File Diff Report

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<?in-line-formulae description="In-line Formulae" end="lead"?>{overscore (v)}(t)=v(t)+e(t)<?in-line-formulae description="In-line Formulae" end="tail"?>

<?in-line-formulae description="In-line Formulae" end="lead"?> <o ostyle="single">v</o>(t)=v(t)+e(t)<?in-line-formulae description="In-line Formulae" end="tail"?>

Where v(t) is the parameter of interest (the refrigerant charge indicator) at time t; α(t) is a rate of change in the parameter value at the time t; m is the average rate of change in α(t); and {overscore (v)}(t) is the estimate of the variable charge based on data acquired at time t. The added term ε(t) is called an innovation process in Kalman filter terminology. This allows deviations from the model and enables adaptation to changing degradation rates if the sensor data point in a certain direction. The sensor data at each time provides the estimated data for the future value parameter of interest and smoothes out noisy estimates or random terms.

Where v(t) is the parameter of interest (the refrigerant charge indicator) at time t; α(t) is a rate of change in the parameter value at the time t; m is the average rate of change in α(t); and <o ostyle="single">v</o>(t) is the estimate of the variable charge based on data acquired at time t. The added term ε(t) is called an innovation process in Kalman filter terminology. This allows deviations from the model and enables adaptation to changing degradation rates if the sensor data point in a certain direction. The sensor data at each time provides the estimated data for the future value parameter of interest and smoothes out noisy estimates or random terms.

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In this embodiment, preferably, the signal processing means 26 also determines specific volume of the fluid. The specific volume can be determined from the “REM calculation” as specific volume cubic feet/pound” in Appendix A. For this calculation, the pressure is independently measured with a pressure gauge and the temperature is calculated from the speed of sound, as described above. Additionally, the signal processing means 24 can determine Reynolds number for the fluid in the pipe from the specific volume and viscosity and consequently PF. It does this in the following way. The determination of the kinematic viscosity (kvis), the profile factor PF and the Reynolds number can be obtained from “REM calculation of meter factor” in Appendix A, where L represents log. The profile correction factor, PF, relates to axial velocity averaged along the acoustic path between the diagonal transducers, {overscore (v)}, with the axial velocity average across the cross sectional area of the flow, {double overscore (v)}. This is expressed as:

In this embodiment, preferably, the signal processing means 26 also determines specific volume of the fluid. The specific volume can be determined from the “REM calculation” as specific volume cubic feet/pound” in Appendix A. For this calculation, the pressure is independently measured with a pressure gauge and the temperature is calculated from the speed of sound, as described above. Additionally, the signal processing means 24 can determine Reynolds number for the fluid in the pipe from the specific volume and viscosity and consequently PF. It does this in the following way. The determination of the kinematic viscosity (kvis), the profile factor PF and the Reynolds number can be obtained from “REM calculation of meter factor” in Appendix A, where L represents log. The profile correction factor, PF, relates to axial velocity averaged along the acoustic path between the diagonal transducers, <o ostyle="single">v</o>, with the axial velocity average across the cross sectional area of the flow, <o ostyle="double">v</o>. This is expressed as:

<li id="ul0006-0001" num="0148">(1) Average fluid velocity, {double overscore (v)}.</li>

<li id="ul0006-0001" num="0148">(1) Average fluid velocity, <o ostyle="double">v</o>.</li>

<?in-line-formulae description="In-line Formulae" end="lead"?>Re=Reynolds number=D{double overscore (v)}/υ<?in-line-formulae description="In-line Formulae" end="tail"?>

<?in-line-formulae description="In-line Formulae" end="lead"?>Re=Reynolds number=D <o ostyle="double">v</o>/υ<?in-line-formulae description="In-line Formulae" end="tail"?>

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wherein n is the number of RR intervals, j is the index of the RR intervals, RRj is the jth value of an {overscore (RR)} interval, and RR is the mean of the RR intervals. However, the pulse variation can be generated in many ways, and generally, pulse variation indeed refers to the division of the power of the QRS complexes as a function of the frequency of occurrence. This is why the pulse variation can also be measured as a value proportional to the magnitude of the total or partial power of the pulse spectrum. The pulse variation may also be calculated for instance by means of the height or width of the distribution pattern of the pulse variation or a magnitude derived from them. The measurement of the pulse spectrum may utilize Welch's averaged periodogram method for generating the power spectral density, an eigenvalue decomposition, such as the PMUSIC (Pseudospectrum using Multiple Signal Classification), the AR spectral decomposition (Auto Regressive Spectral Decomposition), the MSSD index (Mean Square Successive Difference), which is the square of squared differences that occur in the vicinity of normal RR intervals, Porges' filtering method or the like.

wherein n is the number of RR intervals, j is the index of the RR intervals, RRj is the jth value of an <o ostyle="single">RR</o> interval, and RR is the mean of the RR intervals. However, the pulse variation can be generated in many ways, and generally, pulse variation indeed refers to the division of the power of the QRS complexes as a function of the frequency of occurrence. This is why the pulse variation can also be measured as a value proportional to the magnitude of the total or partial power of the pulse spectrum. The pulse variation may also be calculated for instance by means of the height or width of the distribution pattern of the pulse variation or a magnitude derived from them. The measurement of the pulse spectrum may utilize Welch's averaged periodogram method for generating the power spectral density, an eigenvalue decomposition, such as the PMUSIC (Pseudospectrum using Multiple Signal Classification), the AR spectral decomposition (Auto Regressive Spectral Decomposition), the MSSD index (Mean Square Successive Difference), which is the square of squared differences that occur in the vicinity of normal RR intervals, Porges' filtering method or the like.

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<?in-line-formulae description="In-line Formulae" end="lead"?>Enrm3=√{square root over (<E3,E3>)} (12)<?in-line-formulae description="In-line Formulae" end="tail"?>

<?in-line-formulae description="In-line Formulae" end="lead"?>Enrm3=√{square root over (<E3,E3>)} (12)<?in-line-formulae description="In-line Formulae" end="tail"?>

<?in-line-formulae description="In-line Formulae" end="lead"?>Emnrm=√{square root over (<Em,Em>)} (20)<?in-line-formulae description="In-line Formulae" end="tail"?>

<?in-line-formulae description="In-line Formulae" end="lead"?>Emnrm=√{square root over (<Em,Em>)} (20)<?in-line-formulae description="In-line Formulae" end="tail"?>

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To obtain an optimum relationship between the adsorption capacity of the adsorption material of the present invention and its breakthrough behavior, the ratio of the mean particle diameter of the granular or spherical activated carbon particles to the mean fiber diameter of the activated carbon fibers should be selected in a certain range. Especially good results are obtained, if the mean particle diameter of the granular or spherical activated carbon particles ({overscore (d)}activatedcarbonparticle) is greater than the mean fiber diameter of the activated carbon fibers ({overscore (d)}activatedcarbonfiber) by a factor of at least three, preferably by a factor of at least four, more preferably by a factor of at least five, and most preferably by a factor of at lest six. Thus, in accordance with a preferred embodiment: {overscore (d)}activatedcarbonparticle/{overscore (d)}activatedcarbonfiber>3, preferably >4, more preferably >5, and most preferably >6.

To obtain an optimum relationship between the adsorption capacity of the adsorption material of the present invention and its breakthrough behavior, the ratio of the mean particle diameter of the granular or spherical activated carbon particles to the mean fiber diameter of the activated carbon fibers should be selected in a certain range. Especially good results are obtained, if the mean particle diameter of the granular or spherical activated carbon particles ( <o ostyle="single">d</o>activatedcarbonparticle) is greater than the mean fiber diameter of the activated carbon fibers ( <o ostyle="single">d</o>activatedcarbonfiber) by a factor of at least three, preferably by a factor of at least four, more preferably by a factor of at least five, and most preferably by a factor of at lest six. Thus, in accordance with a preferred embodiment: <o ostyle="single">d</o>activatedcarbonparticle/ <o ostyle="single">d</o>activatedcarbonfiber>3, preferably >4, more preferably >5, and most preferably >6.

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In order to calculate the radius of curvature ρsT of the face T of the infinitesimal teeth it is necessary to find previously the radius of curvature of S3 at points F1 to FM during their calculation in steps d) and e) of the second phase. For this the expression (Ec. 2) is applied to the refraction at these points of the rays coming from I. In this case, for each point Fk and denoting by {overscore (AB)} the length of the segment of edges A and B, we have ρi={overscore (IFk)}, ρr=∞ in step d) and ρr={overscore (R′Fk)} in step e).

In order to calculate the radius of curvature ρsT of the face T of the infinitesimal teeth it is necessary to find previously the radius of curvature of S3 at points F1 to FM during their calculation in steps d) and e) of the second phase. For this the expression (Ec. 2) is applied to the refraction at these points of the rays coming from I. In this case, for each point Fk and denoting by <o ostyle="single">AB</o> the length of the segment of edges A and B, we have ρi= <o ostyle="single">IFk</o>, ρr=∞ in step d) and ρr= <o ostyle="single">R′Fk</o> in step e).

It is in step f), in which the points Gk are calculated on the basis of the points Fk, where the desired values of ρsT should be calculated. The calculation involves the use of the expression (Ec. 2) for the three successive incidences undergone by the ray that goes (in the reverse direction) from R toward Fk. Given that in step f) the points and the normals to the surfaces are calculated, the angles of incidence and of refraction/reflection, like the refractive indices, are known parameters in the three incidences. In the first, at Fk, as the radius of curvature ρs is already known and ρi={overscore (RFk)}, from (Ec. 2) we obtain the radius of curvature of the refracted wavefront ρr1. For the second incidence, which occurs on the face V of the tooth calculated at Gk, the radius of curvature of the incident wavefront is ρi={overscore (GkFk)}−ρi and the radius of curvature of the surface is known (ρsV=∞), so that from (Ec. 2) we obtain the radius of curvature of the refracted wavefront ρr2. Finally, for the third incidence, which occurs on the face T of the tooth, it is known that ρi=−ρr2 and ρr3=∞, so that (Ec. 2) can be solved with the radius of curvature ρsT as an unknown, which was the desired value.

It is in step f), in which the points Gk are calculated on the basis of the points Fk, where the desired values of ρsT should be calculated. The calculation involves the use of the expression (Ec. 2) for the three successive incidences undergone by the ray that goes (in the reverse direction) from R toward Fk. Given that in step f) the points and the normals to the surfaces are calculated, the angles of incidence and of refraction/reflection, like the refractive indices, are known parameters in the three incidences. In the first, at Fk, as the radius of curvature ρs is already known and ρi= <o ostyle="single">RFk</o>, from (Ec. 2) we obtain the radius of curvature of the refracted wavefront ρr1. For the second incidence, which occurs on the face V of the tooth calculated at Gk, the radius of curvature of the incident wavefront is ρi= <o ostyle="single">GkFk</o>−ρi and the radius of curvature of the surface is known (ρsV=∞), so that from (Ec. 2) we obtain the radius of curvature of the refracted wavefront ρr2. Finally, for the third incidence, which occurs on the face T of the tooth, it is known that ρi=−ρr2 and ρr3=∞, so that (Ec. 2) can be solved with the radius of curvature ρsT as an unknown, which was the desired value.

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<entry>Mean ({overscore (X)})</entry>	<entry>Mean ( <o ostyle="single">X</o>)</entry>
<entry>Xi − {overscore (X)}</entry>	<entry>Xi − <o ostyle="single">X</o></entry>

<entry> MEAN Xi {overscore (X)}</entry>	<entry> MEAN Xi <o ostyle="single">X</o></entry>
<entry>Xi − {overscore (X)}</entry>	<entry>Xi − <o ostyle="single">X</o></entry>

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When two harmonic vibrations A1 cos(ωt+φ1) and A2 cos(ωt+φ2) of the same frequency occur along the same directions, then the resulting vibration Ā cos(ωt+{overscore (φ)}) has an amplitude defined from Ā2=A12+A22+2A1A2 cos(φ1−φ2). The analyzer thus transforms the pattern of (x,y)-dependent phase difference into the pattern of transmitted light intensity I(x,y)=Ā2. The intensity of light passed through the crossed polarizers and the nematic slab between them follows from Eq. (1) as

When two harmonic vibrations A1 cos(ωt+φ1) and A2 cos(ωt+φ2) of the same frequency occur along the same directions, then the resulting vibration Ā cos(ωt+ <o ostyle="single">φ</o>) has an amplitude defined from Ā2=A12+A22+2A1A2 cos(φ1−φ2). The analyzer thus transforms the pattern of (x,y)-dependent phase difference into the pattern of transmitted light intensity I(x,y)=Ā2. The intensity of light passed through the crossed polarizers and the nematic slab between them follows from Eq. (1) as

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<entry>WGF 11-mer: NH2-AQPYPQGNHEA-COOH</entry>

<entry>WGF 11-mer: NH2-AQPYPQGNHEA-COOH</entry>

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A random copolymer having the formula illustrated in <figref idref="DRAWINGS">FIG. 8</figref> was prepared wherein Z was a diethyl amino group (NR6R7 with R6 and R7 being CH2CH3) and R1 was CH3. The copolymer (I-a) was prepared using N,N-(diethyl amino)ethyl methacrylate (DEAEM) (Sigma-Aldrich, St. Louis, Mo.), poly(ethylene glycol) methyl ether methacrylate (PEGMEM, {overscore (M)}n=300) (Sigma-Aldrich), Potassium t-butoxide (KtBuO) (Sigma-Aldrich) as the initiator, and tetrahydrofuran (THF) (Sigma-Aldrich) as the solvent. Prior to polymerization, both the PEGMEM and the DEAEM monomer were stirred over calcium hydride for at least 24 hours. The dried DEAEM monomer was then distilled under vacuum immediately prior to use. The THF was also dried over sodium metal in the presence of benzophenone until a purple color was present. Once dried, the THF was then distilled under argon and used immediately. Potassium t-butoxide (KtBuO) was used under dry, inert atmosphere with no purification.

A random copolymer having the formula illustrated in <figref idref="DRAWINGS">FIG. 8</figref> was prepared wherein Z was a diethyl amino group (NR6R7 with R6 and R7 being CH2CH3) and R1 was CH3. The copolymer (I-a) was prepared using N,N-(diethyl amino)ethyl methacrylate (DEAEM) (Sigma-Aldrich, St. Louis, Mo.), poly(ethylene glycol) methyl ether methacrylate (PEGMEM, <o ostyle="single">M</o>n=300) (Sigma-Aldrich), Potassium t-butoxide (KtBuO) (Sigma-Aldrich) as the initiator, and tetrahydrofuran (THF) (Sigma-Aldrich) as the solvent. Prior to polymerization, both the PEGMEM and the DEAEM monomer were stirred over calcium hydride for at least 24 hours. The dried DEAEM monomer was then distilled under vacuum immediately prior to use. The THF was also dried over sodium metal in the presence of benzophenone until a purple color was present. Once dried, the THF was then distilled under argon and used immediately. Potassium t-butoxide (KtBuO) was used under dry, inert atmosphere with no purification.

<entry>{overscore (M)}<sub>n</sub></entry>	<entry> <o ostyle="single">M</o><sub>n</sub></entry>
<entry>{overscore (M)}<sub>n</sub></entry>	<entry> <o ostyle="single">M</o><sub>n</sub></entry>

<entry>{overscore (M)}n</entry>

GPC results relative to poly(methyl methacrylate) standards were drastically lower than what was expected based on initiator concentration (Table 1). The polydispersity index (PDI), however, was on the order that is expected for anionic polymerization. In the absence of premature termination or slow initiation, both of which would cause a much broader molecular weight distribution, there is little explanation of a {overscore (M)}n much lower than the expected {overscore (M)}n. Due to the high mass fraction of the polymer contained in the pendent groups of the PDEAEM homopolymer and PEGMEM/DEAEM copolymers, it was believed that a relative calibration to the linear polystyrene or poly(methyl methacrylate) could yield measured molecular weights much lower than their actual values. In order to verify the relative calibration measurements light scattering was used to obtain an absolute molecular weight measurement.

GPC results relative to poly(methyl methacrylate) standards were drastically lower than what was expected based on initiator concentration (Table 1). The polydispersity index (PDI), however, was on the order that is expected for anionic polymerization. In the absence of premature termination or slow initiation, both of which would cause a much broader molecular weight distribution, there is little explanation of a <o ostyle="single">M</o>n much lower than the expected <o ostyle="single">M</o>n. Due to the high mass fraction of the polymer contained in the pendent groups of the PDEAEM homopolymer and PEGMEM/DEAEM copolymers, it was believed that a relative calibration to the linear polystyrene or poly(methyl methacrylate) could yield measured molecular weights much lower than their actual values. In order to verify the relative calibration measurements light scattering was used to obtain an absolute molecular weight measurement.

The values for {overscore (M)}n resulting from laser light scattering were much higher than the values obtained from relative RI measurements. The {overscore (M)}n values were also slightly higher than the target values, which could be due to the fact that the initiator was not titrated prior to each polymerization. If some of the potassium t-butoxide became inactive then the amount of active initiator would be lower, resulting in higher molecular weight values. If an exact {overscore (M)}n was desired, such a practice could be performed immediately prior to the polymerization.

The values for <o ostyle="single">M</o>n resulting from laser light scattering were much higher than the values obtained from relative RI measurements. The <o ostyle="single">M</o>n values were also slightly higher than the target values, which could be due to the fact that the initiator was not titrated prior to each polymerization. If some of the potassium t-butoxide became inactive then the amount of active initiator would be lower, resulting in higher molecular weight values. If an exact <o ostyle="single">M</o>n was desired, such a practice could be performed immediately prior to the polymerization.

