Existence of the equilibrium distribution

2006 ◽  
pp. 41-49
Keyword(s):  
Equilibrium Distribution

The effect of systematic errors of the equilibrium distribution concentrations on the number of stages of countercurrent extraction with various consumption of extractant

1989 ◽  
Vol 54 (4) ◽  
pp. 981-989
Author(s):  
Ján Dojčanský ◽  
Soňa Bafrncová ◽  
Július Surový
Keyword(s):  
Equilibrium Distribution ◽  
Systematic Errors ◽  
Mutual Solubility ◽  
Operating Conditions ◽  
Liquid Equilibrium ◽  
Countercurrent Extraction ◽  
Absolute Deviation ◽  
Line Slope ◽  
Tie Line ◽  
Calculated Number

On using five hypothetical systems differing in the extent of mutual solubility of components, tie-line slope, and type of binodal curve, the effect is evaluated of systematic errors in the form of absolute deviation in the liquid-liquid equilibrium distribution concentrations on the accuracy of calculated number of theoretical stages of isothermal countercurrent extraction under various operating conditions.

scholarly journals Analysis of Genetic Structure and Dispersal Patterns in a Population of Sea Beet

Genetics ◽  
1998 ◽  
Vol 149 (4) ◽  
pp. 1975-1985
Author(s):  
Jarle Tufto ◽  
Alan F Raybould ◽  
Kjetil Hindar ◽  
Steinar Engen
Keyword(s):  
Equilibrium Distribution ◽  
Pollen Dispersal ◽  
Migration Pattern ◽  
Likelihood Ratio Tests ◽  
Frequency Data ◽  
Gene Frequencies ◽  
Dispersal Patterns ◽  
Parametric Bootstrapping ◽  
Estimated Parameters ◽  
Multivariate Stochastic Process

Abstract A model of the migration pattern in a metapopulation of sea beet (Beta vulgaris L. ssp. maritima), based on the continuous distributions of seed and pollen movements, is fitted to gene frequency data at 12 isozyme and RFLP loci by maximum likelihood by using an approximation of the simultaneous equilibrium distribution of the gene frequencies generated by the underlying multivariate stochastic process of genetic drift in the population. Several alternative restrictions of the general model are fitted to the data, including the island model, a model of complete isolation, and a model in which the seed and pollen dispersal variances are equal. Several likelihood ratio tests between these alternatives are performed, and median bias in the estimated parameters is corrected by using parametric bootstrapping. To assess the fit of the selected model, the predicted covariances are compared with covariances computed from the data directly. The dependency of estimated parameters on the ratio between effective and absolute subpopulation sizes, which is treated as a known parameter in the analysis, is also examined. Finally, we note that the data also appear to contain some information about this ratio.

High field 1H NMR Studies of Sol-Gel Kinetics

1986 ◽  
Vol 73 ◽  
Author(s):  
Bruce D. Kay ◽  
Roger A. Assink
Keyword(s):  
Equilibrium Distribution ◽  
Sol Gel ◽  
Nmr Studies ◽  
H Nmr ◽  
Rate Limiting Step ◽  
Rate Of Hydrolysis ◽  
Acid Catalyzed ◽  
Product Species ◽  
Rate Limiting ◽  
Kinetics Of

ABSTRACTHigh resolution 1H NMR spectroscopy at high magnetic fields is employed to study the reaction kinetics of the Si(OCH3)4:CH3OH:H2O sol-gel system. Both the overall extent of reaction as a function of time and the equilibrium distribution of species are measured. In acid catalyzed solution, condensation is the rate limiting step while in base catalyzed solution, hydrolysis becomes rate limiting. A kinetic model in which the rate of hydrolysis is assumed to be independent of the adjacent functional groups is presented. This model correctly predicts the distribution of product species during the initial stages of the sol-gel reaction.

scholarly journals A Markov model for Selmer ranks in families of twists

2014 ◽  
Vol 150 (7) ◽  
pp. 1077-1106 ◽  
Author(s):  
Zev Klagsbrun ◽  
Barry Mazur ◽  
Karl Rubin
Keyword(s):  
Markov Process ◽  
Markov Model ◽  
Elliptic Curve ◽  
Arbitrary Number ◽  
Equilibrium Distribution ◽  
Two Dimensional ◽  
Absolute Galois Group ◽  
Quadratic Twists ◽  
The Family ◽  
Positive Integers

