Related papers: The Constant Astigmatism Equation. New Exact Solut…
We introduce an algebraic formula producing infinitely many exact solutions of the constant astigmatism equation $ z_{yy} + ({1}/{z})_{xx} + 2 = 0 $ from a given seed. A construction of corresponding surfaces of constant astigmatism is then…
We present novel convex-optimization-based solutions to the problem of blind beamforming of constant modulus signals, and to the related problem of linearly constrained blind beamforming of constant modulus signals. These solutions ensure…
We introduce a nonlocal transformation to generate exact solutions of the constant astigmatism equation $z_{yy} + (1/z)_{xx} + 2 = 0$. The transformation is related to the special case of the famous B\"acklund transformation of the…
We propose a new approach to solve an NP complete problem by means of stochastic limit.
In this article, we introduce the notion of stochastic symmetry of a differential equation. It consists in a stochastic flow that acts over a solution of a differential equation and produces another solution of the same equation. In the…
A novel approach to an old symmetry problem is developed. A new proof is given for the following symmetry problem, studied earlier.
We demonstrate how one can describe explicitly the present arbitrariness in solutions of relativistic wave equations in external electromagnetic fields of special form. This arbitrariness is connected to the existence of a transformation,…
In this study, a new form of quadratic spline is obtained, where the coefficients are determined explicitly by variational methods. Convergence is studied and parity conservation is demonstrated. Finally, the method is applied to solve…
We consider the problem of closeness of solutions of an exact and an averaged difference equations on an infinite interval. Appropriate assertions are derived from one special theorem on the stability under constantly acting perturbations.
The general solution to the Complex Bateman equation is constructed. It is given in implicit form in terms of a functional relationship for the unknown function. The known solution of the usual Bateman equation is recovered as a special…
Blind equalization is a classic yet open problem. Statistic-based algorithms, such as constant modulus (CM), were widely investigated. One inherent issue with blind algorithms is the phase ambiguity of equalized signals. In this letter, we…
This paper concerns a spectral estimation problem in which we want to find a spectral density function that is consistent with estimated second-order statistics. It is an inverse problem admitting multiple solutions, and selection of a…
This paper shows how to build a formal analytical solution for a differential equation of arbitrary order and with variable coefficients. It proofs that the most known approximated solutions for such a problem can be derived from the…
In this article we study the existence and uniqueness of solutions of stochastic continuity equation with irregular coefficients.
The Constraint Satisfaction Problem (CSP) framework offers a simple and sound basis for representing and solving simple decision problems, without uncertainty. This paper is devoted to an extension of the CSP framework enabling us to deal…
In this work we propose a new kind of parameterized outer estimate of the united solution set to an interval parametric linear system. The new method has several advantages compared to the methods obtaining parameterized solutions…
We propose a new kind of stochastic absolute value equations involving absolute values of variables. By utilizing an equivalence relation to stochastic bilinear program, we investigate the expected value formulation for the proposed…
The recent development of calibration algorithms has been driven into two major directions: (1) an increasing accuracy of mathematical approaches and (2) an increasing flexibility in usage by reducing the dependency on calibration objects.…
We construct the closed form solution of an elastic beam with axial load using Lie symmetry method. A beam with spatially varying physical properties such as mass and second moment of inertia is considered. The governing fourth order…
We show that Pinney's equation [2] with a constant coefficient can be reduced to its linear part by a simple change of variables. Also, Pinney's original solution is simplified slightly.