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<li id="ul0002-0003" num="0017">B) at least one polyol having on average at least 1.8 and not more than 3.0 Zerewitinoff-active hydrogen atoms and a number-average molecular weight {overscore (M)}n of 450 to 10,000;

<li id="ul0001-0002" num="0018">C) at least one low molecular weight polyol or polyamine having on average at least 1.8 and not more than 3.0 Zerewitinoff-active hydrogen atoms and a number-average molecular weight {overscore (M)}n of 60 to 400 as a chain lengthener;

<li id="ul0001-0002" num="0018">C) at least one low molecular weight polyol or polyamine having on average at least 1.8 and not more than 3.0 Zerewitinoff-active hydrogen atoms and a number-average molecular weight <o ostyle="single">M</o>n of 60 to 400 as a chain lengthener;

<li id="ul0001-0003" num="0019">D) from 1 to 15 wt. %, based on the total weight of the TPU, of at least one organic phosphorus-containing compound based on phosphonate or phosphine oxide having on average at least 1.5 and not more than 3.0 Zerewitinoff-active hydrogen atoms and a number-average molecular weight {overscore (M)}n of 60 to 10,000, corresponding to the following structural formula:</li>

<li id="ul0001-0003" num="0019">D) from 1 to 15 wt. %, based on the total weight of the TPU, of at least one organic phosphorus-containing compound based on phosphonate or phosphine oxide having on average at least 1.5 and not more than 3.0 Zerewitinoff-active hydrogen atoms and a number-average molecular weight <o ostyle="single">M</o>n of 60 to 10,000, corresponding to the following structural formula:</li>

<li id="ul0005-0003" num="0029">F) from 0 to 70 wt. %, based on the total weight of the TPU, of at least one further flameproofing agent which contains no Zerewitinoff-active hydrogen atoms and has a number-average molecular weight {overscore (M)}n of 60 to 10,000;

<p id="p-0021" num="0035">Zerewitinoff-active polyols which are suitable to be used as component B) in the products of the present invention are those having on average at least 1.8 to not more than 3.0 Zerewitinoff-active hydrogen atoms and a number-average molecular weight {overscore (M)}<sub>n </sub>of 450 to 10,000. These often contain small amounts of non-linear compounds as a result of their production. Thus, these are often referred to as “substantially linear polyols”. Polyester-, polyether- or polycarbonate-diols or mixtures of these are preferred.</p>	<p id="p-0021" num="0035">Zerewitinoff-active polyols which are suitable to be used as component B) in the products of the present invention are those having on average at least 1.8 to not more than 3.0 Zerewitinoff-active hydrogen atoms and a number-average molecular weight <o ostyle="single">M</o><sub>n </sub>of 450 to 10,000. These often contain small amounts of non-linear compounds as a result of their production. Thus, these are often referred to as “substantially linear polyols”. Polyester-, polyether- or polycarbonate-diols or mixtures of these are preferred.</p>
<p id="p-0022" num="0036">In addition to compounds containing amino groups, thiol groups or carboxyl groups, compounds containing two to three, preferably two hydroxyl groups are included, and in particular, specifically those with number-average molecular weights {overscore (M)}<sub>n </sub>of 450 to 6,000. It is particularly preferred that these have a number-average molecular weight {overscore (M)}<sub>n </sub>of 600 to 4,500. Among the preferred compounds are, for example, polyesters, polyethers, polycarbonates and polyester-amides containing hydroxyl groups.</p>	<p id="p-0022" num="0036">In addition to compounds containing amino groups, thiol groups or carboxyl groups, compounds containing two to three, preferably two hydroxyl groups are included, and in particular, specifically those with number-average molecular weights <o ostyle="single">M</o><sub>n </sub>of 450 to 6,000. It is particularly preferred that these have a number-average molecular weight <o ostyle="single">M</o><sub>n </sub>of 600 to 4,500. Among the preferred compounds are, for example, polyesters, polyethers, polycarbonates and polyester-amides containing hydroxyl groups.</p>
<p id="p-0023" num="0037">Suitable polyether-diols to be used as component B) of the invention can be prepared, for example, by reacting one or more alkylene oxides having 2 to 4 carbon atoms in the alkylene radical with a starter molecule which contains two active hydrogen atoms in bonded form. Alkylene oxides which may be mentioned include, e.g. ethylene oxide, 1,2-propylene oxide, epichlorohydrin and 1,2-butylene oxide and 2,3-butylene oxide. Ethylene oxide, propylene oxide and mixtures of 1,2-propylene oxide and ethylene oxide are preferably used. The alkylene oxides can be used individually, alternately in succession or as mixtures. Possible starter molecules include, for example, water, amino alcohols, such as N-alkyl-diethanolamines, for example N-methyl-diethanolamine, and diols, such as ethylene glycol, 1,3-propylene glycol, 1,4-butanediol and 1,6-hexanediol. Mixtures of starter molecules can also optionally be employed. Suitable polyether-ols are furthermore the polymerization products of tetrahydrofuran which contain hydroxyl groups. It is also possible to employ trifunctional polyethers in amounts of 0 to 30 wt. %, based on the weight of the bifunctional polyethers. The amount of the trifunctional polyethers used is limited to an amount such that a product which is still thermoplastically processable is formed. The substantially linear polyether-diols preferably have number-average molecular weights {overscore (M)}<sub>n </sub>of 450 to 6,000. They can be used either individually or in the form of mixtures with one another.</p>	<p id="p-0023" num="0037">Suitable polyether-diols to be used as component B) of the invention can be prepared, for example, by reacting one or more alkylene oxides having 2 to 4 carbon atoms in the alkylene radical with a starter molecule which contains two active hydrogen atoms in bonded form. Alkylene oxides which may be mentioned include, e.g. ethylene oxide, 1,2-propylene oxide, epichlorohydrin and 1,2-butylene oxide and 2,3-butylene oxide. Ethylene oxide, propylene oxide and mixtures of 1,2-propylene oxide and ethylene oxide are preferably used. The alkylene oxides can be used individually, alternately in succession or as mixtures. Possible starter molecules include, for example, water, amino alcohols, such as N-alkyl-diethanolamines, for example N-methyl-diethanolamine, and diols, such as ethylene glycol, 1,3-propylene glycol, 1,4-butanediol and 1,6-hexanediol. Mixtures of starter molecules can also optionally be employed. Suitable polyether-ols are furthermore the polymerization products of tetrahydrofuran which contain hydroxyl groups. It is also possible to employ trifunctional polyethers in amounts of 0 to 30 wt. %, based on the weight of the bifunctional polyethers. The amount of the trifunctional polyethers used is limited to an amount such that a product which is still thermoplastically processable is formed. The substantially linear polyether-diols preferably have number-average molecular weights <o ostyle="single">M</o><sub>n </sub>of 450 to 6,000. They can be used either individually or in the form of mixtures with one another.</p>
<p id="p-0024" num="0038">Suitable polyester-diols to be used as component B) in the present invention can be prepared, for example, from dicarboxylic acids having 2 to 12 carbon atoms, preferably 4 to 6 carbon atoms, and polyhydric alcohols. Possible dicarboxylic acids include, for example: aliphatic dicarboxylic acids, such as succinic acid, glutaric acid, adipic acid, suberic acid, azelaic acid and sebacic acid, or aromatic dicarboxylic acids, such as phthalic acid, isophthalic acid and terephthalic acid. The dicarboxylic acids can be used individually or as mixtures, e.g. in the form of a succinic, glutaric and adipic acid mixture. For the preparation of the polyester-diols it may be advantageous, where appropriate, to use the corresponding dicarboxylic acid derivatives, such as carboxylic acid diesters having 1 to 4 carbon atoms in the alcohol radical, carboxylic acid anhydrides or carboxylic acid chlorides, instead of the dicarboxylic acids. Examples of suitable polyhydric alcohols include glycols having 2 to 10, preferably 2 to 6 carbon atoms, such as, e.g. ethylene glycol, diethylene glycol, 1,4-butanediol, 1,5-pentanediol, 1,6-hexanediol, 1,10-decanediol, 2,2-dimethyl- 1,3-propanediol, 1,3-propanediol or dipropylene glycol. The polyhydric alcohols can be used by themselves or as a mixture with one another, depending on the desired properties. Compounds which are also suitable for use as component B) include esters of carbonic acid with the diols mentioned, and particularly those diols having 4 to 6 carbon atoms, such as 1,4-butanediol or 1,6-hexanediol, condensation products of ω-hydroxycarboxylic acids, such as ω-hydroxycaproic acid, or polymerization products of lactones, such as, e.g. ω-caprolactones which are optionally substituted. Polyester-diols which are preferably used are ethanediol polyadipates, 1,4-butanediol polyadipates, ethanediol- 1,4-butanediol polyadipates, 1,6-hexanediol-neopentylglycol polyadipates, 1,6-hexanediol- 1,4-butanediol polyadipates and polycaprolactones. The polyester-diols have number-average molecular weights {overscore (M)}<sub>n </sub>of 450 to 10,000 and can be used individually or in the form of mixtures with one another.</p>	<p id="p-0024" num="0038">Suitable polyester-diols to be used as component B) in the present invention can be prepared, for example, from dicarboxylic acids having 2 to 12 carbon atoms, preferably 4 to 6 carbon atoms, and polyhydric alcohols. Possible dicarboxylic acids include, for example: aliphatic dicarboxylic acids, such as succinic acid, glutaric acid, adipic acid, suberic acid, azelaic acid and sebacic acid, or aromatic dicarboxylic acids, such as phthalic acid, isophthalic acid and terephthalic acid. The dicarboxylic acids can be used individually or as mixtures, e.g. in the form of a succinic, glutaric and adipic acid mixture. For the preparation of the polyester-diols it may be advantageous, where appropriate, to use the corresponding dicarboxylic acid derivatives, such as carboxylic acid diesters having 1 to 4 carbon atoms in the alcohol radical, carboxylic acid anhydrides or carboxylic acid chlorides, instead of the dicarboxylic acids. Examples of suitable polyhydric alcohols include glycols having 2 to 10, preferably 2 to 6 carbon atoms, such as, e.g. ethylene glycol, diethylene glycol, 1,4-butanediol, 1,5-pentanediol, 1,6-hexanediol, 1,10-decanediol, 2,2-dimethyl- 1,3-propanediol, 1,3-propanediol or dipropylene glycol. The polyhydric alcohols can be used by themselves or as a mixture with one another, depending on the desired properties. Compounds which are also suitable for use as component B) include esters of carbonic acid with the diols mentioned, and particularly those diols having 4 to 6 carbon atoms, such as 1,4-butanediol or 1,6-hexanediol, condensation products of ω-hydroxycarboxylic acids, such as ω-hydroxycaproic acid, or polymerization products of lactones, such as, e.g. ω-caprolactones which are optionally substituted. Polyester-diols which are preferably used are ethanediol polyadipates, 1,4-butanediol polyadipates, ethanediol- 1,4-butanediol polyadipates, 1,6-hexanediol-neopentylglycol polyadipates, 1,6-hexanediol- 1,4-butanediol polyadipates and polycaprolactones. The polyester-diols have number-average molecular weights <o ostyle="single">M</o><sub>n </sub>of 450 to 10,000 and can be used individually or in the form of mixtures with one another.</p>

The flameproofing agents D) have a number-average molecular weight {overscore (M)}n of 60 to 10,000, preferably 100 to 5,000, particularly preferably 100 to 1,000.

The flameproofing agents D) have a number-average molecular weight <o ostyle="single">M</o>n of 60 to 10,000, preferably 100 to 5,000, particularly preferably 100 to 1,000.

<li id="ul0012-0003" num="0066">B) at least one polyol having on average at least 1.8 and not more than 3.0 Zerewitinoff-active hydrogen atoms and a number-average molecular weight {overscore (M)}n of 450 to 10,000;</li>

<li id="ul0013-0001" num="0068">C) at least one low molecular weight polyol or polyamine having on average at least 1.8 and not more than 3.0 Zerewitinoff-active hydrogen atoms and a number-average molecular weight {overscore (M)}n of 60 to 400 as a chain lengthener,</li>

<li id="ul0013-0001" num="0068">C) at least one low molecular weight polyol or polyamine having on average at least 1.8 and not more than 3.0 Zerewitinoff-active hydrogen atoms and a number-average molecular weight <o ostyle="single">M</o>n of 60 to 400 as a chain lengthener,</li>

<li id="ul0013-0003" num="0070">D) from 1 to 15 wt. %, based on the total weight of the TPU, of at least one organic phosphorus-containing compound based on phosphonate or phosphine oxide having on average at least 1.5 and not more than 3.0 Zerewitinoff-active hydrogen atoms and a number-average molecular weight {overscore (M)}n of 60 to 10,000, corresponding to the following structural formula:</li>

<li id="ul0013-0003" num="0070">D) from 1 to 15 wt. %, based on the total weight of the TPU, of at least one organic phosphorus-containing compound based on phosphonate or phosphine oxide having on average at least 1.5 and not more than 3.0 Zerewitinoff-active hydrogen atoms and a number-average molecular weight <o ostyle="single">M</o>n of 60 to 10,000, corresponding to the following structural formula:</li>

<li id="ul0018-0004" num="0083">F) from 0 to 70 wt. %, based on the total weight of the TPU, of at least one further flameproofing agent which contains no Zerewitinoff-active hydrogen atoms and has a number-average molecular weight {overscore (M)}n of 60 to 10,000,

<claim-text>B) at least one polyether polyol having on average at least 1.8 and not more than 3.0 Zerewitinoff-active hydrogen atoms and a number-average molecular weight {overscore (M)}n of 450 to 10,000;</claim-text>

<claim-text>B) at least one polyether polyol having on average at least 1.8 and not more than 3.0 Zerewitinoff-active hydrogen atoms and a number-average molecular weight <o ostyle="single">M</o>n of 450 to 10,000;</claim-text>

<claim-text>C) at least one low molecular weight polyol or polyamine having on average at least 1.8 and not more than 3.0 Zerewitinoff-active hydrogen atoms and a number-average molecular weight {overscore (M)}n of 60 to 400 as a chain lengthener;</claim-text>

<claim-text>C) at least one low molecular weight polyol or polyamine having on average at least 1.8 and not more than 3.0 Zerewitinoff-active hydrogen atoms and a number-average molecular weight <o ostyle="single">M</o>n of 60 to 400 as a chain lengthener;</claim-text>

<claim-text>D) from 1 to 15 wt. %, based on the total weight of the TPU, of at least one organic phosphorus-containing compound having on average at least 2.0 Zerewitinoff-active hydrogen atoms and a number-average molecular weight {overscore (M)}n of 60 to 10,000, wherein said organic phosphorus-containing compound is selected from the group consisting of (1) one or more phosphonates which correspond to the structural formula:</claim-text>

<claim-text>D) from 1 to 15 wt. %, based on the total weight of the TPU, of at least one organic phosphorus-containing compound having on average at least 2.0 Zerewitinoff-active hydrogen atoms and a number-average molecular weight <o ostyle="single">M</o>n of 60 to 10,000, wherein said organic phosphorus-containing compound is selected from the group consisting of (1) one or more phosphonates which correspond to the structural formula:</claim-text>

<claim-text>F) from 0 to 70 wt. %, based on the total weight of the TPU, of at least one further flameproofing agent which contains no Zerewitinoff-active hydrogen atoms and has a number-average molecular weight {overscore (M)}n of 60 to 10,000;</claim-text>

<claim-text>F) from 0 to 70 wt. %, based on the total weight of the TPU, of at least one further flameproofing agent which contains no Zerewitinoff-active hydrogen atoms and has a number-average molecular weight <o ostyle="single">M</o>n of 60 to 10,000;</claim-text>

<claim-text>C) at least one low molecular weight polyol or polyamine having on average at least 1.8 and not more than 3.0 Zerewitinoff-active hydrogen atoms and a number-average molecular weight <o ostyle="single">M</o>n of 60 to 400 as a chain lengthener;</claim-text>

<claim-text>D) from 1 to 15 wt. %, based on the total weight of the TPU, of at least one organic phosphorus-containing compound having on average at least 2.0 Zerewitinoff-active hydrogen atoms and a number-average molecular weight <o ostyle="single">M</o>n of 60 to 10,000, wherein said organic phosphorus-containing compound is selected from the group consisting of (1) one or more phosphonates which correspond to the structural formula:</claim-text>

<claim-text>F) 0 to 70 wt. %, based on the total weight of the TPU, of at least one further flameproofing agent which contains no Zerewitinoff-active hydrogen atoms and has a number-average molecular weight {overscore (M)}n of 60 to 10,000,</claim-text>

<claim-text>F) 0 to 70 wt. %, based on the total weight of the TPU, of at least one further flameproofing agent which contains no Zerewitinoff-active hydrogen atoms and has a number-average molecular weight <o ostyle="single">M</o>n of 60 to 10,000,</claim-text>

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If the number of times the mass of the sample S is measured reaches N, the main control unit 150 calculates the average {overscore (m′)} of the masses m′ of the sample S using an averaging operation program at step S412, and displays the average through the display unit (not shown) at step S414.

If the number of times the mass of the sample S is measured reaches N, the main control unit 150 calculates the average <o ostyle="single">m′</o> of the masses m′ of the sample S using an averaging operation program at step S412, and displays the average through the display unit (not shown) at step S414.

Further, similar to the first embodiment, if the statistical processing mode is set, steps S402, S404, S602, S604 and S606 are repeatedly performed N times at steps S608 and S610, and the average {overscore (m″)} of measured masses is calculated at step S612. Further, the calculated average mass {overscore (m″)} is displayed through a display unit (not shown) at step S614.

Further, similar to the first embodiment, if the statistical processing mode is set, steps S402, S404, S602, S604 and S606 are repeatedly performed N times at steps S608 and S610, and the average <o ostyle="single">m″</o> of measured masses is calculated at step S612. Further, the calculated average mass <o ostyle="single">m″</o> is displayed through a display unit (not shown) at step S614.

<p id="p-0105" num="0104">In the mass measurement method according to the fourth embodiment of the present invention in <figref idref="DRAWINGS">FIG. 8</figref>, the average mass {overscore (m′)} of the masses of the sample S is calculated in a statistical processing mode in the mass measurement method of the first embodiment, and the calculated average mass {overscore (m′)} is used together with the mass measurement method using the sample exchange measurement of the second and third embodiments.</p>	<p id="p-0105" num="0104">In the mass measurement method according to the fourth embodiment of the present invention in <figref idref="DRAWINGS">FIG. 8</figref>, the average mass <o ostyle="single">m′</o> of the masses of the sample S is calculated in a statistical processing mode in the mass measurement method of the first embodiment, and the calculated average mass <o ostyle="single">m′</o> is used together with the mass measurement method using the sample exchange measurement of the second and third embodiments.</p>
<p id="p-0106" num="0105">That is, after the average mass {overscore (m′)} of the sample S is calculated at steps S<b>402</b> to S<b>412</b> in the first embodiment, the locations of the sample S and the standard sample CS are exchanged to measure the mass of the sample as in the second and third embodiments.</p>	<p id="p-0106" num="0105">That is, after the average mass <o ostyle="single">m′</o> of the sample S is calculated at steps S<b>402</b> to S<b>412</b> in the first embodiment, the locations of the sample S and the standard sample CS are exchanged to measure the mass of the sample as in the second and third embodiments.</p>
<p id="p-0107" num="0106">First, after the average mass {overscore (m′)} of the sample S is measured at steps S<b>402</b> to S<b>412</b>, the linear motion controller <b>132</b> outputs a driving control signal and drives the linear motor <b>130</b> under the control of the main control unit <b>150</b> with the locations of the sample S and the standard sample exchanged at step S<b>802</b>.</p>	<p id="p-0107" num="0106">First, after the average mass <o ostyle="single">m′</o> of the sample S is measured at steps S<b>402</b> to S<b>412</b>, the linear motion controller <b>132</b> outputs a driving control signal and drives the linear motor <b>130</b> under the control of the main control unit <b>150</b> with the locations of the sample S and the standard sample exchanged at step S<b>802</b>.</p>

Further, the main control unit 150 compares the mass m″″, calculated at step S806, with the average mass {overscore (m′)}, calculated at step S412, at step S808. If the difference therebetween |{overscore (m′)}−m″″| is equal to or greater than a predetermined value ε, the entire process is executed again. Conversely, if the difference between calculated masses |{overscore (m′)}−m″″| is less than the predetermined value ε, it is determined that the measured mass is an accurate final mass, so that the mass m″″ of the sample S measured at step S806 is displayed through a display unit (not shown) at steps S810 and S812.

