Related papers: State space formulas for stable rational matrix so…
In human society, a lot of social phenomena can be concluded into a mathematical problem called the bipartite matching, one of the most well known model is the marriage problem proposed by Gale and Shapley. In this article, we try to find…
We consider the decision problem for quantifier-free formulas whose atoms are linear inequalities interpreted over the reals or rationals. This problem may be decided using satisfiability modulo theory (SMT), using a mixture of a SAT solver…
The rational $Q$-system is an efficient method to solve Bethe ansatz equations for quantum integrable spin chains. We construct the rational $Q$-systems for generic Bethe ansatz equations described by an $A_{\ell-1}$ quiver, which include…
We discuss the existence and nonexistence of solutions to the steady-state Gierer-Meinhardt system $$ \begin{cases} \displaystyle -\Delta u=\frac{u^p}{v^q}+\lambda \rho(x) \,, u>0 &\quad\mbox{ in }\mathbb{R}^N\setminus K,\\[0.1in]…
Let $R$ be a commutative complex unital semisimple Banach algebra with the involution $\cdot ^\star$. Sufficient conditions are given for the existence of a stabilizing solution to the $H^\infty$ Riccati equation when the matricial data has…
We investigate the presence of static solutions in models described by real scalar field in two-dimensional spacetime. After taking advantage of a procedure introduced sometime ago, we solve intricate nonlinear ordinary differential…
We construct a rational integrable system (the rational top) on a coadjoint orbit of ${\rm SL}_N$ Lie group. It is described by the Lax operator with spectral parameter and classical non-dynamical skew-symmetric $r$-matrix. In the case of…
This paper describes a suite of algorithms for constructing low-rank approximations of an input matrix from a random linear image of the matrix, called a sketch. These methods can preserve structural properties of the input matrix, such as…
We propose an energy-driven stochastic master equation for the density matrix as a dynamical model for quantum state reduction. In contrast, most previous studies of state reduction have considered stochastic extensions of the Schr\"odinger…
We study spatially periodic orbits for a coupled map lattice of sine circle maps with nearest neighbour coupling and periodic boundary conditions. The stability analysis for an arbitrary spatial period k is carried out in terms of the…
We propose a new integer programming formulation for the problem of finding a maximum stable set of a graph based on representatives of stable sets. In addition, we investigate exact solutions provided by a Lagrangian decomposition of this…
We investigate the regularity in $L^p$ ($p>2$) of the gradient of any weak solution of a Cauchy problem with mixed Neumann-power type boundary conditions. Under suitable assumptions we prove the existence of weak solutions that satisfy…
We introduce a version of algebraic $K$-theory for coefficient systems of rings which is valued in genuine $G$-spectra for a finite group $G$. We use this construction to build a genuine $G$-spectrum $K_G(\mathbb{Z}[\underline{\pi_1(X)}])$…
While it is well known that nonlinear methods of approximation can often perform dramatically better than linear methods, there are still questions on how to measure the optimal performance possible for such methods. This paper studies…
Consider a multivariable state space system and associated transfer function G({\lambda}). The aim of this paper is to define and analyze two vector spaces of matrix pencils associated with the matrix G({\lambda}) and show that almost all…
In this paper we consider the system of the non-steady Navier-Stokes equations with mixed boundary conditions. We study the existence and uniqueness of a solution of this system. We define Banach spaces $X$ and $Y$, respectively, to be the…
In this paper, a new framework, named as graphical state space model, is proposed for the real time optimal estimation of a class of nonlinear state space model. By discretizing this kind of system model as an equation which can not be…
We generalize the theory of underlying one-step methods to strictly stable general linear methods (GLMs) solving nonautonomous ordinary differential equations (ODEs) that satisfy a global Lipschitz condition. We combine this theory with the…
It is well known that the linear stability of solutions of partial differential equations which are integrable can be very efficiently investigated by means of spectral methods. We present here a direct construction of the eigenmodes of the…
Although there are many results on the global solvability and the precise description of the large time behaviors of solutions to the initial-boundary value problems of the one-dimensional viscous radiative and reactive gas in bounded…