Computation of exact equilibrium values for n-player divide-the-dollar legislative bargaining games as in Baron and Ferejohn (1989) with general quota voting rules, recognition probabilities, and discount factors, can be achieved by solving at most n bivariate square linear systems of equations. The approach recovers Eraslan’s (2002) uniqueness result and relies on a characterization of equilib...

Last time, we talked about a very simple solver for Laplacian-based systems of linear equations, i.e., systems of linear equations of the form Ax = b, where the constraint matrix A is the Laplacian of a graph. This is not fully-general—Laplacians are SPSD matrices of a particular form—but equations of this form arise in many applications, certain other SPSD problems such as those based on SDD m...

An algorithm for the solution of linear systems of equations where the coe cient matrix is diagonal plus a semi{separable matrix is considered. The algorithm is stable with linear complexity. Furthermore it is suitable for an implementation on a system of two processors.

Let {wi,j}1≤i≤n,1≤j≤s ⊂ Lm = F (X1, . . . , Xm)[ ∂ ∂X1 , . . . , ∂ ∂Xm ] be linear partial differential operators of orders with respect to ∂ ∂X1 , . . . , ∂ ∂Xm at most d. We prove an upper bound n(4mdmin{n, s}) (2(m−t)) on the leading coefficient of the Hilbert-Kolchin polynomial of the left Lm-module 〈{w1,j , . . . , wn,j}1≤j≤s〉 ⊂ L n m having the differential type t (also being equal to the...

in this paper we have solved analytically the schrödinger equation for a microscopic particle in a one-dimensional box with two infinite walls, which the potential function inside it, has a linear form. based on the solutions of this special quantum mechanical system, we have shown that as the quantum number approaches infinity the expectation values of microscopic particle position and square ...

We propose a hybrid algorithm for solving the NP-hard absolute value equation (AVE): Ax−|x| = b, where A is an n×n square matrix. The algorithm makes no assumptions on the AVE other than solvability and consists of solving iteratively a linear system of equations followed by a linear program. The algorithm was tested on 100 consecutively generated random solvable instances of the AVE with n =50...

The paper studies language equations of the type X ⋄ L = R and L ⋄ Y = R, where L and R are given languages and ⋄ is an invertible binary word(language) operation. For most of the considered insertion and deletion operations, the existence of both a solution and a singleton solution to these equations proves to be decidable for given regular L and R. In case L is a context-free language and R i...

This paper presents an interactive mathematical tutor application to assist middle school students with solving single-variable linear and quadratic equations and two-variable systems of linear equations. The system uses a gestural, pen-based interface to mimic and enhance the traditional step-by-step method of solving algebraic problems on paper. After the student handwrites each step, the sys...