构造一般Dixon 结式矩阵的快速算法

近几年来, 基于Dixon 结式的消去法被广泛地用来求解非线性多项式方程组, 因此国际上许多学者开始研究构造Dixon 结式矩阵的有效算法. 本文将目前最为有效的只能处理2个变元3个方程情形的递归算法扩展到n个变元n+1个多项式方程的一般情形, 并且将该算法在Maple下编程实现. 通过Maple随机产生的多项式的比较实验, 可以看出, 比之现有的所有方法, 本程序具有更高的效率. 特别是应用此程序, 首次以48阶的Dixon结式矩阵的形式, 给出了4个一般的关于每个变元的次数不超过2次的曲面存在公共交点的必要条件.     

圆柱形微凹坑排布形式对织构表面摩擦性能的影响

利用数值模拟方法研究了具有微圆柱凹坑织构平面在往复运动下的摩擦学性能,分析了微圆坑深度、半径和织构单元位置偏移率等织构几何参数以及表面间相对运动速度对摩擦力和动压承载能力的影响.结果表明:织构单元位置偏移率由0增加到0.5时摩擦表面间的动压承载能力最大增幅约34.9倍,同时摩擦力也随着位置偏移率的增加而小幅增加;增加微织构单元半径可以同时提升承载能力和减小摩擦;而摩擦力和承载能力均随着微织构单元深度在10~60μm区间的增加呈现先增加后减小的趋势,且均在20μm时取得最大值.     

OPTIMAL SUMMATION INTERVAL AND NONEXISTENCE OF POSITIVE SOLUTIONS TO A DISCRETE SYSTEM

In this paper, we are concerned with properties of positive solutions of the following Euler-Lagrange system associated with the weighted Hardy-Littlewood-Sobolev inequality in discrete form{uj =∑ k ∈Zn u~q_k/(1 + |j|)α(1 + |k- j|)λ(1 + |k|)β,(0.1)vj =∑ k ∈Zn u~p_k/(1 + |j|)β(1 + |k- j|)λ(1 + |k|),where u, v 0, 1 p, q ∞, 0 λ n, 0 ≤α + β≤ n- λ,1p+1λ+αnand1p+1+1q+1≤λ+α+βn:=λˉn. We first show that positive solutions of(0.1) have the optimal summation interval under assumptions that u ∈ lp+1(Zn) and v ∈ lq+1(Zn). Then we show that problem(0.1) has no positive solution if 0 λˉ pq ≤ 1 or pq 1 and max{(n-)(q+1)pq-1,(n-λˉ)(p+1)pq-1} ≥λˉ.     

基于真度理论的α-反向三Ⅰ问题的形式解

在多值逻辑系统L*n中,基于真度理论提出了模糊推理的α-反向三Ⅰ问题,并给出了α-反向三ⅠMP、α-反向三ⅠMT问题解的具体形式,在系统L*n中建立了α-反向三Ⅰ问题的形式化推理机制,为模糊推理的α-反向三Ⅰ算法奠定了逻辑基础。     

学会运用换元法

<正>同学们知道,换元法是中学数学中最为常见的也是基本的数学方法之一.通常情况下,一个数学问题,通过某种换元,不但可以简化问题的表述形式,而且更为容易地透过问题情境,揭示问题本质.因此,面对一个数学问题,增强换元解题意识,正确地使用换元方法,是在解题过程中应当关注的.那么,利用换元法     

一类乘积形式的离散不等式及其应用

该文在文献[2]的基础上,研究了一类新的乘积形式的离散不等式.把参考文献中不等式右端第一个因子中包含的未知函数u推广成未知函数的幂函数u~2,运用变量替换技巧、放大技巧、微分中值定理、反函数技巧、常量与变量的辩证关系,给出了不等式中未知函数的估计.最后,阐述了所得的结果可以用来给出乘积形式差分方程解的绝对值的上界估计.     

ζ(2k)的一种简便算法

给出了Riemannζ函数中ζ(s)=∑1/ns,当s=2k(k∈N+)时的欧拉公式的简便证明方法和若干应用.     

Non-probabilistic solutions of imprecisely defined fractional-order diffusion equations

The fractional diffusion equation is one of the most important partial differential equations（PDEs） to model problems in mathematical physics. These PDEs are more practical when those are combined with uncertainties. Accordingly, this paper investigates the numerical solution of a non-probabilistic viz. fuzzy fractional-order diffusion equation subjected to various external forces. A fuzzy diffusion equation having fractional order 0 〈 α≤ 1 with fuzzy initial condition is taken into consideration. Fuzziness appearing in the initial conditions is modelled through convex normalized triangular and Gaussian fuzzy numbers. A new computational technique is proposed based on double parametric form of fuzzy numbers to handle the fuzzy fractional diffusion equation. Using the single parametric form of fuzzy numbers, the original fuzzy diffusion equation is converted first into an interval-based fuzzy differential equation. Next, this equation is transformed into crisp form by using the proposed double parametric form of fuzzy numbers. Finally, the same is solved by Adomian decomposition method（ADM） symbolically to obtain the uncertain bounds of the solution. Computed results are depicted in terms of plots. Results obtained by the proposed method are compared with the existing results in special cases.     

SUPERSYMMETRIC INVARIANCE AND UNIVERSAL CENTRAL EXTENSIONS OF LIE SUPERTRIPLE SYSTEMS

In this article, we discuss some properties of a supersymmetric invariant bilinear form on Lie supertriple systems. In particular, a supersymmetric invariant bilinear form on Lie supertriple systems can be extended to its standard imbedding Lie superalgebras. Furthermore, we generalize Garland＇s theory of universal central extensions for Lie supertriple systems following the classical one for Lie superalgebras. We solve the problems of lifting automorphisms and lifting derivations.     

一道三元变量问题的思考与探究

近年来,多元变量问题备受命题者的青睐,成为高考考查的重点和难点,这类问题涉及知识面广、综合性强、解法灵活多变,其呈现形式复杂且常考常新,多数学生根本找不到解决问题的切入点,所以很多学生耗时却做不动或者望而却步.如何将多元变量问题转化为学生熟悉的问题就成为解决问题的关键.本文结合相关试题,仅把一类三元变量求取值范围转化为线性规划的问题进行了梳理,供大家参考.