Further, the main control unit 150 compares the mass m″″, calculated at step S806, with the average mass <o ostyle="single">m′</o>, calculated at step S412, at step S808. If the difference therebetween | <o ostyle="single">m′</o>−m″″| is equal to or greater than a predetermined value ε, the entire process is executed again. Conversely, if the difference between calculated masses | <o ostyle="single">m′</o>−m″″| is less than the predetermined value ε, it is determined that the measured mass is an accurate final mass, so that the mass m″″ of the sample S measured at step S806 is displayed through a display unit (not shown) at steps S810 and S812.

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<p id="p-0014" num="0013"><figref idref="DRAWINGS">FIG. 5</figref> is a circuit diagram illustrating a known ratioed logic circuit to implement the function {overscore ((A·B)+(C·D))}{overscore ((A·B)+(C·D))}.</p>	<p id="p-0014" num="0013"><figref idref="DRAWINGS">FIG. 5</figref> is a circuit diagram illustrating a known ratioed logic circuit to implement the function <o ostyle="single">(A·B)+(C·D)</o> <o ostyle="single">(A·B)+(C·D)</o>.</p>
<p id="p-0015" num="0014"><figref idref="DRAWINGS">FIG. 6</figref> is a circuit diagram illustrating a ratioed logic circuit with contention interrupt to implement the function {overscore ((A·B)+(C·D))}{overscore ((A·B)+(C·D))}, in accordance with an embodiment of the present invention.</p>	<p id="p-0015" num="0014"><figref idref="DRAWINGS">FIG. 6</figref> is a circuit diagram illustrating a ratioed logic circuit with contention interrupt to implement the function <o ostyle="single">(A·B)+(C·D)</o> <o ostyle="single">(A·B)+(C·D)</o>, in accordance with an embodiment of the present invention.</p>
<p id="p-0016" num="0015"><figref idref="DRAWINGS">FIG. 7</figref> is a circuit diagram illustrating a known ratioed logic circuit to implement the function {overscore ((A·B)+(C·D)+(E·F))}{overscore ((A·B)+(C·D)+(E·F))}{overscore ((A·B)+(C·D)+(E·F))}.</p>	<p id="p-0016" num="0015"><figref idref="DRAWINGS">FIG. 7</figref> is a circuit diagram illustrating a known ratioed logic circuit to implement the function <o ostyle="single">(A·B)+(C·D)+(E·F)</o> <o ostyle="single">(A·B)+(C·D)+(E·F)</o> <o ostyle="single">(A·B)+(C·D)+(E·F)</o>.</p>
<p id="p-0017" num="0016"><figref idref="DRAWINGS">FIG. 8</figref> is a circuit diagram illustrating a ratioed logic circuit with contention interrupt to implement the function {overscore ((A·B)+(C·D)+(E·F))}{overscore ((A·B)+(C·D)+(E·F))}{overscore ((A·B)+(C·D)+(E·F))}, in accordance with an embodiment of the present invention.</p>	<p id="p-0017" num="0016"><figref idref="DRAWINGS">FIG. 8</figref> is a circuit diagram illustrating a ratioed logic circuit with contention interrupt to implement the function <o ostyle="single">(A·B)+(C·D)+(E·F)</o> <o ostyle="single">(A·B)+(C·D)+(E·F)</o> <o ostyle="single">(A·B)+(C·D)+(E·F)</o>, in accordance with an embodiment of the present invention.</p>
<p id="p-0018" num="0017"><figref idref="DRAWINGS">FIG. 9</figref> is a circuit diagram of a known ratioed logic circuit to implement the function {overscore (A+(B·C))}.</p>	<p id="p-0018" num="0017"><figref idref="DRAWINGS">FIG. 9</figref> is a circuit diagram of a known ratioed logic circuit to implement the function <o ostyle="single">A+(B·C)</o>.</p>
<p id="p-0019" num="0018"><figref idref="DRAWINGS">FIG. 10</figref> is a circuit diagram of a ratioed logic circuit with contention interrupt to implement the function {overscore (A+(B·C))}, in accordance with an embodiment of the present invention.</p>	<p id="p-0019" num="0018"><figref idref="DRAWINGS">FIG. 10</figref> is a circuit diagram of a ratioed logic circuit with contention interrupt to implement the function <o ostyle="single">A+(B·C)</o>, in accordance with an embodiment of the present invention.</p>
<p id="p-0020" num="0019"><figref idref="DRAWINGS">FIG. 11</figref> is a circuit diagram of a ratioed logic circuit to implement the function {overscore (A+(B·C)+D)}.</p>	<p id="p-0020" num="0019"><figref idref="DRAWINGS">FIG. 11</figref> is a circuit diagram of a ratioed logic circuit to implement the function <o ostyle="single">A+(B·C)+D</o>.</p>
<p id="p-0021" num="0020"><figref idref="DRAWINGS">FIG. 12</figref> is a circuit diagram of a ratioed logic circuit with contention interrupt to implement the function {overscore (A+(B·C)+D)}, in accordance with an embodiment of the present invention</p>	<p id="p-0021" num="0020"><figref idref="DRAWINGS">FIG. 12</figref> is a circuit diagram of a ratioed logic circuit with contention interrupt to implement the function <o ostyle="single">A+(B·C)+D</o>, in accordance with an embodiment of the present invention</p>

<?in-line-formulae description="In-line Formulae" end="lead"?>OUT={overscore ((A·B)+(C·D))}{overscore ((A·B)+(C·D))} (Equation 1)<?in-line-formulae description="In-line Formulae" end="tail"?>

<?in-line-formulae description="In-line Formulae" end="lead"?>OUT= <o ostyle="single">(A·B)+(C·D)</o> <o ostyle="single">(A·B)+(C·D)</o> (Equation 1)<?in-line-formulae description="In-line Formulae" end="tail"?>

<?in-line-formulae description="In-line Formulae" end="lead"?>OUT={overscore ((A·B)+(C·D)+(E·F))}{overscore ((A·B)+(C·D)+(E·F))}{overscore ((A·B)+(C·D)+(E·F))}. (Equation 2)<?in-line-formulae description="In-line Formulae" end="tail"?>

<?in-line-formulae description="In-line Formulae" end="lead"?>OUT= <o ostyle="single">(A·B)+(C·D)+(E·F)</o> <o ostyle="single">(A·B)+(C·D)+(E·F)</o> <o ostyle="single">(A·B)+(C·D)+(E·F)</o>. (Equation 2)<?in-line-formulae description="In-line Formulae" end="tail"?>

<?in-line-formulae description="In-line Formulae" end="lead"?>OUT={overscore (A+(B·C))} (Equation 3)<?in-line-formulae description="In-line Formulae" end="tail"?>

<?in-line-formulae description="In-line Formulae" end="lead"?>OUT= <o ostyle="single">A+(B·C)</o> (Equation 3)<?in-line-formulae description="In-line Formulae" end="tail"?>

<?in-line-formulae description="In-line Formulae" end="lead"?>OUT={overscore (A+(B·C)+D)} (Equation 4)<?in-line-formulae description="In-line Formulae" end="tail"?>

<?in-line-formulae description="In-line Formulae" end="lead"?>OUT= <o ostyle="single">A+(B·C)+D</o> (Equation 4)<?in-line-formulae description="In-line Formulae" end="tail"?>

<claim-text>28. The apparatus of <claim-ref idref="CLM-00026">claim 26</claim-ref>, wherein the logical function comprises OUT={overscore ((A·B)+(C·D))}{overscore ((A·B)+(C·D))}, where OUT represents an output signal generated on the output, A, B, C, and D represent input signals received on the multiple inputs, “+” represents a logical OR, and “·” represents a logical AND, and wherein the decoder comprises a logical NOR gate coupled to logically NOR inversions of the portion of the multiple inputs not coupled to the pull up network.</claim-text>

<claim-text>28. The apparatus of <claim-ref idref="CLM-00026">claim 26</claim-ref>, wherein the logical function comprises OUT= <o ostyle="single">(A·B)+(C·D)</o> <o ostyle="single">(A·B)+(C·D)</o>, where OUT represents an output signal generated on the output, A, B, C, and D represent input signals received on the multiple inputs, “+” represents a logical OR, and “·” represents a logical AND, and wherein the decoder comprises a logical NOR gate coupled to logically NOR inversions of the portion of the multiple inputs not coupled to the pull up network.</claim-text>

<claim-text>29. The apparatus of <claim-ref idref="CLM-00026">claim 26</claim-ref>, wherein the logical function comprises OUT={overscore ((A·B)+(C·D)+(E·F))}{overscore ((A·B)+(C·D)+(E·F))}{overscore ((A·B)+(C·D)+(E·F))}, where OUT represents an output signal generated on the output, A, B, C, D, E, and F represent input signals received on the multiple inputs, “+” represents a logical OR, and “·” represents a logical AND.</claim-text>

<claim-text>29. The apparatus of <claim-ref idref="CLM-00026">claim 26</claim-ref>, wherein the logical function comprises OUT= <o ostyle="single">(A·B)+(C·D)+(E·F)</o> <o ostyle="single">(A·B)+(C·D)+(E·F)</o> <o ostyle="single">(A·B)+(C·D)+(E·F)</o>, where OUT represents an output signal generated on the output, A, B, C, D, E, and F represent input signals received on the multiple inputs, “+” represents a logical OR, and “·” represents a logical AND.</claim-text>

<claim-text>31. The apparatus of <claim-ref idref="CLM-00026">claim 26</claim-ref>, wherein the logical function comprises OUT={overscore (A+(B·C))}, where OUT represents an output signal generated on the output, A, B, and C represent input signals received on the multiple inputs, “+” represents a logical OR, and “·” represents a logical AND, and wherein the decoder comprises a logical inverter coupled to logically invert an inversion of one of the multiple inputs.</claim-text>

<claim-text>31. The apparatus of <claim-ref idref="CLM-00026">claim 26</claim-ref>, wherein the logical function comprises OUT= <o ostyle="single">A+(B·C)</o>, where OUT represents an output signal generated on the output, A, B, and C represent input signals received on the multiple inputs, “+” represents a logical OR, and “·” represents a logical AND, and wherein the decoder comprises a logical inverter coupled to logically invert an inversion of one of the multiple inputs.</claim-text>

<claim-text>32. The apparatus of <claim-ref idref="CLM-00026">claim 26</claim-ref>, wherein the logical function comprises OUT={overscore (A+(B·C)+D)}, where OUT represents an output signal generated on the output, A, B, C, and D represent input signals received on the multiple inputs, “+” represents a logical OR, and “·” represents a logical AND, and wherein the decoder comprises a logical NAND gate coupled to logically NAND the inversions of the second portion of the multiple inputs not coupled to the pull up network.</claim-text>

<claim-text>32. The apparatus of <claim-ref idref="CLM-00026">claim 26</claim-ref>, wherein the logical function comprises OUT= <o ostyle="single">A+(B·C)+D</o>, where OUT represents an output signal generated on the output, A, B, C, and D represent input signals received on the multiple inputs, “+” represents a logical OR, and “·” represents a logical AND, and wherein the decoder comprises a logical NAND gate coupled to logically NAND the inversions of the second portion of the multiple inputs not coupled to the pull up network.</claim-text>

<claim-text>38. The method of <claim-ref idref="CLM-00035">claim 35</claim-ref>, wherein the logical function comprises {overscore ((A·B)+(C·D))}{overscore ((A·B)+(C·D))}, where A, B, C, and D represent the received digital logic signals, “+” represents a logical OR, and “·” represents a logical AND, and wherein determining whether a contention state exists comprises:

<claim-text>38. The method of <claim-ref idref="CLM-00035">claim 35</claim-ref>, wherein the logical function comprises <o ostyle="single">(A·B)+(C·D)</o> <o ostyle="single">(A·B)+(C·D)</o>, where A, B, C, and D represent the received digital logic signals, “+” represents a logical OR, and “·” represents a logical AND, and wherein determining whether a contention state exists comprises:

<claim-text>39. The method of <claim-ref idref="CLM-00035">claim 35</claim-ref>, wherein the logical function comprises {overscore ((A·B)+(C·D)+(E·F))}{overscore ((A·B)+(C·D)+(E·F))}{overscore ((A·B)+(C·D)+(E·F))}, where A, B, C, D, E, and F represent the received digital logic signals, “+” represents a logical OR, and “·” represents a logical AND, and wherein determining whether a contention state exists comprises:

<claim-text>39. The method of <claim-ref idref="CLM-00035">claim 35</claim-ref>, wherein the logical function comprises <o ostyle="single">(A·B)+(C·D)+(E·F)</o> <o ostyle="single">(A·B)+(C·D)+(E·F)</o> <o ostyle="single">(A·B)+(C·D)+(E·F)</o>, where A, B, C, D, E, and F represent the received digital logic signals, “+” represents a logical OR, and “·” represents a logical AND, and wherein determining whether a contention state exists comprises:

<claim-text>40. The method of <claim-ref idref="CLM-00035">claim 35</claim-ref>, wherein the logical function comprises {overscore (A+(B·C))}, where A, B, and C represent the received digital logic signals, “+” represents a logical OR, and “·” represents a logical AND, and wherein determining whether a contention state exists comprises:

<claim-text>40. The method of <claim-ref idref="CLM-00035">claim 35</claim-ref>, wherein the logical function comprises <o ostyle="single">A+(B·C)</o>, where A, B, and C represent the received digital logic signals, “+” represents a logical OR, and “·” represents a logical AND, and wherein determining whether a contention state exists comprises:

<claim-text>41. The method of <claim-ref idref="CLM-00035">claim 35</claim-ref>, wherein the logical function comprises {overscore (A+(B·C)+D)}, where A, B, C, and D represent the received digital logic signals, “+” represents a logical OR, and “·” represents a logical AND, and wherein determining whether a contention state exists comprises:

<claim-text>41. The method of <claim-ref idref="CLM-00035">claim 35</claim-ref>, wherein the logical function comprises <o ostyle="single">A+(B·C)+D</o>, where A, B, C, and D represent the received digital logic signals, “+” represents a logical OR, and “·” represents a logical AND, and wherein determining whether a contention state exists comprises:

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<p id="p-0004" num="0003"><figref idref="DRAWINGS">FIG. 1</figref> shows a prior art POR circuit <b>100</b> for generating a power-on reset signal RST for an associated IC device (not shown for simplicity). POR circuit <b>100</b> includes a PMOS transistor <b>101</b>, NMOS transistors <b>102</b>–<b>104</b>, a diode-connected NMOS transistor <b>105</b>, resistors <b>106</b>–<b>107</b>, and an inverter <b>108</b>. Resistors <b>106</b>–<b>107</b> and diode <b>105</b>, which are connected in series between a supply voltage VDD and ground potential, form a voltage divider at node <b>111</b>, which is coupled to the input of a CMOS inverter <b>110</b> formed by PMOS transistor <b>101</b> and NMOS transistor <b>102</b>. The output <b>112</b> of CMOS inverter <b>110</b> provides RST. NMOS transistors <b>103</b> and <b>104</b> are connected in series between output node <b>112</b> and ground potential, with the gate of transistor <b>103</b> coupled to node <b>111</b> and the gate of transistor <b>104</b> coupled to the output of inverter <b>108</b>. Inverter <b>108</b> is configured to logically invert RST to generate its complement {overscore (RST)}.</p>	<p id="p-0004" num="0003"><figref idref="DRAWINGS">FIG. 1</figref> shows a prior art POR circuit <b>100</b> for generating a power-on reset signal RST for an associated IC device (not shown for simplicity). POR circuit <b>100</b> includes a PMOS transistor <b>101</b>, NMOS transistors <b>102</b>–<b>104</b>, a diode-connected NMOS transistor <b>105</b>, resistors <b>106</b>–<b>107</b>, and an inverter <b>108</b>. Resistors <b>106</b>–<b>107</b> and diode <b>105</b>, which are connected in series between a supply voltage VDD and ground potential, form a voltage divider at node <b>111</b>, which is coupled to the input of a CMOS inverter <b>110</b> formed by PMOS transistor <b>101</b> and NMOS transistor <b>102</b>. The output <b>112</b> of CMOS inverter <b>110</b> provides RST. NMOS transistors <b>103</b> and <b>104</b> are connected in series between output node <b>112</b> and ground potential, with the gate of transistor <b>103</b> coupled to node <b>111</b> and the gate of transistor <b>104</b> coupled to the output of inverter <b>108</b>. Inverter <b>108</b> is configured to logically invert RST to generate its complement <o ostyle="single">RST</o>.</p>
<p id="p-0005" num="0004">When POR circuit <b>100</b> is powered-up, VDD rises from 0 volts to its normal operating voltage. Node <b>111</b>, which is initially at or near ground potential, turns on PMOS transistor <b>101</b> and turns off NMOS transistors <b>102</b> and <b>103</b>, thereby charging node <b>112</b> toward VDD through PMOS transistor <b>101</b>. The resulting logic high state of RST is inverted by inverter <b>108</b> to generate a logic low {overscore (RST)} that maintains NMOS transistor <b>104</b> in a non-conductive state. The increasing operating voltage VDD also charges node <b>111</b> through resistor <b>106</b>, albeit more slowly than node <b>112</b>. When the voltage at node <b>111</b> reaches the trip point of CMOS inverter <b>110</b>, PMOS transistor <b>101</b> turns off and NMOS transistor <b>102</b> turns on, thereby discharging node <b>112</b> to ground potential and de-asserting RST to logic low.</p>	<p id="p-0005" num="0004">When POR circuit <b>100</b> is powered-up, VDD rises from 0 volts to its normal operating voltage. Node <b>111</b>, which is initially at or near ground potential, turns on PMOS transistor <b>101</b> and turns off NMOS transistors <b>102</b> and <b>103</b>, thereby charging node <b>112</b> toward VDD through PMOS transistor <b>101</b>. The resulting logic high state of RST is inverted by inverter <b>108</b> to generate a logic low <o ostyle="single">RST</o> that maintains NMOS transistor <b>104</b> in a non-conductive state. The increasing operating voltage VDD also charges node <b>111</b> through resistor <b>106</b>, albeit more slowly than node <b>112</b>. When the voltage at node <b>111</b> reaches the trip point of CMOS inverter <b>110</b>, PMOS transistor <b>101</b> turns off and NMOS transistor <b>102</b> turns on, thereby discharging node <b>112</b> to ground potential and de-asserting RST to logic low.</p>
<p id="p-0006" num="0005">The rising voltage at node <b>111</b> also turns on transistor <b>103</b>, and inverter <b>108</b> inverts RST to generate a logic high {overscore (RST)} which turns on NMOS transistor <b>104</b>. Thus, when RST is de-asserted to logic low, transistors <b>103</b> and <b>104</b> provide an additional discharge path to ground potential for output node <b>112</b>.</p>	<p id="p-0006" num="0005">The rising voltage at node <b>111</b> also turns on transistor <b>103</b>, and inverter <b>108</b> inverts RST to generate a logic high <o ostyle="single">RST</o> which turns on NMOS transistor <b>104</b>. Thus, when RST is de-asserted to logic low, transistors <b>103</b> and <b>104</b> provide an additional discharge path to ground potential for output node <b>112</b>.</p>
<p id="p-0007" num="0006">POR circuit <b>100</b> can also assert RST to logic high when VDD decreases below an acceptable level. For example, when VDD decreases below its normal operating voltage, the voltage at node <b>111</b> also decreases. When the voltage on node <b>111</b> falls below the trip point of CMOS inverter <b>110</b>, NMOS transistors <b>102</b> and <b>103</b> turn off and PMOS transistor <b>101</b> turns on, thereby charging node <b>112</b> toward VDD to assert RST to logic high. Inverter <b>108</b> inverts RST to generate a logic low {overscore (RST)} which turns off NMOS transistor <b>104</b>, thereby isolating output node <b>112</b> from ground potential.</p>	<p id="p-0007" num="0006">POR circuit <b>100</b> can also assert RST to logic high when VDD decreases below an acceptable level. For example, when VDD decreases below its normal operating voltage, the voltage at node <b>111</b> also decreases. When the voltage on node <b>111</b> falls below the trip point of CMOS inverter <b>110</b>, NMOS transistors <b>102</b> and <b>103</b> turn off and PMOS transistor <b>101</b> turns on, thereby charging node <b>112</b> toward VDD to assert RST to logic high. Inverter <b>108</b> inverts RST to generate a logic low <o ostyle="single">RST</o> which turns off NMOS transistor <b>104</b>, thereby isolating output node <b>112</b> from ground potential.</p>

