On the Global Character of the Difference Equation X n + 1 =

We investigate the global stability, the periodic character, and the boundedness nature of solutions of the difference equation x n +1 = f + n x n m (2 k +1) + i x n m 2 l A + x n m 2 l , n =0,1,… where k and l are non-negative integers, the parameters f , n , i , A are non-negative real numbers with f + n + i >0, and the initial conditions are non-negative real numbers. We show that the solutions exhibit a trichotomy character depending upon the parameters n , i and A .     

第一类超Cartan域上的不变度量

首先证明超Cartan域Y_I(k;N;m,n)为凸域的充分必要条件是2k■m;接着讨论了在超Cartan域上四类经典的不变度量,即Bergman度量、Caratheodory度量、Kobayashi度量和Einstein-Kahler度量的等价性;最后通过计算得到了超Cartan域Y_I(1;N;2,n)和Y_I(2;N;2,n)上的Caratheodory度量(和Kobayashi度量)的显表达式.     

On the Periodic Character of Some Difference Equations

We consider positive solutions of the following difference equation x n =max A x n m k , B x n m m , n =0,1,…, where A , B are any positive real numbers and k , m are any positive integers. We prove that every positive solution is eventually periodic and determine the period in terms of the parameters A , B , k , and m .     

Equivalent Conditions for the Consistency of the Helmholtz Decomposition of Muckenhoupt Ap-Weighted Lp-Spaces

Analysis Mathematica - We are concerned with basic properties of the Helmholtz decomposition of the Muckenhoupt Ap-weighted Lp-space ( $$L_w^p(\Omega )$$ )n for any domain Ω in ?n (n...     

两个完全图的乘积的树宽

本文确定了乘积图Km×Kn的树宽.我们的结果是若m和n都是偶数,且m≥n,或m是奇数而n是偶数,或m和n都是奇数且n≥m,则Km×Kn的树宽是TW(Km×Kn)=n(m+1)/2-1.这恰好是图Km×Kn的带宽.     

Rationality of the Knizhnik-Zamolodchikov equation solution

We construct an explicit solution of the Knizhnik-Zamolodchikov system with n = 4 and m = 2 in the terms of hypergeometric functions. We prove that this solution is rational when the parameter ρ is integer. We show that the Knizhnik-Zamolodchikov system has no rational solution in the case where n = 5, m = 5, and ρ is integer.     

球面上热核的渐近展开

具体计算了球面Ｓｎ（１）（ｎ２）上热核的渐近展开式中前五项的系数，而根据已有的公式只能算出前四项．最后给出了展开式一般项的递推公式，发现它与Ｂｅｒｎｏｕｌｉ数有未曾想到的联系．根据不变量理论，我们可以确定任意ｎ维紧致无边Ｒｉｅｍａｎｎ流形上热核的渐近展开式中第五项的系数．     

自然数乘法分拆个数及因子个数上界估计

我们证明，若n充分大，则其乘法分拆数小于n/lnn，这几乎解决了关于自然数乘法分拆数的一个猜测,也得到了自然数因子个数的一个上界估计。     

一类马尔可夫序列最大值的极限律

主要研究一类马尔可夫序列{Xn,n≥0}的最大值的极限分布.导出了这类序列最大值和最小值的分布表达式,利用经典极值理论,建立了规范化最大值max{X0,X1,…,Xn}与i.i.d序列{ξn,n≥1}的规范化最大值max{1ξ,2ξ,…,ξn+1}具有相同极限律的条件.     

Complete settling of the multiplier conjecture for the case of n =3pr

In this paper we improve the character approach to the multiplier conjecture that we presented after 1992, and thus we have made considerable progress in the case of n=3n1. We prove that in the case of n = 3n1 Second multiplier theorem remains true if the assumption "n1 ＞λ" is replaced by "(n1, λ)=1".Consequentially we prove that if we let D be a (v, κ,λ)-difference set in an abelian group G, and n=3pr for some prime p, (p,v)=1, then p is a numerical multiplier of D.     

第一类典型域上的Bloch常数

引入第一类典型域R_I(m,n)上的全纯映照子族H_k(R_I(m,n)),当k→+∞时,该映照族就是R_I(m,n)上的局部双全纯映照族.建立了H_k(R_I(m,n))上的Bonk偏差定理.当k=1和k→+∞时,其结果分别都回到了FitzGerad和龚升关于典型域R_I(m,n)上的Bonk偏差定理.当m=n=1时,其结果又回到了Liu和Minda在单位圆盘上的偏差定理.应用偏差定理,给出了映照族H_k(R_I(m,n))上的Bloch常数估计,其结果补全了从k=1和k→+∞之间的R_I(m,n)上Bloch常数估计的所有结果,而且把单位球上的Bloch常数估计推广到R_I(m,n)上.     

