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61.
We consider semilinear Neumann equations with an indefinite and unbounded potential. We establish the existence and uniqueness of positive solutions. We show that our setting incorporates as special cases several parametric equations of interest (such as the equidiffusive logistic equation). 相似文献
62.
63.
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
64.
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
65.
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.
66.
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
67.
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
68.
Mourad E. H. Ismail 《The Ramanujan Journal》2006,11(3):349-353
We give short elementary proofs of a formula of Ramanujan as interpreted by Bradley, and a companion formula originally proved
by W. Chu. We also give an elementary proof of a generalization of an identity originally proved using modular functions and
used to study a generating function for the number of partitions with specified crank.
Research partially supported by NSF grant DMS 99-70865.
2000 Mathematics Subject Classification Primary—39A70, 11P83; Secondary—33C20 相似文献
69.
The fourth power mean of the general 2-dimensional Kloostermann sums mod <Emphasis Type="Italic">p</Emphasis> 下载免费PDF全文
The main purpose of this paper is using the analytic methods and the properties of Gauss sums to study the computational problem of one kind fourth power mean of the general 2-dimensional Kloostermann sums mod p, and give an exact computational formula for it. 相似文献
70.