一类具有转向点问题的n阶近似解

用Langer变换和Olver变换求得一类具有转向点问题的n阶近似解:y(x)=v(x)ψ(x),其中ψ=λ12-14×(x2-1)14,2332=-λx∫11-τ2dτ,v(z)=A(z,λ)ξ(λ23z)+B(z,λ)'ζ(λ23z).并探讨了其特征值问题,得到λn=4n+1112,n=0,1,2….由此给出了该类问题的解的一般性结论.     

一类带约束的二维弱奇异积分方程的一般解及其应用*

本文给出二维弱奇异积分方程作用着约束方程的比[1]为更一般的解P式中k和产是给出的连续函数;(s,φ)是原点在M(r,θ)的局部极坐标;(r,θ)是原点在O(0.0)的总体极坐标;F(r_*,θ)=c_*(常数)是研究域Q的边界围线?Q:g(ω)=F(r,θ)/[πkφ₀];g'=dg/dω,ω=N-r2sin2(θ+φ₀);φ₀,N为中值.[1]的(2.19)型的解仅为F(r,θ)=ω时上述解的特例.文中给出刚性圆锥和弹性半空间接触问题的解作为应用例子.此解较Love(1939)的解简明.     

一类非线性Volterra积分微分方程的周期解

本文借助laplace变换及不动点理论,研究了系统(?)=Ax+integral from n=0 to t(c(t-s)x(s)ds)+F(t,x)的周期解的存在性。唯一性问题,给出了一组充分条件.     

Smarandache函数的几类相关方程的解

设φ(n),S(n)分别表示正整数n的Euler函数和Smarandache函数,利用初等的方法和技巧,依据Smarandache函数计算公式,给出k的方程φ(p~αm)=S(p~(ακ))的所有解,其中p为素数,α,m为正整数且gcd(m,p)=1,由此得到方程φ(n)=S(n~k)的所有解(n,k)进而确定了满足条件S(n)|σ(n)的全部正整数n.最后,根据莫比乌斯变换反演定理证明了方程φ(n)=∑_(d|n)S(d)仅有两个解,分别为n=2~5和n=3×2~5.     

直线爆炸所形成的柱面波的近似分析解

由直线爆炸所形成的柱面波,文献[1]得到了数值解。本文对于绝热指数γ=C_p/C_v较大的情形,取ε=1/γ2为小参数,用伸缩坐标法得到了问题的一级近似分析解。算例(γ=3)表明,近似解与准确解(数值解)十分符合。     

用Householder变换实现从L2到L∞空间的最佳逼近

本文用数值代数中常用的Householder变换法不仅求得超定线性方程组的L_2解,同时利用其保存信息,通过定向扰动(DP算法)还可求出其L_∞解,其算法稳定、简便,而且可以得出L_2解与L_∞解之差的精确表达式。这对于数值函数的线性模空间中的最佳逼近的比较,以及用之于实际的曲线(面)拟合有较大的实用意义。§1详细列出用H变换实现DP算法的步骤及有关的理论结果;§2给出了一般意义下的DP算法的几何解释;§3给出了L_2解和L_∞解之差的精确表达式和数值例子。     

也谈一类线性方程组的解的公式

<正> 对于线性方程组(2),[1]只对 m=0,h=1的情形进行了讨论,没有给出解的公式.而[2]即使给出了解的公式,那也只是在 m 为整数,且 h=1的特殊情况下得出的.且所给出的公式使用时也很麻烦.面对着这个问题,本文将给出当 m 与 h 为任意实数时方程组(2)的解的公式.     

Karmarkar算法的一点注记

Karmarkar算法是解如下形式的LP: min c~Tx s.t.Ax=0 (1) e~Tx=1,x≥0。其中A∈Z~(m×n)为行满秩矩阵,c∈Z~n,e=(1,…,1)∈Z~n,x∈R~n。设(1)有内点可行解且其最优值为零。文[1]中给出解(1)的基本算法和改进算法,并通过势函数给出了证明。其证明过程是复杂的,且决定迭代步长的参数α=0.25。文[2]论证了α取值可增为1/3。文     

获得非线性微分方程显式解析解的两种新算法

基于AC=BD的思想来求解非线性微分方程(组)。设Au=0为给定的待求解的方程,Dv=0是容易求解的方程。如果可以获得变换u=Cv使得v满足Dv=0,则能够得到Au=0的解。为了说明该种途径,本文举例给出几种变换C的表达式。     

二阶具有非正系数的NFDE与RFDE的非振动解类型与判别

本文讨论二阶具有非正系数的中立型与滞后型泛函微分方程,给出了这些方程的非振动解的类型以及判别条件。 对于cO情形(中立型),本文给出了四种S~*类的非振动解:对于|c|相似文献   

错误系统结构的相似变换研究

分析了现实世界中事物的可变性,以及人们利用事物可变性的可能性.在此基础上,我们研究了对串联、并联、扩缩、蕴含、反馈等六种基本结构的相似变换的系统结构的图示表示,并利用错误函数和逻辑命题去形式化描述它们的变化形式和规律.接着给出了事物可变性的结构图示和六种基本变换的变换方式,变换参数和变换体系.     

