Related papers: On the explicit formula for Gauss-Jordan eliminati…
A Gaussian elimination form of inverse iteration within the complex coordinate approach is shown to produce a simple uniform method of finding both real bound state energies and complex resonant state energies for several problems which…
We develop a general criterion for cut elimination in sequent calculi for propositional modal logics, which rests on absorption of cut, contraction, weakening and inversion by the purely modal part of the rule system. Our criterion applies…
In recent years, G\"odel's ontological proof and variations of it were formalized and analyzed with automated tools in various ways. We supplement these analyses with a modeling in an automated environment based on first-order logic…
Several preconditioned AOR methods have been proposed to solve system of linear equations $Ax=b$, where $A \in \mathbb{R}^{n \times n}$ is a unit Z-matrix. The aim of this paper is to give a comparison result for a class of preconditioners…
An expression for the coefficients of a linear iterative equation in terms of the parameters of the source equation is given both for equations in standard form and for equations in reduced normal form. The operator generating an iterative…
A recently proposed integral representation for permanents is rederived using only elementary combinatorics. For this proof the assumption that the matrix, for which the permanent is calculated, has an inverse is not necessary.
The explicit solution of the discrete time filtering problems with exponential criteria for a general Gaussian signal is obtained through an approach based on a conditional Cameron-Martin type formula. This key formula is derived for…
Resultants and Gr\"obner bases are crucial tools in studying polynomial elimination theory. We investigate relations between the variety of the resultant of two polynomials and the variety of the ideal they generate. Then we focus on the…
This paper is intended to provide an introduction to cut elimination which is accessible to a broad mathematical audience. Gentzen's cut elimination theorem is not as well known as it deserves to be, and it is tied to a lot of interesting…
We describe a method for inverting Gentzen's cut-elimination in classical first-order logic. Our algorithm is based on first computign a compressed representation of the terms present in the cut-free proof and then cut-formulas that realize…
We introduce a natural notion of determinant in matrix JB$^*$-algebras, i.e., for hermitian matrices of biquaternions and for hermitian $3\times 3$ matrices of complex octonions. We establish several properties of these determinants which…
In this paper, the result of applying iterative univariate resultant constructions to multivariate polynomials is analyzed. We consider the input polynomials as generic polynomials of a given degree and exhibit explicit decompositions into…
Quite often, verification tasks for distributed systems are accomplished via counter abstractions. Such abstractions can sometimes be justified via simulations and bisimulations. In this work, we supply logical foundations to this practice,…
In this paper, we give several matrix representations for the Horadam quaternions. We derive several identities related to these quaternions by using the matrix method. Since quaternion multiplication is not commutative, some of our results…
Efficient matrix determinant calculations have been studied since the 19th century. Computers expand the range of determinants that are practically calculable to include matrices with symbolic entries. However, the fastest determinant…
The paper presents a cut-elimination procedure for intuitionistic propositional logic in which cut is eliminated directly, without introducing the multiple-cut rule mix, and in which pushing cut above contraction is one of the reduction…
A method is presented that reduces the number of terms of systems of linear equations (algebraic, ordinary and partial differential equations). As a byproduct these systems have a tendency to become partially decoupled and are more likely…
A counter-intuitive result of Gauss (formulae (1.6), (1.7) below) is made less mysterious by virtue of being generalized through the introduction of an additional parameter.
We present several identities involving quasi-minors of noncommutative generic matrices. These identities are specialized to quantum matrices, yielding q-analogues of various classical determinantal formulas.
We consider a specific form of explicitly correlated Gaussians -- with tensor pre-factors -- which appear naturally when dealing with certain few-body systems in nuclear and particle physics. We derive analytic matrix elements with these…