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In this paper, by using the theories and methods of mathematical analysis and computer algebra, a new algorithm of symbolic integral was established, a new Maple procedure myint for it was established, too. And it was applied to the automatic proving the mean-value theorems for derivatives. The results indicated that the algorithm of symbolic integral had been established in this paper had advantage of simple idea, excellent property for operation and powerful competence. This would be useful for the problem of solving differential equations, automatic proving some mathematical theorems, and so on. [Copyright &y& Elsevier]

An algorithm for finding the largest singular value of a nonnegative rectangular tensor was recently proposed by Chang, Qi, and Zhou [J. Math. Anal. Appl., 2010, 370: 284-294]. In this paper, we establish a linear convergence rate of the Chang-Qi-Zhou algorithm under a reasonable assumption. [ABSTRACT FROM AUTHOR]

Abstract: Many useful morphological filters are built as long concatenations of erosions and dilations: openings, closings, size distributions, sequential filters, etc. This paper proposes a new algorithm implementing morphological dilation and erosion of functions. It supports rectangular structuring element, runs in linear time w.r.t. the image size and constant time w.r.t. the structuring element size, and has minimal memory usage. It has zero algorithm latency and processes data in stream. These properties are inherited by operators composed by concatenation, and allow their efficient implementation. We show how to compute in one pass an Alternate Sequential Filter (ASF n ) regardless the number of stages n. This algorithm opens the way to such time-critical applications where the complexity and memory requirements of serial morphological operators represented a bottleneck limiting their usability. [Copyright &y& Elsevier]

Abstract: This paper presents a new algorithm that computes the local algebras of the roots of a zero-dimensional polynomial equation system, with a number of operations in the coefficient field that is polynomial in the number of variables, in the evaluation cost of the equations and in a Bézout number. [Copyright &y& Elsevier]

Abstract: A locally connected spanning tree of a graph G is a spanning tree T of G such that the set of all neighbors of in T induces a connected subgraph of G for every . The purpose of this paper is to give linear-time algorithms for finding locally connected spanning trees on strongly chordal graphs and proper circular-arc graphs, respectively. [Copyright &y& Elsevier]

Abstract: In this paper, by using the theories and methods of mathematics analysis, ordinary differential equation and computer algebra, a reliable algorithm for solving ordinary differential equation (ODE) was established, and a new Maple procedure mechodeproc was established, too. The results of the examples indicated that the procedure mechodeproc based on Taylor polynomial method was simple and effective, and could provide an accuracy approximate solution or exact solution of the ordinary differential equation. This would be useful for solving differential equation. [Copyright &y& Elsevier]

Abstract: Resultant is a classical algebraic tool for determining whether or not a polynomial systems have a common root without explicitly solving for the roots. But, the complexity of resultants can be very high in practice. In this paper, by using the theories and methods of computer algebra, two reliable algorithms for computing multi-resultant problems-Dixon resultant and Macaulay resultant were established, two new Maple procedures dixonres and macaulayres were established, too. Some examples are presented to illustrate the implementations of the programs. This would be useful for solving a system of polynomial equations. [Copyright &y& Elsevier]

Abstract: In this paper, by using the theories and methods of mathematical analysis and computer algebra, a reliable algorithm of Padé approximation method for solving nonlinear singular perturbation problems was established, a new Maple procedure spp was established, too. The procedure spp give not only the approximate analytic solutions but also the numerical solutions of SPP. Six examples are presented to illustrate the implementation of the program. The method is very simple and effective for most of singular perturbation problems. This would be useful for solving differential equations. [Copyright &y& Elsevier]

Abstract: Let be a finite group. It is easy to compute the character of corresponding to a given complex representation, but much more difficult to compute a representation affording a given character. In part this is due to the fact that a class of equivalent representations contains no natural canonical representation. Although there is a large literature devoted to computing representations, and methods are known for particular classes of groups, we know of no general method which has been proposed which is practical for any but small groups. We shall describe an algorithm for computing an irreducible matrix representation which affords a given character of a given group . The algorithm uses properties of the structure of which can be computed efficiently by a program such as GAP, theoretical results from representation theory, theorems from group theory (including the classification of finite simple groups), and linear algebra. All results in this paper have been implemented in the GAP package REPSN. [Copyright &y& Elsevier]