相关论文: On the unique solution of the generalized absolute…

This paper establishes several new facts on generalized polyhedral convex sets and shows how they can be used in vector optimization. Among other things, a scalarization formula for the efficient solution sets of generalized vector…

We present explicit sufficient conditions that guarantee the existence and uniqueness of the feasible load-flow solution for distribution networks with a generic topology (radial or meshed) modeled with positive sequence equivalents. In the…

Consider the nonlinear matrix equation X-sum_{i=1}^{m}A_{i}^{*}X^{-1}A_{i}=Q. This paper shows that there exists a unique positive definite solution to the equation without any restriction on A_{i}. Three perturbation bounds for the unique…

We consider the generalized continuous-time Lyapunov equation: $$ A^*XB + B^*XA =-Q, $$ where $Q$ is an $N\times N$ Hermitian positive definite matrix and $A,B$ are arbitrary $N\times N$ matrices. Under some conditions, using the coupled…

In a recent paper, a distributed algorithm was proposed for solving linear algebraic equations of the form $Ax = b$ assuming that the equation has at least one solution. The equation is presumed to be solved by $m$ agents assuming that each…

Finding the stochastic equilibria for finite-state stochastic matrices amounts to solving an eigen\-vector problem $\pi = \pi P$. Various techniques for doing so are known, some extremely computationally intensive. Herein we shall aim to…

We give a new elementary proof of existence and uniqueness of a solution to the Sylvester equation $AX-XB=Y$

This paper introduces, up to the author's knowledge, for the first time the generalized initial value problem. In this problem, given an ordinary differential equation defined in some set, the initial conditions are mapped to a subset of…

A special series is introduced in this paper to yield solution of the first-order linear vector differential equation. It is proved that if the differential equation satisfied by the first term of this series can be solved exactly, then…

A novel approach is introduced to a very widely occurring problem, providing a complete, explicit resolution of it: minimisation of a convex quadratic under a general quadratic, equality or inequality, constraint. Completeness comes via…

A fundamental result in linear algebra states that if a homogenous linear equation system has only the trivial solution, then there are at most as many variables as equations. We prove the following generalisation of this phenomenon. If a…

A shift splitting modified Newton-type (SSMN) iteration method is introduced for solving large sparse generalized absolute value equations (GAVEs). The SSMN method is established by replacing the regularized splitting of the coefficient…

We present the exact solution to the linearized Maxwell equations in space-time slightly curved by a gravitational wave. We show that in general, even dealing with a first-order theory in the strength of the gravitational field, the…

We give two conditions that are necessary and sufficient for the uniqueness of Filippov solutions of scalar, autonomous ordinary differential equations with discontinuous velocity fields. When only one of the two conditions is satisfied, we…

We introduce a new theory of generalised solutions which applies to fully nonlinear PDE systems of any order and allows for merely measurable maps as solutions. This approach bypasses the standard problems arising by the application of…

Using the Bethe ansatz, we obtain the exact solution of the master equation for the totally asymmetric exclusion process on an infinite one-dimensional lattice. We derive explicit expressions for the conditional probabilities P(x_1, ...…

W.E. Roth (1952) proved that the matrix equation $AX-XB=C$ has a solution if and only if the matrices $\left[\begin{matrix}A&C\\0&B\end{matrix}\right]$ and $\left[\begin{matrix}A&0\\0&B\end{matrix}\right]$ are similar. A. Dmytryshyn and B.…

In this paper, we provide a necessary and sufficient condition ensuring the property of exponential dichotomy for periodic linear systems of generalized differential equations. This condition allow us to revisit a recent result of…

An interesting observation is that most pairs of weakly homogeneous mappings have no strongly monotonic property, which is one of the key conditions to ensure the unique solvability of the generalized variational inequality. This paper…

First order algebraic differential equations are considered. An necessary condition for a first order algebraic differential equation to have a rational general solution is given: the algebraic genus of the equation should be zero.…