The Asymptotics of Estimate of the Projection Directions Concerning Sliced inverse Regression

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Conceptions of function translation: obstacles, intuitions, and rerouting

A horizontal translation of a function is the focus of this study. We examine the explanations provided by secondary school students and secondary school teachers to a translation of a function, focusing on the example of the parabola y=(x−3)² and its relationship to y=x². The participants’ explanations focused on attending to patterns, locating the zero of the function, and the point-wise calculation of function values. The results confirm that the horizontal shift of the parabola is, at least initially, inconsistent with expectations and counterintuitive to most participants. We articulate possible sources of this perceived inconsistency and describe a pedagogical approach aimed at resolving it.     

Maximal Subsemigroups of Finite Transformation Semigroups K（n, r）

Let Tn be the full transformation semigroup on the n-element set Xn. For an arbitrary integer r such that 2 ≤ r ≤ n-1, we completely describe the maximal subsemigroups of the semigroup K(n, r) = {α∈Tn : |im α| ≤ r}. We also formulate the cardinal number of such subsemigroups which is an answer to Problem 46 of Tetrad in 1969, concerning the number of subsemigroups of Tn.     

Les transformations de Cremona stellaires

On construit explicitement toutes les transformations de Cremona de qui satisfont à la propriété suivante: il existe tels que les droites par sont envoyées sur les droites par . On caractérise de plusieurs manières ces transformations et pour chaque entier non-négatif on donne des formules pour la dimension de l'ensemble constitué de celles qui ont degré .

ABSTRACT. We construct the Cremona transformations of satisfying the following property: there exist such that the image of all straight lines through are straight lines through . We characterise these transformations, and for all non-negative integer we give a formula for the dimension of the set of those whose degree is .

     

Clifford algebra and the Lorentz transformation with (p, q) form

In this paper, the concepts of Lorentz inner product with (p, q) form, the Lorentz space and the Lorentz transformation with (p, q) form are given by using Clifford algebra. It is shown that L_m^p,q is the Lorentz transformation with (p, q) form, and the matrix equality relation of Minkowski space with (n − 1, 1) form is given. The examples are given to illustrate the corresponding results.     

Transformation graph

The transformation graph G^-+- of a graph G is the graph with vertex set V(G)E(G), in which two vertices u and v are joined by an edge if one of the following conditions holds: (i) u,vV(G) and they are not adjacent in G, (ii) u,vE(G) and they are adjacent in G, (iii) one of u and v is in V(G) while the other is in E(G), and they are not incident in G. In this paper, for any graph G, we determine the connectivity and the independence number of G^-+-. Furthermore, for a graph G of order n4, we show that G^-+- is hamiltonian if and only if G is not isomorphic to any graph in {2K₁+K₂,K₁+K₃}{K_1,n-1,K_1,n-1+e,K_1,n-2+K₁}.     

模糊错误逻辑论域分解转化联结词研究

主要给出了模糊错误逻辑论域分解转化联结词所涉及的概念、运算及其模糊错误逻辑论域分解转化联结词与/nf l内涵分离、/nf h内涵分化、∥nhb内涵互补、—∥nhd l内涵对立等的关系作了一点研究。     

The capacitated general windy routing problem with turn penalties

In this paper we present the capacitated general windy routing problem with turn penalties. This new problem subsumes many important and well-known arc and node routing problems, and it takes into account turn penalties and forbidden turns, which are crucial in many real-life applications, particularly in downtown areas and for large vehicles. We provide a way to solve this problem both optimally and heuristically by transforming it into a generalized vehicle routing problem.     

Abundance of Semigroups of Transformations Restricted by an Equivalence

Let σ be an equivalence on X, and let E(X, σ) denote the semigroup (under composition) of all f: X → X such that σ ? ker(f). In this article, we show that the semigroup E(X, σ) is right abundant but not left abundant whenever |X| ≥3 and σ is non-trivial.