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Linear Expression (linear + expression)

Distribution by Scientific Domains
Chemistry42%

Selected Abstracts

Linear Expression of the Mathematical Relationship between Electroosmotic Mobility and Buffer Concentration

CHINESE JOURNAL OF CHEMISTRY, Issue 1 2006
Xu Xu
Abstract It was believed that electroosmotic mobility ,eo is inversely proportional to the square root of the ionic strength I. But the linear relationship for regression analysis was expressed differently in different papers. The paper studied the linear expression of the mathematical relationship between ,eo and c (background buffer concentration) by mathematical transform and real experimental data. ,eo values of fused silica capillary were determined in four buffer systems. Their experimental conditions were controlled carefully for decreasing temperature difference ,T and pH difference ,pH in 50 µm ID capillary, in which no double layer overlap existed. The linear relationship between the reciprocal of electroosmotic mobility and the square root of concentration (or ionic strength) was derived by mathematical method. The regression analysis of experimental data was shown to well correspond to the relationship. The constants in regression equation could be well defined and the calculated results were acceptable. [source]

SIMD Optimization of Linear Expressions for Programmable Graphics Hardware

COMPUTER GRAPHICS FORUM, Issue 4 2004
Chandrajit Bajaj
Abstract The increased programmability of graphics hardware allows efficient graphical processing unit (GPU) implementations of a wide range of general computations on commodity PCs. An important factor in such implementations is how to fully exploit the SIMD computing capacities offered by modern graphics processors. Linear expressions in the form of, where A is a matrix, and and are vectors, constitute one of the most basic operations in many scientific computations. In this paper, we propose a SIMD code optimization technique that enables efficient shader codes to be generated for evaluating linear expressions. It is shown that performance can be improved considerably by efficiently packing arithmetic operations into four-wide SIMD instructions through reordering of the operations in linear expressions. We demonstrate that the presented technique can be used effectively for programming both vertex and pixel shaders for a variety of mathematical applications, including integrating differential equations and solving a sparse linear system of equations using iterative methods. [source]

Flow Characterization of Peach Products During Extrusion

JOURNAL OF FOOD SCIENCE, Issue 3 2000
H. Akdogan
ABSTRACT: Suitability of Bingham, Herschel-Bulkley, Casson, and Mizrahi-Berk models, to characterize the flow behavior of peach products during extrusion was investigated. The Casson equation sufficiently described the flow of peach extrudates within the 49 to 125 s -1 shear rate range. As concentration increased, yield stress and consistency coefficients increased. A rheological model was proposed to describe the viscosity of peach extrudates. The model incorporates the effect of shear rate by the Casson equation and the effect of concentration by a linear expression. The model provided good fit to the experimental data for peach extrudates reconstituted from drum-dried peach purees. [source]

On the relation between electron temperatures in the O+ and O++ zones in high-metallicity H ii regions

MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 4 2006
Leonid S. Pilyugin
ABSTRACT We suggest a new way to establish the relation between the electron temperature t3 within the [O iii] zone and the electron temperature t2 within the [O ii] zone in high-metallicity (12 + log(O/H) > 8.25) H ii regions. The t2,t3 diagram is constructed by applying our method to a sample of 372 H ii regions. We find that the correlation between t2 and t3 is tight and can be approximated by a linear expression. The new t2,t3 relation can be used to determine t2 and accurate abundances in high-metallicity H ii regions with a measured t3. It can also be used in conjunction with the ff relation for the determination of t3 and t2 and oxygen abundances in high-metallicity H ii regions, where the [O iii],4363 auroral line is not detected. The derived t2,t3 relation is independent of photoionization models of H ii regions. [source]

Linear Expression of the Mathematical Relationship between Electroosmotic Mobility and Buffer Concentration

CHINESE JOURNAL OF CHEMISTRY, Issue 1 2006
Xu Xu
Abstract It was believed that electroosmotic mobility ,eo is inversely proportional to the square root of the ionic strength I. But the linear relationship for regression analysis was expressed differently in different papers. The paper studied the linear expression of the mathematical relationship between ,eo and c (background buffer concentration) by mathematical transform and real experimental data. ,eo values of fused silica capillary were determined in four buffer systems. Their experimental conditions were controlled carefully for decreasing temperature difference ,T and pH difference ,pH in 50 µm ID capillary, in which no double layer overlap existed. The linear relationship between the reciprocal of electroosmotic mobility and the square root of concentration (or ionic strength) was derived by mathematical method. The regression analysis of experimental data was shown to well correspond to the relationship. The constants in regression equation could be well defined and the calculated results were acceptable. [source]

SIMD Optimization of Linear Expressions for Programmable Graphics Hardware

COMPUTER GRAPHICS FORUM, Issue 4 2004
Chandrajit Bajaj
Abstract The increased programmability of graphics hardware allows efficient graphical processing unit (GPU) implementations of a wide range of general computations on commodity PCs. An important factor in such implementations is how to fully exploit the SIMD computing capacities offered by modern graphics processors. Linear expressions in the form of, where A is a matrix, and and are vectors, constitute one of the most basic operations in many scientific computations. In this paper, we propose a SIMD code optimization technique that enables efficient shader codes to be generated for evaluating linear expressions. It is shown that performance can be improved considerably by efficiently packing arithmetic operations into four-wide SIMD instructions through reordering of the operations in linear expressions. We demonstrate that the presented technique can be used effectively for programming both vertex and pixel shaders for a variety of mathematical applications, including integrating differential equations and solving a sparse linear system of equations using iterative methods. [source]