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<p id="p-0041" num="0040">The first phase detector and charge pump sync portion <b>401</b> is used such that a delay time of the VCDL circuit portion <b>405</b> of the reference clock REF_CLK has a value between 0.5 T and 1.5 T. The first phase detector and charge pump sync portion <b>401</b> in response to a reset signal {overscore (RESET)} detects the phase of the first phase clock signal P<b>0</b> and the fifth phase clock signal P<b>180</b> and generates a charge pump enable signal CP_EN and a first control voltage R_VCTL.</p>	<p id="p-0041" num="0040">The first phase detector and charge pump sync portion <b>401</b> is used such that a delay time of the VCDL circuit portion <b>405</b> of the reference clock REF_CLK has a value between 0.5 T and 1.5 T. The first phase detector and charge pump sync portion <b>401</b> in response to a reset signal <o ostyle="single">RESET</o> detects the phase of the first phase clock signal P<b>0</b> and the fifth phase clock signal P<b>180</b> and generates a charge pump enable signal CP_EN and a first control voltage R_VCTL.</p>
<p id="p-0042" num="0041"><figref idref="DRAWINGS">FIG. 5</figref> shows in detail the first phase detector and charge pump sync portion <b>401</b>. Referring to <figref idref="DRAWINGS">FIG. 5</figref>, a first phase detection portion <b>510</b> includes a D-flipflop <b>511</b> for outputting the first phase clock signal P<b>0</b> in response to the fifth phase clock signal and an S-R latch <b>512</b> for generating a charge pump enable signal CP_EN in response to the output of the D-flipflop <b>511</b> and the reset signal {overscore (RESET)}.</p>	<p id="p-0042" num="0041"><figref idref="DRAWINGS">FIG. 5</figref> shows in detail the first phase detector and charge pump sync portion <b>401</b>. Referring to <figref idref="DRAWINGS">FIG. 5</figref>, a first phase detection portion <b>510</b> includes a D-flipflop <b>511</b> for outputting the first phase clock signal P<b>0</b> in response to the fifth phase clock signal and an S-R latch <b>512</b> for generating a charge pump enable signal CP_EN in response to the output of the D-flipflop <b>511</b> and the reset signal <o ostyle="single">RESET</o>.</p>
<p id="p-0043" num="0042">The charge pump sync portion <b>520</b> generates a first control voltage R_VCTL in response to the reset signal {overscore (RESET)}, the output of the S-R latch <b>512</b>, and a bias signal Vb. The charge pump sync portion <b>520</b> includes a PMOS transistor <b>521</b> and first through third NMOS transistors <b>522</b>, <b>523</b>, and <b>524</b> which are connected in series between a power voltage VDD and a ground voltage VSS. Gates of the PMOS transistor <b>521</b> and the second NMOS transistors <b>522</b>, <b>523</b>, and <b>524</b> are connected to the reset signal {overscore (RESET)}, a gate of the first NMOS transistor <b>522</b> is connected to an output of the S-R latch <b>512</b>, and a gate of the third NMOS transistor <b>524</b> is connected to the bias signal Vb. Drains of the PMOS transistor <b>521</b> and the first NMOS transistor <b>522</b> become the first control voltage R_VCTL. The first control voltage R_VCTL is provided to the first loop filter <b>403</b> which is formed of a capacitor.</p>	<p id="p-0043" num="0042">The charge pump sync portion <b>520</b> generates a first control voltage R_VCTL in response to the reset signal <o ostyle="single">RESET</o>, the output of the S-R latch <b>512</b>, and a bias signal Vb. The charge pump sync portion <b>520</b> includes a PMOS transistor <b>521</b> and first through third NMOS transistors <b>522</b>, <b>523</b>, and <b>524</b> which are connected in series between a power voltage VDD and a ground voltage VSS. Gates of the PMOS transistor <b>521</b> and the second NMOS transistors <b>522</b>, <b>523</b>, and <b>524</b> are connected to the reset signal <o ostyle="single">RESET</o>, a gate of the first NMOS transistor <b>522</b> is connected to an output of the S-R latch <b>512</b>, and a gate of the third NMOS transistor <b>524</b> is connected to the bias signal Vb. Drains of the PMOS transistor <b>521</b> and the first NMOS transistor <b>522</b> become the first control voltage R_VCTL. The first control voltage R_VCTL is provided to the first loop filter <b>403</b> which is formed of a capacitor.</p>

The operation of the reference DLL 301 is described below. When the reset signal {overscore (RESET)} is activated, the first control voltage R_VCTL becomes the power voltage VDD and the delay time of the VCDL circuit portion 405 has the minimum value. The minimum delay time must be less than T. When the reset signal {overscore (RESET)} is deactivated, the delay time of the VCDL circuit portion 405 increases close to T. The second phase detector and charge pump portion 402 operate until the delay time of the VCDL circuit portion 405 is T. When the delay time of the VCDL circuit portion 405 is T, edges of the first phase clock signal P0 and the ninth phase clock signal P360 are accurately matched.

The operation of the reference DLL 301 is described below. When the reset signal <o ostyle="single">RESET</o> is activated, the first control voltage R_VCTL becomes the power voltage VDD and the delay time of the VCDL circuit portion 405 has the minimum value. The minimum delay time must be less than T. When the reset signal <o ostyle="single">RESET</o> is deactivated, the delay time of the VCDL circuit portion 405 increases close to T. The second phase detector and charge pump portion 402 operate until the delay time of the VCDL circuit portion 405 is T. When the delay time of the VCDL circuit portion 405 is T, edges of the first phase clock signal P0 and the ninth phase clock signal P360 are accurately matched.

\\QA012\C$\REDBOOK_VERIFICATION\RAWCOMPAREDATA\PROD_010907-XML\US07161404-20070109.XML	\\QA012\C$\REDBOOK_VERIFICATION\RAWCOMPAREDATA\TEST_010907-XML\US07161404-20070109.XML

<figref idref="DRAWINGS">FIG. 4</figref> is a block diagram of one embodiment of hardened latch 400 fabricated on a die using a complementary metal-oxide semiconductor (CMOS) manufacturing process. Hardened latch 400 includes first latch 403 coupled to second latch 406. Hardened latch 400 receives a data signal at input port 409 and a clock signal at input port 412 and generates data output signal {overscore (Q)} at output port 415. In operation, for one embodiment, data contained in the data signal at input port 409 is stored in latch 400 on a rising edge of the clock signal at port 412. The stored data is available as data signal {overscore (Q)} at output port 415. The stored data is protected from a single event upset (SEU) at a data storage node in either first latch 403 or second latch 406 by coupling first latch 403 to second latch 406. Hardened latch 400 is also immune to a series of SEUs occurring at internal data storage nodes of first latch 403 and second latch 406.

<figref idref="DRAWINGS">FIG. 4</figref> is a block diagram of one embodiment of hardened latch 400 fabricated on a die using a complementary metal-oxide semiconductor (CMOS) manufacturing process. Hardened latch 400 includes first latch 403 coupled to second latch 406. Hardened latch 400 receives a data signal at input port 409 and a clock signal at input port 412 and generates data output signal <o ostyle="single">Q</o> at output port 415. In operation, for one embodiment, data contained in the data signal at input port 409 is stored in latch 400 on a rising edge of the clock signal at port 412. The stored data is available as data signal <o ostyle="single">Q</o> at output port 415. The stored data is protected from a single event upset (SEU) at a data storage node in either first latch 403 or second latch 406 by coupling first latch 403 to second latch 406. Hardened latch 400 is also immune to a series of SEUs occurring at internal data storage nodes of first latch 403 and second latch 406.

In operation, writing to hardened latch 500 is performed via transmission gates 518 and 524. The latch is protected for an SEU occurring on a single internal node, which implies that at least two nodes have to be modified simultaneously in order to change the state of latch 500. Transmission gates 518 and 524 are sized so that the gate delay of the two gates is equal. For one embodiment, the size of each of the transmission gates 518 and 524 is equal to the size of the transmission gate 318 of the unhardened latch shown in <figref idref="DRAWINGS">FIG. 3</figref>. Output buffer 521 is sized so that when coupled to transmission gates 518 and 524 only a small increase in the D to {overscore (Q)} delay is incurred when compared with the D to {overscore (Q)} delay of the unhardened latch shown in <figref idref="DRAWINGS">FIG. 3</figref>. For one embodiment, output buffer 521 includes two output buffer transistors and the size of each of the two output buffer transistors is equal to the size of the output buffer transistors of the unhardened latch shown in <figref idref="DRAWINGS">FIG. 3</figref>.

In operation, writing to hardened latch 500 is performed via transmission gates 518 and 524. The latch is protected for an SEU occurring on a single internal node, which implies that at least two nodes have to be modified simultaneously in order to change the state of latch 500. Transmission gates 518 and 524 are sized so that the gate delay of the two gates is equal. For one embodiment, the size of each of the transmission gates 518 and 524 is equal to the size of the transmission gate 318 of the unhardened latch shown in <figref idref="DRAWINGS">FIG. 3</figref>. Output buffer 521 is sized so that when coupled to transmission gates 518 and 524 only a small increase in the D to <o ostyle="single">Q</o> delay is incurred when compared with the D to <o ostyle="single">Q</o> delay of the unhardened latch shown in <figref idref="DRAWINGS">FIG. 3</figref>. For one embodiment, output buffer 521 includes two output buffer transistors and the size of each of the two output buffer transistors is equal to the size of the output buffer transistors of the unhardened latch shown in <figref idref="DRAWINGS">FIG. 3</figref>.

At one stable state, nodes 527 and 536 store 1 and nodes 530 and 533 store 0. The output value at port 609 is 0. An SEU on either node 527 or 530 results in node 527 having value 0 and node 530 having value 1, because of coupling between nodes 527 and 530. Output buffer 612 attempts to drive output port 609 high. Nodes 533 and 536 retain their original values 0 and 1, respectively. Output buffer 615 attempts to hold output port 609 at its correct value 0. There is a contention between buffer 612 and 615. In one embodiment, the nMOS and pMOS transistors of buffers 612 and 615 are sized so that the D to {overscore (Q)} delay is minimized. The pMOS transistor of buffer 612 is weaker than the nMOS transistor of buffer 615 and output port 609 preserves its correct value 0 only marginally degraded. An SEU on either node 533 or node 536 results in node 536 having value 0 and node 533 having value 1, because of coupling between nodes 536 and 533. Buffer 615 attempts to raise the voltage on output port 615. Nodes 527 and 530 retain their original values 1 and 0, respectively. The pMOS transistor of buffer 615 is weaker than the nMOS transistor of buffer 612 and output port 609 retains its correct value 0 only marginally degraded. In this stable state corresponding to logic value 0 at output port 609, transients at output port 609 are suppressed.

At one stable state, nodes 527 and 536 store 1 and nodes 530 and 533 store 0. The output value at port 609 is 0. An SEU on either node 527 or 530 results in node 527 having value 0 and node 530 having value 1, because of coupling between nodes 527 and 530. Output buffer 612 attempts to drive output port 609 high. Nodes 533 and 536 retain their original values 0 and 1, respectively. Output buffer 615 attempts to hold output port 609 at its correct value 0. There is a contention between buffer 612 and 615. In one embodiment, the nMOS and pMOS transistors of buffers 612 and 615 are sized so that the D to <o ostyle="single">Q</o> delay is minimized. The pMOS transistor of buffer 612 is weaker than the nMOS transistor of buffer 615 and output port 609 preserves its correct value 0 only marginally degraded. An SEU on either node 533 or node 536 results in node 536 having value 0 and node 533 having value 1, because of coupling between nodes 536 and 533. Buffer 615 attempts to raise the voltage on output port 615. Nodes 527 and 530 retain their original values 1 and 0, respectively. The pMOS transistor of buffer 615 is weaker than the nMOS transistor of buffer 612 and output port 609 retains its correct value 0 only marginally degraded. In this stable state corresponding to logic value 0 at output port 609, transients at output port 609 are suppressed.

Thus, the probability of a propagated error in subsequent logic stages is reduced by about 50% for the hardened latch in <figref idref="DRAWINGS">FIG. 6</figref> when compared with the hardened latch of <figref idref="DRAWINGS">FIG. 5</figref>, and at the same time the D to {overscore (Q)} delay of the latch of <figref idref="DRAWINGS">FIG. 6</figref> is smaller than the corresponding delay of the hardened latch of <figref idref="DRAWINGS">FIG. 5</figref>. In addition, with all other transistor sizes equal to the sizes of the unhardened latch shown in <figref idref="DRAWINGS">FIG. 3</figref>, there is no penalty on D to {overscore (Q)} delay, and setup and hold times of the latch in <figref idref="DRAWINGS">FIG. 5</figref> or the latch in <figref idref="DRAWINGS">FIG. 6</figref>. Depending on the size of the transistors of split buffers 612 and 615, the penalty on area and power consumption is typically about 50%.

Thus, the probability of a propagated error in subsequent logic stages is reduced by about 50% for the hardened latch in <figref idref="DRAWINGS">FIG. 6</figref> when compared with the hardened latch of <figref idref="DRAWINGS">FIG. 5</figref>, and at the same time the D to <o ostyle="single">Q</o> delay of the latch of <figref idref="DRAWINGS">FIG. 6</figref> is smaller than the corresponding delay of the hardened latch of <figref idref="DRAWINGS">FIG. 5</figref>. In addition, with all other transistor sizes equal to the sizes of the unhardened latch shown in <figref idref="DRAWINGS">FIG. 3</figref>, there is no penalty on D to <o ostyle="single">Q</o> delay, and setup and hold times of the latch in <figref idref="DRAWINGS">FIG. 5</figref> or the latch in <figref idref="DRAWINGS">FIG. 6</figref>. Depending on the size of the transistors of split buffers 612 and 615, the penalty on area and power consumption is typically about 50%.

<figref idref="DRAWINGS">FIG. 7</figref> is a schematic diagram of an alternate embodiment of hardened latch 700 having Miller C output buffer 701. The SEU performance of hardened latch 700 is superior to the SEU performance of either hardened latch 500 or hardened latch 600. An SEU can modify at most one of the nodes 527 and 536 at a time. The output port 703 can be modified only if both nodes 527 and 536 change simultaneously, which is possible only during writing into the cell via transmission gates 518 and 524. During the recovery time, the bit value stored at output port 703 retains its original value dynamically. A drawback of hardened latch of <figref idref="DRAWINGS">FIG. 7</figref> is that the D to {overscore (Q)} delay approximately doubles, while the setup and hold times remain essentially unchanged compared to the hardened latches shown in <figref idref="DRAWINGS">FIGS. 5 and 6</figref>.

<figref idref="DRAWINGS">FIG. 7</figref> is a schematic diagram of an alternate embodiment of hardened latch 700 having Miller C output buffer 701. The SEU performance of hardened latch 700 is superior to the SEU performance of either hardened latch 500 or hardened latch 600. An SEU can modify at most one of the nodes 527 and 536 at a time. The output port 703 can be modified only if both nodes 527 and 536 change simultaneously, which is possible only during writing into the cell via transmission gates 518 and 524. During the recovery time, the bit value stored at output port 703 retains its original value dynamically. A drawback of hardened latch of <figref idref="DRAWINGS">FIG. 7</figref> is that the D to <o ostyle="single">Q</o> delay approximately doubles, while the setup and hold times remain essentially unchanged compared to the hardened latches shown in <figref idref="DRAWINGS">FIGS. 5 and 6</figref>.

