共查询到19条相似文献,搜索用时 109 毫秒
1.
Ye Maodong 《数学年刊B辑(英文版)》1990,11(3):359-362
Let f (x) ∈ C [-1, 1], p_n~* (x) be the best approximation polynomial of degree n tof (x). G. Iorentz conjectured that if for all n, p_(2n)~* (x) = p_(2n+1)~* (x), then f is even; and ifp_(2n+1)~* (x) = p_(2n+2)~* (x), p_o~* (z) = 0, then f is odd. In this paper, it is proved that, under the L_1-norm, the Lorentz conjecture is validconditionally, i. e. if (i) (1-x~2) f (x) can be extended to an absolutely convergentTehebyshev sories; (ii) for every n, f (x) - p_(2n+1)~* (x) has exactly 2n + 2 zeros (or, in thearcond situation, f (x) - p_(2n+2)~* (x) has exaetly 2n+3 zeros), then Lorentz conjecture isvalid. 相似文献
2.
设A和B是含单位元的C~*代数,s∈A和t∈B是可逆自伴元,对任意的x∈A及z∈B,定义x~+=s~(-1)x~*s,z~+=t~(-1)z~*t。假定A是实秩零的并且Φ:A→B是有界线性满射。证明了对任意的 都成立的充要条件是Φ(1)可逆,Φ(1)~+Φ(1)=Φ(1)Φ(1)~+∈Z(B)(B的中心),并且存在从A到B上的满+同态Ψ,使得对所有的x∈A都有Φ(x)=Φ(1)Ψ(x)成立。对于一般C~*代数上保正交性的线性映射Φ,在假定Φ(1)可逆的条件下,也得到类似的结果。 相似文献
3.
设x:M→S~(n+1)是(n+1)-维单位球面上不含脐点的超曲面,在S~(n+1)的Moebius变换群下浸入x的四个基本不变量是:一个黎曼度量g称为Moebius度量;一个1-形式Φ称为Moebius形式;一个对称的(0,2)张量A称为Blaschke张量和一个对称的(0,2)张量B称为Moebius第二基本形式.对称的(0,2)张量D=A+λB也是Moebius不变量,其中λ是常数,D称为浸入x的仿Blaschke张量.李海中和王长平研究了满足条件:(i)Φ=0;(ii)A+λB+μg=0的超曲面,其中λ和μ都是函数,他们证明了λ和μ都是常数,并且给出了这类超曲面的分类,也就是在Φ=0的条件下D只有一个互异的特征值的超曲面的分类.本文对S~5上满足如下条件的超曲面进行了完全分类:(i)Φ=0,(ii)对某常数λ,D具有常数特征值. 相似文献
4.
高斯公式应用小议 总被引:1,自引:0,他引:1
在利用高斯公式计算曲面积分时 ,许多学生往往忽视了对定理条件的考察。比如 :同济四版《高等数学》下册总习题十的第 3 ( 4)题就是一例。例 1 :计算 ∑xdydz +ydzdx +zdxdy( x2 +y2 +z2 ) 3 ,其中 ∑:1 -z5=( x -2 ) 21 6+( y -1 ) 29( z≥ 0 )上侧。多数学生在利用高斯公式求解时 ,做法如下 :解 :令 P =x( x2 +y2 +z2 ) 3 ,Q =y( x2 +y2 +z2 ) 3 ,R =zx2 +y2 +z2 ) 3 ,补 ∑1:z =0 ( x -2 ) 21 6+( y -1 ) 29≤ 1 下侧。于是由高斯公式得 : ∑+ ∑ 1Pdydz +Qdzdx +Rdxdy = Ω P x+ Q y+ R z dv Ω0 dv =0 ,其中Ω为由 ∑ +∑1所围区… 相似文献
5.
课 题 换元法适用年级 初二年级学期 2 0 0 3— 2 0 0 4学年度第一学期 已知x=(x2 + 3x-2 ) 2 + 3 (x2 + 3x-2 ) -2 ,x2 + 2x-2≠0 ,求x2 + 4x的值 .分析与解答 令 x2 + 3x -2 =t①则 t2 + 3t-2 =x②① -②得(x-t) (x +t) + 3 (x-t) =t-x,∴ x =t或x +t+ 4=0 .x =t时 ,x2 + 3x -2 =x ,x2 + 2x-2 =0不合题意 ,舍 .x+t+ 4=0时 ,x2 + 4x -2 =0 .∴ x2 + 4x =2 .名人名言志不强者智不达———墨 翟老师课堂用题1 .分解因式 (x2 +x + 1 ) (x2 +x + 2 ) -1 2 .2 .比较A与B的大小 .其中A =3 6892 2 1 3 271 2 43 2 1 0 1 , B =3… 相似文献
6.
