三角代数上中心化子的刻画

设[T]是一个三角代数,[φ:T→T]是一个可加映射。证明了如果存在正整数[m,n,r],使得[(m+n)φ(ar+1)-(mφ(a)ar+][narφ(a))∈Z(T)]对任意的[a∈T]成立,那么存在[λ∈Z(T)],使得对任意的[a∈T,]有[φ(a)=λa]。     

一种新的(A,x,y)知识的零知识证明协议

基于线性假设下的Cramer-shoup加密方案和SDH假设,提出一种新的(A,x,y)知识的零知识证明协议。该协议比文献[2]中SDH对(A,x)知识的零知识证明协议多了一个参数。     

催化剂反应中一类非线性边值问题的有限元配点法

§1.引 言 Galerkin方法是求解微分方程边值问题应用最广的一类有限元方法.文[1]利用配置点Galerkin方法研究了边值问题Ly=(a(x)y')+c(x)y=f(x),x∈I=(0,1)y(0)=y(1)=0的近似解.本文利用配置点Galerkin方法研究如下催化剂反应中质量转换问题:Ly=xy"(x)+(s-1)y'(x)+xq(x)y=xf(x,y),x∈I, (1)y'(0)=0, -y'(1)=A(y(1)-1) (2)     

Ω上三重积分优化复化Simpson数值算法

设空间区域 Ω={(x,y,z)|α≤x≤b,φ_1(x)≤y≤φ_2(x),φ_1(x,y)≤z≤φ_2(x,y)}。(1)f(x,y,z)在Ω及其邻域内具有四阶连续偏导数,φ_1(x)与φ_2(x)在[α,a]内可导,φ_1(x,y)与φ_2(x,y)在Ω的投影(xoy面)区域上具有连续偏导数。下面介绍三重积分 I=∫∫∫f(x,y,z)dxdydz (2)的优化复化Simpson数值积分算法。首先将Ω进行划分,把[α,b]分为2m等分,步长与分点为 h_1=(b-α) /2m,x_i=α+ih_1(i=0,1,2,…,2m)。 (3)在x_(2i+1)处把[φ_1(x_(2i+1)),φ_2(x_(2i+1))分为2n等分,步长与分点为 g_(1,2i+1) =((φ_2(x_(2i+1)))-(φ_1(x_(2i+1))))/2n (i=o,1,2,…,m-1), (4) y_(2i+1,j)=φ_1(x_(2i+1))+jg_(1,2i+1) (j=0,1,2,…,2n)。     

解一阶线性常微分方程组一般边值问题的线性最小二乘法

设有一阶线性常微分方程组边值问题 y_i＇(x)=sum from i=1 to n [a_(ij)(x)y_i(x)+f_i(x)]0相似文献   

泛逻辑泛运算模型之间的关系*

研究泛逻辑的泛与运算模型、泛或运算模型与模糊非之间的关系。证明了零级泛与运算模型T(x,y,h)、零级泛或运算模型S(x, y, h)与强非N(x)=1-x形成De Morgan三元组,当h∈(0, 0.75), 零级泛或运算S(x, y, h)=(min(xm+ym, 1))1/m, N(x)=(1-xm)1/m时, T, S, N形成一个强De Morgan三元组。进一步证明了一级泛与运算模型T(x, y, h, k)、一级泛或运算模型S(x, y, h, k)与N(x)=(1-xn)1/n满足De Morgan定律;特别当h∈(0, 075), 一级泛或运算模型S(x, y, h, k)=(min(xnm+ynm, 1))1/nm, N(x)=(1-xnm)1/nm时, T, S, N形成一个强De Morgan三元组。     

一类递归方程的解

<正> 文献[1]指出,在设计快速算法和平行算法的“结构递归”技术中,计算效率的分析常常表现为下列递归方程的求解:T(cx)=aT(x)+Q(x).例如,Strassen 矩阵乘法的运算量 M(x)决定于方程M(2x)=7M(x)+18x~2满足 M(2)=25的特解;FFT 算法的运算量 W(x)也是方程     

有关三次样条函数的曲线拟合及扦值问题

本文主要解决生产实践中提出的向题,给定一组节点x_0相似文献   

一种新的基于弱T范数簇的神经元模型

提出了一种新的能实现多种连续逻辑运算的神经元模型。利用该神经元模型可实现多种逻辑运算,包括一种从min(x,y)连续变化到max(0,x y-1）的弱T范数簇,从max(x,y)到min(1,x y)连续变化的弱S范数簇,从min（x,y)连续变化到max(x,y)的平均运算等等,并且利用OWA算子,该模型可以很容量地推广到多元运算。     

转移逻辑(I)

在古典的二值逻辑CL(Classical Logic)中,每一命题X的真值取自二元集合{0,1},即T(X)=0与T(X)=1为两种极端的稳定状态;因此CL只能作为客观事物静止状态的粗略反映,以后发展了模糊逻辑FL(Fuzzy Logic),每一命题变量可在闭区间[0,1]上取值,T(X)=a(0≤a≤1),表明X属于某一状态的程度为a,不属于此状态的程度为     

