共查询到20条相似文献,搜索用时 31 毫秒
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In this paper, we develop a stochastic calculus related to a fractional Brownian sheet as in the case of the standard Brownian sheet. Let be a fractional Brownian sheet with Hurst parameters H=(H1,H2), and (2[0,1],B(2[0,1]),μ) a measure space. By using the techniques of stochastic calculus of variations, we introduce stochastic line integrals along all sufficiently smooth curves γ in 2[0,1], and four types of stochastic surface integrals: , i=1,2, , , , . As an application of these stochastic integrals, we prove an Itô formula for fractional Brownian sheet with Hurst parameters H1,H2∈(1/4,1). Our proof is based on the repeated applications of Itô formula for one-parameter Gaussian process. 相似文献
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Let ψ(x) denote the digamma function, that is, the logarithmic derivative of Euler's Γ-function. Let q be a positive integer greater than 1 and γ denote Euler's constant. We show that all the numbers
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Yaming Yu 《Journal of Mathematical Analysis and Applications》2009,352(2):967-970
Let Γ(x) denote Euler's gamma function. The following inequality is proved: for y>0 and x>1 we have
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Goto numbers for certain parameter ideals Q in a Noetherian local ring (A,m) with Gorenstein associated graded ring are explored. As an application, the structure of quasi-socle ideals I=Q:mq (q≥1) in a one-dimensional local complete intersection and the question of when the graded rings are Cohen-Macaulay are studied in the case where the ideals I are integral over Q. 相似文献
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We consider point sets in the m-dimensional affine space where each squared Euclidean distance of two points is a square in Fq. It turns out that the situation in is rather similar to the one of integral distances in Euclidean spaces. Therefore we expect the results over finite fields to be useful for the Euclidean case.We completely determine the automorphism group of these spaces which preserves integral distances. For some small parameters m and q we determine the maximum cardinality I(m,q) of integral point sets in . We provide upper bounds and lower bounds on I(m,q). If we map integral distances to edges in a graph, we can define a graph Gm,q with vertex set . It turns out that Gm,q is strongly regular for some cases. 相似文献
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Gabriele Ranieri 《Journal of Number Theory》2008,128(6):1576-1586
Let p be an odd prime and q=pm, where m is a positive integer. Let ζq be a qth primitive root of 1 and Oq be the ring of integers in Q(ζq). In [I. Gaál, L. Robertson, Power integral bases in prime-power cyclotomic fields, J. Number Theory 120 (2006) 372-384] I. Gaál and L. Robertson show that if , where is the class number of , then if α∈Oq is a generator of Oq (in other words Z[α]=Oq) either α is equals to a conjugate of an integer translate of ζq or is an odd integer. In this paper we show that we can remove the hypothesis over . In other words we show that if α∈Oq is a generator of Oq then either α is a conjugate of an integer translate of ζq or is an odd integer. 相似文献
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Mingjin Wang 《Journal of Mathematical Analysis and Applications》2008,341(2):1487-1494
In this paper, we use the Andrews-Askey integral and the q-Chu-Vandermonde formula to derive a more general integral formula. Applications of the new integral formula are also given, which include to derive the q-Pfaff-Saalschütz formula and the terminating Sears's transformation formula. 相似文献
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In this paper we give a simple proof of inequalities of integrals of functions which are the composition of nonnegative continuous convex functions on a vector space Rm and vector-valued functions in a weakly compact subset of a Banach vector space generated by m-spaces for 1?p<+∞. Also, the same inequalities hold if these vector-valued functions are in a weakly* compact subset of a Banach vector space generated by m-spaces instead. 相似文献
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C.K Arthur Lim 《Journal of Mathematical Analysis and Applications》2004,296(2):594-602
In this paper, we are concerned with orbital integrals on a class of real reductive Lie groups with non-compact Iwasawa K-component. The class contains all connected semisimple Lie groups with infinite center. We establish that any given orbital integral over general orbits with compactly supported continuous functions for a group G in is convergent. Moreover, it is essentially the limit of corresponding orbital integrals for its quotient groups in Harish-Chandra's class. Thus the study of orbital integrals for groups in class reduces to those of Harish-Chandra's class. The abstract theory for this limiting technique is developed in the general context of locally compact groups and linear functionals arising from orbital integrals. We point out that the abstract theory can be modified easily to include weighted orbital integrals as well. As an application of this limiting technique, we deduce the explicit Plancherel formula for any group in class . 相似文献
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Lubomir Gavrilov Iliya D. Iliev 《Journal of Mathematical Analysis and Applications》2009,357(1):69-1669
We study the stratum in the set of all quadratic differential systems , with a center, known as the codimension-four case Q4. It has a center and a node and a rational first integral. The limit cycles under small quadratic perturbations in the system are determined by the zeros of the first Poincaré-Pontryagin-Melnikov integral I. We show that the orbits of the unperturbed system are elliptic curves, and I is a complete elliptic integral. Then using Picard-Fuchs equations and the Petrov's method (based on the argument principle), we set an upper bound of eight for the number of limit cycles produced from the period annulus around the center. 相似文献
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Alex V. Kontorovich 《Journal of Number Theory》2006,117(1):1-13
For every positive integer n, the quantum integer [n]q is the polynomial [n]q=1+q+q2+?+qn-1. A quadratic addition rule for quantum integers consists of sequences of polynomials , , and such that for all m and n. This paper gives a complete classification of quadratic addition rules, and also considers sequences of polynomials that satisfy the associated functional equation . 相似文献
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Non-singular plane algebraic curves over with a Singer group of PGL(3,q) in their automorphism group are classified. Apart from three distinguished points, the set of -rational points of such curves can be partitioned into 2−(q2+q+1,q+1,1) designs each isomorphic to the finite projective plane . 相似文献
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In this paper we consider the stability of the inverse problem of determining a function q(x) in a wave equation in a bounded smooth domain in Rn from boundary observations. This information is enclosed in the hyperbolic (dynamic) Dirichlet-to-Neumann map associated to the solutions to the wave equation. We prove in the case of n?2 that q(x) is uniquely determined by the range restricted to a subboundary of the Dirichlet-to-Neumann map whose stability is a type of double logarithm. 相似文献
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