The equation that approximately traces the trajectory in the concentration phase space of chemical kinetics is derived based on the rate of entropy production. The equation coincides with the true chemical kinetics equation to first order in a variable that characterizes the degree of quasi-equilibrium for each reaction, and the equation approximates the trajectory along at least final part of ...

Linear dimensionality reduction techniques, notably principal component analysis, are widely used in climate data analysis as a means to aid in the interpretation of datasets of high dimensionality. These linear methods may not be appropriate for the analysis of data arising from nonlinear processes occurring in the climate system. Numerous techniques for nonlinear dimensionality reduction have...

we classify the paracontact riemannian manifolds that their rieman-nian curvature satisfies in the certain condition and we show that thisclassification is hold for the special cases semi-symmetric and locally sym-metric spaces. finally we study paracontact riemannian manifolds satis-fying r(x, ξ).s = 0, where s is the ricci tensor.

In this work, we propose a proximal algorithm for unconstrained optimization on the cone of symmetric semidefinite positive matrices. It appears to be the first in the proximal class on the set of methods that convert a Symmetric Definite Positive Optimization in Nonlinear Optimization. It replaces the main iteration of the conceptual proximal point algorithm by a sequence of nonlinear programm...

commutative properties of four-dimensional generalized symmetric pseudo-riemannian manifolds were considered. specially, in this paper, we studied skew-tsankov and jacobi-tsankov conditions in 4-dimensional pseudo-riemannian generalized symmetric manifolds.