AbstractWe study the distribution of 2-Selmer ranks in the family of quadratic twists of an elliptic curve $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}E$ over an arbitrary number field $K$. Under the assumption that ${\rm Gal}(K(E[2])/K) \ {\cong }\ S_3$, we show that the density (counted in a nonstandard way) of twists with Selmer rank $r$ exists for all positive integers $r$, and is given via an equilibrium distribution, depending only on a single parameter (the ‘disparity’), of a certain Markov process that is itself independent of $E$ and $K$. More generally, our results also apply to $p$-Selmer ranks of twists of two-dimensional self-dual ${\bf F}_p$-representations of the absolute Galois group of $K$ by characters of order $p$.

Equilibrium distribution of radioxenon in tissue: xenon-hemoglobin association curve

1961 ◽  
Vol 16 (6) ◽  
pp. 1065-1070 ◽  
Author(s):  
Hadley L. Conn
Keyword(s):  
Partition Coefficients ◽  
Equilibrium Distribution ◽  
Hemoglobin Concentration ◽  
Gas Diffusion ◽  
In Vivo Studies ◽  
Diffusion Method ◽  
Body Tissues ◽  
Gas Diffusion Method

In vitro and in vivo studies were made of the equilibrium distribution of radioxenon in various organs and tissues of the dog and the xenon uptake compared with a water standard. Tissue-blood partition coefficients were calculated. The radioxenon-hemoglobin association curve was determined for dog and human hemoglobin and methemoglobin. The uptake of radioxenon by blood, due in particular to xenon-hemoglobin affinity, was appreciably greater than uptake either by water or by most other body tissues. Fat and brain were notable exceptions. Consequently, tissue-blood partition coefficients were about eight for fat, one for brain, and significantly less than one for other tissues studied. Acceptable accuracy for blood flow determinations with a radioxenon inert gas diffusion method would seem to depend on the use of a partition coefficient correction in turn corrected at least for the existing hemoglobin concentration. The uptake of xenon by hemoglobin had the characteristics of a solubility or a quasi-solubility phenomenon. The problem of the nature of the interaction is apparently not resolved. Submitted on June 19, 1961

Lighting Equilibrium Distribution Maps and Their Application to Face Recognition Under Difficult Lighting Conditions

2017 ◽  
Vol 31 (03) ◽  
pp. 1756003 ◽  
Author(s):  
Jun Dong ◽  
Xue Yuan ◽  
Fanlun Xiong
Keyword(s):  
Face Recognition ◽  
Equilibrium Distribution ◽  
Main Idea ◽  
Data Sets ◽  
Test Image ◽  
Distribution Maps ◽  
Lighting Conditions ◽  
Map Construction ◽  
Compensation Methods ◽  
Approximation Coefficients

In this paper, a novel facial-patch based recognition framework is proposed to deal with the problem of face recognition (FR) on the serious illumination condition. First, a novel lighting equilibrium distribution maps (LEDM) for illumination normalization is proposed. In LEDM, an image is analyzed in logarithm domain with wavelet transform, and the approximation coefficients of the image are mapped according to a reference-illumination map in order to normalize the distribution of illumination energy due to different lighting effects. Meanwhile, the detail coefficients are enhanced to achieve detail information emphasis. The LEDM is obtained by blurring the distances between the test image and the reference illumination map in the logarithm domain, which may express the entire distribution of illumination variations. Then, a facial-patch based framework and a credit degree based facial patches synthesizing algorithm are proposed. Each normalized face images is divided into several stacked patches. And, all patches are individually classified, then each patch from the test image casts a vote toward the parent image classification. A novel credit degree map is established based on the LEDM, which is deciding a credit degree for each facial patch. The main idea of credit degree map construction is the over-and under-illuminated regions should be assigned lower credit degree than well-illuminated regions. Finally, results are obtained by the credit degree based facial patches synthesizing. The proposed method provides state-of-the-art performance on three data sets that are widely used for testing FR under different illumination conditions: Extended Yale-B, CAS-PEAL-R1, and CMUPIE. Experimental results show that our FR frame outperforms several existing illumination compensation methods.

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