τ-function of discrete isomonodromy transformations and probability

Isomonodromy Transformations of Linear Systems of Difference Equations

We introduce and study “isomonodromy” transformations of the matrix linear difference equation Y (z + 1) = A(z)Y (z) with polynomial (or rational) A(z). Our main result is a construction of an isomonodromy action of Zm(n+1)−1 on the space of coefficients A(z) (here m is the size of matrices and n is the degree of A(z)). The (birational) action of certain rank n subgroups can be described by dif...

Transformations to symmetry based on the probability weighted characteristic function

On Possibility/probability Transformations

The problem of converting possibility measures into probability measures has received attention in the past, but not by so many scholars. This question is philosophically interesting as part of the debate between probability and fuzzy sets. The imbedding of fuzzy sets into random set theory as done by Goodman and Nguyen (1985), Wang Peizhuang (1983), among others, has solved this question in pr...

Discrete Mathematics and Probability

Effects of Probability Function on the Performance of Stochastic Programming

Stochastic programming is a valuable optimization tool where used when some or all of the design parameters of an optimization problem are defined by stochastic variables rather than by deterministic quantities. Depending on the nature of equations involved in the problem, a stochastic optimization problem is called a stochastic linear or nonlinear programming problem. In this paper,a stochasti...