一类非线性递归序列的极限

探讨了形如Fn+2=a1Fnb1+1+a2Fbn2+1,n 1的非线性递归序列{Fn}的极限问题,给出了在满足一定条件时,序列{Fn}的极限值与初始值无关.     

On the Dynamics of Homeomorphisms on the Unit Ball of Rn

Positivity - Consider a compact convex subset X of R n (n ≥ 2) with non-empty interior and let H(X) be the set of all homeomorphisms from X onto X endowed with the supremum metric. We are...     

On the Relation Between the Determinant and the Permanent on Symmetric Matrices

Let H n ( F ) be the space of n -square symmetric matrices over the field F . We generalize the main result of [M.H. Lim (1979). A note on the relation between the determinant and the permanent. Linear and Multilinear Algebra , 7 , 145-147], proving that the determinant is not convertible into the permanent on H n ( F ), provided that n ? 3, F has at least n elements and the characteristic of F is not 2. The case n = 2 is also studied.     

人口方程的总和生育率的控制

研究了年龄递进的人口分布参数控制方程,当控制变量β(t)发生改变时,可以找到两个阶梯函数βn(t)和βn(t)同时逼近β(t),并得出当n→∞时,Pn(r,t)和Pn(r,t)也同时逼近P(r,t).     

关于分圆多项式的Schinzel等式

对一无平方因子的奇数ｎ＞１，　分圆多项式φｎ（ｘ）　　满足Ｓｃｈｉｎｚｅｌ等式，　φｎ（ｘ）＝Ｐ２ｎ，ｍ（ｘ）－（－１／ｍ）ｍｘＱ２ｎ，ｍ（ｘ），　　这里Ｐｎ，ｍ（ｘ）和　Ｑｎ，ｍ（ｘ）是整系数多项式且　ｍ｜ｎ．本文给出两个简明的公式来计算　Ｐｎ，ｍ（ｘ）　和　Ｑｎ，ｍ（ｘ）　　．     

Pairs of square-free values of the type n2 + 1, n2 + 2

Czechoslovak Mathematical Journal - We show that there exist infinitely many consecutive square-free numbers of the form n2 + 1, n2 + 2. We also establish an asymptotic formula for the number of...     

On the Multiplicity and the Cohen-Macaulayness of Fiber Cones of Graded Modules

Let (A,m) be a Noetherian local ring with maximal ideal m,I an ideal of A,J an m-primary ideal of A,N a finitely generated A-module,S =⊕n≥0 Sn a finitely generated standard graded algebra over A and M =⊕n≥0 Mn a finitely generated graded S-module.We characterize the multiplicity and the Cohen-Macaulayness of the fiber cone FJ(M) =⊕n≥0 Mn/JMn.As an application,we obtain some results on the multiplicity and the Cohen-Macaulayness of the fiber cone ⊕n≥0 InN/JInN.     

An Extremal Problem Concerning the Derivatives of a Polynomial at Its Roots

Let w be a monic polynomial of degree n +1 with roots x_j in the interval [−1, 1]. We consider the problem of finding the roots x_j for which the minimum of ¦ w '( x_j )¦, for 0≤ j ≤ n , is as large as possible. We prove that the Clenshaw–Curtis points cos( j π/ n ) are the only solution when n is even and that they get asymptotically close to the solution for odd values of n , as n goes to infinity. Our problem is related to the problem of minimizing the norm of inverse Vandermonde matrices.     

On the essential dimension of a finite group

Let f(x) = aixi be a monic polynomial of degree n whosecoefficients are algebraically independent variables over a base field k of characteristic 0. We say that a polynomial g(x) isgenerating (for the symmetric group) if it can be obtained from f(x) by a nondegenerate Tschirnhaus transformation. We show that the minimal number dk(n) of algebraically independent coefficients of such a polynomial is at least [n/2]. This generalizes a classical theorem of Felix Klein on quintic polynomials and is related to an algebraic form of Hilberts 13th problem.Our approach to this question (and generalizations) is basedon the idea of the essential dimension of a finite group G:the smallest possible dimension of an algebraic G-variety over k to which one can compress a faithful linear representation of G. We show that dk(n) is just the essential dimension of the symmetricgroup Sn. We give results on the essential dimension ofother groups. In the last section we relate the notion of essential dimension to versal polynomials and discuss their relationship to the generic polynomials of Kuyk, Saltman and DeMeyer.