共查询到20条相似文献,搜索用时 15 毫秒
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Let Cp be the Schatten p-class for p>0. Generalizations of the parallelogram law for the Schatten 2-norms have been given in the following form: if A={A1,A2,…,An} and B={B1,B2,…,Bn} are two sets of operators in, then C2
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Hao Pan 《Journal of Number Theory》2006,117(1):216-221
Let k,m,n?2 be integers. Let A be a subset of {0,1,…,n} with 0∈A and the greatest common divisor of all elements of A is 1. Suppose that
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In this paper, we present families of quasi-convex sequences converging to zero in the circle group T, and the group J3 of 3-adic integers. These sequences are determined by increasing sequences of integers. For an increasing sequence , put gn=an+1−an. We prove that
- (a)
- the set {0}∪{±3−(an+1)|n∈N} is quasi-convex in T if and only if a0>0 and gn>1 for every n∈N;
- (b)
- the set {0}∪{±an3|n∈N} is quasi-convex in the group J3 of 3-adic integers if and only if gn>1 for every n∈N.
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Szabolcs Baják 《Applied mathematics and computation》2010,216(11):3219-3227
We solve the so-called invariance equation in the class of two-variable Stolarsky means {Sp,q:p,q∈R}, i.e., we find necessary and sufficient conditions on the six parameters a, b, c, d, p, q such that the identity
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Rosihan M. Ali V. Ravichandran 《Journal of Mathematical Analysis and Applications》2006,324(1):663-668
Let A,B,D,E∈[−1,1]. Conditions on A,B,D and E are determined so that
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We completely describe those positive Borel measures μ in the unit disc D such that the Bergman space Ap(w)⊂Lq(μ), 0<p,q<∞, where w belongs to a large class W of rapidly decreasing weights which includes the exponential weights , α>0, and some double exponential type weights.As an application of that result, we characterize the boundedness and the compactness of Tg:Ap(w)→Aq(w), 0<p,q<∞, w∈W, where Tg is the integration operator
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Using purely elementary methods, necessary and sufficient conditions are given for the existence of 2T-periodic and 4T-periodic solutions around the upper equilibrium of the mathematical pendulum when the suspension point is vibrating with period 2T. The equation of the motion is of the formwhere l, g are constants andA, T are positive constants. The exact stability zones for the upper equilibrium are presented.
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$$\ddot{\theta}-\frac{1}{l}(g+a(t)) \theta=0,$$
$$a(t) := \begin{cases} A &\text{if } 2kT\leq t < (2k+1)T,\\ -A &\text{if } (2k+1)T\leq t < (2k+2)T,\end{cases}\quad (k=0,1,\dots);$$
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Given a sequence A = (a 1, …, a n ) of real numbers, a block B of A is either a set B = {a i , a i+1, …, a j } where i ≤ j or the empty set. The size b of a block B is the sum of its elements. We show that when each a i ∈ [0, 1] and k is a positive integer, there is a partition of A into k blocks B 1, …, B k with |b i ?b j | ≤ 1 for every i, j. We extend this result in several directions. 相似文献
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Qi-Yan Shi 《Journal of Mathematical Analysis and Applications》2005,311(1):182-190
Let Ω=N{−1,1} and {ωj} be independent random variables taking values in {−1,1} with equal probability. Endowed with the product topology and under the operation of pointwise product, Ω is a compact Abelian group, the so-called Cantor group. Let a,b,c be real numbers with 1+a+b+c>0, 1+a−b−c>0, 1−a+b−c>0 and 1−a−b+c>0. Finite products on Ω,
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Tom Sanders 《Israel Journal of Mathematics》2010,179(1):1-28
