Multiscale signal analysis has been used since the early 1990s as a powerful tool for image processing. Nonlinear PDEs and multiscale morphological filters can be used to create nonlinear operators that have advantages over linear operators, notably preserving important features such as edges in images. In this report, we present the nonlinear Hamilton-Jacobi PDEs commonly used as filters for i...

In this paper, stochastic generalizations of some fixed point for operators satisfying random contractively generalized hybrid and some other contractive condition have been proved. We discuss also the existence of a solution to a nonlinear random integral equation in Banah spaces.

Since Lotka and Volterra’s seminal and pioneering works (see [10]) many decades ago, modeling of interacting, competing species have received considerable attention in the fields of biology, ecology, mathematics (for example, see [3, 9]). In their remarkably simple deterministic model, Lotka and Volterra considered two coupled nonlinear differential equations that mimic the temporal evolution o...

CONTENTS Introduction. 0. Pseudodifferential operators and linear PDE. §0.1 The Fourier integral representation and symbol classes §0.2 Schwartz kernels of pseudodifferential operators §0.3 Adjoints and products §0.4 Elliptic operators and parametrices §0.5 L 2 estimates §0.6 Gårding's inequality §0.7 The sharp Gårding inequality §0.8 Hyperbolic evolution equations §0.9 Egorov's theorem §0.10 M...

in this paper, stochastic generalizations of some fixed point for operators satisfying random contractively generalized hybrid and some other contractive condition have been proved. we discuss also the existence of a solution to a nonlinear random integral equation in banah spaces.

In this paper a new population-based algorithm for nonlinear modeling is proposed. Its advantage is the automatic selection of evolutionary operators and their parameters for individuals in population. In this approach evolutionary operators are selected from a large set of operators, however only the solutions that use low number of operators are promoted in population. Moreover, assigned oper...

Using the nonlinear coherent states method, a formalism for the construction of the coherent states associated to ”inverse bosonic operators” and their dual family has been proposed. Generalizing the approach, the ”inverse of f -deformed ladder operators” corresponding to the nonlinear coherent states in the context of quantum optics and the associated coherent states have been introduced. Fina...

Links of factorization theory, supersymmetry and Darboux transformations as isospectral deformations of difference operators are considered in the context of soliton theory. The dressing chain equations for factorizing operators of a spectral problem are derived. The chain equations itselves yield nonlinear systems which closure generates solutions of the equations as well as of the nonlinear s...