In this paper, we present an extension of \G-networks" which includes queues with network state-dependent service rate, routing intensities and triggered batch signal movement. We prove that these networks have a geometric product form invariant measure. We establish su cient conditions for the existence of a solution to tra c equations.

In this paper, a  fuzzy numerical procedure for solving fuzzy linear Volterra integro-differential equations of the second kind under strong  generalized differentiability is designed. Unlike the existing numerical methods, we do not replace the original fuzzy equation by a $2times 2$ system ofcrisp equations, that is the main difference between our method  and other numerical methods.Error ana...

 Abstract: There are some methods for solving integro-differential equations. In this work, we solve the general-order Feredholm integro-differential equations. The Petrov-Galerkin method by considering Chebyshev multiwavelet basis is used. By using the orthonormality property of basis elements in discretizing the equation, we can reduce an equation to a linear system with small dimension. For ...

The article proposes the continuation and development of apparatus derived numbers, which allows us to study behavior several variables functions properties systems solutions differential equations without their differentiability. conditions criteria for using partial external derivatives numbers are proposed, obtained earlier results can be applied in stability ordinary systems.

We introduce a ultradiscretization with parity variables of the q-difference Painlevé VI system of equations. We show that ultradiscrete limit of Riccati-type solutions of q-Painlevé VI satisfies the ultradiscrete Painlevé VI system of equations with the parity variables, which is valid by using the parity variables. We study some solutions of the ultradiscrete Riccati-type equation and those o...

For the Euler equations in a thin domain Qε = Ω×(0, ε), Ω a rectangle in R, with initial data in (W (Qε)), q > 3, bounded uniformly in ε, the classical solution is shown to exist on a time interval (0, T (ε)), where T ( ) → +∞ as → 0. We compare this solution with that of a system of limiting equations on Ω.