A generalized Riemann- Stieltjes integral on time scales and discontinuous dynamical equations

This paper is concerned with a generalization of the Riemann- Stieltjes integral on time scales for deal with some aspects of discontinuous dynamic equations in which Riemann-Stieltjes integral does not works. © 2011 Academic Publications.

On Li’s Coefficients for Some Classes of L-Functions

AMS Subj. Classification: 11M41, 11M26, 11S40

Class Number Two for Real Quadratic Fields of Richaud-Degert Type

2000 Mathematics Subject Classification: Primary: 11D09, 11A55, 11C08, 11R11, 11R29; Secondary: 11R65, 11S40; 11R09.

RIEMANN ZETA ZEROS AND PRIME NUMBER SPECTRA IN QUANTUM FIELD THEORY

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Teorema de Riemann-Roch, morfismos de Frobenius e a hipótese de Riemann

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Generalized Fractional Evolution Equation

2000 Mathematics Subject Classification: Primary 46F25, 26A33; Secondary: 46G20

On-line processing of wh-questions in children with G-SLI and typically developing children

Background: The computational grammatical complexity ( CGC) hypothesis claims that children with G(rammatical)-specific language impairment ( SLI) have a domain-specific deficit in the computational system affecting syntactic dependencies involving 'movement'. One type of such syntactic dependencies is filler-gap dependencies. In contrast, the Generalized Slowing Hypothesis claims that SLI children have a domain-general deficit affecting processing speed and capacity. Aims: To test contrasting accounts of SLI we investigate processing of syntactic (filler-gap) dependencies in wh-questions. Methods & Procedures: Fourteen 10; 2 - 17; 2 G-SLI children, 14 age- matched and 17 vocabulary-matched controls were studied using the cross- modal picturepriming paradigm. Outcomes & Results: G-SLI children's processing speed was significantly slower than the age controls, but not younger vocabulary controls. The G- SLI children and vocabulary controls did not differ on memory span. However, the typically developing and G-SLI children showed a qualitatively different processing pattern. The age and vocabulary controls showed priming at the gap, indicating that they process wh-questions through syntactic filler-gap dependencies. In contrast, G-SLI children showed priming only at the verb. Conclusions: The findings indicate that G-SLI children fail to establish reliably a syntactic filler- gap dependency and instead interpret wh-questions via lexical thematic information. These data challenge the Generalized Slowing Hypothesis account, but support the CGC hypothesis, according to which G-SLI children have a particular deficit in the computational system affecting syntactic dependencies involving 'movement'. As effective remediation often depends on aetiological insight, the discovery of the nature of the syntactic deficit, along side a possible compensatory use of semantics to facilitate sentence processing, can be used to direct therapy. However, the therapeutic strategy to be used, and whether such similar strengths and weaknesses within the language system are found in other SLI subgroups are empirical issues that warrant further research.

Abelian torsion groups with a countably compact group topology

Comfort and Remus [W.W. Comfort, D. Remus, Abelian torsion groups with a pseudo-compact group topology, Forum Math. 6 (3) (1994) 323-337] characterized algebraically the Abelian torsion groups that admit a pseudocompact group topology using the Ulm-Kaplansky invariants. We show, under a condition weaker than the Generalized Continuum Hypothesis, that an Abelian torsion group (of any cardinality) admits a pseudocompact group topology if and only if it admits a countably compact group topology. Dikranjan and Tkachenko [D. Dikranjan. M. Tkachenko, Algebraic structure of small countably compact Abelian groups, Forum Math. 15 (6) (2003) 811-837], and Dikranjan and Shakhmatov [D. Dikranjan. D. Shakhmatov, Forcing hereditarily separable compact-like group topologies on Abelian groups, Topology Appl. 151 (1-3) (2005) 2-54] showed this equivalence for groups of cardinality not greater than 2(c). We also show, from the existence of a selective ultrafilter, that there are countably compact groups without non-trivial convergent sequences of cardinality kappa(omega), for any infinite cardinal kappa. In particular, it is consistent that for every cardinal kappa there are countably compact groups without non-trivial convergent sequences whose weight lambda has countable cofinality and lambda > kappa. (C) 2009 Elsevier B.V. All rights reserved.

Conjectures and theorems in the theory of entire functions

Motivated by the recent solution of Karlin's conjecture, properties of functions in the Laguerre-Polya class are investigated. The main result of this paper establishes new moment inequalities fur a class of entire functions represented by Fourier transforms. The paper concludes with several conjectures and open problems involving the Laguerre-Polya class and the Riemann xi -function.

Higher order turän inequalities

The celebrated Turân inequalities P 2 n(x)-P n-x(x)P n+1(x) ≥ 0, x ε[-1,1], n ≥ 1, where P n(x) denotes the Legendre polynomial of degree n, are extended to inequalities for sums of products of four classical orthogonal polynomials. The proof is based on an extension of the inequalities γ 2 n - γ n-1γ n+1 ≥ 0, n ≥ 1, which hold for the Maclaurin coefficients of the real entire function ψ in the Laguerre-Pölya class, ψ(x) = ∑ ∞ n=0 γ nx n / n!. ©1998 American Mathematical Society.

Integral Transforms Method to Solve a Time-Space Fractional Diffusion Equation

Mathematical Subject Classification 2010: 35R11, 42A38, 26A33, 33E12.

Maximum Principle and Its Application for the Time-Fractional Diffusion Equations

MSC 2010: 26A33, 33E12, 35B45, 35B50, 35K99, 45K05 Dedicated to Professor Rudolf Gorenflo on the occasion of his 80th anniversary

Second Order Optimality Conditions in Nonsmooth Unconstrained Optimization

AMS subject classification: 49J52, 90C30.

Almost Disjoint Families of Representing Sets

The thesis is concerned with a number of problems in Combinatorial Set Theory. The Generalized Continuum Hypothesis is assumed. Suppose X and K are non-zero cardinals. By successively identifying K with airwise disjoint sets of power K, a function/: X-*•K can be viewed as a transversal of a pairwise disjoint (X, K)family A . Questions about families of functions in K can thus bethought of as referring to families of transversals of A. We wish to consider generalizations of such questions to almost disjoint families; in particular we are interested in extensions of the following two problems: (i) What is the 'maximum' cardinality of an almost disjoint family of functions each mapping X into K? (ii) Describe the cardinalities of maximal almost disjoint families of functions each mapping X into K. Article in Bulletin of the Australian Mathematical Society 27(03):477 - 479 · June 1983