A gain graph is a graph whose edges are labelled invertibly from a group. A weighted gain graph is a gain graph with vertex weights from a semigroup, where the gain group is lattice ordered and acts on the weight semigroup. For weighted gain graphs we establish basic properties and we present general dichromatic and tree-expansion polynomials that are Tutte invariants (they satisfy Tutte’s dele...

‎The main purpose of this paper is to study the numerical solution of nonlinear Volterra integral equations with constant delays, based on the multistep collocation method. These methods for approximating the solution in each subinterval are obtained by fixed number of previous steps and fixed number of collocation points in current and next subintervals. Also, we analyze the convergence of the...

This is a survey of open problems in different parts of combinatorial and additive number theory. 1. What sets are sumsets? Let N,N0, Z, and Z d denote, respectively, the sets of positive integers, nonnegative integers, integers, and d-dimensional integral lattice points. LetG denote an arbitrary abelian group and let X denote an arbitrary abelian semigroup, written additively. Let |S| denote t...

In this paper we study an integro-differential equation describing granular flow dynamics with slow erosion. This nonlinear partial differential equation is a conservation law where the flux contains an integral term. Through a generalized wave front tracking algorithm, approximate solutions are constructed and shown to converge strongly to a Lipschitz semigroup.

Let S be a locally compact foundation semigroup with identity and                          be its semigroup algebra. Let X be a weak*-closed left translation invariant subspace of    In this paper, we prove that  X  is invariantly  complemented in   if and  only if  the left ideal  of    has a bounded approximate identity. We also prove that a foundation semigroup with identity S is left amenab...

in the present paper we give a partially negative answer to a conjecture of ghahramani, runde and willis. we also discuss the derivation problem for both foundation semigroup algebras and clifford semigroup algebras. in particular, we prove that if s is a topological clifford semigroup for which es is finite, then h1(m(s),m(s))={0}.