共查询到20条相似文献,搜索用时 156 毫秒
1.
在数学的学习当中 ,仅仅掌握课本中定理的证明是不够的 ,而应该深入反思其本质所在 ,在拓广思路的基础上 ,探讨它的新证法 .下面看我们对绝对值不等式定理的思考 .已知a ,b∈R ,求证|a|- |b|≤ |a b|≤ |a| |b|.(高中《代数》下册P 2 6定理 1)证明此题的关键是设法脱去绝对值符号 .思考 1 两边平方的方法 .证法 1 先证 |a b|≤ |a| |b|.①∵ |a b|2 =a2 2ab b2 ≤ |a|2 2 |a|·|b| |b|2 =( |a| |b|) 2 ,∴ |a b|≤ |a| |b|.再证 |a|- |b|≤ |a b|.②若 |a|- |b|≤ 0时 ,|a|- |b|≤ |a … 相似文献
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“|a| - |b|≤ |a±b|≤ |a| + |b|”是高中数学新教材第二册 (上 )第 2 0页的一个重要不等式定理 ,它是处理含有绝对值问题的一个重要工具 ,课本限于篇幅 ,主要介绍它在证明不等式中的应用 ,而其它方面很少涉及 ,且何时取等号也未指明 ,本文对此加以补充并例谈其应用 .1 定理的补注1)等号成立的条件|a +b| =|a| + |b|当且仅当ab≥ 0 ;|a -b| =|a| + |b|当且仅当ab≤ 0 ;|a| - |b| =|a +b|当且仅当 (a +b)b≤ 0 ;|a| - |b| =|a -b|当且仅当 (a -b)b≥ 0 .2 )不等号成立的条件|a +b| <|a| + |b|当且仅当ab <0 ;|a -b| <|a| + |b|当且仅当ab … 相似文献
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不等式“|a|- |b|≤ |a b|≤ |a| |b|[1] ”(以下简称 [1])是高中数学的一个重要知识点 ,考试大纲说明中对此有明确要求 :会应用不等式“|a|- |b|≤ |a b|≤ |a| |b|”.事实上 ,如何有效地、灵活地应用不等式 [1]证明有关综合性代数推理题是高中数学的难点 .以下简述知识要点 相似文献
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“|a| -|b|≤ |a±b|≤ |a| + |b|”是高中数学中的一个重要不等式定理 ,它是处理含有绝对值问题的一个重要工具 .课本主要介绍它在证明不等式中的应用 ,而其它方面很少涉及 ,且何时取等号也未指明 ,但在高考中却多次考查到 .为此本文加以补充并例谈其应用 .一、定理的补注1.等号成立的条件|a +b| =|a| + |b| ab≥ 0 ;|a -b| =|a| + |b| ab≤ 0 ;|a| -|b| =|a +b| (a +b)b≤ 0 ;|a| -|b| =|a -b| (a -b)b≥ 0 .2 .字母a ,b的范围其实a ,b不仅在实数中成立 ,且在复数集中也成立 .同时右边不等式… 相似文献
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考虑了一类带Sobolev-Hardy指数的椭圆型方程组{-Δu-μu/|x|2=α/α+β|μ|α-2u|v|β/|x|s+σp/p+q|u|p-2u|v|q,x∈B,-Δu-μu/|x|2=β/α+β|μ|α|v|β-2v/|x|s+σp/p+q|u|p|v|q-2,x∈B,其中0≤μμ,-4,μ=((N-2)~2)/4,σ0,0≤s2,N6+s,α+β=2~*(s)=(2(N-s))/(N-2),p,q≥1,2≤p+q2~*(s),B■R~N为以原点为心的一个开球.利用逼近方法及喷泉定理,得到了上述方程组无穷多个球对称解的存在性. 相似文献
