Using the theory of orthogonal polynomials, their associated recursion relations and differential formulas we develop a new method for evaluating integrals that include orthogonal polynomials. The method is illustrated by obtaining the following integral result that involves the Bessel function and associated Laguerre polynomial: integral(infinity)(0) x(v)e(-x/2) J(v)(mu x)L-n(2v)(x)dx = 2(v)Ga...

Background: Previous studies have reported anomalous resting brain activity in the electroencephalogram (EEG) of alcoholics, often reflected as increased power in the beta and theta frequency bands. The effects of binge drinking, the most common pattern of excessive alcohol consumption during adolescence and youth, on brain activity at rest is still poorly known. In this study, we sought to ass...

1. Overview of the Madelung Problem 2. Analytic Consequences of the Andrews Identity 3. Connection with Multiple Zeta Sums 4. An -Series for M(s) 5. Integral Representations for the Madelung Constant 6. Number-Theoretical Implications: Sums of Three Squares 7. Open Problems Acknowledgments References From a modern theta-function identity of G. E. Andrews we derive new representations for the ce...

We examined the adjustment of leaf angle (L theta) and foliar chlorophyll and xanthophyll chemistry in Eucalyptus nitens (Deane and Maiden) Maiden seedlings maintained in various nitrogen (N)-supply treatments over a 6-month period. Adjustment of L theta toward the vertical was greatest under conditions of foliar N deficiency and became incrementally more horizontal with increasing foliar N con...

The government organizations in Africa, Asia and South America are adopting OSS solutions because of its low cost and availability of cheap skilled programmers in their countries to customize the software to their needs. In a study conducted to track the usage of OSS, it was found that OSS is extensively promoted in countries like India, China and Taiwan followed by South Korea, Malaysia, Singa...

The firing characteristics of 1437 CA1 pyramidal neurons were studied in relation to both spatial location and the phase of the theta rhythm in healthy young and old rats performing a simple spatial task on a rectangular track. The old rats had previously been found to be deficient on the Morris spatial learning task. Age effects on the theta rhythm per se were minimal. Theta amplitude and freq...

EEG correlates of mathematical and trait anxiety level were studied in 52 healthy Russian-speakers during execution of error-recognition tasks with lexical, arithmetic and algebraic conditions. Event-related spectral perturbations were used as a measure of brain activity. The ERSP plots revealed alpha/beta desynchronizations within a 500-3000 ms interval after task onset and slow-wave synchroni...

An edge-labeling f of a graph G is an injection from E(G) to the set of integers. The edge-bandwidth of G is B 0 (G) = min f fB 0 (f)g, where B 0 (f) is the maximum diierence between labels of incident edges of G. The m-theta graph (l 1 ; : : : ; l m g is the graph consisting of m pairwise internally disjoint paths with common endpoints and lengths l 1 l m. We determine the edge-bandwidth of al...

Abstract Fefferman (Acta Math 24:9–36, 1970, Theorem 2 $$'$$ ′ ) has proved the weak (1,1) boundedness for a class of oscillating singular integrals that includes spectral multipliers Euclidean Laplacian $$\Delta ,$$ Δ , </mml:mr...

In this thesis, we formulate and partially prove conjectures à la MazurTate for two cases of L-functions. Suppose given a L-function L(M,K, s) attached to an arithmetic object M over a number field K (a “motive”) so that L can be twisted by characters of the Galois group G of an extension of K. To this pair (L,G), one may hope to associate a theta element Θ(L,G) ∈ A[G], where A is a well define...