\\QA012\C$\REDBOOK_VERIFICATION\RAWCOMPAREDATA\PROD_010907-XML\US07161523-20070109.XML	\\QA012\C$\REDBOOK_VERIFICATION\RAWCOMPAREDATA\TEST_010907-XML\US07161523-20070109.XML

<?in-line-formulae description="In-line Formulae" end="lead"?>if ({overscore (c)}j+1·cj)<img id="CUSTOM-CHARACTER-00001" he="2.79mm" wi="3.89mm" file="US07161523-20070109-P00001.TIF" alt="custom character" img-content="character" img-format="tif"/>(trimj+=∂, trimj+1−=∂) Equation 3<?in-line-formulae description="In-line Formulae" end="tail"?>

<?in-line-formulae description="In-line Formulae" end="lead"?>if ( <o ostyle="single">c</o>j+1·cj)<img id="CUSTOM-CHARACTER-00001" he="2.79mm" wi="3.89mm" file="US07161523-20070109-P00001.TIF" alt="custom character" img-content="character" img-format="tif"/>(trimj+=∂, trimj+1−=∂) Equation 3<?in-line-formulae description="In-line Formulae" end="tail"?>

\\QA012\C$\REDBOOK_VERIFICATION\RAWCOMPAREDATA\PROD_010907-XML\US07161529-20070109.XML	\\QA012\C$\REDBOOK_VERIFICATION\RAWCOMPAREDATA\TEST_010907-XML\US07161529-20070109.XML

<?in-line-formulae description="In-line Formulae" end="lead"?>DP=√{square root over (R2−(HR−HT)2)} Eqn. 5<?in-line-formulae description="In-line Formulae" end="tail"?>

<?in-line-formulae description="In-line Formulae" end="lead"?>DP=√{square root over (R2−(HR−HT)2)} Eqn. 5<?in-line-formulae description="In-line Formulae" end="tail"?>

\\QA012\C$\REDBOOK_VERIFICATION\RAWCOMPAREDATA\PROD_010907-XML\US07161532-20070109.XML	\\QA012\C$\REDBOOK_VERIFICATION\RAWCOMPAREDATA\TEST_010907-XML\US07161532-20070109.XML

<?in-line-formulae description="In-line Formulae" end="lead"?>ρi=√{square root over (({overscore (x)}i−{overscore (x)})2)}+c·Δt+ε<?in-line-formulae description="In-line Formulae" end="tail"?>

<?in-line-formulae description="In-line Formulae" end="lead"?>ρi=√{square root over (({overscore (x)}i−{overscore (x)}R)2)}+√{square root over (({overscore (x)}R−{overscore (x)})2)}+c·t<?in-line-formulae description="In-line Formulae" end="tail"?>

<?in-line-formulae description="In-line Formulae" end="lead"?>ρi=√{square root over (( <o ostyle="single">x</o>i− <o ostyle="single">x</o>R)2)}+√{square root over (( <o ostyle="single">x</o>R− <o ostyle="single">x</o>)2)}+c·t<?in-line-formulae description="In-line Formulae" end="tail"?>

\\QA012\C$\REDBOOK_VERIFICATION\RAWCOMPAREDATA\PROD_010907-XML\US07161597-20070109.XML	\\QA012\C$\REDBOOK_VERIFICATION\RAWCOMPAREDATA\TEST_010907-XML\US07161597-20070109.XML

<p id="p-0076" num="0108">To illustrate a scenario where the starting point and the end point of an edge are not located on pixel borders, method <b>200</b> is now explained in reference to <figref idref="DRAWINGS">FIG. 3</figref>. The image file provides an edge {overscore (P<b>0</b>P<b>3</b>)} that has a starting point P<b>0</b> in pixel <b>0</b> and an end point P<b>3</b> in a pixel <b>2</b>. Edge {overscore (P<b>0</b>P<b>3</b>)} intersects the border between pixels <b>0</b> and <b>1</b> at a point P<b>1</b>, and the border between pixels <b>1</b> and <b>2</b> at a point P<b>2</b>. Points P<b>1</b> and P<b>2</b> are conventionally calculated from points P<b>0</b> and P<b>3</b>, and the slope of edge {overscore (P<b>0</b>P<b>3</b>)}.</p>	<p id="p-0076" num="0108">To illustrate a scenario where the starting point and the end point of an edge are not located on pixel borders, method <b>200</b> is now explained in reference to <figref idref="DRAWINGS">FIG. 3</figref>. The image file provides an edge <o ostyle="single">P<b>0</b>P<b>3</b></o> that has a starting point P<b>0</b> in pixel <b>0</b> and an end point P<b>3</b> in a pixel <b>2</b>. Edge <o ostyle="single">P<b>0</b>P<b>3</b></o> intersects the border between pixels <b>0</b> and <b>1</b> at a point P<b>1</b>, and the border between pixels <b>1</b> and <b>2</b> at a point P<b>2</b>. Points P<b>1</b> and P<b>2</b> are conventionally calculated from points P<b>0</b> and P<b>3</b>, and the slope of edge <o ostyle="single">P<b>0</b>P<b>3</b></o>.</p>
<p id="p-0077" num="0109">In a first iteration through method <b>200</b>, the graphic engine processes the portion of edge {overscore (P<b>0</b>P<b>3</b>)} in pixel <b>0</b>. In step <b>201</b>, the graphic engine computes and initializes the variables for point P<b>0</b>. Most notably, the graphic engine computes dx<b>0</b>. As the edge does not start and end within one pixel, dx<b>1</b> is initialized as 0. In step <b>202</b>, the graphic engine determines there is no exceeded area from rasterizing a previous scan line because edge {overscore (P<b>0</b>P<b>3</b>)} starts in the current scan line. Thus, step <b>202</b> is followed by step <b>205</b>. In step <b>205</b>, the graphic engine determines that dx<b>0</b> does not equal to 0 because point P<b>0</b> is not located on the left border of pixel <b>0</b>. Thus, step <b>205</b> is followed by step <b>206</b>. In step <b>206</b>, the graphic engine computes dy<b>0</b> for point P<b>0</b>. In step <b>208</b>, the graphic engine computes area<b>0</b> from dy<b>0</b>. In step <b>210</b>, the graphic engine decrements dx by dx<b>0</b>, and dy by dy<b>0</b>. In step <b>214</b>, the graphic engine decrements da by area<b>0</b>, which is not part of the area projected by edge {overscore (P<b>0</b>P<b>3</b>)} in pixel <b>0</b>. In step <b>215</b>, the graphic engine sets dx<b>0</b> equal to 0.</p>	<p id="p-0077" num="0109">In a first iteration through method <b>200</b>, the graphic engine processes the portion of edge <o ostyle="single">P<b>0</b>P<b>3</b></o> in pixel <b>0</b>. In step <b>201</b>, the graphic engine computes and initializes the variables for point P<b>0</b>. Most notably, the graphic engine computes dx<b>0</b>. As the edge does not start and end within one pixel, dx<b>1</b> is initialized as 0. In step <b>202</b>, the graphic engine determines there is no exceeded area from rasterizing a previous scan line because edge <o ostyle="single">P<b>0</b>P<b>3</b></o> starts in the current scan line. Thus, step <b>202</b> is followed by step <b>205</b>. In step <b>205</b>, the graphic engine determines that dx<b>0</b> does not equal to 0 because point P<b>0</b> is not located on the left border of pixel <b>0</b>. Thus, step <b>205</b> is followed by step <b>206</b>. In step <b>206</b>, the graphic engine computes dy<b>0</b> for point P<b>0</b>. In step <b>208</b>, the graphic engine computes area<b>0</b> from dy<b>0</b>. In step <b>210</b>, the graphic engine decrements dx by dx<b>0</b>, and dy by dy<b>0</b>. In step <b>214</b>, the graphic engine decrements da by area<b>0</b>, which is not part of the area projected by edge <o ostyle="single">P<b>0</b>P<b>3</b></o> in pixel <b>0</b>. In step <b>215</b>, the graphic engine sets dx<b>0</b> equal to 0.</p>
<p id="p-0078" num="0110">In step <b>216</b>, the graphic engine determines that dx<b>1</b> is equal to 0 because point P<b>0</b> is not an end point located inside pixel <b>0</b>. Thus, step <b>216</b> is followed by step <b>228</b>. In step <b>228</b>, the graphic engine increments da by the carryover area, which was initialized to 0. In step <b>230</b>, the graphic engine increments x_current by dx, and y_current by dy, to advance from point P<b>0</b> in pixel <b>0</b> to point P<b>1</b> in pixel <b>1</b>. In step <b>234</b>, the graphic engine increments dy_metering by dy to track when edge {overscore (P<b>0</b>P<b>3</b>)} reaches the next scan line.</p>	<p id="p-0078" num="0110">In step <b>216</b>, the graphic engine determines that dx<b>1</b> is equal to 0 because point P<b>0</b> is not an end point located inside pixel <b>0</b>. Thus, step <b>216</b> is followed by step <b>228</b>. In step <b>228</b>, the graphic engine increments da by the carryover area, which was initialized to 0. In step <b>230</b>, the graphic engine increments x_current by dx, and y_current by dy, to advance from point P<b>0</b> in pixel <b>0</b> to point P<b>1</b> in pixel <b>1</b>. In step <b>234</b>, the graphic engine increments dy_metering by dy to track when edge <o ostyle="single">P<b>0</b>P<b>3</b></o> reaches the next scan line.</p>
<p id="p-0079" num="0111">In step <b>238</b>, the graphic engine determines that dy_metering is less than GF_ONE because edge {overscore (P<b>0</b>P<b>3</b>)} is still in the current scan line. Thus, step <b>238</b> is followed by step <b>246</b>. In step <b>246</b>, the graphic engine saves the value of da as the area projected by edge {overscore (P<b>0</b>P<b>3</b>)} in pixel <b>0</b>. In step <b>247</b>, the graphic engine decrements dx_left by dx to track when the end of edge {overscore (P<b>0</b>P<b>3</b>)} will be reached. In step <b>248</b>, the graphic engine determines that dx_left is not equal to 0 because it has not reahed the end of edge {overscore (P<b>0</b>P<b>3</b>)}. Thus, step <b>248</b> is followed by step <b>250</b>. In step <b>250</b>, the graphic engine does not calulate dx<b>1</b> because the next pixel (pixel <b>1</b>) is not the last pixel that edge {overscore (P<b>0</b>P<b>3</b>)} touches. In step <b>251</b>, the graphic engine increments the carryover area, which was initialized to 0, by dy. In step <b>252</b>, the graphic engine reinitializes dx, dy, and da. Step <b>252</b> is followed by step <b>205</b> and the methods repeats for point P<b>1</b> in pixel <b>1</b>.</p>	<p id="p-0079" num="0111">In step <b>238</b>, the graphic engine determines that dy_metering is less than GF_ONE because edge <o ostyle="single">P<b>0</b>P<b>3</b></o> is still in the current scan line. Thus, step <b>238</b> is followed by step <b>246</b>. In step <b>246</b>, the graphic engine saves the value of da as the area projected by edge <o ostyle="single">P<b>0</b>P<b>3</b></o> in pixel <b>0</b>. In step <b>247</b>, the graphic engine decrements dx_left by dx to track when the end of edge <o ostyle="single">P<b>0</b>P<b>3</b></o> will be reached. In step <b>248</b>, the graphic engine determines that dx_left is not equal to 0 because it has not reahed the end of edge <o ostyle="single">P<b>0</b>P<b>3</b></o>. Thus, step <b>248</b> is followed by step <b>250</b>. In step <b>250</b>, the graphic engine does not calulate dx<b>1</b> because the next pixel (pixel <b>1</b>) is not the last pixel that edge <o ostyle="single">P<b>0</b>P<b>3</b></o> touches. In step <b>251</b>, the graphic engine increments the carryover area, which was initialized to 0, by dy. In step <b>252</b>, the graphic engine reinitializes dx, dy, and da. Step <b>252</b> is followed by step <b>205</b> and the methods repeats for point P<b>1</b> in pixel <b>1</b>.</p>
<p id="p-0080" num="0112">In a second iteration through method <b>200</b>, the graphic engine processes point P<b>1</b> in pixel <b>1</b>. In step <b>205</b>, the graphic engine determines that dx<b>0</b> is set to 0. Thus, step <b>205</b> is followed by step <b>216</b>. In step <b>216</b>, the graphic engine determines that dx<b>1</b> is equal to 0 because point P<b>1</b> is not an end point located inside pixel <b>1</b>. Thus, step <b>216</b> is followed by step <b>228</b>. In step <b>228</b>, the graphic engine increments da by the carryover area calculated in the previous iteration at step <b>251</b>. In step <b>230</b>, the graphic engine increments x_current by dx, and y_current by dy, to advance from point P<b>1</b> in pixel <b>1</b> to point P<b>2</b> in pixel <b>2</b>. In step <b>234</b>, the graphic engine increments dy_metering by dy to track when edge {overscore (P<b>0</b>P<b>3</b>)} reaches the next scan line.</p>	<p id="p-0080" num="0112">In a second iteration through method <b>200</b>, the graphic engine processes point P<b>1</b> in pixel <b>1</b>. In step <b>205</b>, the graphic engine determines that dx<b>0</b> is set to 0. Thus, step <b>205</b> is followed by step <b>216</b>. In step <b>216</b>, the graphic engine determines that dx<b>1</b> is equal to 0 because point P<b>1</b> is not an end point located inside pixel <b>1</b>. Thus, step <b>216</b> is followed by step <b>228</b>. In step <b>228</b>, the graphic engine increments da by the carryover area calculated in the previous iteration at step <b>251</b>. In step <b>230</b>, the graphic engine increments x_current by dx, and y_current by dy, to advance from point P<b>1</b> in pixel <b>1</b> to point P<b>2</b> in pixel <b>2</b>. In step <b>234</b>, the graphic engine increments dy_metering by dy to track when edge <o ostyle="single">P<b>0</b>P<b>3</b></o> reaches the next scan line.</p>
<p id="p-0081" num="0113">In step <b>238</b>, the graphic engine determines that dy_metering is less than GF_ONE because edge {overscore (P<b>0</b>P<b>3</b>)} is still in the current scan line. Thus, step <b>238</b> is followed by step <b>246</b>. In step <b>246</b>, the graphic engine saves the value of da as the projected area by edge {overscore (P<b>0</b>P<b>3</b>)} in pixel <b>1</b>. In step <b>247</b>, the graphic engine decrements dx_left by dx to track when the end of edge {overscore (P<b>0</b>P<b>3</b>)} will be reached. In step <b>248</b>, the graphic engine determines that dx_left is not equal to 0 because it has not reached the end of edge {overscore (P<b>0</b>P<b>3</b>)}. Thus, step <b>248</b> is followed by step <b>250</b>. In step <b>250</b>, the graphic engine calculates dx<b>1</b> because the next pixel (pixel <b>2</b>) is the last pixel that edge {overscore (P<b>0</b>P<b>3</b>)} touches. In step <b>251</b>, the graphic engine increments the carryover area by dy. In step <b>252</b>, the graphic engine reinitializes dx, dy, and da. Step <b>252</b> is followed by step <b>205</b> and the methods repeats for point P<b>2</b> in pixel <b>2</b>.</p>	<p id="p-0081" num="0113">In step <b>238</b>, the graphic engine determines that dy_metering is less than GF_ONE because edge <o ostyle="single">P<b>0</b>P<b>3</b></o> is still in the current scan line. Thus, step <b>238</b> is followed by step <b>246</b>. In step <b>246</b>, the graphic engine saves the value of da as the projected area by edge <o ostyle="single">P<b>0</b>P<b>3</b></o> in pixel <b>1</b>. In step <b>247</b>, the graphic engine decrements dx_left by dx to track when the end of edge <o ostyle="single">P<b>0</b>P<b>3</b></o> will be reached. In step <b>248</b>, the graphic engine determines that dx_left is not equal to 0 because it has not reached the end of edge <o ostyle="single">P<b>0</b>P<b>3</b></o>. Thus, step <b>248</b> is followed by step <b>250</b>. In step <b>250</b>, the graphic engine calculates dx<b>1</b> because the next pixel (pixel <b>2</b>) is the last pixel that edge <o ostyle="single">P<b>0</b>P<b>3</b></o> touches. In step <b>251</b>, the graphic engine increments the carryover area by dy. In step <b>252</b>, the graphic engine reinitializes dx, dy, and da. Step <b>252</b> is followed by step <b>205</b> and the methods repeats for point P<b>2</b> in pixel <b>2</b>.</p>

<p id="p-0083" num="0115">In step <b>218</b>, the graphic engine determines dy<b>1</b> for point P<b>2</b>. In step <b>220</b>, the graphic engine determines area<b>1</b> from dy<b>1</b>. In step <b>222</b>, the graphic engine decrements dx by dx<b>1</b>, and dy by dy<b>1</b>. In step <b>226</b>, the graphic engine decrements da by area<b>1</b>, which is not an area projected by edge {overscore (P<b>0</b>P<b>3</b>)} in pixel <b>2</b>.</p>	<p id="p-0083" num="0115">In step <b>218</b>, the graphic engine determines dy<b>1</b> for point P<b>2</b>. In step <b>220</b>, the graphic engine determines area<b>1</b> from dy<b>1</b>. In step <b>222</b>, the graphic engine decrements dx by dx<b>1</b>, and dy by dy<b>1</b>. In step <b>226</b>, the graphic engine decrements da by area<b>1</b>, which is not an area projected by edge <o ostyle="single">P<b>0</b>P<b>3</b></o> in pixel <b>2</b>.</p>
<p id="p-0084" num="0116">In step <b>228</b>, the graphic engine increments da by the carryover area calculated in the previous iteration at step <b>251</b>. In step <b>230</b>, the graphic engine increments x_current by dx, and y_current by dy, to advance from point P<b>2</b> in pixel <b>2</b> to point P<b>3</b> in pixel <b>2</b>. In step <b>234</b>, the graphic engine increments dy_metering by dy to track when edge {overscore (P<b>0</b>P<b>3</b>)} reaches the next scan line.</p>	<p id="p-0084" num="0116">In step <b>228</b>, the graphic engine increments da by the carryover area calculated in the previous iteration at step <b>251</b>. In step <b>230</b>, the graphic engine increments x_current by dx, and y_current by dy, to advance from point P<b>2</b> in pixel <b>2</b> to point P<b>3</b> in pixel <b>2</b>. In step <b>234</b>, the graphic engine increments dy_metering by dy to track when edge <o ostyle="single">P<b>0</b>P<b>3</b></o> reaches the next scan line.</p>
<p id="p-0085" num="0117">In step <b>238</b>, the graphic engine determines that dy_metering is less than GF_ONE because edge {overscore (P<b>0</b>P<b>3</b>)} is still in the current scan line. Thus, step <b>238</b> is followed by step <b>246</b>. In step <b>246</b>, the graphic engine saves the value of da as the projected area by edge {overscore (P<b>0</b>P<b>3</b>)} in pixel <b>2</b>. In step <b>247</b>, the graphic engine decrements dx_left by dx to track when the end of edge {overscore (P<b>0</b>P<b>3</b>)} will be reached. In step <b>248</b>, the graphic engine determines that dx_left is equal to 0 because it has reached the end of edge {overscore (P<b>0</b>P<b>3</b>)}. Thus, step <b>248</b> is followed by step <b>254</b>, which ends method <b>200</b>.</p>	<p id="p-0085" num="0117">In step <b>238</b>, the graphic engine determines that dy_metering is less than GF_ONE because edge <o ostyle="single">P<b>0</b>P<b>3</b></o> is still in the current scan line. Thus, step <b>238</b> is followed by step <b>246</b>. In step <b>246</b>, the graphic engine saves the value of da as the projected area by edge <o ostyle="single">P<b>0</b>P<b>3</b></o> in pixel <b>2</b>. In step <b>247</b>, the graphic engine decrements dx_left by dx to track when the end of edge <o ostyle="single">P<b>0</b>P<b>3</b></o> will be reached. In step <b>248</b>, the graphic engine determines that dx_left is equal to 0 because it has reached the end of edge <o ostyle="single">P<b>0</b>P<b>3</b></o>. Thus, step <b>248</b> is followed by step <b>254</b>, which ends method <b>200</b>.</p>