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选择题 :1 若1x<x ,则x的取值范围是 ( )(A) (-∞ ,- 1 )∪ (1 , ∞ ) .(B) (- 1 ,0 )∪ (1 , ∞ ) .(C) (- 1 ,1 ) .(D) (- 1 ,0 )∪ (0 ,1 ) .2 不等式logx 45 <1的解集是 ( )(A) {x| 0 <x <45 }.(B) {x|x >45 }.(C) {x| 45 <x <1 }.(D) {x| 0 <x <45 }∪ {x|x >1 }.3 若 |a| <1 ,|b| <1 ,则 |a b| |a -b|与 2的大小关系是 ( )(A) |a b| |a -b| >2 .(B) |a b| |a -b| <2 .(C) |a b| |a -b| =2 .(D)不确定 .4 设x∈R ,则 (1 - |x| ) (1 x) >0成立的充分… 相似文献
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On the Bergman Kernels of Some Special Reinhardt Domains 总被引:1,自引:1,他引:0
We consider the Reinhardt domains of the following types:E_1 = {z = (z_1,z_2)∈C~2: |z_1}~(2K)+ |z_2|<1,K>0},E_2 = {z = (z_1,z_2)∈C~2: |z_1| + |z_2|<1},E_3 = {z = (z_1,z_2,z_3)∈ C~3: |z_1| + |z_2|~2 + |z_3|~2<1},E_4 = {z = (z_1,z_2,z_3)∈ C~3: |z_1| + |z_2| + |z_3|~2<1},E_5 = {z = (z_1,z_2,z_3)∈ C~3: |z_1| + |z_2| + |z_3|<1}. 相似文献
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对于完备格L上给定的|I|×|I|的矩阵R,若存在|I|×|I|的L上的矩阵S满足S⊙S=R,则称S为R的平方根,其中I表示指标集|I|的基数,⊙在本文中指的是sup-T合成算子并且T是无限∨分配的保序的算子。本文给出了完备格上基于sup-T合成算子的矩阵平方根存在的充要条件以及相应的理论上的算法求解所有的平方根。 相似文献
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J. F. Mena-Jurado R. Paya-Albert A. Rodriguez-Palacios 《Israel Journal of Mathematics》1985,51(1-2):33-67
Let |·| be a fixed absolute norm onR
2. We introduce semi-|·|-summands (resp. |·|-summands) as a natural extension of semi-L-summands (resp.L-summands). We prove that the following statements are equivalent. (i) Every semi-|·|-summand is a |·|-summand, (ii) (1, 0)
is not a vertex of the closed unit ball ofR
2 with the norm |·|. In particular semi-L
p-summands areL
p-summands whenever 1<p≦∞. The concept of semi-|·|-ideal (resp. |·|-ideal) is introduced in order to extend the one of semi-M-ideal (resp.M-ideal). The following statements are shown to be equivalent. (i) Every semi-|·|-ideal is a |·|-ideal, (ii) every |·|-ideal
is a |·|-summand, (iii) (0, 1) is an extreme point of the closed unit ball ofR
2 with the norm |·|. From semi-|·|-ideals we define semi-|·|-idealoids in the same way as semi-|·|-ideals arise from semi-|·|-summands.
