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Zeta Functions and the Log-behavior of Combinatorial Sequences
log-convexity Riemann zeta function Bernoulli number Bell number Bessel zeta function Narayana number Hö lder's inequality
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2014/6/3
In this paper, we use the Riemann zeta function ζ(x) and the Bessel zeta function ζμ(x) to study the log-behavior of combinatorial sequences. We prove that ζ(x) is log-convex for x>1. As a consequence...
Congruences of Multipartition Functions Modulo Powers of Primes
modular form partition multipartition Ramanujan-type congruence
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2014/6/3
Let pr(n) denote the number of r-component multipartitions of n, and let Sγ λ be the space spanned by η(24z)γφ(24z), where η(z) is the Dedekind’s eta function and η(z) is a holomorphic modular form i...
Proof of a Positivity Conjecture on Schur Functions
symmetric function Schur function multiplier sequence totally positive sequence
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2014/6/3
In the study of Zeilberger's conjecture on an integer sequence related to the Catalan numbers, Lassalle proposed the following conjecture. Let (t)n denote the rising factorial, and let ΛR denote the a...
Partition Identities for Ramanujan's Third Order Mock Theta Functions
mock theta function Ramanujan's identities partition identity Fine's theorem involution
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2014/6/3
We find two involutions on partitions that lead to partition identities for Ramanujan's third order mock theta functions φ(-q) and ψ(-q). We also give an involution for Fine's partition identity on th...
Perturbations and operator trace functions
Perturbations operator trace functions
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2011/2/21
We study the spectral functional A 7→ Tr f(D + A) for a suitable function f, a self-adjoint operator D having compact resolvent, and a certain class of bounded self-adjoint operators A.
Properties of harmonic meromorphic functions which are starlike of complex order with respect to conjugate points
harmonic meromorphic
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2010/11/1
This paper defines and investigates a class of meromorphic univalent harmonic functions that are starlike of complex order with respect to conjugate points. The authors obtain convolution and convex c...
On certain subclass of harmonic univalent functions defined by a generalized Ruscheweyh derivatives operator
Harmonic univalent functions Ruscheweyh derivative
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2010/9/20
In this paper, the class SH(α, β; n, λ) of univalent harmonic and sense-preserving mappings in the unit disk is introduced. The distortion inequalities and extreme points for functions in the class SH...
Paths of inner-related functions
Paths inner-related functions
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2011/2/24
We characterize the connected components of the subset CN∗ of H∞ formed by the products bh, where b is Carleson-Newman Blaschke product and h ∈ H∞ is an inver-tible function.
Notes about extended real- and set-valued functions
extended real- set-valued functions
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2010/11/19
An order theoretic and algebraic framework for the extended real numbers is established which includes extensions of the usual difference to expressions involving $-\infty$ and/or $+\infty$, so-calle...
The Spin-weighted Spheroidal Wave functions in the Case of s=1/2
Wave functions Mathematical Physics
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2010/11/18
The spin-weighted spheroidal equations in the case s=1/2 is thoroughly studied in the paper by means of the perturbation method in supersymmetry quantum mechanics. The first-five terms of the super-p...
Length Functions for Semigroup Embeddings
Membership problem Word problem Embeddings of Semigroups
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2010/12/6
Following the work done in [O] for groups, we describe, for a given semigroup S, which functions l : S → N can be realized up to equivalence as length functions g 7→ |g|H by embedding S into a finitel...
Multivalent meromorphic starlike functions with negative coefficients
Meromorphic Starlike Negative Coefficients
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2010/9/13
Coefficient inequalities, distortion theorems and class preserving integral operators are obtained for p-valent meromorphic starlike functions of order α (0 ≤ α < p) with negative coefficients.
On fuzzy topological ring valued fuzzy continuous functions
fuzzy topological ring (FTR) fuzzy ideal
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2010/9/13
The collection of all fuzzy continuous functions from a fts Y to a fuzzy topological ring (in short, FTR) Z, denoted by FC(Y,Z) induces a ring structure from that of Z. This paper explores the structu...
Kernels for products of L-functions
Kernels products of L-functions
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2010/11/30
The Rankin-Cohen bracket of two Eisenstein series provides a kernel yielding products of the
periods of Hecke eigenforms at critical values. Extending this idea leads to a new type of Eisenstein seri...
Further Notes on a Family of Continuous, Non-differentiable Functions
continuous nowhere di erentiable fractal Hausdor dimension
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2011/2/23
We examine a parametrized family of functions Fa, all of which are continuous and some of which are nowhere or almost nowhere di erentiable.