<p id="p-0086" num="0118">To illustrate a scenario when an edge extends into the next scan line in one unit step, method <b>200</b> is now explained in reference to <figref idref="DRAWINGS">FIG. 4</figref>. <figref idref="DRAWINGS">FIG. 4</figref> shows an edge {overscore (P<b>4</b>P<b>9</b>)} having a starting point P<b>4</b> in a pixel <b>4</b> and an end point P<b>9</b> in a pixel <b>7</b>′. Edge {overscore (P<b>4</b>P<b>9</b>)} intersects the border between pixels <b>4</b> and <b>5</b> at a point P<b>5</b>, the border between pixels <b>5</b> and <b>6</b> at a point P<b>6</b>, and the border between pixels <b>6</b> and <b>6</b>′ at a point P<b>7</b>. Points P<b>5</b>, P<b>6</b>, and P<b>7</b> are conventionally calculated from points P<b>4</b> and P<b>8</b>, and the slope of edge {overscore (P<b>4</b>P<b>9</b>)}.</p>	<p id="p-0086" num="0118">To illustrate a scenario when an edge extends into the next scan line in one unit step, method <b>200</b> is now explained in reference to <figref idref="DRAWINGS">FIG. 4</figref>. <figref idref="DRAWINGS">FIG. 4</figref> shows an edge <o ostyle="single">P<b>4</b>P<b>9</b></o> having a starting point P<b>4</b> in a pixel <b>4</b> and an end point P<b>9</b> in a pixel <b>7</b>′. Edge <o ostyle="single">P<b>4</b>P<b>9</b></o> intersects the border between pixels <b>4</b> and <b>5</b> at a point P<b>5</b>, the border between pixels <b>5</b> and <b>6</b> at a point P<b>6</b>, and the border between pixels <b>6</b> and <b>6</b>′ at a point P<b>7</b>. Points P<b>5</b>, P<b>6</b>, and P<b>7</b> are conventionally calculated from points P<b>4</b> and P<b>8</b>, and the slope of edge <o ostyle="single">P<b>4</b>P<b>9</b></o>.</p>
<p id="p-0087" num="0119">In a first iteration through method <b>200</b>, the graphic engine starts with the portion of edge {overscore (P<b>4</b>P<b>9</b>)} in pixel <b>4</b>. In step <b>201</b>, the graphic engine computes and initializes the parameters for point P<b>4</b>. Most notably, the graphic engine computes dx<b>0</b>. As the edge does not start and end in one pixel, dx<b>1</b> is initialized as 0. In step <b>202</b>, the graphic engine determines there is no exceeded area from rasterizing a previous scan line and proceeds to step <b>205</b>. In step <b>205</b>, the graphic engine determines that dx<b>0</b> does not equal to 0 because point P<b>4</b> is not located on the left border of pixel <b>0</b>. Thus, step <b>205</b> is followed by step <b>206</b>. In step <b>206</b>, the graphic engine determines dy<b>0</b> for point P<b>4</b>. In step <b>208</b>, the graphic engine determines area<b>0</b> from dy<b>0</b>. In step <b>210</b>, the graphic engine decrements dx by dx<b>0</b>, and dy by dy<b>0</b>. In step <b>214</b>, the graphic engine decrements da by area<b>0</b>, which is not an area projected by edge {overscore (P<b>4</b>P<b>9</b>)} in pixel <b>4</b>.</p>	<p id="p-0087" num="0119">In a first iteration through method <b>200</b>, the graphic engine starts with the portion of edge <o ostyle="single">P<b>4</b>P<b>9</b></o> in pixel <b>4</b>. In step <b>201</b>, the graphic engine computes and initializes the parameters for point P<b>4</b>. Most notably, the graphic engine computes dx<b>0</b>. As the edge does not start and end in one pixel, dx<b>1</b> is initialized as 0. In step <b>202</b>, the graphic engine determines there is no exceeded area from rasterizing a previous scan line and proceeds to step <b>205</b>. In step <b>205</b>, the graphic engine determines that dx<b>0</b> does not equal to 0 because point P<b>4</b> is not located on the left border of pixel <b>0</b>. Thus, step <b>205</b> is followed by step <b>206</b>. In step <b>206</b>, the graphic engine determines dy<b>0</b> for point P<b>4</b>. In step <b>208</b>, the graphic engine determines area<b>0</b> from dy<b>0</b>. In step <b>210</b>, the graphic engine decrements dx by dx<b>0</b>, and dy by dy<b>0</b>. In step <b>214</b>, the graphic engine decrements da by area<b>0</b>, which is not an area projected by edge <o ostyle="single">P<b>4</b>P<b>9</b></o> in pixel <b>4</b>.</p>
<p id="p-0088" num="0120">In step <b>216</b>, the graphic engine determines that dx<b>1</b> of point P<b>4</b> is equal to 0 because point P<b>4</b> is not an end point located inside pixel <b>4</b>. Thus, step <b>216</b> is followed by step <b>228</b>. In step <b>228</b>, the graphic engine increments da by the carryover area, which was initialized as 0. In step <b>230</b>, the graphic engine increments x_current by dx, and y_current by dy, to advance from point P<b>4</b> in pixel <b>4</b> to point P<b>5</b> in pixel <b>5</b>. In step <b>234</b>, the graphic engine increments dy_metering by dy to track when edge {overscore (P<b>4</b>P<b>9</b>)} reaches the next scan line.</p>	<p id="p-0088" num="0120">In step <b>216</b>, the graphic engine determines that dx<b>1</b> of point P<b>4</b> is equal to 0 because point P<b>4</b> is not an end point located inside pixel <b>4</b>. Thus, step <b>216</b> is followed by step <b>228</b>. In step <b>228</b>, the graphic engine increments da by the carryover area, which was initialized as 0. In step <b>230</b>, the graphic engine increments x_current by dx, and y_current by dy, to advance from point P<b>4</b> in pixel <b>4</b> to point P<b>5</b> in pixel <b>5</b>. In step <b>234</b>, the graphic engine increments dy_metering by dy to track when edge <o ostyle="single">P<b>4</b>P<b>9</b></o> reaches the next scan line.</p>
<p id="p-0089" num="0121">In step <b>238</b>, the graphic engine determines that dy_metering is less than GF_ONE and proceeds to step <b>246</b>. In step <b>246</b>, the graphic engine saves the value of da as the area projected by edge {overscore (P<b>4</b>P<b>9</b>)} in pixel <b>4</b>. In step <b>247</b>, the graphic engine decrements dx_left by dx to track when it reaches the end of edge {overscore (P<b>4</b>P<b>9</b>)}. In step <b>248</b>, the graphic engine determines that dx_left is not equal to 0 and proceeds to step <b>250</b>. In step <b>250</b>, the graphic engine does not calculate dx<b>1</b> because the next pixel (pixel <b>5</b>) is not the last pixel that edge {overscore (P<b>4</b>P<b>9</b>)} touches. In step <b>251</b>, the graphic engine increments the carryover area, which was initialized to 0, by dy. In step <b>252</b>, the graphic engine reinitializes dx, dy, and da. Step <b>252</b> is followed by step <b>205</b> and the methods repeats for point P<b>5</b> in pixel <b>5</b>.</p>	<p id="p-0089" num="0121">In step <b>238</b>, the graphic engine determines that dy_metering is less than GF_ONE and proceeds to step <b>246</b>. In step <b>246</b>, the graphic engine saves the value of da as the area projected by edge <o ostyle="single">P<b>4</b>P<b>9</b></o> in pixel <b>4</b>. In step <b>247</b>, the graphic engine decrements dx_left by dx to track when it reaches the end of edge <o ostyle="single">P<b>4</b>P<b>9</b></o>. In step <b>248</b>, the graphic engine determines that dx_left is not equal to 0 and proceeds to step <b>250</b>. In step <b>250</b>, the graphic engine does not calculate dx<b>1</b> because the next pixel (pixel <b>5</b>) is not the last pixel that edge <o ostyle="single">P<b>4</b>P<b>9</b></o> touches. In step <b>251</b>, the graphic engine increments the carryover area, which was initialized to 0, by dy. In step <b>252</b>, the graphic engine reinitializes dx, dy, and da. Step <b>252</b> is followed by step <b>205</b> and the methods repeats for point P<b>5</b> in pixel <b>5</b>.</p>

In a third iteration through method 200, the graphic engine processes point P6 in pixel 6. In step 205, the graphic engine determines that dx0 is set to 0 and proceeds to step 216. In step 216, the graphic engine determines that dx1 of point P6 is equal to 0 because point 6 is not an end point located inside pixel 6. Thus, step 216 is followed by step 228. In step 228, the graphic engine computes increments da by the carryover area calculated in the previous iteration. In step 230, the graphic engine increments x_current by dx and y_current by dy to advance from point P6 to point P8. In step 234, the graphic engine increments dy_metering by dy to track when edge {overscore (P4P9)} reaches the next scan line.

In a third iteration through method 200, the graphic engine processes point P6 in pixel 6. In step 205, the graphic engine determines that dx0 is set to 0 and proceeds to step 216. In step 216, the graphic engine determines that dx1 of point P6 is equal to 0 because point 6 is not an end point located inside pixel 6. Thus, step 216 is followed by step 228. In step 228, the graphic engine computes increments da by the carryover area calculated in the previous iteration. In step 230, the graphic engine increments x_current by dx and y_current by dy to advance from point P6 to point P8. In step 234, the graphic engine increments dy_metering by dy to track when edge <o ostyle="single">P4P9</o> reaches the next scan line.

In step 238, the graphic engine determines that dy_metering is greater than GF_ONE because edge {overscore (P4P9)} extends into the next scan line in one unit step. Thus, step 238 is followed by optional step 239. In optional step 239, the graphic engine sets the flag for parameter sum_fill. In step 240, the graphic engine decrements dy_metering by GF_ONE. In step 242, the graphic engine computes the exceeded area in pixel 6′ from dy_metering. In step 244, the graphic engine decrements da by the exceeded area, which is not part of the area projected by edge {overscore (P4P9)} in pixel 6. In step 245, the graphic engine saves da as the area projected by edge {overscore (P4P9)} in pixel 6. In step 245A, the graphic engine saves the exceeded area of edge {overscore (P4P9)} in pixel 6′ so it can be used when the graphic engine processes edge {overscore (P4P9)} in the next scan line. In step 245B, the graphic engine saves the carryover area projected onto a pixel 7′ by the exceeded area in pixel 6′, which is simply dy_metering. Step 245B is followed by step 254, which ends method 200.

In step 238, the graphic engine determines that dy_metering is greater than GF_ONE because edge <o ostyle="single">P4P9</o> extends into the next scan line in one unit step. Thus, step 238 is followed by optional step 239. In optional step 239, the graphic engine sets the flag for parameter sum_fill. In step 240, the graphic engine decrements dy_metering by GF_ONE. In step 242, the graphic engine computes the exceeded area in pixel 6′ from dy_metering. In step 244, the graphic engine decrements da by the exceeded area, which is not part of the area projected by edge <o ostyle="single">P4P9</o> in pixel 6. In step 245, the graphic engine saves da as the area projected by edge <o ostyle="single">P4P9</o> in pixel 6. In step 245A, the graphic engine saves the exceeded area of edge <o ostyle="single">P4P9</o> in pixel 6′ so it can be used when the graphic engine processes edge <o ostyle="single">P4P9</o> in the next scan line. In step 245B, the graphic engine saves the carryover area projected onto a pixel 7′ by the exceeded area in pixel 6′, which is simply dy_metering. Step 245B is followed by step 254, which ends method 200.

\\QA012\C$\REDBOOK_VERIFICATION\RAWCOMPAREDATA\PROD_010907-XML\US07161676-20070109.XML	\\QA012\C$\REDBOOK_VERIFICATION\RAWCOMPAREDATA\TEST_010907-XML\US07161676-20070109.XML

<?in-line-formulae description="In-line Formulae" end="lead"?>ΔE=√{square root over (ΔL2+Δa2+Δb2)}<?in-line-formulae description="In-line Formulae" end="tail"?>

<?in-line-formulae description="In-line Formulae" end="lead"?>ΔE=√{square root over (ΔL2+Δa2+Δb2)}<?in-line-formulae description="In-line Formulae" end="tail"?>

\\QA012\C$\REDBOOK_VERIFICATION\RAWCOMPAREDATA\PROD_010907-XML\US07161680-20070109.XML	\\QA012\C$\REDBOOK_VERIFICATION\RAWCOMPAREDATA\TEST_010907-XML\US07161680-20070109.XML

The set of values used for pj and εm,j for different values of m and j will depend in part on whether the components of the measured conjugated quadratures are to be joint measurements or non-joint measurements. The average times {overscore (t)}d1 and {overscore (t)}d2 of the times of the respective pulses of the duplets of pulses corresponding to components of the conjugated quadratures that are associated with cos φA<sub2>1</sub2>C<sub2>1 </sub2>and sin φA<sub2>1</sub2>C<sub2>1</sub2>, respectively, are given by the equations

The set of values used for pj and εm,j for different values of m and j will depend in part on whether the components of the measured conjugated quadratures are to be joint measurements or non-joint measurements. The average times <o ostyle="single">t</o>d1 and <o ostyle="single">t</o>d2 of the times of the respective pulses of the duplets of pulses corresponding to components of the conjugated quadratures that are associated with cos φA<sub2>1</sub2>C<sub2>1 </sub2>and sin φA<sub2>1</sub2>C<sub2>1</sub2>, respectively, are given by the equations

It is also apparent from Eq. (5) that the difference between the two average times {overscore (t)}d1 and {overscore (t)}d2 can be arranged to be non-zero by selecting the set of values of pj such that the sum of pj over the domain of j is different from the value of 2. It is important to note that in this case where the difference in the average times is non-zero, the first and second components of conjugated quadratures corresponding to the average times {overscore (t)}d1 and {overscore (t)}d2 may either be two different components of a conjugated quadratures or the same component of two different conjugated quadratures.

It is also apparent from Eq. (5) that the difference between the two average times <o ostyle="single">t</o>d1 and <o ostyle="single">t</o>d2 can be arranged to be non-zero by selecting the set of values of pj such that the sum of pj over the domain of j is different from the value of 2. It is important to note that in this case where the difference in the average times is non-zero, the first and second components of conjugated quadratures corresponding to the average times <o ostyle="single">t</o>d1 and <o ostyle="single">t</o>d2 may either be two different components of a conjugated quadratures or the same component of two different conjugated quadratures.

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<?in-line-formulae description="In-line Formulae" end="lead"?>F{Pout}=R2Pbias210−2LF{(1−S2(√{square root over (2RmPin)} sin 2πt/Vs))2}RL<?in-line-formulae description="In-line Formulae" end="tail"?>

<?in-line-formulae description="In-line Formulae" end="lead"?>F{Pout}=R2Pbias210−2LF{(1−S2(√{square root over (2RmPin)} sin 2πt/Vs))2}RL<?in-line-formulae description="In-line Formulae" end="tail"?>

<?in-line-formulae description="In-line Formulae" end="lead"?>10 log [F{Pout}]=10 log [R2Pbias210−2LF{(1−S2({square root over (2RmPin)} sin 2πt/Vs))2}RL]<?in-line-formulae description="In-line Formulae" end="tail"?>

<?in-line-formulae description="In-line Formulae" end="lead"?>10 log [F{Pout}]=10 log [R2Pbias210−2LF{(1−S2({square root over (2RmPin)} sin 2πt/Vs))2}RL]<?in-line-formulae description="In-line Formulae" end="tail"?>

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<figref idref="DRAWINGS">FIG. 4</figref> shows an example of a hexagonal close pack (HCP) cell with the [11{overscore (2)}0] plane indicated with dashed lines. In the case of HCP Co-alloys, the magnetic axes of the crystallites are parallel to the plane that is orthogonal to the basal planes of the hexagonal unit cell (i.e. the magnetic axes are parallel to the [11{overscore (2)}0] plane).

<figref idref="DRAWINGS">FIG. 4</figref> shows an example of a hexagonal close pack (HCP) cell with the [11 <o ostyle="single">2</o>0] plane indicated with dashed lines. In the case of HCP Co-alloys, the magnetic axes of the crystallites are parallel to the plane that is orthogonal to the basal planes of the hexagonal unit cell (i.e. the magnetic axes are parallel to the [11 <o ostyle="single">2</o>0] plane).

In magnetic media, “Orientation” is typically achieved by growing the magnetic alloy on suitable underlayers grown in turn on substrates which are circumferentially textured. U.S. Pat. No. 5,989,674 describes the influence that a textured substrate has on the growth of an underlayer structure. When deposited on a properly textured substrate, the lattice parameters of the BCC Cr and Cr-alloys along the radial direction are greater than the corresponding lattice parameters along the track direction. This anisotropic strain relaxation leads to a better lattice match of the [11{overscore (2)}0] prismatic plane of the HCP Co-alloy, which is deposited on top of the underlayer, along the track direction. Consequently, the magnetic axis of a crystallite predominantly aligns along the track direction. “Orientation” requires that the Co-alloy crystallites grow with their [11{overscore (2)}0] plane parallel to the substrate. To ensure this, the underlayer material is grown with its [002] plane parallel to the substrate plane.

In magnetic media, “Orientation” is typically achieved by growing the magnetic alloy on suitable underlayers grown in turn on substrates which are circumferentially textured. U.S. Pat. No. 5,989,674 describes the influence that a textured substrate has on the growth of an underlayer structure. When deposited on a properly textured substrate, the lattice parameters of the BCC Cr and Cr-alloys along the radial direction are greater than the corresponding lattice parameters along the track direction. This anisotropic strain relaxation leads to a better lattice match of the [11 <o ostyle="single">2</o>0] prismatic plane of the HCP Co-alloy, which is deposited on top of the underlayer, along the track direction. Consequently, the magnetic axis of a crystallite predominantly aligns along the track direction. “Orientation” requires that the Co-alloy crystallites grow with their [11 <o ostyle="single">2</o>0] plane parallel to the substrate. To ensure this, the underlayer material is grown with its [002] plane parallel to the substrate plane.

