INVOLUTIVE BASES UNDER COMPOSITION

In this paper, the behaviors of involutive bases under composition operation are studied. For two kinds of involutive bases, i.e., Pommaret bases, Janet bases, we study their behavior problems under composition. Some further problems are also proposed.     

THE GROEBNER BASIS UNDER COMPOSITION I

IIntroductlonIn rece尬 p叩ers Hoon Hong addressed the problem of*them behaviour ofGroebner basesund。composition ofpolynomlals(see[1])二 This prob卜m can be stated as follows:Let G be a Groebner basis of the ideal g6n。ated by F under some t。m ordering,w     

THE UNIVERSAL GROEBNER BASIS UNDER COMPOSITION

Composition is the operation of replacing variables in a polynomial with other polynomials. The main question in this paper is: when does composition commute with universal Groebner basis computation? We prove that this happens iff the composition is single variable. This has a natural application in the computation of universal Groebner bases of composed polynomials.     

SOME STUDIES ON GROeBNER BASES FOR MODULES AND APPLICATIONS

Hong’s theorem for Groebner bases under polynomial composition is generalized to module case with more general consideration.Similar generalization is also considered when the coefficient field is replaced by a Dedekind domain.     

THE LINEAR ARBORICITY OF COMPOSITION GRAPHS

The linear arboricity la(G) of a graph G is the minimum number of linear forests which partition the edges of G. Akiyama, Exoo and Harary conjectured that la(G) = [△(G) 1/2] for any regular graph G. In this paper, we prove the conjecture for some composition graphs, in particular, for complete multipartite graphs.     

THE MINIMAL CHARACTERISTIC BASIS OF A POLYNOMIAL IDEAL

The concept of minimal characteristic basis(abbr.char basis) of a polynomial ideal ispresened to give the uniqueness of the char basis of an ideal.For the prime ideal,we give an algorithmto construct the minimal char basis from generators of the given ideal.     

LIFE DISTRIBUTION OF SERIES UNDER THE SUCCESSIVE DAMAGE MODEL

We analyse further the reliability behaviour of series and parallel systems in the successive damage model initiated by Downton. The results are compared with those obtained for other models with different bivariate distributions.     

交货期固定的工件准时完工数——最大排序问题的多项式时间算法

给出了求解交货期固定的工件准时完工数最大的排序问题的多项式时间算法。     

DETERMINATION OF THE DENSEST SUBGRAPH

Define the density d(G) of a graph G as ε(G)/v(G). A polynomial algorithm forfinding the densest subgraph of a graph is provided. Some results related to the density ofthe densest subgraph of a graph are obtained as well.     

ON THE CONSTRUCTION OF GROEBNER BASIS OF A POLYNOMIAL IDEAL BASED ON RIQUIER-JANET THEORY

As a consequence of a previons study of algebraic differential geometry(see [WU1]) theremay be associated to certain special kinds of differential ideals some well-behaved basis enjoyingsome well-behaved properties.If the differential ideals are further specialized so that theycorrespond to ordinary polynomial ideals then such a well-behaved basis will become the usualGroebner basis of the polynomial ideals while the latter is not known for differential ideals.     

LINEAR COMPLEXITY AND THE MINIMAL POLYNOMIAL OF LINEAR RECURRING SEQUENCES OVER Z/(m)

In this note we discuss the annihilating properties of sequences over Z/(m).Byconsidering the linear complexity and the annihilator structure,we derive the uniqueness conditionfor the minimal polynomial,and some related results of decimation sequences.     

ADMISSIBILITY OF LINEAR ESTIMATORS OF REGRESSION COEFFICIENTS IN THE CLASS OF ALL ESTIMATORS UNDER THE MATRIX LOSS FUNCTION

For the general fixed effects linear model:Y=Xτ+ε,ε～N(0,V)(or N(0,σ~2V)),V≥0,we obtain the necessary and sufficient condition for LY+α to be admissible for Sτ in the class of allestimators under matrix loss function(d-Sτ)(d-Sτ)′;for the general random effects linear model:Y=Xβ+ε,(?)where (?)=XV_(11)X′+XV_(12)+V_(21)X′+V_(22)≥0,we also obtain the necessary and sufficient condition for LY+α to be admissible for Sα+Qβin the class of all estimators under matrix loss function(d-Sα-Qβ)(d-Sα-Qβ)′.     

FIXED POINTS OF THE ITH POWER OF DIFFERENTIAL POLYNOMIALS GENERATED BY SOLUTIONS OF DIFFERENTIAL EQUATIONS

In this paper,we study the problem on the fixed points of the lth power of linear differential polynomials generated by second order linear differential equations.Because of the control of differential equation,we can obtain some precise estimate of their fixed points.     

A NOTE ON THE STOCHASTIC ROOTS OF STOCHASTIC MATRICES

In this paper, we study the stochastic root matrices of stochastic matrices. All stochastic roots of2×2 stochastic matrices are found explicitly.A method based on characteristic polynomial of matrix isdeveloped to find all real root matrices that are functions of the original 3×3 matrix, including allpossible(function)stochastic root matrices. In addition, we comment on some numerical methods forcomputing stochastic root matrices of stochastic matrices.     

一类带有安装时间的单机成组排序问题

针对一类带有准备时间和安装时间的单机成组排序问题,给出了求解最优排序的多项式算法。其中每个工件都具有自己的准备时间,组和组之间具有安装时间,并且安装时间和已经加工完工件的加工时间有关。所有工件在机器上加工时,一次只能加工一个工件,工件不可中断,组内工件连续加工,组和组之间需要安装时间。对目标函数为极小化最大完工时间的单机成组排序问题,给出了求解最优排序的多项式算法。原问题不是成组问题,为此在原问题的基础上添加了工件的成组问题且组内每个工件都具有自己准备时间,其结果是依然能给出求解最优排序的多项式算法。