Nonlinear cross-correlation equations in finite and semi-infinite intervals are studied by means of Fourier transform and Cauchy integral techniques. The equations are reduced to a bilinear conjugacy problem for two analytic functions on the real axis which can be solved in explicit form. In particular, Engibaryan’s equations from nonlinear factorization theory of Wiener-Hopf integral equations...

The applicability of the Fisher equation, which combines diffusion with logistic nonlinearity, to population dynamics of bacterial colonies is studied with the help of explicit analytic solutions for the spatial distribution of a stationary bacterial population under a static mask. The mask protects bacteria from ultraviolet light. The solution, which is in terms of Jacobian elliptic functions,...

The theory of finite-rank perturbations allows for the determination spectral information broad classes operators using tools analytic function theory. In this work, are applied to powers derivative operator, providing a full account from self-adjoint boundary conditions computing aspects operators' matrix-valued measures. particular, support and weights Clark (spectral) measures computed via c...

Volumetric light transport effects are significant for many materials like skin, smoke, clouds, snow or water. In particular, one must consider the multiple scattering of light within the volume. While it is possible to simulate such media using volumetric Monte Carlo or finite element techniques, those methods are very computationally expensive. On the other hand, simple analytic models have s...

In fact, Hochstadt gives an explicit formula for the discriminant which will be reproduced below. Since Hochstadt’s work there has been a considerable interest in finite-band potentials, i.e., potentials q such that the spectrum of the operator associated with d2/dx 2 + q consists of finitely many regular analytic arcs, due to their close relationship with the Korteweg-de Vries hierarchy and he...

This paper is concerned with estimating the internal state of a dynamic system by processing measurements taken from the system output. An exact analytic representation of the probability density functions characterizing the estimate may not be possible to obtain. Even when available, it may be too complex or not practical because, for example, recursive application is required. Hence, approxim...

in this paper, an enhanced computational code was developed using finite-volume method for solving the incompressible natural convection flow within the cylindrical cavities. grids were generated by an easy method with a view to computer program providing. an explicit integration algorithm was applied to find the steady state condition. also instead of the conventional algorithms of simple, sim...

The finite analytic numerical method is developed to solve two-point boundary value problems of ordinary differential equations. The basic idea of the finite analytic method is the incorporation of the local analytic solution of the governing equation in the numerical solution of the boundary value problem. In this study, the finite analytic solution is developed for both linear and nonlinear s...