线性常系数非齐次微分方程的特解公式 总被引:1,自引:0,他引:1
邓云辉 《数学的实践与认识》2009,39(5)
用初等方法得到n阶线性常系数非齐次方程y(n)+a1y(n-1)+…+any=Pm(x)eλx特解y*的求解公式,使求y*的计算比较简单. 相似文献
7.
1引 言
1960年Meyer-K(o)nig W.和Zeller K.在[6]中提出了Meyer-K(o)nig-Zeller算子
Mn(f,x)=∞∑k=0f(k/(n+k))mn,k(x),0≤x<1,Mn(f,1):=f(1),mn,k(x)=(n+kk)xk(1-x)n+1,在[1,2,5,7,9,10,12]中对于此算子的逼近性质及各种修正了的Meyer-K(o)nig-Zeller算子作了研究,其中重要的变形是Kantorovich型的积分算子: M*n(f;x)=∞∑k=0((n+k)(n+k+1))/n∫(k+1)/(n+k+1)k/(n+k)f(u)dumn,k(x),x∈[0,),其中Mn(f,1):=f(1),mn,k(x)=(n+kk)xk(1+x)n+1,mn,-1(x):=0. V.Totik在[8]中给出了M*n(f;x)的Lp-逼近(1≤p<∞),王建力在[11]研究了其加权Lp-逼近(1≤p<∞).本文引进新的K+泛函,利用Ditzian-Totik模ω2ψ(f,t)研究了该算子的点态逼近性质,得到了它的逼近正、逆及等价定理. 相似文献
8.
问题 求由曲线 C:b2 y2 =(b +x) 2 (a2 - x2 ) (b≥ a >0 )包围的面积 .1 分析1.1 曲线 C的几何特征由曲线 C的方程知 ,x轴为曲线的对称轴 ,不妨考察曲线 C在 x轴的上半部分 ,并记其为曲线 C1 :y = a2 - x2 +xb a2 - x2 (|x|≤ a) .曲线 C1 可看成是由半圆 C* :y =a2 - x2 (|x|≤ a)演变而来 :在曲线y = a2 - x2 (0≤ x≤ a)上 (第一象限部分的四分之一圆 )上任取一点 A1 (x0 ,y0 ) ,并将其平移到 A′1 (x0 ,y0 +x0b a2 - x20 ) ,同时在曲线 :y =a2 - x2 (- a≤ x≤ 0 )上 (第二象限部分的四分之一圆 )取与 A1 关于 y轴… 相似文献
9.
高一年级1.已知m ,n ,p∈A ={x |x - 1|≤ 3且x∈Z}.试求logm +nP的不同值的个数 .2 .已知函数 f(x)为偶函数 ,对于定义域R内在任意x ,都有 f(x) =f( 4-x) ,且当x∈ [0 ,2 ]时 ,f(x)=1-x2 ,求x∈ [2 0 0 2 ,2 0 0 4 ]时f(x)的解析式 .3 .已知函数 f(x) =- 2x +2 ,x∈ [12 ,1] ,设 f(x)的反函数为y =g(x) ,a1 =1,a2 =g(a1 ) ,… ,an =g(an-1 ) ,求数列 {an}的通项公式高二年级1.已知函数f(x) =lg(log3 2 x -klog2 x +2 ) ,若f(x)在( 1,+∞ )上均有意义 .试求实数k的取值范围 .2 .设a∈k,函数 f(x) =ax2 +x -a ( - 1≤x≤ 1) .( 1)若 |a|≤ … 相似文献
10.
数列是高考的热点 ,是学生进一步学习的基础 .数列与函数知识的综合应用是学生学习的难点 ,下面列举这方面的例子进行分析 .例 1 已知函数f(x)在 ( - 1,1)上有定义 ,f 12 =- 1,且满足x ,y∈ ( - 1,1)有 f(x) +f(y) =f x + y1+xy .1)证明 :f(x)在 ( - 1,1)上为奇函数 ;2 )对数列x1 =12 ,xn + 1 =2xn1+x2 n,求 f(xn) ;3)求证 1f(x1 ) + 1f(x2 ) +… + 1f(xn) >- 2n + 5n + 2 .解 1)令x =y =0 ,则 2 f( 0 ) =f( 0 ) ,∴ f( 0 )= 0 .令 y =-x∈ ( - 1,1) ,则f(x) + f( -x) =f( 0 ) =0 ,∴ f( -x) =- f(x) ,即f(x)为 ( - 1,1)上的奇函数 .( 2 … 相似文献
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12.