<figref idref="DRAWINGS">FIG. 6</figref> shows an example of the epitaxial relationships between a HCP magnetic layer and a BCC CrMo layer. BCC atoms 32 are shown on a BCC lattice 36. The [002] plane is shown parallel to the page. The four BCC atoms 32 are not from one crystalline cell, but rather are from specific corners of four adjoining BCC cells. Four HCP atoms 34 comprise the [11{overscore (2)}0] plane 38 of the HCP structure.

<figref idref="DRAWINGS">FIG. 6</figref> shows an example of the epitaxial relationships between a HCP magnetic layer and a BCC CrMo layer. BCC atoms 32 are shown on a BCC lattice 36. The [002] plane is shown parallel to the page. The four BCC atoms 32 are not from one crystalline cell, but rather are from specific corners of four adjoining BCC cells. Four HCP atoms 34 comprise the [11 <o ostyle="single">2</o>0] plane 38 of the HCP structure.

A high angle of incidence deposition (i.e. ≧30 degrees) of the hard bias and seed layers 10, 14 is employed to produce uniaxial anisotropy in the hard bias layer 10. In contrast, current art hard bias deposition employing ion beam growth technology employ angles between 10–20 degrees with respect to the normal of the film plane. Ion beam deposition has been successful in experimental trials. It is possible that other vapor phase growth methods can be employed as long as the particle flux direction is well defined. It is surmised that the orientation in the hard bias layer 10 originates from the anisotropic growth of the seed layer 12 which is induced by the ion beam directionality and growth geometry. Therefore, when the lattice plane is viewed from the normal direction, the atomic arrangement in the seed layer 12 is anisotropic. Consequently, when the hard bias layer 10 is grown at a shallower angle, the degree of lattice matching for the HCP Co-alloy [11{overscore (2)}0] plane is favored along the beam direction, thus producing uniaxial magnetic anisotropy.

A high angle of incidence deposition (i.e. ≧30 degrees) of the hard bias and seed layers 10, 14 is employed to produce uniaxial anisotropy in the hard bias layer 10. In contrast, current art hard bias deposition employing ion beam growth technology employ angles between 10–20 degrees with respect to the normal of the film plane. Ion beam deposition has been successful in experimental trials. It is possible that other vapor phase growth methods can be employed as long as the particle flux direction is well defined. It is surmised that the orientation in the hard bias layer 10 originates from the anisotropic growth of the seed layer 12 which is induced by the ion beam directionality and growth geometry. Therefore, when the lattice plane is viewed from the normal direction, the atomic arrangement in the seed layer 12 is anisotropic. Consequently, when the hard bias layer 10 is grown at a shallower angle, the degree of lattice matching for the HCP Co-alloy [11 <o ostyle="single">2</o>0] plane is favored along the beam direction, thus producing uniaxial magnetic anisotropy.

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The operation of a memory device according to the present invention will be explained hereafter in relation with <figref idref="DRAWINGS">FIG. 2</figref>, which illustrates the variation along time of various control and/or output signals of a dynamic memory according to the present invention, in an operation of precharge of a storage element 2 (<figref idref="DRAWINGS">FIG. 1</figref>) or of read terminals SA1 and SA2. <figref idref="DRAWINGS">FIGS. 2A</figref>, 2B, 2C, 2D, 2E, and 2F respectively show control signals RESTORE, WL, PBL, BLPASS, SELN ({overscore (SELP)}), and PSA. <figref idref="DRAWINGS">FIGS. 2G to 2J</figref> illustrate the voltage variations along time, respectively, on line BLd, at point STORE, and on terminals SA1 and SA2.

The operation of a memory device according to the present invention will be explained hereafter in relation with <figref idref="DRAWINGS">FIG. 2</figref>, which illustrates the variation along time of various control and/or output signals of a dynamic memory according to the present invention, in an operation of precharge of a storage element 2 (<figref idref="DRAWINGS">FIG. 1</figref>) or of read terminals SA1 and SA2. <figref idref="DRAWINGS">FIGS. 2A</figref>, 2B, 2C, 2D, 2E, and 2F respectively show control signals RESTORE, WL, PBL, BLPASS, SELN ( <o ostyle="single">SELP</o>), and PSA. <figref idref="DRAWINGS">FIGS. 2G to 2J</figref> illustrate the voltage variations along time, respectively, on line BLd, at point STORE, and on terminals SA1 and SA2.

Successive read and refresh operations of a datum contained in a storage element 2 will be detailed hereafter in relation with <figref idref="DRAWINGS">FIG. 3</figref>, which illustrates the variation along time of various control and/or output signals of a dynamic memory according to the present invention. <figref idref="DRAWINGS">FIG. 3A</figref> shows signal RESTORE. <figref idref="DRAWINGS">FIG. 3B</figref> shows signal WL. <figref idref="DRAWINGS">FIG. 3C</figref> shows signal PBL. <figref idref="DRAWINGS">FIG. 3D</figref> shows signal BLPASS. <figref idref="DRAWINGS">FIG. 3E</figref> shows signal SELN ({overscore (SELP)}). <figref idref="DRAWINGS">FIG. 3F</figref> shows signal PSA. <figref idref="DRAWINGS">FIGS. 3G</figref> ad 3H illustrate the variations along time, respectively, on direct bit line BLd and reference bit lines BLr. <figref idref="DRAWINGS">FIGS. 31 and 3J</figref> illustrate the voltage variation along time, respectively, on storage nodes STORE and STOREref. <figref idref="DRAWINGS">FIGS. 3K and 3L</figref> illustrate the voltage variations along time, respectively, on terminals SA1 and SA2.

Successive read and refresh operations of a datum contained in a storage element 2 will be detailed hereafter in relation with <figref idref="DRAWINGS">FIG. 3</figref>, which illustrates the variation along time of various control and/or output signals of a dynamic memory according to the present invention. <figref idref="DRAWINGS">FIG. 3A</figref> shows signal RESTORE. <figref idref="DRAWINGS">FIG. 3B</figref> shows signal WL. <figref idref="DRAWINGS">FIG. 3C</figref> shows signal PBL. <figref idref="DRAWINGS">FIG. 3D</figref> shows signal BLPASS. <figref idref="DRAWINGS">FIG. 3E</figref> shows signal SELN ( <o ostyle="single">SELP</o>). <figref idref="DRAWINGS">FIG. 3F</figref> shows signal PSA. <figref idref="DRAWINGS">FIGS. 3G</figref> ad 3H illustrate the variations along time, respectively, on direct bit line BLd and reference bit lines BLr. <figref idref="DRAWINGS">FIGS. 31 and 3J</figref> illustrate the voltage variation along time, respectively, on storage nodes STORE and STOREref. <figref idref="DRAWINGS">FIGS. 3K and 3L</figref> illustrate the voltage variations along time, respectively, on terminals SA1 and SA2.

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<?in-line-formulae description="In-line Formulae" end="lead"?>{overscore (x)}(m)={overscore (S)}(m)b(m)+{overscore (n)}(m) (19)<?in-line-formulae description="In-line Formulae" end="tail"?>

<?in-line-formulae description="In-line Formulae" end="lead"?> <o ostyle="single">x</o>(m)= <o ostyle="single">S</o>(m)b(m)+ <o ostyle="single">n</o>(m) (19)<?in-line-formulae description="In-line Formulae" end="tail"?>

in which S<img id="CUSTOM-CHARACTER-00001" he="1.78mm" wi="1.78mm" file="US07161975-20070109-P00001.TIF" alt="custom character" img-content="character" img-format="tif"/>and Sℑ are the separate real and imaginary parts of S, respectively. Similar notation is used for the complex input signal x and noise n. S and x are replaced by {overscore (S)} and {overscore (x)} in the development of equation (16), as described above, and the decision operator α( ) is replaced simply by a sign operation (taking the sign of the soft decision to determine the hard decision value). Subject to these changes, the method of <figref idref="DRAWINGS">FIG. 6</figref> is used to initialize the decision values substantially as described above.

in which S<img id="CUSTOM-CHARACTER-00001" he="1.78mm" wi="1.78mm" file="US07161975-20070109-P00001.TIF" alt="custom character" img-content="character" img-format="tif"/>and Sℑ are the separate real and imaginary parts of S, respectively. Similar notation is used for the complex input signal x and noise n. S and x are replaced by <o ostyle="single">S</o> and <o ostyle="single">x</o> in the development of equation (16), as described above, and the decision operator α( ) is replaced simply by a sign operation (taking the sign of the soft decision to determine the hard decision value). Subject to these changes, the method of <figref idref="DRAWINGS">FIG. 6</figref> is used to initialize the decision values substantially as described above.

<?in-line-formulae description="In-line Formulae" end="lead"?>f(φ)=∥{overscore (x)}−{overscore (S)}ejφ∥2 (20)<?in-line-formulae description="In-line Formulae" end="tail"?>

<?in-line-formulae description="In-line Formulae" end="lead"?>f(φ)=∥ <o ostyle="single">x</o>− <o ostyle="single">S</o>ejφ∥2 (20)<?in-line-formulae description="In-line Formulae" end="tail"?>

Equation (20) combines both the unit circle and real axis constraints that apply to the BPSK constellation. Again, the ALPS procedure may be applied to z and T, as determined by the methods of <figref idref="DRAWINGS">FIG. 6</figref> using {overscore (S)} and {overscore (x)}.

<?in-line-formulae description="In-line Formulae" end="lead"?>Lk(bk):=∥{overscore (F)}kbk*∥2 (36)<?in-line-formulae description="In-line Formulae" end="tail"?>

<?in-line-formulae description="In-line Formulae" end="lead"?>Lk(bk):=∥ <o ostyle="single">F</o>kbk*∥2 (36)<?in-line-formulae description="In-line Formulae" end="tail"?>

a real matrix made by stacking the real and imaginary parts of F, in the manner of {overscore (S)} described above. The maximization of Lk over the real constellation of bk is ambiguous, in that the maximum can be determined only up to multiplication of bk by a real scalar (such as −1).

a real matrix made by stacking the real and imaginary parts of F, in the manner of <o ostyle="single">S</o> described above. The maximization of Lk over the real constellation of bk is ambiguous, in that the maximum can be determined only up to multiplication of bk by a real scalar (such as −1).

To maximize the value of equation (36) for each k, processor 99 preferably performs a singular value decomposition (SVD) of {overscore (F)}k, as is known in the art:

To maximize the value of equation (36) for each k, processor 99 preferably performs a singular value decomposition (SVD) of <o ostyle="single">F</o>k, as is known in the art:

<?in-line-formulae description="In-line Formulae" end="lead"?>{overscore (F)}k=UkΣkVkT (37)<?in-line-formulae description="In-line Formulae" end="tail"?>

<?in-line-formulae description="In-line Formulae" end="lead"?> <o ostyle="single">F</o>k=UkΣkVkT (37)<?in-line-formulae description="In-line Formulae" end="tail"?>

Based on the above decomposition of {overscore (F)}k, processor 99 can determine a vector of hard decision values {circumflex over (b)}k simply by taking the sign of each element of {tilde over (b)}k, at a decision step 102. As noted earlier, the determination of the elements of {circumflex over (b)}k is uncertain as to multiplication by ±1, and other means must be applied in order to resolve this ambiguity. (One possibility is the use of known pilot signals, as described below.) Given the hard decision values of the symbols {circumflex over (b)}k, the channel response vector for each user k can be determined by substituting these values into equation (29), in which the chip matrix D has been replaced by the equivalent fingerprint matrix Fk:

Based on the above decomposition of <o ostyle="single">F</o>k, processor 99 can determine a vector of hard decision values {circumflex over (b)}k simply by taking the sign of each element of {tilde over (b)}k, at a decision step 102. As noted earlier, the determination of the elements of {circumflex over (b)}k is uncertain as to multiplication by ±1, and other means must be applied in order to resolve this ambiguity. (One possibility is the use of known pilot signals, as described below.) Given the hard decision values of the symbols {circumflex over (b)}k, the channel response vector for each user k can be determined by substituting these values into equation (29), in which the chip matrix D has been replaced by the equivalent fingerprint matrix Fk:

<?in-line-formulae description="In-line Formulae" end="lead"?>τk=arg max∥{overscore (F)}k(τk){circumflex over (b)}k(τk)∥2 (41)<?in-line-formulae description="In-line Formulae" end="tail"?>

<?in-line-formulae description="In-line Formulae" end="lead"?>τk=arg max∥ <o ostyle="single">F</o>k(τk){circumflex over (b)}k(τk)∥2 (41)<?in-line-formulae description="In-line Formulae" end="tail"?>

Here Fk is the fingerprint matrix defined above, taken in the absence of pilot signals. The fingerprint matrix is extended by the pilot fingerprint, given by nk=PkHx. Applying the SVD of equation (37) to {overscore (nkFk)} gives a soft decision value (assuming BPSK modulation):

Here Fk is the fingerprint matrix defined above, taken in the absence of pilot signals. The fingerprint matrix is extended by the pilot fingerprint, given by nk=PkHx. Applying the SVD of equation (37) to <o ostyle="single">nkFk</o> gives a soft decision value (assuming BPSK modulation):

<claim-text>9. The receiver according to <claim-ref idref="CLM-00008">claim 8</claim-ref>, wherein the multi-user detection circuitry is arranged to invert the expression by finding the phase angle φk of each of the elements of b that minimizes a norm given by ∥{overscore (x)}−{overscore (S)}b∥2.</claim-text>

<claim-text>9. The receiver according to <claim-ref idref="CLM-00008">claim 8</claim-ref>, wherein the multi-user detection circuitry is arranged to invert the expression by finding the phase angle φk of each of the elements of b that minimizes a norm given by ∥ <o ostyle="single">x</o>− <o ostyle="single">S</o>b∥2.</claim-text>

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<figref idref="DRAWINGS">FIG. 2</figref> illustrates an encoder circuit 200 according to an embodiment. A domino gate 202 includes an input transistor 204 controlled by the data input to the bus line 102. A domino gate 206 includes an input transistor 208 controlled by the value of the data input to the bus on the previous cycle, and supplied by a clocked FF 210, which stores the complement of the previous data input value. The domino gates 202 and 206 are clocked by a Φ1 clock signal, and the clocked FF 210 is clocked by the complement of the Φ1 clock signal, {overscore (Φ1)}.

During pre-charge, when Φ1 is LOW and {overscore (Φ1)} is HIGH, node A, node B, and node C are all HIGH. The value on node A depends on the value of the current data input, and the value on node B depends on the value of the previous data input.

During pre-charge, when Φ1 is LOW and <o ostyle="single">Φ1</o> is HIGH, node A, node B, and node C are all HIGH. The value on node A depends on the value of the current data input, and the value on node B depends on the value of the previous data input.

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According to the present invention, modified Blum-Shub-Smale machines (hereinafter referred to as “BSS' machines”) operate over a finite field ZN for a fixed prime number N. Such a machine includes (1) a state space ZNS, (2) an output space ZNO, (3) an input space ZNI, and (4) a directed graph with p numbered nodes; where S, O, and I are positive integers. The set {overscore (S)}={0, . . . , p−1}×ZNS×ZNO×ZNI is called the full state space of the Blum-Shub-Smale-like machine. The first component is the node number, the next S components are the automaton's internal work space, the O components after that, the output, and lastly, the I input components. The graph of the automaton has two main types of node variants:

According to the present invention, modified Blum-Shub-Smale machines (hereinafter referred to as “BSS' machines”) operate over a finite field ZN for a fixed prime number N. Such a machine includes (1) a state space ZNS, (2) an output space ZNO, (3) an input space ZNI, and (4) a directed graph with p numbered nodes; where S, O, and I are positive integers. The set <o ostyle="single">S</o>={0, . . . , p−1}×ZNS×ZNO×ZNI is called the full state space of the Blum-Shub-Smale-like machine. The first component is the node number, the next S components are the automaton's internal work space, the O components after that, the output, and lastly, the I input components. The graph of the automaton has two main types of node variants:

When a polynomial representation, H, of a Mealy machine is to be encrypted using multivariate polynomials, there are some constraints on the selection of encryption keys. As in the univariate case, there are S function components of H, which are fed back into variables, and O function components which are not. This will only work as intended if (ci, ri, si)=(cl+i, rl+i, sl+i) for all 1≦i≦{overscore (1)}, where {overscore (1)} is such that Σj=I {overscore (1)}cj≧S. In the following set D=Σj=1{overscore (1)}cj. In any case, D may not exceed the number of variables, so in the case where there are more function components than variables, there may be function components free of such restrictions when deciding upon triples for encryption. Thus, the first {overscore (1)} partially encrypted blocks of H's components must use the same key pairs as the first {overscore (1)} partially decrypted blocks of H's variables. Recall that H's variables are written {right arrow over (x)}(n), {right arrow over (y)}(n), and that {right arrow over (x)} is the state of the Mealy machine. Therefore the first {overscore (1)} vectors/blocks {right arrow over (w)}i(n) will represent {right arrow over (x)}(n) and possibly a little of {right arrow over (y)}(n), and the remaining vectors/blocks will represent the rest of {right arrow over (y)}(n)—the input to the Mealy machine. The partially encrypted version of H, written Er,s∘H, may for the case D=S be written as:

When a polynomial representation, H, of a Mealy machine is to be encrypted using multivariate polynomials, there are some constraints on the selection of encryption keys. As in the univariate case, there are S function components of H, which are fed back into variables, and O function components which are not. This will only work as intended if (ci, ri, si)=(cl+i, rl+i, sl+i) for all 1≦i≦ <o ostyle="single">1</o>, where <o ostyle="single">1</o> is such that Σj=I <o ostyle="single">1</o>cj≧S. In the following set D=Σj=1 <o ostyle="single">1</o>cj. In any case, D may not exceed the number of variables, so in the case where there are more function components than variables, there may be function components free of such restrictions when deciding upon triples for encryption. Thus, the first <o ostyle="single">1</o> partially encrypted blocks of H's components must use the same key pairs as the first <o ostyle="single">1</o> partially decrypted blocks of H's variables. Recall that H's variables are written {right arrow over (x)}(n), {right arrow over (y)}(n), and that {right arrow over (x)} is the state of the Mealy machine. Therefore the first <o ostyle="single">1</o> vectors/blocks {right arrow over (w)}i(n) will represent {right arrow over (x)}(n) and possibly a little of {right arrow over (y)}(n), and the remaining vectors/blocks will represent the rest of {right arrow over (y)}(n)—the input to the Mealy machine. The partially encrypted version of H, written Er,s∘H, may for the case D=S be written as:

For the BSS' machines, the resulting expression resembles the above expressions, but is slightly simpler. There is one variable vector {right arrow over (x)}(n) with 1+S+O+I components. H has 1+S+O components. As with the Mealy machine, the triples (ci, ri, si) must equal (cl+i, rl+i, sl+i) for 1≦i≦{overscore (1)}, where {overscore (1)} is such that Σj=1īcj≧1+S and Σj=1{overscore (1)}−1 cj≦1+S. Set D=Σj=1{overscore (1)}cj. In any case, D may not exceed the number of variables, so in the case where there are more function components than variables, there may be function components free of such restrictions when deciding upon triples for encryption. The partially encrypted state and output data after n applications of H is defined as {right arrow over (w)}

For the BSS' machines, the resulting expression resembles the above expressions, but is slightly simpler. There is one variable vector {right arrow over (x)}(n) with 1+S+O+I components. H has 1+S+O components. As with the Mealy machine, the triples (ci, ri, si) must equal (cl+i, rl+i, sl+i) for 1≦i≦ <o ostyle="single">1</o>, where <o ostyle="single">1</o> is such that Σj=1īcj≧1+S and Σj=1 <o ostyle="single">1</o>−1 cj≦1+S. Set D=Σj=1 <o ostyle="single">1</o>cj. In any case, D may not exceed the number of variables, so in the case where there are more function components than variables, there may be function components free of such restrictions when deciding upon triples for encryption. The partially encrypted state and output data after n applications of H is defined as {right arrow over (w)}

The resulting machine is called {overscore (M)}.

