Related papers: Minimum Variance Solution of Underdetermined Syste…

In this paper we characterize the definiteness of the discrete symplectic system, study a nonhomogeneous discrete symplectic system, and introduce the minimal and maximal linear relations associated with these systems. Fundamental…

In this short article, some properties of matrices of moving least-squares approximation have been proven.The used technique is based on singular-value decomposition and inequalities for singular-values. Some inequalities for the norm of…

Dynamic Mode Decomposition (DMD) has emerged as a powerful tool for analyzing the dynamics of non-linear systems from experimental datasets. Recently, several attempts have extended DMD to the context of low-rank approximations. This…

Reasoning with minimal models has always been at the core of many knowledge representation techniques, but we still have only a limited understanding of this problem in Description Logics (DLs). Minimization of some selected predicates,…

Mathematical Program Networks (MPNs) are introduced in this work. An MPN is a collection of interdependent Mathematical Programs (MPs) which are to be solved simultaneously, while respecting the connectivity pattern of the network defining…

We give a necessary and sufficient condition for a system of linear inhomogeneous fractional differential equations to have at least one bounded solution. We also obtain an explicit description for the set of all bounded (or decay)…

Linearized models of power systems are often desirable to formulate tractable control and optimization problems that still reflect real-world physics adequately under various operating conditions. In this paper, we propose an approach that…

Separable nonlinear least squares (SNLS)problem is a special class of nonlinear least squares (NLS)problems, whose objective function is a mixture of linear and nonlinear functions. It has many applications in many different areas,…

The alternating minimization (AM) method is a fundamental method for minimizing convex functions whose variable consists of two blocks. How to efficiently solve each subproblems when applying the AM method is the most concerned task. In…

We explore Young measure solutions of systems of conservation laws through an alternative variational method that introduces a suitable, non-negative error functional to measure departure of feasible fields from being a weak solution. Young…

In this paper, we consider the problem of minimizing a linear functional subject to uncertain linear and bilinear matrix inequalities, which depend in a possibly nonlinear way on a vector of uncertain parameters. Motivated by recent results…

Solving a singular linear system for an individual vector solution is an ill-posed problem with a condition number infinity. From an alternative perspective, however, the general solution of a singular system is of a bounded sensitivity as…

In this paper, we study the problem of finding the least square solutions of over-determined linear algebraic equations over networks in a distributed manner. Each node has access to one of the linear equations and holds a dynamic state. We…

We study the number of monochromatic solution to linear equation in $\{1,\dots,n\}$ when we color the set by at least three colors. We consider the $r$-commonness for $r\geq 3$ of linear equation with odd number of terms, and we also prove…

The uncertainty relation is a fundamental concept in quantum theory, plays a pivotal role in various quantum information processing tasks. In this study, we explore the additive uncertainty relation pertaining to two or more observables, in…

Explicit formulas for the mean and variance of linear stochastic differential equations are derived in terms of an exponential matrix. This result improved a previous one by means of which the mean and variance are expressed in terms of a…

We describe the explicit form of a left greatest common divisor and a least common multiple of solutions of a solvable linear matrix equation over a commutative elementary divisor domain. We prove that these left greatest common divisor and…

Let K be a field of characteristic 0. We consider linear equations a1*x1+...+an*xn=1 in unknowns x1,...,xn from G, where a1,...,an are non-zero elements of K, and where G is a subgroup of the multiplicative group of non-zero elements of K.…

The minimal set of Shannon-type inequalities (referred to as elemental inequalities), plays a central role in determining whether a given inequality is Shannon-type. Often, there arises a situation where one needs to check whether a given…

A new relativistic invariant version of nonlinear Maxwell equations is offerred. Some properties of these equations are considered.