A nonlinear stochastic integral equation of the Hammerstein type in the form x(t; c) = h(t; co) + f k(t, s; co)f (s, x(s; co)) dy (s) is studied where t E S, a v-finite measure space with certain properties, co E Q, the supporting set of a probability measure space (Q, A, P), and the integral is a Bochner integral. A random solution of the equation is defined to be a second order vector-valued ...

This article is concerned with the nonlinear singular perturbation problem due to small diffusivity in nonlinear evolution equations of Chaffee-Infante type. The boundary layer appearing at the boundary of the domain is fully described by a corrector which is “explicitly” constructed. This corrector allows us to obtain convergence in Sobolev spaces up to the boundary. AMS Subject Classification...

In this paper, we study the functional equation, f(x+y)f(x)f(y) = d sinx sin y. Some generalizations of the above functional equation are also considered.

In this paper we study the Lindley-type equation W = max{0, B − A−W}. Its main characteristic is that it is a non-increasing monotone function in its main argument W. Our main goal is to derive a closed-form expression of the steady-state distribution of W. In general this is not possible, so we shall state a sufficient condition that allows us to do so. We also examine stability issues, derive...

Describing a problem in terms of a system of equations is common to many branches of science and engineering. Due to their size and complexity, constructing and solving such systems often warrants the use of computers. A class of equation-based languages has grown out of the desire to describe equation systems using the wellunderstood and mature techniques from conventional programming language...

Several Miura type transformations for the Boussinesq equation are found and the corresponding integrable systems constructed.

Nonlinear generalization of the Dirac equation extending the standard paradigm of nonlinear Hamiltonians is discussed. “Faster-than-light telegraphs” are absent for all theories formulated within the new framework. A new metric for infinite dimensional Lie algebras associated with Lie-Poisson dynamics is introduced.

The Weyl equation (massless Dirac equation) is studied in a family of metrics of the Gödel type. The field equation is solved exactly for one member of the family. PACS numbers 04.20q,04.20.Jb,04.40+c,98.80.k

‎we study dual integral equations which appear in formulation of the‎ ‎potential distribution of an electrified plate with mixed boundary‎ ‎conditions‎. ‎these equations will be converted to a system of‎ ‎singular integral equations with cauchy type kernels‎. ‎using‎ ‎chebyshev polynomials‎, ‎we propose a method to approximate the‎ ‎solution of cauchy type singular integral equation which will ...