This paper is concerned with solving large-scale eigenvalue problems by algebraic substructuring. Algebraic substructuring refers to the process of applying matrix reordering and partitioning algorithms to divide a large sparse matrix into smaller submatrices from which a subset of spectral components are extracted and combined to form approximate solutions to the original problem. Through an a...

We prove algebraic equations satissed by the area generating function for directed animals on an innnite family of regular, non-planar, two-dimensional graphs.

We discuss the existence results for a fuzzy initial value problem of linear differential-algebraic equations and provide an explicit representation for the solution. A few illustrative examples are given. © 2014 Elsevier B.V. All rights reserved.

In this article we propose a method of performing arithmetic operations on variables with unknown distribution. The approach to the evaluation results of arithmetic operations can select probability intervals of the algebraic equations and their systems solutions, of differential equations and their systems in case of histogram evaluation of the empirical density distributions of random paramet...

—This document presents an introduction of two commonly used power system differential algebraic equations for studying electromechanical oscillation and transient stability. Two types of generator models are used to formulate the power system model, respectively: the second-order classical model and the fourth-order generator model. An example is provided on the IEEE 9-bus system.

In this paper, we classify ruled surfaces in Lorentz-Minkowski 3-spaces satisfying some algebraic equations in terms of the second Gaussian curvature, the mean curvature and the Gaussian curvature.

A braided Yang-Baxter Algebra in a Theory of two coupled Lattice Quantum KdV: algebraic properties and ABA representations. Abstract A generalization of the Yang-Baxter algebra is found in quantizing the mon-odromy matrix of two (m)KdV equations discretized on a space lattice. This braided Yang-Baxter equation still ensures that the transfer matrix generates operators in involution which form t...

This paper presents solne inrprovements to the matrix-sigll-fllnction algorithn~ for the alge\,raic Riccati equation. A simple reorganization changes nonsynnnetric watrix inversion5 into syinmetric niatrix inversions. Scaling accelerates convergence of the basic iteration ant1 yields a new qnadratic formula for certain 2-by-2 algebraic Riccati eqnation5. Numerical experience suggests the algori...