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Abstract: In the paper, the author establishes several integral representations and properties of Stirling numbers of the first kind. [Copyright &y& Elsevier]

Abstract: We prove an extension of the Ocone–Karatzas integral representation, valid for all functions on the classical Wiener space. We also establish an elementary chain rule formula and combine the two results to compute explicit integral representations for some classes of composite random variables. [Copyright &y& Elsevier]

We obtain an integral representation of even functions of two variables for which the kernel [ k( x + y) + k( x − y)], x, y ∈ R, is positive definite. [ABSTRACT FROM AUTHOR]

Let F be a finite extension of ℚ. Using the mod p Satake transform, we define what it means for an irreducible admissible smooth representation of an F-split p-adic reductive group over $\overline{ \mathbb{F}}_{p}$ to be supersingular. We then give the classification of irreducible admissible smooth GL( F)-representations over $\overline{ \mathbb{F}}_{p}$ in terms of supersingular representations. As a consequence we deduce that supersingular is the same as supercuspidal. These results generalise the work of Barthel-Livné for n=2. For general split reductive groups we obtain similar results under stronger hypotheses. [ABSTRACT FROM AUTHOR]

Abstract: The main object of this paper is to investigate several general families of hypergeometric polynomials and their associated multiple integral representations. By suitably specializing our main results, the corresponding integral representations are deduced for such familiar classes of hypergeometric polynomials as (for example) the generalized Bedient polynomials and the generalized Cesàro polynomials. Each of the integral representations, which are derived in this paper, may be viewed also as a linearization relationship for the product of two different members of the associated family of hypergeometric polynomials. [Copyright &y& Elsevier]

The field scattered by a plane composed of several homogenous layers on a perfectly reflecting plane is generally given by its plane wave expansion (Fourier representation). We here develop another approach to express the field, more suitable for point source illumination. For this, we sum the contributions of modes corresponding to zeros gj (or poles – gj) of the reflection coefficient of the imperfectly reflecting surface, developing an original integral representation and its expansions, valid for arbitrary mode which can be passive or active. Particular attention has been paid to active modes with Regj < 0, and to the vicinity of the mode with gj = – 1. We then obtain novel exact expressions for the field in acoustics and for potentials in electromagnetism. [ABSTRACT FROM PUBLISHER]

A numerical algorithm for calculating the generalized Mittag-Leffler Eα,≈(z) function for arbitrary complex argument z and real parameters α > 0 and β ϵ ℝ is presented. The algorithm uses the Taylor series, the exponentially improved asymptotic series, and integral representations to obtain optimal stability and accuracy of the algorithm. Special care is applied to the limits of validity of the different schemes to avoid instabilities in the algorithm. [ABSTRACT FROM AUTHOR]

Abstract: In this article, we study the semigroup approach for the mathematical analysis of the inverse coefficient problems of identifying the unknown coefficient in the linear parabolic equation , with Dirichlet boundary conditions , . Main goal of this study is to investigate the distinguishability of the input–output mappings , via semigroup theory. In this paper, we show that if the null space of the semigroup consists of only zero function, then the input–output mappings and have the distinguishability property. Moreover, the values and of the unknown diffusion coefficient at and , respectively, can be determined explicitly by making use of measured output data (boundary observations) or/and . In addition to these, the values and of the unknown coefficient at and , respectively, are also determined via the input data. Furthermore, it is shown that measured output data and can be determined analytically, by an integral representation. Hence the input–output mappings , are given explicitly in terms of the semigroup. Finally by using all these results, we construct the local representations of the unknown coefficient at the end points and . [Copyright &y& Elsevier]

We investigate the class of ±1 polynomials evaluated at q defined as: A(q) = {ϵ0 + ϵ1q + … + ϵmqm : ϵi Є {-1, 1}} and usually called spectrum, and show that, if q is the root of the polynomial xn - xn-1 - … - xk+1 + xk + xk-1 + … + x + 1 between 1 and 2, and n > 2k + 3, then A(q) is discrete, which means that it does not have any accumulation points. [ABSTRACT FROM AUTHOR]

An integral representation formula in terms of the normal Gauss map for minimal surfaces in the 3-dimensional Heisenberg group with canonical left invariant metric is obtained. [ABSTRACT FROM AUTHOR]

Functions of several octonion variables are investigated and integral representation theorems for them are proved. By using these theorems, solutions of $$\tilde \partial - equations$$ are studied. More generally, functions of several Cayley-Dickson variables are considered. Integral formulas of the Martinelli-Bochner, Leray, and Koppelman type used in complex analysis are proved in a new generalized form for functions of Cayley-Dickson variables instead of complex variables. Moreover, analogues of Stein manifolds over Cayley-Dickson graded algebras are defined and investigated. [ABSTRACT FROM AUTHOR]

Let the integers 1, . . . , n be assigned colors. Szemerédi's theorem implies that if there is a dense color class then there is an arithmetic progression of length three in that color. We study the conditions on the color classes forcing totally multicolored arithmetic progressions of length 3. Let f( n) be the smallest integer k such that there is a coloring of {1, . . . , n} without totally multicolored arithmetic progressions of length three and such that each color appears on at most k integers. We provide an exact value for f( n) when n is sufficiently large, and all extremal colorings. In particular, we show that f( n)=8 n/17+ O(1). This completely answers a question of Alon, Caro and Tuza. [ABSTRACT FROM AUTHOR]

This correspondence presents two variable-rate encoding algorithms that achieve capacity for the (d, k) constraint when k = 2d + 1, or when k - d + 1 is not prime. The first algorithm, symbol sliding, is a generalized version of the bit flipping algorithm introduced by Aviran et al. In addition in achieving capacity for (d, 2d + 1) constraints, it comes close to capacity in other cases. The second algorithm is based on interleaving and is a generalized version of the bit stuffing algorithm introduced by Bender and Wolf. This method uses fewer than k - d biased bit streams to achieve capacity for (d, k) constraints with k - d + 1 not prime. In particular, the encoder for (d, d + 2m - 1) constraints 2 ≤ m < ∞ requires only m biased bit streams. [ABSTRACT FROM AUTHOR]

We study the generating function of rooted and unrooted hyperforests in a general complete hypergraph with n vertices by using a novel Grassmann representation of their generating functions. We show that this new approach encodes the known results about the exponential generating functions for the different number of vertices. We also consider some applications, such as counting hyperforests in the k-uniform complete hypergraph and the one complete in hyperedges of all dimensions. Some general features of the asymptotic regimes for a large number of connected components are discussed. [ABSTRACT FROM AUTHOR]