Related papers: Category of a map and nonlinear analysis
Natural data offer a hard challenge to data analysis. One set of tools is being developed by several teams to face this difficult task: Persistent topology. After a brief introduction to this theory, some applications to the analysis and…
We discuss the homological algebra of representation theory of finite dimensional algebras and finite groups. We present various methods for the construction and the study of equivalences of derived categories: local group theory, geometry…
The Cauchy-type problem for a nonlinear differential equation involving Hilfer fractional derivative is considered. We prove existence, uniqueness and continuous dependence of a solution for Cauchy-type problem using successive…
In this article, we consider nonlinear complementarity problem. We introduce a new homotopy function for finding the solution of nonlinear complementarity problem through the trajectory . We show that the homotopy path approaching the…
In this paper, we consider the {\it tensor absolute value equations} (TAVEs), which is a newly introduced problem in the context of multilinear systems. Although the system of TAVEs is an interesting generalization of matrix {\it absolute…
A new syntactic characterization of problems complete via Turing reductions is presented. General canonical forms are developed in order to define such problems. One of these forms allows us to define complete problems on ordered…
We consider an ordinary nonlinear differential equation with generalized coefficients as an equation in differentials in algebra of new generalized functions. Then the solution of such equation will be a new generalized function. In the…
The authors suggest a new powerful tool for solving group classification problems, that is applied to obtaining the complete group classification in the class of nonlinear Schr\"odinger equations of the form…
This paper presents a comprehensive survey of methods which can be utilized to search for solutions to systems of nonlinear equations (SNEs). Our objectives with this survey are to synthesize pertinent literature in this field by presenting…
We argue that reducing nonlinear programming problems to a simple canonical form is an effective way to analyze them, specially when the problem is degenerate and the usual linear independence hypothesis does not hold. To illustrate this…
We classify nontrivial, nonnegative, positively homogeneous solutions of the equation \begin{equation*} \Delta u=\gamma u^{\gamma-1} \end{equation*} in the plane. The problem is motivated by the analysis of the classical Alt-Phillips free…
The paper aims to show the equivalency between nonlinear complementarity problem and the system of nonlinear equations. We propose a homotopy method with vector parameter $\lambda$ in finding the solution of nonlinear complementarity…
This work investigates the application of the Newton's method for the numerical solution of a nonlinear boundary value problem formulated through an ordinary differential equation (ODE). Nonlinear ODEs arise in various mathematical modeling…
We classify the solutions to an overdetermined elliptic problem in the plane in the finite connectivity case. This is achieved by establishing a one-to-one correspondence between the solutions to this problem and a certain type of minimal…
The vector-matrix Riemann boundary value problem for the unit disk with piecewise constant matrix is constructively solved by a method of functional equations. By functional equations we mean iterative functional equations with shifts…
A model "remarkable" fin equation is singled out from a class of nonlinear (1+1)-dimensional fin equations. For this equation a number of exact solutions are constructed by means of using both classical Lie algorithm and different modern…
These are classified by the direction of approximation (from above or below), the set family types (partition or covering) of simple functions, the coefficient signature (non-negative or signed), and cardinal number of terms of simple…
Let $\A$ be an algebra and let $f(x_1,...,x_d)$ be a multilinear polynomial in noncommuting indeterminates $x_i$. We consider the problem of describing linear maps $\phi:\A\to \A$ that preserve zeros of $f$. Under certain technical…
On an example of the open nonlinear electrodynamic system - transverse non-homogeneous, isotropic, nonlinear (a Kerr-like dielectric nonlinearity) dielectric layer, the algorithms of solution of the diffraction problem of a plane wave on…
On the base of Lie algebraic and differential geometry methods, a wide class of multidimensional nonlinear systems is obtained, and the integration scheme for such equations is proposed.