共查询到20条相似文献,搜索用时 140 毫秒
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我们知道不等式|a+b|≤|a|+|b|是高中代数下册中25页的一个定理,它在解有关绝对值问题中有着重要的应用.我们现对这个不等式取舍等号的条件进行分析,不难得到两条重要的推论:1.|a+b|=|a|+|b|ab≥0;2.|a+b|<|a|+|b|ab<0.这两个基本的互逆关系,显示了数学协调美的内力,充分体现了数学问题的相互转化的作用,标志着它们必有优美的应用.下面举例说明.例1 (上海市1984年中学数学竞赛题)方程|2x-1|+|x-2|=|x+1|的实数解为.解 原方程可化为|2x-… 相似文献
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求复数模的最值常见错误浅析353100福建省建瓯一中叶家旺复数模的最值的求法是复数中的一个重要知识点.通常方法有:代数法、三角法、图象法、利用|z|2=Z·Z.利用||z1|-|z2||≤|z1±z2|≤|z1|+|z2|.等基本方法.学生在应用上述... 相似文献
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§1. IntroductionIn1967,Teicherprovedthat[1]E(Supn|Sn|nL2n)p<+∞, iffEX2log+|X|L2|X|<+∞,p=2E|X|p<+∞,p>2 . Where{X,Xn,n≥1}isasequenceofi.i.drealrandomvariableswithmeanszero.In1995,Thesimilarresultshavebeensetupfori.i.drandomvariables{X,Xnn≥1}withmean… 相似文献
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该文研究Bernstein多项式的绝对收敛性.证明了,对每个x∈[0,1],一个有界变差函数的Bernstein多项式序列是绝对|C,1|可和的,而且给出了Berstein多项式序列的绝对|C,1|和式的余项的估计. 相似文献
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在函数这一章的复习中,笔者发现学生在解有关函数性质问题时,经常发生一些不该有的错误.本文仅就此发表一点看法.例1判断函数f(x)=1-x2|x+2|-2的奇偶性.错解∵f(-x)=1-(-x)2|-x+2|-2=1-x2|x-2|-2.∴f(-x)≠... 相似文献
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若f(x,y)在不动点为鞍点的特征值满足λ1>1>|λ2|>0,|λ1·λ2|<1,则f(x,y)限制在鞍点的局部有公式α=1+1nr是局部熵,α是局部分维数.把公式应用到Henon映射中,当α=1.4,b=0.3时,得到1nr=0.454,α=1.244. 相似文献
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J. R. Cannon 《Annali di Matematica Pura ed Applicata》1964,65(1):377-387
Summary Let u(x, t) satisfy the heat equation in a region D in the x−t plane and vanish initially. Let |u|<M0 in D and |u
i
2
|<∈ in D* ⊂ D. Then, in D−D*, |u|<
, where B=B(x, t) satisfies O<B<1 and B(x, t) and M1 are given explicity by simple formulas. The a priori bound is applied to an error analysis of a numerical procedure for continuing
solutions of the heat equation in the space variable.