The resulting machine is called <o ostyle="single">M</o>.

Given {overscore (M)}'s state after n state-transitions, {right arrow over (x)}(n), and the (n+1)st input {right arrow over (y)}(n), the next state transition and output is computed by the mapping:

Given <o ostyle="single">M</o>'s state after n state-transitions, {right arrow over (x)}(n), and the (n+1)st input {right arrow over (y)}(n), the next state transition and output is computed by the mapping:

The set of node numbers from 1 top can be written {overscore (N)}. A BSS machine thus has p nodes in all. The full state space of a Blum-Shub-Smale machine is then {overscore (N)}×RS. It is possible to express the computation of a Blum-Shub-Smale machine using only the “computing endomorphism”

The set of node numbers from 1 top can be written <o ostyle="single">N</o>. A BSS machine thus has p nodes in all. The full state space of a Blum-Shub-Smale machine is then <o ostyle="single">N</o>×RS. It is possible to express the computation of a Blum-Shub-Smale machine using only the “computing endomorphism”

<?in-line-formulae description="In-line Formulae" end="lead"?>H:{overscore (N)}×RS→{overscore (N)}×RS.<?in-line-formulae description="In-line Formulae" end="tail"?>

<?in-line-formulae description="In-line Formulae" end="lead"?>H: <o ostyle="single">N</o>×RS→ <o ostyle="single">N</o>×RS.<?in-line-formulae description="In-line Formulae" end="tail"?>

When y∈{overscore (N)}, an(y)=1 if and only if n=y, otherwise an(y)=0. For y∉{overscore (N)},an(y) produces nonsense. It is necessary to know that β(y,σ)=β(y, χ({right arrow over (x)})) is expressible as a polynomial, for which an expression can be found in the article by Blum, Shub, and Smale. When computing β(y,σ) for a node, σ=χ({right arrow over (x)}) must be evaluated. Over a finite field it is possible to express χ as a polynomial.

When y∈ <o ostyle="single">N</o>, an(y)=1 if and only if n=y, otherwise an(y)=0. For y∉ <o ostyle="single">N</o>,an(y) produces nonsense. It is necessary to know that β(y,σ)=β(y, χ({right arrow over (x)})) is expressible as a polynomial, for which an expression can be found in the article by Blum, Shub, and Smale. When computing β(y,σ) for a node, σ=χ({right arrow over (x)}) must be evaluated. Over a finite field it is possible to express χ as a polynomial.

Since the modified machines are constructed over <img id="CUSTOM-CHARACTER-00015" he="3.13mm" wi="2.46mm" file="US07162032-20070109-P00002.TIF" alt="custom character" img-content="character" img-format="tif"/>N, which contains only non-negative integers, the original version of the branch node becomes meaningless. Instead, the next-node function takes the form β: {overscore (N)}×<img id="CUSTOM-CHARACTER-00016" he="3.13mm" wi="2.46mm" file="US07162032-20070109-P00002.TIF" alt="custom character" img-content="character" img-format="tif"/>N→{overscore (N)}. To simplify, require {overscore (N)}⊂<img id="CUSTOM-CHARACTER-00017" he="3.13mm" wi="2.46mm" file="US07162032-20070109-P00002.TIF" alt="custom character" img-content="character" img-format="tif"/>N, even though one could make do with a smaller prime than some N≧p for the state-space. This implies that β is extended to β:ZN2→ZN.

Since the modified machines are constructed over <img id="CUSTOM-CHARACTER-00015" he="3.13mm" wi="2.46mm" file="US07162032-20070109-P00002.TIF" alt="custom character" img-content="character" img-format="tif"/>N, which contains only non-negative integers, the original version of the branch node becomes meaningless. Instead, the next-node function takes the form β: <o ostyle="single">N</o>×<img id="CUSTOM-CHARACTER-00016" he="3.13mm" wi="2.46mm" file="US07162032-20070109-P00002.TIF" alt="custom character" img-content="character" img-format="tif"/>N→ <o ostyle="single">N</o>. To simplify, require <o ostyle="single">N</o>⊂<img id="CUSTOM-CHARACTER-00017" he="3.13mm" wi="2.46mm" file="US07162032-20070109-P00002.TIF" alt="custom character" img-content="character" img-format="tif"/>N, even though one could make do with a smaller prime than some N≧p for the state-space. This implies that β is extended to β:ZN2→ZN.

\\QA012\C$\REDBOOK_VERIFICATION\RAWCOMPAREDATA\PROD_010907-XML\US07162056-20070109.XML	\\QA012\C$\REDBOOK_VERIFICATION\RAWCOMPAREDATA\TEST_010907-XML\US07162056-20070109.XML

<?in-line-formulae description="In-line Formulae" end="lead"?>M=√{square root over (Ix2+Iy2)} (Eq. 4)<?in-line-formulae description="In-line Formulae" end="tail"?>

<?in-line-formulae description="In-line Formulae" end="lead"?>M=√{square root over (Ix2+Iy2)} (Eq. 4)<?in-line-formulae description="In-line Formulae" end="tail"?>

\\QA012\C$\REDBOOK_VERIFICATION\RAWCOMPAREDATA\PROD_010907-XML\US07162069-20070109.XML	\\QA012\C$\REDBOOK_VERIFICATION\RAWCOMPAREDATA\TEST_010907-XML\US07162069-20070109.XML

<li id="ul0001-0001" num="0025">i) calculation of average {overscore (h)} for each row and column.</li>

<li id="ul0001-0001" num="0025">i) calculation of average <o ostyle="single">h</o> for each row and column.</li>

<?in-line-formulae description="In-line Formulae" end="lead"?>column: Δx(x,y)=|h(x,y)−{overscore (h)}(x)|<?in-line-formulae description="In-line Formulae" end="tail"?>

<?in-line-formulae description="In-line Formulae" end="lead"?>column: Δx(x,y)=|h(x,y)− <o ostyle="single">h</o>(x)|<?in-line-formulae description="In-line Formulae" end="tail"?>

<?in-line-formulae description="In-line Formulae" end="lead"?>row: Δy(x,y)=|h(x,y)−{overscore (h)}(y)|<?in-line-formulae description="In-line Formulae" end="tail"?>

<?in-line-formulae description="In-line Formulae" end="lead"?>row: Δy(x,y)=|h(x,y)− <o ostyle="single">h</o>(y)|<?in-line-formulae description="In-line Formulae" end="tail"?>

\\QA012\C$\REDBOOK_VERIFICATION\RAWCOMPAREDATA\PROD_010907-XML\US07162210-20070109.XML	\\QA012\C$\REDBOOK_VERIFICATION\RAWCOMPAREDATA\TEST_010907-XML\US07162210-20070109.XML

<li id="ul0008-0002" num="0072">un, n={overscore (1,N)}<−1, 2, . . . , N is the pilot signal complex correlation responses,</li>

<?in-line-formulae description="In-line Formulae" end="lead"?>xn(tj), j=1, 2, . . . , n={overscore (1,N)}<−1, 2, . . . , N<?in-line-formulae description="In-line Formulae" end="tail"?>

<?in-line-formulae description="In-line Formulae" end="lead"?>xn(tj), j=1, 2, . . . , n= <o ostyle="single">1,N</o><−1, 2, . . . , N<?in-line-formulae description="In-line Formulae" end="tail"?>

The complex correlation responses of the pilot signal un and the correlation matrix elements Knm, n,m={overscore (1,N)}<−1, 2, . . . , N are generated using the sliding window from J samples (chips) of the input signal as shown for example, in <figref idref="DRAWINGS">FIG. 2</figref>.

The complex correlation responses of the pilot signal un and the correlation matrix elements Knm, n,m= <o ostyle="single">1,N</o><−1, 2, . . . , N are generated using the sliding window from J samples (chips) of the input signal as shown for example, in <figref idref="DRAWINGS">FIG. 2</figref>.

where wn, n={overscore (1,N)}<−1, 2, . . . , N are the weight vectors (coordinates of simplex vertices) of the preceding adaptation step.

where wn, n= <o ostyle="single">1,N</o><−1, 2, . . . , N are the weight vectors (coordinates of simplex vertices) of the preceding adaptation step.

\\QA012\C$\REDBOOK_VERIFICATION\RAWCOMPAREDATA\PROD_010907-XML\US07162338-20070109.XML	\\QA012\C$\REDBOOK_VERIFICATION\RAWCOMPAREDATA\TEST_010907-XML\US07162338-20070109.XML

A composite pose {overscore (S)} can be provided by the SLAM process and can be expressed by {overscore (S)}=({overscore (x)}, {overscore (y)}, {overscore (θ)})T. This composite pose {overscore (S)} can be provided as an input to, for example, a robot behavior control program such as a behavioral program for vacuum cleaning. In alternative examples of computing a composite pose {overscore (S)}, the composite pose can be weighted using probabilities and/or importance factors, can be averaged by selecting data only from high probability particles, and the like. The process advances from the optional state 1394 to a state 1398.

A composite pose <o ostyle="single">S</o> can be provided by the SLAM process and can be expressed by <o ostyle="single">S</o>=( <o ostyle="single">x</o>, <o ostyle="single">y</o>, <o ostyle="single">θ</o>)T. This composite pose <o ostyle="single">S</o> can be provided as an input to, for example, a robot behavior control program such as a behavioral program for vacuum cleaning. In alternative examples of computing a composite pose <o ostyle="single">S</o>, the composite pose can be weighted using probabilities and/or importance factors, can be averaged by selecting data only from high probability particles, and the like. The process advances from the optional state 1394 to a state 1398.

\\QA012\C$\REDBOOK_VERIFICATION\RAWCOMPAREDATA\PROD_010907-XML\US07162340-20070109.XML	\\QA012\C$\REDBOOK_VERIFICATION\RAWCOMPAREDATA\TEST_010907-XML\US07162340-20070109.XML

The output distance is provided by D(x, y), as a direct measurement of data matching, wherein xi is the library of predetermined data, and yi is the recent history of data. In either equation, the variable m is the number of samples of data. Additionally, variable {overscore (xi)} is the average (mean) value for attribute i occurring in the library of prerecorded data, and {overscore (yi)} is the average (mean) value for attribute i occurring in the recent history of data.

The output distance is provided by D(x, y), as a direct measurement of data matching, wherein xi is the library of predetermined data, and yi is the recent history of data. In either equation, the variable m is the number of samples of data. Additionally, variable <o ostyle="single">xi</o> is the average (mean) value for attribute i occurring in the library of prerecorded data, and <o ostyle="single">yi</o> is the average (mean) value for attribute i occurring in the recent history of data.

\\QA012\C$\REDBOOK_VERIFICATION\RAWCOMPAREDATA\PROD_010907-XML\US07162359-20070109.XML	\\QA012\C$\REDBOOK_VERIFICATION\RAWCOMPAREDATA\TEST_010907-XML\US07162359-20070109.XML

<?in-line-formulae description="In-line Formulae" end="lead"?>{overscore (σ(k))}=s1·{overscore (VO2)}(k)+s2·{overscore (VO2)}(k−1) (25)<?in-line-formulae description="In-line Formulae" end="tail"?>

<?in-line-formulae description="In-line Formulae" end="lead"?> <o ostyle="single">σ(k)</o>=s1· <o ostyle="single">VO2</o>(k)+s2· <o ostyle="single">VO2</o>(k−1) (25)<?in-line-formulae description="In-line Formulae" end="tail"?>

\\QA012\C$\REDBOOK_VERIFICATION\RAWCOMPAREDATA\PROD_010907-XML\US07162371-20070109.XML	\\QA012\C$\REDBOOK_VERIFICATION\RAWCOMPAREDATA\TEST_010907-XML\US07162371-20070109.XML

<sequence-list file="US07162371-20070109-SEQLST.XML" carriers="internal-electronic" seq-file-type="ST.25"/>

<sequence-list file="US07162371-20070109-S00001.XML" carriers="internal-electronic" seq-file-type="ST.25"/>

\\QA012\C$\REDBOOK_VERIFICATION\RAWCOMPAREDATA\PROD_010907-XML\US07162741-20070109.XML	\\QA012\C$\REDBOOK_VERIFICATION\RAWCOMPAREDATA\TEST_010907-XML\US07162741-20070109.XML

In order to make predictions using the mixture (equation (3)), we must keep track of the sum of all the tree weights at time t, ΣTwTt. An efficient way to do this is to keep the sum of all subtree weights for each node. We define {overscore (w)}t(u) to be the sum of all subtrees rooted at node u:

In order to make predictions using the mixture (equation (3)), we must keep track of the sum of all the tree weights at time t, ΣTwTt. An efficient way to do this is to keep the sum of all subtree weights for each node. We define <o ostyle="single">w</o>t(u) to be the sum of all subtrees rooted at node u:

To update the weights of the nodes we use the following rules. We first initialize w1(u)=1 for ∀u and {overscore (w)}1(u) for ∀u.

To update the weights of the nodes we use the following rules. We first initialize w1(u)=1 for ∀u and <o ostyle="single">w</o>1(u) for ∀u.

For {overscore (w)}t(u) if xt∈u:

For <o ostyle="single">w</o>t(u) if xt∈u:

<?in-line-formulae description="In-line Formulae" end="lead"?>{overscore (w)}t+1(u)={overscore (w)}t(u) (A16)<?in-line-formulae description="In-line Formulae" end="tail"?>

<?in-line-formulae description="In-line Formulae" end="lead"?> <o ostyle="single">w</o>t+1(u)= <o ostyle="single">w</o>t(u) (A16)<?in-line-formulae description="In-line Formulae" end="tail"?>

\\QA012\C$\REDBOOK_VERIFICATION\RAWCOMPAREDATA\PROD_010907-XML\USD0535002-20070109.XML	\\QA012\C$\REDBOOK_VERIFICATION\RAWCOMPAREDATA\TEST_010907-XML\USD0535002-20070109.XML

<last-name>Mu{overscore (n)}oz Martinez</last-name>

<last-name>Muñoz Martinez</last-name>

\\QA012\C$\REDBOOK_VERIFICATION\RAWCOMPAREDATA\PROD_010907-XML\USRE039460-20070109.XML	\\QA012\C$\REDBOOK_VERIFICATION\RAWCOMPAREDATA\TEST_010907-XML\USRE039460-20070109.XML

For the inverse approach, consider that in a closed three dimensional region Ω with the boundary surface Γ, as shown in <figref idref="DRAWINGS">FIG. 1a</figref>, a subregion Ω0⊂Ω, called the synthesis controlled subdomain is defined and within this region the function {tilde over (B)}(r,z) is prescribed. The problem consists of searching for a boundary function J(R,ξ) that produces the field {overscore (B)}(r,z) in Ω0 as close to the target field {tilde over (B)}(r,z) as is possible. The basic formulation begins with the integration of the equation (10) giving

For the inverse approach, consider that in a closed three dimensional region Ω with the boundary surface Γ, as shown in <figref idref="DRAWINGS">FIG. 1a</figref>, a subregion Ω0⊂Ω, called the synthesis controlled subdomain is defined and within this region the function {tilde over (B)}(r,z) is prescribed. The problem consists of searching for a boundary function J(R,ξ) that produces the field <o ostyle="single">B</o>(r,z) in Ω0 as close to the target field {tilde over (B)}(r,z) as is possible. The basic formulation begins with the integration of the equation (10) giving

The current densities shown in FIGS. 5(a) and 5(b) are converted into coil configurations using the non-linear optimization technique described above. Consider three magnet structures with L=0.8 m, 1.0 m and 1.5 m, and with the radius of the free bore being R=0.5 m. Also assume that the dsv is located at the center of the magnet with a radius of r=0.21 m. For these cases, 150 sample points evenly spaced over the dsv and including its surface were selected as exemplified in FIG. 7. The constant target field {overscore (B)}z was set to 1.0 Tesla at each sample point of the dsv. The resulting continuous current density function shown in <figref idref="DRAWINGS">FIG. 5a</figref> is clearly oscillating. According to these current distributions, initially, 11 coils are required for the 0.8 m magnet, 9 coils for the 1.0 m magnet, and 5 coils for the 1.5 m magnet to reasonably approximate the continuous current distribution. See FIG. 2. For convenience of initial design, the same turns density was used for all the coils and a constant transport current was assumed.

The current densities shown in FIGS. 5(a) and 5(b) are converted into coil configurations using the non-linear optimization technique described above. Consider three magnet structures with L=0.8 m, 1.0 m and 1.5 m, and with the radius of the free bore being R=0.5 m. Also assume that the dsv is located at the center of the magnet with a radius of r=0.21 m. For these cases, 150 sample points evenly spaced over the dsv and including its surface were selected as exemplified in FIG. 7. The constant target field <o ostyle="single">B</o>z was set to 1.0 Tesla at each sample point of the dsv. The resulting continuous current density function shown in <figref idref="DRAWINGS">FIG. 5a</figref> is clearly oscillating. According to these current distributions, initially, 11 coils are required for the 0.8 m magnet, 9 coils for the 1.0 m magnet, and 5 coils for the 1.5 m magnet to reasonably approximate the continuous current distribution. See FIG. 2. For convenience of initial design, the same turns density was used for all the coils and a constant transport current was assumed.

\\QA012\C$\REDBOOK_VERIFICATION\RAWCOMPAREDATA\PROD_010907-XML\USRE039464-20070109.XML	\\QA012\C$\REDBOOK_VERIFICATION\RAWCOMPAREDATA\TEST_010907-XML\USRE039464-20070109.XML

<sequence-list file="USRE039464-20070109-SEQLST.XML" carriers="internal-electronic" seq-file-type="ST.25"/>

<sequence-list file="USRE039464-20070109-S00001.XML" carriers="internal-electronic" seq-file-type="ST.25"/>