A continuous linear map T from a Banach algebra A into another B approximately preserves the zero products if ‖T(a)T(b)‖ ≤ α‖a‖‖b‖ (a,b ∈ A, ab = 0) for some small positive α. This paper is mainly concerned with the question of whether any continuous linear surjective map T: A → B that approximately preserves the zero products is close to a continuous homomorphism from A onto B with respect to the operator norm. We show that this is indeed the case for amenable group algebras. 相似文献
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P. Chansangiam 《Journal of Mathematical Analysis and Applications》2009,356(2):525-276
Let B(H) be the space of all bounded linear operators on a complex separable Hilbert space H. Bohr inequality for Hilbert space operators asserts that for A,B∈B(H) and p,q>1 real numbers such that 1/p+1/q=1,
2|A+B|?p2|A|+q2|B| 相似文献
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Motivated by a question of Sárközy, we study the gaps in the product sequence B = A · A = {b 1 < b 2 < …} of all products a i a j with a i , a j ∈ A when A has upper Banach density α > 0. We prove that there are infinitely many gaps b n+1 ? b n ? α ?3 and that for t ≥ 2 there are infinitely many t-gaps b n+t ? b n ? t 2 α ?4. Furthermore, we prove that these estimates are best possible.We also discuss a related question about the cardinality of the quotient set A/A = {a i /a j , a i , a j ∈ A} when A ? {1, …, N} and |A| = αN. 相似文献
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We find the greatest value α 1 and α 2, and the least values β 1 and β 2, such that the double inequalities α 1 S(a,b)?+?(1???α 1) A(a,b)?T(a,b)?β 1 S(a,b)?+?(1???β 1) A(a,b) and \(S^{\alpha_{2}}(a,b)A^{1-\alpha_{2}}(a,b)< T(a,b)< S^{\beta_{2}}(a,b)A^{1-\beta_{2}}(a,b)\) hold for all a,b?>?0 with a?≠?b. As applications, we get two new bounds for the complete elliptic integral of the second kind in terms of elementary functions. Here, S(a,b)?=?[(a 2?+?b 2)/2]1/2, A(a,b)?=?(a?+?b)/2, and \(T(a,b)=\frac{2}{\pi}\int\limits_{0}^{{\pi}/{2}}\sqrt{a^2{\cos^2{\theta}}+b^2{\sin^2{\theta}}}{\rm d}\theta\) denote the root-square, arithmetic, and Toader means of two positive numbers a and b, respectively. 相似文献
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Marek Niezgoda 《Linear algebra and its applications》2010,433(1):136-640
Let a,b>0 and let Z∈Mn(R) such that Z lies into the operator ball of diameter [aI,bI]. Then for all positive definite A∈Mn(R),
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We establish the weak Harnack estimates for locally bounded sub- and superquasiminimizers u of with f subject to the general structural conditions where p : Ω →] 1, ∞[ is a variable exponent. The upper weak Harnack estimate is proved under the assumption that b, g ∈ L t (Ω) for some t > n/p ?, and the lower weak Harnack estimate is proved under the stronger assumption that b, g ∈ L ∞(Ω). As applications we obtain the Harnack inequality for quasiminimizers and the fact that locally bounded quasisuperminimizers have Lebesgue points everywhere whenever b, g ∈ L ∞(Ω). Throughout the paper, we make the standard assumption that the variable exponent p is logarithmically Hölder-continuous.
相似文献
$${\int}_{\Omega} f(x,u,\nabla u)\,dx $$
$$|z|^{p(x)} - b(x)|y|^{p(x)}-g(x) \leq f(x,y,z) \leq \mu|z|^{p(x)} + b(x)|y|^{p(x)} + g(x), $$
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Let A?B?0 with A>0, t∈[0,1] and p?1. Then we shall show that
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Gyula Károlyi 《Journal of Combinatorial Theory, Series A》2009,116(3):741-746
Let A≠B be nonempty subsets of the group of integers modulo a prime p. If p?|A|+|B|−2, then at least |A|+|B|−2 different residue classes can be represented as a+b, where a∈A, b∈B and a≠b. This result complements the solution of a problem of Erd?s and Heilbronn obtained by Alon, Nathanson, and Ruzsa. 相似文献