Work was performed under the auspices of the U. S. Atomic Energy Commission. 相似文献
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Tomasz Beberok 《Journal of Geometric Analysis》2016,26(4):2883-2892
In this paper we obtain the closed forms of some hypergeometric functions. As an application, we obtain the explicit forms of the Bergman kernel functions for Reinhardt domains \(\{|z_3|^{\lambda } < |z_1|^{2p} + |z_2|^2, \ |z_1|^{2p} + |z_2|^2 < |z_1|^{p} \}\) and \(\{|z_4|^{\lambda } < (|z_1|^2 + |z_2|^2)^{p} + |z_3|^2, \ (|z_1|^2 + |z_2|^2)^{p} + |z_3|^2 < (|z_1|^2 + |z_2|^2 )^{p/2} \}\). 相似文献
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V. Tryhuk 《Czechoslovak Mathematical Journal》2008,58(3):605-635
In this article, the equivalence and symmetries of underdetermined differential equations and differential equations with
deviations of the first order are considered with respect to the pseudogroup of transformations . That means, the transformed unknown function is obtained by means of the change of the independent variable and subsequent multiplication by a nonvanishing factor. Instead
of the common direct calculations, we use some more advanced tools from differential geometry; however, the exposition is
self-contained and only the most fundamental properties of differential forms are employed. We refer to analogous achievements
in literature. In particular, the generalized higher symmetry problem involving a finite number of invariants of the kind
is compared to similar results obtained by means of auxiliary functional equations. 相似文献
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Let F(z) be an analytic function in |z| < 1. If F(z) has only a finite number
of algebraic singularities on the unit circle |z| = 1, then Darbouxs method can be
used to give an asymptotic expansion for the coefficient of zn in the Maclaurin
expansion of F(z). However, the validity of this expansion ceases to hold, when
the singularities are allowed to approach each other. A special case of this
confluence was studied by Fields in 1968. His results have been considered
by others to be
too complicated, and desires have been expressed to investigate whether
any simplification is feasible. In this paper, we shall show that simplification is
indeed possible. In the case of two coalescing algebraic singularities, our
expansion involves only two Bessel functions of the first kind. 相似文献
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We obtain conditions for the nonexistence of global solutions and estimates of existence time for local solutions to the problem $$\frac{{d^k y}}{{dt^k }} \geqslant a_1 (t)\left| y \right|^{q_1 } + a_2 (t)\left| y \right|^{q_2 } + \cdots + a_n (t)\left| y \right|^{q_n } .$$ The proofs are based on the method of trial functions developed by Mitidieri and Pokhozhaev. 相似文献
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We consider second-order subelliptic operators with complex coefficients over a connected Lie group G. If the principal coefficients are right uniformly continuous then we prove that the operators generate strongly continuous holomorphic semigroups with kernels K satisfying Gaussian bounds. Moreover, the kernels are Hölder continuous and for each 0, 1 and > 0 one has estimates
for g, h, k, l G and all z in a subsector of the sector of holomorphy with
where
denotes the canonical subelliptic modulus and D " the local dimension.These results are established by a blend of elliptic and parabolic techniques in which De Giorgi estimates and Morrey–Campanato spaces play an important role. 相似文献
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一类高阶中立型方程的周期解 总被引:5,自引:0,他引:5
利用Fourier级数理论讨论了一类高阶中立型方程的周期解问题。所得结果改进了司建国(应用数学和力学,第17卷1期:关于高阶常系数中立型方程周期解的讨论)的主要结果,即将该文定理1的条件|b0|<1/2改为|b0|≠1,从而该文的其它定理也可相应得到改进。 相似文献
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I. V. Boikov 《Mathematical Notes》1972,12(2):541-546
A computational scheme of collocation type is proposed for a singular linear integral equation with a power singularity in the regular integral and the justification is given. The results obtained are used to justify the approximate solution of the singular integral equation $$Kx \equiv a(t)x(t) + \frac{{b(t)}}{{\pi i}}\smallint _{\left| \tau \right| = 1} \frac{{x(\tau )d\tau }}{{\tau - t}} + \frac{1}{{2\pi i}}\smallint _{\left| \tau \right| = 1} \frac{{h|t,\tau )x(\tau )}}{{\left| {\tau - t} \right|^\delta }}d\tau = f(t)$$ by a modification of the method of minimal residuals. 相似文献
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L. V. Kovalev 《Journal of Mathematical Sciences》2002,110(6):3111-3120
A simple proof of the recent result by E. G. Emel'yanov concerning the maximum of the conformal radius r(D,1) for a family of simply connected domains with a fixed value r(D,0) is given. A similar problem is solved for a family of convex domains. Exact estimates for functionals of the form
are obtained for families of functions inverse to elements of the classes S and Sm, where S={f:f is regular and univalent in the disk {z:|z| < 1} and f(0)=f'(0)-1=0} and SM=
for
. Bibliography: 7 titles. 相似文献
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Theorems determining Weyl's multipliers for the summability almost everywhere by the |c, 1| method of the series with respect to block-orthonormal systems are proved. In particular, it is stated that if the sequence {(n)} is the Weyl multiplier for the summability almost everywhere by the |c, 1| method of all orthogonal series, then there exists a sequence {N
k} such that {(n)} will be the Weyl multiplier for the summability almost everywhere by the |c, 1| method of all series with respect to the
k
-orthonormal systems. 相似文献