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题目 2008年普通高等学校招生全国统一考试理科数学(必修+选修Ⅱ)第10题
若直线x/a+y/b=1通过点M(cosa,sina),则
A.a+b2≤1 B.a2+b2≥1
C.1/a2+1/b2≤1 D.1/a2+1/b2≥1
评析 本题是在解析几何、三角函数、不等式三方面知识的交汇点上进行设计的,立意新颖,毫无赘言,此谓之精.与考生交流讨论,发现该题思维开放度很高,解法多样,巧夺天工.此谓之妙.下面择其有代表性的解法进行讨论.…… 相似文献
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嵌在各向同性均匀弹性半空间的弹性斜桩顶部,受任意荷载的位移和应力,可分解为在倾斜平面xOz及其法平面yOz内进行分析.将Mindlin力作为基本虚载荷,令集度为未知函数X(t)、Y(t)、Z(t),分别平行于x、y、z轴,的基本载荷沿桩轴t的[0,L]内分布,并在桩顶作用集中力Qx,Qy、Z,力偶矩My、Mx,根据弹性桩的边界条件,将问题归结为一组Fredholm-Volera型的积分方程.文中给出数值解.计算结果的精度可用功的互等定理来检查. 相似文献
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如图,在△ABC中,设∠A、∠B、∠C所对的边分别为a、b、c,过B作BD⊥AC于D点.1.三角形面积公式 在Rt△ADB中, BD=c·sinA.∴S△=1/2AC·BD=1/2bc·sinA.同理S△1/2casinB,S△1/2casinC. 相似文献
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作下列变换可使椭圆x2/a2+y2+b2=1变换成双曲线x2/a2-y2/b2=1.如图,设A1、A2是椭圆x2/2+y2/b2=1长轴的两个端点,P1P2是与A1A2垂直的弦,则直线A1 P1、A2P2的交点轨迹是双曲线x2/a2-y2/b2=1.反之亦然.有关这种变换的实质在文[1]中已作了探讨.本文探究这两条可变换曲线的张角和最值点的性质.…… 相似文献
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一、引言 Conolly、Conolly与Chan、Hadidi、Haight等讨论了输入或服务速率依赖于在场顾客数的各种Mn/Mn/1 型随机服务系统.韩继业进一步研究了到达间隔分布依赖于系统中顾客数的GI/M/c模型. 相似文献
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Two classes of operators with irreducibility and the small and compact perturbations of them 下载免费PDF全文
This paper gives the concepts of finite dimensional irreducible operators((FDI) operators)and infinite dimensional irreducible operators((IDI) operators). Discusses the relationships of(FDI)operators,(IDI) operators and strongly irreducible operators((SI) operators) and illustrates some properties of the three classes of operators. Some sufficient conditions for the finite-dimensional irreducibility of operators which have the forms of upper triangular operator matrices are given. This paper proves that every operator with a singleton spectrum is a small compact perturbation of an(FDI) operator on separable Banach spaces and shows that every bounded linear operator T can be approximated by operators in(Σ FDI)(X) with respect to the strong-operator topology and every compact operator K can be approximated by operators in(Σ FDI)(X) with respect to the norm topology on a Banach space X with a Schauder basis, where(ΣFDI)(X) := {T∈B(X) : T=Σki=1Ti, Ti ∈(FDI), k ∈ N}. 相似文献
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本文证明了:如果两个W~*-三元算子环V和W的cb距离d_(cb)(V,W)很小的时候,其连接冯·诺依曼代数之间的距离也很小.还证明了:和内射的W~*-三元算子环靠的很近的W~*-三元算子环也是内射的.对具有r性质和McDuff性质的W~*-三元算子环,类似的结论也成立. 相似文献
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The central theme of the present paper are band and band-dominated operators, i.e. norm limits of band operators. In the first part, we generalize the results from [24] and [25] concerning the Fredholm properties of band-dominated operators and the applicability of the finite section method to the case of operators with operator-valued coefficients. We characterize these properties in terms of the limit operators of the given band-dominated operator. The main objective of the second part is to apply these results to pseudodifferential operators on cones in
n
which is possible after a suitable discretization.Partially supported by the German Research Foundation (DFG) under Grant Nr. 436 RUS 17/67/98. 相似文献
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The paper is devoted to study of singular integral operators with
fixed singularities at endpoints of contours on weighted Lebesgue spaces with
general Muckenhoupt weights. Compactness of certain integral operators with
fixed singularities is established. The membership of singular integral operators
with fixed singularities to Banach algebras of singular integral operators
on weighted Lebesgue spaces with slowly oscillating Muckenhoupt weights is
proved on the basis of Balakrishnans formula from the theory of strongly
continuous semi-groups of closed linear operators. Symbol calculus for such
operators, Fredholm criteria and index formulas are obtained. 相似文献
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M. A. Bastos Yu. I. Karlovich A. F. dos Santos 《Integral Equations and Operator Theory》2002,42(1):22-56
The invertibility of convolution type operators on unions of intervals is studied. Sufficient conditions of invertibility for some classes of these operators are established. Solvability results forn-term corona problems are obtained using two different approaches: one involving reduction ton–1 Riemann-Hilbert problems in two variables and another involving reduction to two-term corona problems. The invertibility of the convolution operators on a union of intervals is also related to the invertibility of associated convolution operators on single intervals. Formulas for the inverse operators are given.Work partially supported by F. C. T. (Portugal) Project Praxis XXI/2/2.1/MAT/441/94 and by CONACYT (México) grant, Cátedra Patrimonial, No. 990017-EX. 相似文献
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S. ter Horst M. Messerschmidt A.C.M. Ran M. Roelands M. Wortel 《Indagationes Mathematicae》2018,29(5):1350-1361
In recent years the coincidence of the operator relations equivalence after extension (EAE) and Schur coupling (SC) was settled for the Hilbert space case. For Banach space operators, it is known that SC implies EAE, but the converse implication is only known for special classes of operators, such as Fredholm operators with index zero and operators that can in norm be approximated by invertible operators. In this paper we prove that the implication EAE SC also holds for inessential Banach space operators. The inessential operators were introduced as a generalization of the compact operators, and include, besides the compact operators, also the strictly singular and strictly co-singular operators; in fact they form the largest ideal such that the invertible elements in the associated quotient algebra coincide with (the equivalence classes of) the Fredholm operators. 相似文献
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Yury Arlinskiĭ 《Integral Equations and Operator Theory》2011,71(3):417-453
We establish connections between Schur parameters of the Schur class operator-valued functions, the corresponding simple conservative
realizations, lower triangular Toeplitz matrices, and Kreĭn shorted operators. By means of Schur parameters or shorted operators
for defect operators of Toeplitz matrices necessary and sufficient conditions for a simple conservative discrete-time system
to be controllable/observable and for a completely non-unitary contraction to be completely non-isometric/completely non-co-isometric
are obtained. For the Schur problem a characterization of central solution and uniqueness criteria to the solution are given
in terms of shorted operators for defect operators of contractive Toeplitz matrices, corresponding to data. 相似文献
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Nina Zorboska 《Proceedings of the American Mathematical Society》2003,131(3):793-800
We analyze the connection between compactness of operators on the Bergman space and the boundary behaviour of the corresponding Berezin transform. We prove that for a special class of operators that we call radial operators, an oscilation criterion is a sufficient condition under which the compactness of an operator is equivalent to the vanishing of the Berezin transform on the unit circle. We further study a special class of radial operators, i.e., Toeplitz operators with a radial symbol.