On the Law of Importation $(x wedge y) longrightarrow z equiv (x longrightarrow (y longrightarrow z))$ in Fuzzy Logic

The law of importation, given by the equivalence (x Lambda y) rarr z equiv (xrarr (y rarr z)), is a tautology in classical logic. In A-implications defined by Turksen et aL, the above equivalence is taken as an axiom. In this paper, we investigate the general form of the law of importation J(T(x, y), z) = J(x, J(y, z)), where T is a t-norm and J is a fuzzy implication, for the three main classes of fuzzy implications, i.e., R-, S- and QL-implications and also for the recently proposed Yager's classes of fuzzy implications, i.e., f- and g-implications. We give necessary and sufficient conditions under which the law of importation holds for R-, S-, f- and g-implications. In the case of QL-implications, we investigate some specific families of QL-implications. Also, we investigate the general form of the law of importation in the more general setting of uninorms and t-operators for the above classes of fuzzy implications. Following this, we propose a novel modified scheme of compositional rule of inference (CRI) inferencing called the hierarchical CRI, which has some advantages over the classical CRI. Following this, we give some sufficient conditions on the operators employed under which the inference obtained from the classical CRI and the hierarchical CRI become identical, highlighting the significant role played by the law of importation.     

Problemi al contorno per equazioni del tipoy″=f(x,y) trattati come equazioni integrali con metodi alle differenze finite di elevata accuratezza

This work faces the problem of the numerical treatment on digital computers of boundary value problems of the type: $$y'' = f(x,y); y(a) = A,y(b) = B$$ through the reduction into the equivalent integral equation: $$y(x) = \mathop \smallint \limits_a^b g_K (x,\xi )[K^2 y(\xi ) - f(\xi ,y(\xi ))]d\xi $$ whereg _K (x,ξ) is the Green function associated to the differential operator \(\frac{{d^2 }}{{dx^2 }} - K^2 \) . I have extended to this problem a discrete analogue of higher accuracy introduced in [1] with reference to a boundary value problem analised under a differential point of view: this extention costitutes the original part of the work. The above problem is analysed with reference to the discretization error and the convergence of the discrete analogue solution algorithm; the actnal numerical treatment of a few systems follows.     

Families of fifth order Nyström methods for y″=f(x,y) and intervals of periodicity

In this paper all fifth order Nyström methods fory″=f(x, y) based on four evaluations off are presented. Furthermore, we prove that out of these methods there is only one with a non-vanishing interval of periodicity.     

Ein Runge-Kutta-Nyström-Formelpaar der Ordnung 11(12) für Differentialgleichungen der Form y″=f(x,y)

A new explicit, direct Runge-Kutta-Nyström formula-pair of order 11 (12) with 20 function evaluations per step for initial value problems in ordinary differential equations of second order of the special formy″=f(x, y) is derived. Three numerical examples demonstrate the efficacy of the new formula-pair.     

Numerical treatment on digital computers for boundary value problem in ordinary differential equations of the typey' = f(x,y,y')

This paper deals with the numerical solution of boundary value problems of the type: $$y'' = f(x,y,y'); y(a) = A, y(b) = B.$$ In the case when the first derivative does not explicitly appear the problem has been faced by the author in [2], where a new approach has been suggested to improve the results given by the classical methods. In the following pages such an approach is extended to the above complete equation, and a new iterative algorithm is presented to solve the obtained discrete systems.     

A direct method for the numerical solution ofy″=f(x,y)

A direct method has been obtained for the numerical solution ofy″=f(x,y). Stability and error analysis of this method are studied and compared with the classical Runge-Kutta method and Runge-Kutta-Nyström method. Computational examples are also presented.     

Choice of kernel function for density estimation

Let l=f^n(x) be the kernel estimate of a density f(x) from a sample of size n. Wahba [6] has developed an upper bound to E[f(x)-l=f^n(x)]2. In the present paper, we find the kernel function of finite support [m=-T, T] that minimizes Wahba's upper bound. It is Q(y) = (1 + am=-1) (2T)m=-1 [1-m=-a|y|a] where a = 2-pm=-1, p m=ge 1.     

Hermitesche Differenzenverfahren zur Approximation der Lösung von Differentialgleichungen der Formu xy =f(x,y, u,u x,u y )

Hermitean, stable convergent one- and multistep methods of high acuray are developed for the numerical treatment of initial-value problems for the differential equationu _xy =f(x, y, u, u _x ,u _y ). Some methods are tested by well known examples.     

Solutions to the functional equation I(x, y) = I(x, I(x, y)) for three types of fuzzy implications derived from uninorms

This paper investigates an iterative Boolean-like law with fuzzy implications derived from uninorms. More precisely, we characterize the solutions to the functional equation I(x, y) = I(x, I(x, y)) that involve RU-, (U, N)- and QLU-implications generated by the most usual classes of uninorms.