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1.
幂零群的若干充分条件   总被引:11,自引:0,他引:11  
王品超  逮杰清 《数学进展》1998,27(4):331-334
本文利用C-正规子群的性质,得到了若干有限群为幂零群的充分条件,推广了一些著名定理,如Thompson定理及It^o定理。  相似文献   

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1 问题的提出大家知道,当一个三面角的三个面角都固定时,则它们任意两个面的平面角的大小也就确定;它们之间一定存在着某种必然的内在联系;事实上,我们有如下的定理;图1BαC2θ1θOA定理 设O-ABC为一个三面角,∠AOB=φ,∠AOC=θ1,∠BOC=θ2,二面角A-OC-B的平面角为α,则有cosφ=cosθ1cosθ2+sinθ1sinθ2cosα;略证:如图1,AC⊥OC,BC⊥OC,则∠ACB=α;令OA=a,OB=b;在Rt△ACO中,AC=asinθ1,OC=acosθ1;同理,B…  相似文献   

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两个三角不等式   总被引:2,自引:2,他引:0  
定理1在任意△ABC中,A、B、C表示其三内角,则cos3A+cos3B+cos3C≥38.(等号当且仅当△ABC为正三角形时成立)证明由三角恒等式cos3A+cos3B+cos3C=(2R+r)3-3s2r4R3-1(R、r、s为△ABC的外接圆半...  相似文献   

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本文首先利用cointegral和cocleft模余代数概念,得到H为Hopf代数当且仅当H作为H-模余代数是cocleft以及模余代数的一些性质.然后,设C为H-模余代数.令C=C/Ckerε则有.最后,证明了结构定理:当C为cocleftH-模余代数时,作为余代数有同构:C≌C×H  相似文献   

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C^n中的界域上σ—方程局部解的Bochner—Ono公式   总被引:7,自引:0,他引:7  
姚宗元 《数学进展》1993,22(6):553-560
本文利用Ono的局部化方法及Xeнкин的技巧,讨论C^n空间中有界域上σ-方程局部解的存在性,并得到有界域上σ-方程局部解的Bochner-Ono公式,且指出在含参数的局部意义下有简单的一致估计。  相似文献   

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刘健先生在文[1]中提出如下猜想:在任意△ABC中,有cosBcosCsinA2+cosCcosAsinB2+cosAcosBsinC2<1①笔者通过研究,发现了这个不等式的一个指数形式:定理在△ABC中,有cosBcosCsinkA2+cosCco...  相似文献   

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cosnA2+cosnB2+cosnC2的上下确界杨寅(呼和浩特交通学校010023)设A、B、C为三角形的三个内角,题目中的问题久已悬而未决.今用分析方法彻底解决这个问题.定理设A、B、C为三角形的三个内角,n2为自然数,则有min1+222n,...  相似文献   

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本文以多项式(1+x)Vn(x)Vn(x)=cos2n+12θcosθ2,x=cosθ的零点作为插值的节点,构造了一个Lagrange插值多项式算子过程Cn(f,x),给出了其逼近阶估计.同时证明Cn(f,x)亦满足Ditzian-Totik定理.  相似文献   

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一类有趣的三角不等式   总被引:1,自引:1,他引:0  
最近,本文作者通过研究、探索,发现了一类新颖、奇特的三角不等式.定理1在△ABC中,有cos2A+cosB+cosC>34.(1)证∵cosB-C2-sinA2=2sinB2sinC2>0,∴cosB-C2>sinA2,∴cos2A+cosB+cos...  相似文献   

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设(T,Σ,u)是有限测定空间,表示定义在T上取值于X的p幂Bochner可积函数空间。本文主要证明了Lp(T,X)中的一般子集G和Lp(T,Y)型子集为太阳集的特征定理;对实Hibert空间X,得到了子集Lp(T,Y)为Lp(T,X)的半Chebyshev太阳集的特征,同时给出了子集Lp(N,Y)是Lp(N,X)的强Chebyshev子空间的条件。  相似文献   

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We present a rigorous numerical proof based on interval arithmetic computations categorizing the linearized and nonlinear stability of periodic viscous roll waves of the KdV–KS equation modeling weakly unstable flow of a thin fluid film on an incline in the small-amplitude KdV limit. The argument proceeds by verification of a stability condition derived by Bar–Nepomnyashchy and Johnson–Noble–Rodrigues–Zumbrun involving inner products of various elliptic functions arising through the KdV equation. One key point in the analysis is a bootstrap argument balancing the extremely poor sup norm bounds for these functions against the extremely good convergence properties for analytic interpolation in order to obtain a feasible computation time. Another is the way of handling analytic interpolation in several variables by a two-step process carving up the parameter space into manageable pieces for rigorous evaluation. These and other general aspects of the analysis should serve as blueprints for more general analyses of spectral stability.  相似文献   

13.
We propose a geometric method for quantifying the difference between parametrized curves in Euclidean space by introducing a distance function on the space of parametrized curves up to rigid transformations (rotations and translations). Given two curves, the distance between them is defined as the infimum of an energy functional which, roughly speaking, measures the extent to which the jet field of the first curve needs to be rotated to match up with the jet field of the second curve. We show that this energy functional attains a global minimum on the appropriate function space, and we derive a set of first-order ODEs for the minimizer.  相似文献   

14.
We study the structure of the periodic steady-state solutions of forced and damped strongly nonlinear coupled oscillators in the frequency–energy domain by constructing forced and damped frequency – energy plots (FEPs). Specifically, we analyze the steady periodic responses of a two degree-of-freedom system consisting of a grounded forced linear damped oscillator weakly coupled to a strongly nonlinear attachment under condition of 1:1 resonance. By performing complexification/averaging analysis we develop analytical approximations for strongly nonlinear steady-state responses. As an application, we examine vibration isolation of a harmonically forced linear oscillator by transferring and confining the steady-state vibration energy to the weakly coupled strongly nonlinear attachment, thereby drastically reducing its steady-state response. By comparing the nonlinear steady-state response of the linear oscillator to its corresponding frequency response function in the absence of a nonlinear attachment we demonstrate the efficacy of drastic vibration reduction through steady-state nonlinear targeted energy transfer. Hence, our study has practical implications for the effective passive vibration isolation of forced oscillators.  相似文献   

15.
《Applied Mathematical Modelling》2014,38(21-22):5347-5355
This paper investigates the multi-mode resource availability cost problem with recruitment and release dates for resources. This problem is a more realistic model and extended case of the resource availability cost problem. The project contains activities interrelated by finish–start precedence relations with zero time lags, which require a set of renewable resources. First, a mixed integer programming formulation is proposed for the problem. Then, simulated annealing (SA) algorithm is proposed to obtain a satisfying solution for this NP-hard problem. The effectiveness of the proposed algorithm is demonstrated through comprehensive experimentation based on 300 test problems. The results are analyzed and discussed.  相似文献   

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We discuss the interplay between lagrangian distributions and connections in (generalized) symplectic geometry, beginning with the traditional case of symplectic manifolds and then passing to the more general context of poly- and multisymplectic structures on fiber bundles, which is relevant for the covariant hamiltonian formulation of classical field theory. In particular, we generalize Weinstein?s tubular neighborhood theorem for symplectic manifolds carrying a (simple) lagrangian foliation to this situation. In all cases, the Bott connection, or an appropriately extended version thereof, plays a central role.  相似文献   

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