Li Jiayu 《偏微分方程(英文版)》1990,3(3)
Let M be a n-dimensional simply connected, complete Riemannian manifold with constant negative curvature. The heat kernel on M is denoted by H^M_t(x, y) = H^M_t(r(x, y)), where r(x, y) = dist(x, y). We have the explicit formula of H^M_t(x, y) for n=2, 3, and the induction formula of H^M_t(x, y) for n ≥ 4^{[-1]}. But the explicit formula is very complicated for n ≥ 4. ln this paper we give some simple and useful global estimates of H^M_t(x, y), and apply these estimates to the problem of eigenvalue. 相似文献
13.
Milutin Dostanić 《Czechoslovak Mathematical Journal》1999,49(4):707-732
We find an exact asymptotic formula for the singular values of the integral operator of the form
, a Jordan measurable set) where
and L is slowly varying function with some additional properties. The formula is an explicit expression in terms of L and T. 相似文献
14.
An elementary proof of the prime number theorem in the form $$\psi (x) - x = O(x exp\{ - (\log x)^{\tfrac{1}{7}} (log log x)^{ - 2} \} )$$ is given. The proof uses a generalization of Selberg's formula and a tauberian argument. 相似文献
15.
M. V. Mosolova 《Mathematical Notes》1978,23(6):448-452
We establish the formula $$\ln (e^B e^A ) = \smallint _0^t \psi (e^{ - \tau ad_A } e^{ - \tau ad_B } ) e^{ - \tau ad_A } d\tau (A + B),$$ where Ψ(x)=(In x)/(x ? 1); here A and B are elements of a. finite-dimensional Lie algebra which satisfy certain conditions. This formula enables us, in particular, to give a simple proof of the Campbell-Hausdorff theorem. We also give a generalization of the formula to the case of an arbitrary number of factors. 相似文献
16.
R. C. Bhatt 《Israel Journal of Mathematics》1965,3(2):87-88
The exact solution of number of problems in quantum mechanics has been given in terms of Appell’s functionF 2; in an extension of this work I have given here a summation formula, which is as follows:
$$\begin{gathered} \sum\limits_{n = 0}^m {F_2 (a,} - n, - n;1;x,y) \hfill \\ = \frac{{(m + 1)(x - y)^{ - 1} }}{a}[F_2 (a - 1, - m, - m - 1;1,1;x,y) - \rightleftharpoons ] \hfill \\ \end{gathered} $$ 相似文献
17.
Let
. The present note gives the asymptotoc formula of max
.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
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Let C be a nonempty closed convex subset of a uniformly convex and 2-uniformly smooth Banach space E and let Π C be a sunny nonexpansive retraction from E onto C. Let the mappings ${T, S: C \to E}$ be γ 1-strongly accretive, μ 1-Lipschitz continuous and γ 2-strongly accretive, μ 2-Lipschitz continuous, respectively. For arbitrarily chosen initial point ${x^0 \in C}$ , compute the sequences {x k } and {y k } such that ${\begin{array}{ll} \quad y^k = \Pi_C[x^k-\eta S(x^k)],\ x^{k+1} = (1-\alpha^k)x^k+\alpha^k\Pi_C[y^k-\rho T(y^k)],\quad k\geq 0, \end{array}}$ where {α k } is a sequence in [0,1] and ρ, η are two positive constants. Under some mild conditions, we prove that the sequences {x k } and {y k } converge to x* and y*, respectively, where (x*, y*) is a solution of the following system of variational inequality problems in Banach spaces: ${\left\{\begin{array}{l}\langle \rho T(y^*)+x^*-y^*,j(x-x^*)\rangle\geq 0, \quad\forall x \in C,\\langle \eta S(x^*)+y^*-x^*,j(x-y^*)\rangle\geq 0,\quad\forall x \in C.\end{array}\right.}$ Our results extend the main results in Verma (Appl Math Lett 18:1286–1292, 2005) from Hilbert spaces to Banach spaces. We also obtain some corollaries which include some results in the literature as special cases. 相似文献