Geopersia is published biannually by the College of Science, University of Tehran, Iran. The College of Science published Journal of Science, which covered all fields of basic science, from 1968 to 2010. It was then decided that the College’s journals should be more specialized, and hence publication of Geopersia was launched. Articles printed in Geopersia will be available online too. Aims an...

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The concepts of a generalized theta function and of a metaplectic cover of GL2 were introduced by T. Kubota in the 1960s. This theory is concerned with a remarkable class of automorphic forms closely related to the nth-order reciprocity law over an algebraic number field k containing the nth roots of unity. A foundational discussion of the theory for the case of n-fold covers of GLr (r 2* 2) is...

The problems described here concern Weyl group multiple Dirichlet series (WMDs). Let F be a totally complex algebraic number field containing the group μn of n-th roots of unity. We will assume that −1 is an n-th power in F . Let Φ ⊂ R be a reduced root system. Then one can attach to Φ and n a family of multiple Dirichlet series whose coefficients involve products of n-th order Gauss sums. Thes...

In cooperative games, a key question is to find a division of payoffs to coalition members in a fair manner. Nucleolus is one of such solution concepts that provides a stable solution for the grand coalition. We study the computation of the nucleolus of a number of cooperative games, including fractional matching games and fractional edge cover games on general weighted graphs, as well as verte...

We study Yang-Baxter equations with orthosymplectic supersymmetry. extend a new approach of the construction spinor and metaplectic $\hat{\cal R}$-operators orthogonal symplectic symmetries to supersymmetric case symmetry. In this R}$-operator is given by ratio two operator valued Euler Gamma-functions. illustrate calculating such R}$ operators in explicit form for special cases $osp(n|2m)$ alg...

Motivated by the need for succinct representations of all “small” transversals (or hitting sets) of a hypergraph of fixed rank, we study the complexity of computing such a representation. Next, the existence of a minimal hitting set of at least a given size arises as a subproblem. We give one algorithm for hypergraphs of any fixed rank, and we largely improve an earlier algorithm (by H. Fernau,...