In the present paper we consider one class of zero-sum games with discontinuous payoffs which may have no solutions in the sets of pure or mixed strategies. We show that, however, the solution always exists in the set of so-called R-mixed strategies which are the elements of the space R of distributions with discontinuous test functions. The advantages of the new space of distributions (in comp...

Electronic archives are increasingly being used to store information that needs to be available for a long time such as land register information and medical records. In order for the data in such archives to remain useful, their integrity and authenticity must be protected over their entire life span. Also, in many cases it must be possible to prove that the data existed at a certain point in ...

We prove the existence of a solution of a free boundary problem for the transonic small-disturbance equation. The free boundary is the position of a transonic shock dividing two regions of smooth flow. Assuming inviscid, irrotational flow, as modeled by the transonic small-disturbance equation, the equation is hyperbolic upstream where the flow is supersonic, and elliptic in the downstream subs...

In this paper, for solving the finite-dimensional variational inequality problem ðx x ÞFðx ÞP0; 8x 2 X; where F is a C ðr > 1Þ mapping from X to R, X 1⁄4 fx 2 R : gðxÞO0g is nonempty (not necessarily bounded) and gðxÞ :R ! R is a convex Crþ1 mapping, a homotopy method is presented. Under various conditions, existence and convergence of a smooth homotopy path from almost any interior initial poi...

We give a simple proof of existence of solutions of the dispersion management and diffraction management equations for zero average dispersion, respectively diffraction. These solutions are found as maximizers of non-linear and non-local variational problems which are invariant under a large non-compact group. Our proof of existence of maximizer is rather direct and avoids the use of Lions’ con...

We study a coupled system of two parabolic equations in one space dimension. This system is singular because of the presence of one term with the inverse of the gradient of the solution. Our system describes an approximate model of the dynamics of dislocation densities in a bounded channel submitted to an exterior applied stress. The system of equations is written on a bounded interval with Dir...

This document presents the formalization of introductory material from recursion theory — definitions and basic properties of primitive recursive functions, Cantor pairing function and computably enumerable sets (including a proof of existence of a one-complete computably enumerable set and a proof of the Rice’s theorem).

cancellations in the perturbation series of certain completely integrable Hamiltonian systems. and existence of heteroclinic chains in Hamiltonian three time scales systems, Preprint, 1997. Ge1] Gentile, G: A proof of existence of whiskered tori with quasi at homoclinic intersections in a class of almost integrable Hamiltonians systems, Forum Mathematicum 17 Draft #1 DB k?1 (k ? 1)!? 0 C(;) ?1 ...

The most precise measurements are done at present by timing of radiopulsars in binary systems with two neutron stars. The timing measurements of the Taylor-Hulse pulsar give the most precise results on testing of general relativity (GR), finding implicit proof of existence of gravitational waves. We show that the existing measurements, used for checking the variability of the fundamental consta...

We revisit affine diffusion processes on general and on the canonical state space in particular. A detailed study of theoretic and applied aspects of this class of Markov processes is given. In particular, we derive admissibility conditions and provide a full proof of existence and uniqueness through stochastic invariance of the canonical state space. Existence of exponential moments and the fu...