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A class of partial differential equations (a conservation law and four balance laws), with four independent variables and involving sixteen arbitrary continuously differentiable functions, is considered in the framework of equivalence…

The relevant quasipotential near an equilibrium point is determined by a new linear matrix equation, with less unknowns than an existing (possibly nonlinear) one. This also assures the asymptotic fulfillment of the Fokker-Planck equation,…

We relate the graph isomorphism problem to the solvability of certain systems of linear equations with nonnegative variables. This version replaces the two previous versions of this paper.

This paper is concerned with complexity theoretic aspects of a general formulation of quantum game theory that models strategic interactions among rational agents that process and exchange quantum information. In particular, we prove that…

We study more general variational problems on time scales. Previous results are generalized by proving necessary optimality conditions for (i) variational problems involving delta derivatives of more than the first order, and (ii) problems…

Variational methods are employed in situations where exact Bayesian inference becomes intractable due to the difficulty in performing certain integrals. Typically, variational methods postulate a tractable posterior and formulate a lower…

A general sufficient condition for the convergence of subsequences of solutions of non-autonomous, nonlinear difference equations and systems is obtained. For higher order equations the delay sizes and patterns play essential roles in…

In finite games mixed Nash equilibria always exist, but pure equilibria may fail to exist. To assess the relevance of this nonexistence, we consider games where the payoffs are drawn at random. In particular, we focus on games where a large…

We develop new polynomial methods for studying systems of word equations. We use them to improve some earlier results and to analyze how sizes of systems of word equations satisfying certain independence properties depend on the lengths of…

An interesting observation is that most pairs of weakly homogeneous mappings have no strongly monotonic property, which is one of the key conditions to ensure the unique solvability of the generalized variational inequality. This paper…

We present a quasi-integrable two-dimensional lattice equation: i.e., a partial difference equation which satisfies a criterion of integrability, singularity confinement, although it has a chaotic aspect in the sense that the degrees of its…

This article addresses the question of involutiveness and discusses the initial value problem for a class of overdetermined systems of partial differential equations which arise in the theory of integrable systems and are defined by…

We establish necessary optimality conditions for variational problems with a Lagrangian depending on a combined Caputo derivative of variable fractional order. The endpoint of the integral is free, and thus transversality conditions are…

In the paper we study the subject of positivity of systems with sequential fractional difference. We give formulas for the unique solutions of systems in linear and semi-linear cases. The positivity of systems is considered.

This paper deals with an extension of the concept of correlated strategies to Markov stopping games. The Nash equilibrium approach to solving nonzero-sum stopping games may give multiple solutions. An arbitrator can suggest to each player…

We derive strong variance-based uncertainty relations for arbitrary two and more unitary operators by re-examining the mathematical foundation of the uncertainty relation. This is achieved by strengthening the celebrated Cauchy-Schwarz…

In game theory, the concept of Nash equilibrium reflects the collective stability of some individual strategies chosen by selfish agents. The concept pertains to different classes of games, e.g. the sequential games, where the agents play…

We consider the most general correlations that can be obtained by a group of parties whose causal relations are well-defined, although possibly probabilistic and dependent on past parties' operations. We show that, for any fixed number of…

The method of separation of variables is significant, it has been applied to physics, engineering , chemistry and other fields. It allows to reduce the diffculity of problems by separating the variables from partial differential equation…

This work presents a novel policy iteration algorithm to tackle nonzero-sum stochastic impulse games arising naturally in many applications. Despite the obvious impact of solving such problems, there are no suitable numerical methods…