用分部换元法解无理方程

解方程f(x)=0时,令方程中关于x的某部分f_1(x),f_2(x),…,f_n(X)分别为u_1,u_2…,u_n,我们把这种换元法称之为分部换元法。用此法解某些根指数较大而又不易直接化去根号的无理方程,有时较为简便。常见的有以下两种类型。 1.型如v后,变为f(u,v)=0。如能导出u、v的线性齐次式pu+qv=0,则可化为有理方程而解之。例1 解方程2x+1+xx~2+2~(1/2)+     

双曲型守恒律组的一类差分格式及其熵条件

其中u(x,t)=(u_1(x,t),…,u_m(x,t))~T,f(u(x,t))=(f_1(u(x,t)),…,f_m(u(x,t)))~T,f的Jacobian记为 A(u)=?f(u)/?u,具有m个实特征值λ_1(u)≤λ_2(u)≤… ≤λ_m(u)以及完备的古特征向量系{γ_k(u)}_k~m=1.对区域R~+={(x,t)|x∈(-∞,+∞),t∈     

更新序列对于有限Markov链的嵌入

§1 引言数列 f=f~(1),f~(2),…,f~(n),…}称为,一序列,如果f~(i)≥0(i≥1);sum from t=1 to ∞ f~(i)≤1 (1)由产生的更新序列 u-{u_0;u_1,u_2,…,u_n,…}依下式定义(2)更新序列与马氏链关系密切。设 X(n)是离散参数马氏链,其(一步)转移矩阵为P=(P_(ij))_(i,j∈E),(E 为可列集) (3)又记 n 步转移矩阵为 P~((n))=(P_(ij)~((n)))_(i,j∈E),则P~((0))=(单位矩阵),P~((1))=P,P~((n))=P~n (4)这时,对每个 i∈E,数列{P_(i)~((n))}_(n≥0)是更新序列,其所有产生的 f-序列为{f_i~((n))}+_(n≥1):     

Banach空间常微分方程的解

在[4]中,S.V.Du和V.Lakshmikantham利用紧型条件证明了必存在单调序列{v_n}和{w_n},一致收敛于Banach空间常微分方程初值问题u′=f(t,u),u(0)=u_0的最大解和最小解。在本文中我们证明了,如果Banach空间是弱序列完备的,则[4]中的紧型条件(这是[4]中的一个主要条件)是可以删掉的。我们还对Banach空间周期边值问题证明了类似的结果。     

多角形域上的有限元方法及外推

§1.引言 考虑边值问题: L_u=-D_i(a_(ij)D_(ju)+a_0u=f,u|?Ω=0.(1.1)假定L是一致椭圆算子且系数a_(ij),a_0及右端f适当光滑,a_0≥0.Ω为一平面多角形区域,Q={Q_1,Q_2,…,Q_l}为Ω的角点集合.对于任意给定的常数组{α_i}_1~l,0<α_i≤1,     

姿态角计算方法

<正> 本文提出解决问题(dx(t))/(dt)=f(t,x(t),u(t)),x(t_0)=x_0,(1)g(t,x(t),u(t))=0 (2)的一套实用的数值计算方法,其中 t∈[t_0,t_f],t_f 可以是固定的,也可以是不固定的,x(t)=(x_1(t),x_2(t),…,x_n(t))~T∈R~n 是状态向量,u(t)=(u_1(t),u_2(t),u_3(t))~T=((?)_1(t),(?)(t),γ(t))~T∈R~3是火箭的姿态角,f=(f_1,f_2,…,f_n)~T 是 n 维向量值函数,g=(g_1,g_2,g_3)~T 是三维向量值函数.这套方法包括简单迭代法,简化牛顿法及简化梯度法,并给出判断简单迭代法收敛性的一个充分条件的准则.这个准则在具体条件下既简单又实用.     

更新序列、f-序列、P-函数、F-函数族以及典则测度的圈乘运算

苏1己!吉0 .J.‘二刁定义1 .1一个数列f一(f,,fZ…)叫做一个f一序列,如果了,)O(,=l,2,…),习了,(1定义1.2一个数列怒=(。。,。,,…)叫做一个更新序列, (1 .1)如果存在一个f一序列f=(f,,f:,…)使(1 .2)=艺f,:。一;(,=1,2,…) nU介舰UJ‘J、..‘了叫做u的介序列。有时,“叫做由f产生的更新序列。 显然f一序列和它产生的更新序列互为唯一决定(因此在全体更新序列和全体介序列之间建立了一一对应关系),确切言之,有如下结果〔”: 命题1.1设了二(l1,了2,…)是一个f一序列,粉是由了产生的更新序列,则uo=l(1 .3)f‘工f‘2…f‘。艺︸九甲自一一忿…     

A Remark on the Existence of Entire Large and Bounded Solutions to a(k_1, k_2)-Hessian System with Gradient Term

In this paper, we study the existence of positive entire large and bounded radial positive solutions for the following nonlinear system{S_k_1(λ(D_(u1)~2)) + a_1(|x|) |▽_(u_1) |~(k_1)= p_1(|x|) f_1(u_2) for x ∈ R~N,S_k_2(λ(D_(u_2)~2)) + a_2(|x|) |▽_(u2) |~(k_2)= p_2(|x|) f_2(u_1) for x ∈ R~N.Here S_k_i(λ(D_(u_i)~2) is the k_i-Hessian operator, a_1, p_1, f_1, a_2, p_2 and f_2 are continuous functions.     