Proper semi-|·|-idealoids are those which are neither semi-|·|-summands nor semi-|·|-ideals. We prove that there is a proper
semi-|·|-idealoid if and only if (1, 0) is a vertex and (0, 1) is not an extreme point of the closed unit ball ofR
2 with the norm |·|. So there are no proper semi-L
p-idealoids. The paper concludes by showing thatw*-closed semi-|·|-idealoids in a dual Banach space are semi-|·|-summands, so no new concept appears by predualization of semi-|·|-idealoids. 相似文献
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本文考虑如下非线性发展方程组的初边值问题u″+ Au -△ u′-α| v|ρ+ 2 | u|ρu =0 , v″+ Av -△ v′-α| u|ρ+ 2 | v|ρv =0 ,其中 A为 p-Laplace算子 ,α∈ R,ρ>-1均为常数 ,证明了整体解的存在性及渐近性 ,得到了当初始能量为正但有上界时解的爆破性条件 相似文献
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设G为有限群,称G的子群H为ss-置换子群,如果存在G的次正规子群B使得G=HB,且H与B的任意Sylow子群可以交换,即对任意X∈Syl(B)有XH=HX.利用子群的ss-置换性来研究有限群的结构,得到有限群超可解的两个充分条件. 相似文献
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Liuqing Yang 《偏微分方程(英文版)》2012,25(3):199-207
In this paper we mainly study the relation between $|A|^2, |H|^2$ and cosα (α is the Kähler angle) of the blow up flow around the type II singularities of a symplectic mean curvature flow. We also study similar property of an almost calibrated Lagrangian mean curvature flow. We show the nonexistence of type II blow-up flows for a symplectic mean curvature flow satisfying $|A|^2≤λ|H|^2$ and $cosα≥δ>1-\frac{1}{2λ}(½≤α≤ 2)$, or for an almost calibrated Lagrangian mean curvature flow satisfying $|A|^2≤λ|H|^2$ and $cosθ≥δ>max\ {0,1-\frac{1}{λ}}(\frac34≤λ≤ 2)$, where θ is the Lagrangian angle. 相似文献
15.
Sun Xiehua 《数学年刊B辑(英文版)》1987,8(4):468-470
To answer the rest part of the problem of Boas R. P. on derivative of polynomial, it is shown that if $\[p(z)\]$ is a polynomial of degree n such that $\[\mathop {\max }\limits_{\left| z \right| \le 1} \left| {p(z)} \right| \le 1\]$ and $\[{p(z) \ne 0}\]$ in $\[\left| z \right| \le k,0 < k \le 1\]$, then $\[\left| {{p^''}(z)} \right| \le n/(1 + {k^n})\]$ for $\[\left| z \right| \le 1\]$. The above estimate is sharp and the equation holds for $\[p(z) = ({z^n} + {k^n})/(1 + {k^n})\]$. 相似文献
16.
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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D. S. Ananichev 《Russian Mathematics (Iz VUZ)》2010,54(1):1-9
A deterministic incomplete automaton
$
\left| Q \right| + \left\lfloor {\frac{{\left| Q \right| - 1}}
{2}} \right\rfloor
$
\left| Q \right| + \left\lfloor {\frac{{\left| Q \right| - 1}}
{2}} \right\rfloor
and this bound is tight. 相似文献
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Solutions to the $\sigma_k$-Loewner-Nirenberg Problem on Annuli are Locally Lipschitz and Not Differentiable 下载免费PDF全文
Yanyan Li & Luc Nguyen 《数学研究》2021,54(2):123-141
We show for $k \geq 2$ that the locally Lipschitz viscosity solution to the $\sigma_k$-Loewner-Nirenberg problem on a given annulus $\{a < |x| < b\}$ is $C^{1,\frac{1}{k}}_{\rm loc}$ in each of $\{a < |x| \leq \sqrt{ab}\}$ and $\{\sqrt{ab} \leq |x| < b\}$ and has a jump in radial derivative across $|x| = \sqrt{ab}$. Furthermore, the solution is not $C^{1,\gamma}_{\rm loc}$ for any $\gamma > \frac{1}{k}$. Optimal regularity for solutions to the $\sigma_k$-Yamabe problem on annuli with finite constant boundary values is also established. 相似文献
20.
If p(z) is a polynomial of degree n having all its zeros on |z| = k, k ≤ 1, then it is proved[5] that max |z|=1 |p′(z)| ≤ kn1n + kn m|z|=ax1 |p(z)|. In this paper, we generalize the above inequality by extending it to the polar derivative of a polynomial of the type p(z) = cnzn + ∑n j=μ cn jzn j, 1 ≤μ≤ n. We also obtain certain new inequalities concerning the maximum modulus of a polynomial with restricted zeros. 相似文献