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1.
Let B be an unbounded domain located outside an angle domain with vertex at the origin, A ={λn}(n = 1,2,...) be a sequence of complex numbers satisfying sup | arg(λn)| 〈 α 〈 π/2 and denote by M(∧) = {z^λ, λ ∈ ∧} the corresponding system of functions z^λ(λ∈∧). Let α0(z) be a weight function defined on B. We obtain a completeness theorem for the system M(∧) in the Hilbert space L^2 [B, α0].  相似文献   

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To every partition n=n1+n2+...+ns one can associate a vertex operator realization of the Lie algebras a and gln. Using this construction, we obtain reductions of the s-component KP hierarchy, reductions which are related to these partitions. In this way we obtain matrix KdV-type equations. We show that the following two constraints on a KP -function are equivalent: (1) is a -function of the [n1, n2, ..., ns]-th reduced KP hierarchy which satisfies the string equation L–1=0; (2) satisfies the vacuum constraints of the W1+ algebra.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 104, No. 1, pp. 32–42, July, 1995.  相似文献   

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关于[m,n,p_1,p_2,…,p_s]指数型群   总被引:1,自引:0,他引:1  
黎先华 《数学学报》1992,35(2):273-278
本文给出了[m,n,p_1,p_2,…,p_s]指数型群的结构,改进了前人的结果.  相似文献   

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We consider the problem of generating all k-subsets (1 ? k ? m ? n) of the set [1, 2, …, n] in lexicographical order. The running time per k-subset is shown to be constant. The experimental data suggest that our algorithm is about 25% faster than the algorithm proposed by A. Nijenhuis and H. S. Wilf (“Combinatorial Algorithms,” 2nd ed., Academic Press, New York, 1978).  相似文献   

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We obtain exact values of different n-widths for classes of differentiable periodic functions in the space L 2[0, 2π] satisfying the constraint $$ \left( {\int_0^h {\omega _m^p \left( {f^{\left( r \right)} ;t} \right)dt} } \right)^{{1 \mathord{\left/ {\vphantom {1 p}} \right. \kern-\nulldelimiterspace} p}} \leqslant \Phi \left( h \right) $$ , where 0 < h < ∞, 1/r < p ≤ 2, r ∈ ?, and ω m (f (r); t) is the modulus of continuity of mth order of the derivative f (r)(x) ∈ L 2[0, 2π].  相似文献   

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The Kostka–Foulkes polynomials related to a root system can be defined as alternating sums running over the Weyl group associated to . By restricting these sums over the elements of the symmetric group when is of type or , we obtain again a class of Kostka–Foulkes polynomials. When is of type or there exists a duality between these polynomials and some natural -multiplicities and in tensor products [11]. In this paper we first establish identities for the which implies in particular that they can be decomposed as sums of Kostka–Foulkes polynomials with nonnegative integer coefficients. Moreover these coefficients are branching coefficients This allows us to clarify the connection between the -multiplicities and the polynomials defined by Shimozono and Zabrocki. Finally we show that and coincide up to a power of with the one dimension sum introduced by Hatayama and co-workers when all the parts of are equal to , which partially proves some conjectures of Lecouvey and Shimozono and Zabrocki.Presented by P. Littelmann.  相似文献   

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Chebyshev determined $$\mathop {\min }\limits_{(a)} \mathop {\max }\limits_{ - 1 \le x \le 1} |x^n + a_1 x^{n - 1} + \cdots + a_n |$$ as 21?n , which is attained when the polynomial is 21?n T n(x), whereT n(x) = cos(n arc cosx). Zolotarev's First Problem is to determine $$\mathop {\min }\limits_{(a)} \mathop {\max }\limits_{ - 1 \le x \le 1} |x^n - n\sigma x^{n - 1} + a_2 x^{n - 2} + \cdots + a_n |$$ as a function ofn and the parameter σ and to find the extremal polynomials. He solved this in 1878. Another discussion was given by Achieser in 1928, and another by Erdös and Szegö in 1942. The case when 0≤|σ|≤ tan2(π/2n) is quite simple, but that for |σ|> tan2(π/2n) is quite different and very complicated. We give two new versions of the proof and discuss the change in character of the solution. Both make use of the Equal Ripple Theorem.  相似文献   

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Inthispaper,wehaveobtainedthefollowingtheorems.Theorem1 Letφ(x)beaincreasingfunctionon[0,+∞),φ(x)→+∞andφ(x)xbeno-increasing(Whenxislargeenough),andletBbeaseparableBanachspace,XbeaB-valuedrandomvariable,ifi)X∈WM20ii)Xτ-EXτ∈CLT,τ>0,whereXτ=XI{yXy≤τ}ii…  相似文献   

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Under sufficiently general assumptions, we describe sets of entire functions f, sets of growing functions λ, and sets of complex-valued functions H from L p [0, 2π], p ∈ [1, + ∞], for which
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 7, pp. 889–896, July, 1998.  相似文献   

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The problem of minimizing the constant in Jackson-type inequalities with respect to all subspaces of dimensionN, i.e., with respect to the entire set of approximating subspaces of dimensionN, is solved. It is shown that the constant in question is equal to the value of different widths of classL 2 (δ, τ, β, γ, θ). Translated fromMatematicheskie Zametki, Vol. 65, No. 6, pp. 816–820, June, 1999.  相似文献   

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We prove that, in the basis {x 1 & x 2 & x 3, x 1x 2x 3, $ \bar x_1 $ }, for inverse faults at the inputs of functional elements, all Boolean functions f(x 1, x 2, ..., x n ) can be realized by asymptotically optimally reliable circuits operating with unreliability asymptotically (as ? → 0) equal to: ? 3 for the constants 0 and 1, ? for the functions $ \bar x_i $ , and 3? for f(x 1, x 2, ..., x n ) ≠ 0, 1, $ \bar x_i $ , x i , where ? is the error probability at each input of the functional element and i = 1, ..., n. The functions xi, i = 1, ..., n, can be realized absolutely reliably. The complexity of asymptotically optimally reliable circuits is equal in order to the complexity of minimal circuits constructed only from reliable elements.  相似文献   

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The best quadrature formula has been found in the following sense:for afunction whose norm of the second derivative is bounded by a given constant and thebest quadrature formula for the approximate evaluation of integration of that function canminimize the worst possible error if the values of the function and its derivative at certainnodes are known.The best interpolation formula used to get the quadrature formula aboveis also found.Moreover,we compare the best quadrature formula with the open compoundcorrected trapezoidal formula by theoretical analysis and stochastic experiments.  相似文献   

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The equationu(t)=pu(t)+qu(t-) is presented as an archetype (scalar) equation for assessing the quality of integrator/interpolator pairs used to solve retarded differential-difference equations. The relationships ofP-stability andP[, ]-stability, defined with respect to this archetype equation, to stability and order of multistep integrators and to passivity and order of Lagrange interpolators are developed. Composite multistep integrators and composite Lagrange interpolators are considered as a means of obtaining high order pairs stable for all step-sizes over a large portion, if not all, of the (p, q)-domain on which the archetype equation is stable.The research reported herein was supported by grant MCS-7815396 from the National Science Foundation.  相似文献   

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本文以二次函数Y-ax2+bx+c在区间[m,n]上的最值问题为例从数、形、结果三方面来讨论.   ……  相似文献   

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