关于广义Schrodinger型方程组第三边值问题的差分方法

本文讨论下述定解问题的差分解法 u_t(x,t)=Au_(xx)(x,t) f(u),(x,t)∈Q_T=(0,L)×(0,T) u_x(0,t)—σ_1u(0,t)=0,σ_1>0,t∈[0,T]; u_x(L,t) σ_2u(L,t)=0,σ_2>0,t∈[0,T]; u(x,0)=■(x),x∈[0,L].其中u(x,t)=(u_1(x,t),…,u_m(x,t)),f(u)=f(f_1(u),…,f_m(u)),■(x)=(■_1(x),…■_m(x))满足适定性条件,且假定     

寻找最优控制的具有约束算子的梯度算法

§1.具有约束算子的梯度算法 考虑连续的受控系统,其运动轨道及控制满足常微分方程组 x=f(x,u,t),x(t_0)=x_0, (1.1)其中x=(x_1,x_2,…,x_n)~T?E~n是系统的状态变量,u=(u_1,u_2,…,u_r)~T?E~r是系统的控制变量;f(·,·,·)=(f_1(·,·,·),…,f_n(·,·,·))~T是由E~n×E~r×E~1到E~n中的向量值函数;t_0是运动的起始时刻;x_0是运动的初始状态;t_f是运动的终结时刻.为简单起见,下面假定t_0,x_0,t_f均已给定。 我们把定义在区间[t_0,t_f]上的每一个在E~r中取值的分段连续函数u(t)=(u_1(t),u_2(t),…,u_r(t))~T称作系统(1.1)的一个控制。所有这样的控制的集合记作H,给定系     

直觉模糊关系的截集性质

定义了直觉模糊关系的截集以及并给出了它们的基本性质,同时分别讨论了自反、对称、传递直觉模糊关系与经典二元关系之间的等价刻画;其次,提出直觉模糊关系的定义域与值域的概念;最后,分析了直觉模糊关系合成的截集性质.     

Qualities of goods in the models of production

In this paper the models of production in which the qualities of goods are considered are presented. Such models are completely described by the families of matrices or by a function which has some properties which are natural from the economic point of view. The special cases of the models are the well known linear model of production and the van Neumann-Gale's model.     

L－fuzzy集网的R－收敛性质

本文在ＬＦ拓扑空间中建立了Ｌ－ｆｕｚｚｙ集网的弱收敛（Ｒ－收敛）概念，应用文［４］中的Ｒ－闭包，系统讨论了它们的性质，证明了等式ＲｌｉｍＡ＿ｎ＝∧（∨Ａ＿ｍ）＿Ｒ和ＲｌｉｍＡ＿ｎ＝Ａ＿ｎ＝∧（∨Ａ＿ｍ）＿Ｒ并且给出了Ｌ－ｆｕｚｚｙ集网与其子网之间的关系。     

一类三阶牛顿变形方法

A class of third-order convergence methods of solving roots for non-linear equation,which are variant Newton's method,are given.Their convergence properties are proved.They are at least third order convergence near simple root and one order convergence near multiple roots.In the end,numerical tests are given and compared with other known Newton's methods.The results show that the proposed methods have some more advantages than others.They enrich the methods to find the roots of non-linear equations and they are important in both theory and application.     

Estimation of Parameters of Partially Linear Errors-in-variables Models with Replicated Net Points of Observation

A kind of partially linear errors-in-variables models with replicated net points of observation are studied in this paper. Estimators of unknown parameters are given. Under certain regular conditions, it is shown that the estimators of the unknown parameters are strongly consistent and their a.s. convergence rates are achieved.     

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Letbe a sequence of real-valued random variables and be other random variables which are independent of the form sequence. Suppose that are pairwise generalized negatively orthant dependent with heavy tails under the condition that are independent or associated, some asymptotic formulas are established.     

On the Least Number of Fixed Points of an Equivariant Map

The problem on the least number of fixed points of an equivariant map of a compact polyhedron on which a finite group acts is considered. For such a map, the least number of fixed points and the least number of fixed orbits are estimated in terms of invariants of the type of Nielsen numbers. The estimates obtained are sharp. The results are similar to those of P. Wong, but their assumptions are essentially weaker. Some notations are refined. The proofs are constructive.     

IA-Automorphisms of Metabelian Products of Two Abelian Groups

For metabelian products of two Abelian groups with torsion, IA-automorphisms that are not inner and hence are not induced by any automorphisms of the free products of the same Abelian groups are constructed.     

非线性中立双曲型时滞微分方程解的振动判据

讨论一类多滞量非线性中立双曲型时滞微分方程的振动性质，获得了其一切解振动的充分条件。     

Convergence of densities of some functionals of Gaussian processes

The aim of this paper is to establish the uniform convergence of the densities of a sequence of random variables, which are functionals of an underlying Gaussian process, to a normal density. Precise estimates for the uniform distance are derived by using the techniques of Malliavin calculus, combined with Stein?s method for normal approximation. We need to assume some non-degeneracy conditions. First, the study is focused on random variables in a fixed Wiener chaos, and later, the results are extended to the uniform convergence of the derivatives of the densities and to the case of random vectors in some fixed chaos, which are uniformly non-degenerate in the sense of Malliavin calculus. Explicit upper bounds for the uniform norm are obtained for random variables in the second Wiener chaos, and an application to the convergence of densities of the least square estimator for the drift parameter in Ornstein–Uhlenbeck processes is discussed.