Order statistics arising from exponentiated gamma (EG) distribution are considered. Closed from expressions for the single and double moments of order statistics are derived. Measures of skewness and kurtosis of the probability density function of the rth order statistic for different choices of r, n and /theta are presented. Recurrence relations between single and double moments of r...

A new implementation for the computation of the Riemann theta function in the open-source mathematical software Sage is discussed. This implementation is used in two applications. The first is the computation of three-phase solutions of the Kadomtsev-Petviashvili equation using an algorithm due to Dubrovin [11], originally implemented by Dubrovin, Flickinger, and Segur [12]. Our implementation ...

The Riemann theta function is a complex-valued function of g complex variables. It appears in the construction of many (quasi-)periodic solutions of various equations of mathematical physics. In this paper, algorithms for its computation are given. First, a formula is derived allowing the pointwise approximation of Riemann theta functions, with arbitrary, user-specified precision. This formula ...

In his famous "deathbed" letter, Ramanujan "defined" the notion of a mock theta function and offered some examples of functions he believed satisfied his definition. Very recently, Griffin et al. established for the first time that Ramanujan's mock theta functions actually satisfy his own definition. On the other hand, Zwegers' 2002 doctoral thesis [Zwegers S (2002) Mock theta functions. PhD th...

Nucleon structure functions are shown to have a qualitative (or ‘formal’) relation to the classical elliptic theta functions. In particular, θ 1/2 shows a clear resemblance to a non-singlet structure function like xF3. In the appropriate range, the Q2-dependence of the moments of θ 1/2 is in near-quantitative agreement with QCD, and at low-Q2 the moments converge to a common value, as observed ...

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...

We develop the theory of the tempered anabelian and Frobenioid-theoretic aspects of the “étale theta function”, i.e., the Kummer class of the classical formal algebraic theta function associated to a Tate curve over a nonarchimedean local field. In particular, we consider a certain natural “environment” for the study of the étale theta function, which we refer to as a “mono-theta environment”, ...

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...

for any lacunary sequence $theta = (k_{r})$, we define the concepts of $s_{theta}-$limit point and $s_{theta}-$cluster point of a sequence of fuzzy numbers $x = (x_{k})$. we introduce the new sets  $lambda^{f}_{s_{theta}}(x)$, $gamma^{f}_{s_{theta}}(x)$ and prove some inclusion relaions between these and the sets $lambda^{f}_{s}(x)$, $gamma^{f}_{s}(x)$ introduced in ~cite{ayt:slpsfn} by aytar [...

Previous studies indicate that 11,12,15-trihydroxyeicosatrienoic acid (11,12,15-THETA), an endothelium-derived hyperpolarizing factor in the rabbit aorta, mediates a portion of the relaxation response to acetylcholine by sequential metabolism of arachidonic acid by 15-lipoxygenase, hydroperoxide isomerase, and epoxide hydrolase. To determine the stereochemical configuration of the endothelial 1...