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The paper summarizes recent advances in the theory of geometric stable (GS) distributions. The results presented include parametrizations, characterizations, mixture representations, properties, asymptotic and convergent series expansions of densities and distribution functions, moments and tail behavior, simulation, and estimation. 相似文献
64.
In this paper, we establish some differential identities and obtain some Sturm comparison theorems for the second order nonlinear differential equation by using them.and generalize some classicial Sturm comparison theorems. 相似文献
65.
Hsien-Chung Wu 《Applications of Mathematics》2007,52(1):1-23
The procedures for constructing a fuzzy number and a fuzzy-valued function from a family of closed intervals and two families
of real-valued functions, respectively, are proposed in this paper. The constructive methodology follows from the form of
the well-known “Resolution Identity” (decomposition theorem) in fuzzy sets theory. The fuzzy-valued measure is also proposed
by introducing the notion of convergence for a sequence of fuzzy numbers. Under this setting, we develop the fuzzy-valued
integral of fuzzy-valued function with respect to fuzzy-valued measure. Finally, we provide a Dominated Convergence Theorem
for fuzzy-valued integrals. 相似文献
66.
Applications of residues to combinatorial identities 总被引:1,自引:0,他引:1
I-Chiau Huang 《Proceedings of the American Mathematical Society》1997,125(4):1011-1017
A concrete aspect of Grothendieck Duality is used to give local cohomology proofs of combinatorial identities including MacMahon's master theorem, Grosswald identity, identity of Shoo, Tepper identity, and others.
67.
Tran Dan Thu 《Journal of Combinatorial Theory, Series A》2007,114(8):1504-1514
The powerful AZ identity is a sharpening of the famous LYM-inequality. More generally, Ahlswede and Zhang discovered a generalization in which the Bollobás inequality for two set families can be lifted to an identity.In this paper, we show another generalization of the AZ identity. The new identity implies an identity which characterizes the deficiency of the Bollobás inequality for an intersecting Sperner family. We also give some consequences relating to Helly families and LYM-style inequalities. 相似文献
68.
本文研究了非自伴Dirac算子的一般两点边值问题的渐近迹,首先运用平移算子得到了其Cauchy问题解的渐近式,并由此及边界条件,构造了整函数ω(λ),利用它将边界条件分为八种基本类型,最后采用留数的方法,得到了四种主要类型的特征值的渐近迹公式。 相似文献
69.
Volker Runde 《Journal of Mathematical Analysis and Applications》2007,329(1):736-751
Let G be a locally compact group, and let R(G) denote the ring of subsets of G generated by the left cosets of open subsets of G. The Cohen-Host idempotent theorem asserts that a set lies in R(G) if and only if its indicator function is a coefficient function of a unitary representation of G on some Hilbert space. We prove related results for representations of G on certain Banach spaces. We apply our Cohen-Host type theorems to the study of the Figà-Talamanca-Herz algebras Ap(G) with p∈(1,∞). For arbitrary G, we characterize those closed ideals of Ap(G) that have an approximate identity bounded by 1 in terms of their hulls. Furthermore, we characterize those G such that Ap(G) is 1-amenable for some—and, equivalently, for all—p∈(1,∞): these are precisely the abelian groups. 相似文献
70.
Three proofs are given for a reciprocity theorem for a certain q-series found in Ramanujan’s lost notebook. The first proof uses Ramanujan’s 1ψ1 summation theorem, the second employs an identity of N. J. Fine, and the third is combinatorial. Next, we show that the reciprocity
theorem leads to a two variable generalization of the quintuple product identity. The paper concludes with an application
to sums of three squares.
Dedicated to Richard Askey on the occasion of his 70th birthday.
2000 Mathematics Subject Classification Primary—33D15
B. C. Berndt: Research partially supported by grant MDA904-00-1-0015 from the National Security Agency.
A. J. Yee: Research partially supported by a grant from The Number Theory Foundation. 相似文献