Level -1/2 Realization of Quantum N-Toroidal Algebra in Type Cn

We construct a level -1/2 vertex representation of the quantum [Formula: see text]-toroidal algebra of type [Formula: see text], which is a natural generalization of the usual quantum toroidal algebra. The construction also provides a vertex representation of the quantum toroidal algebra for type [Formula: see text] as a by-product.

Systematic study of cluster radioactivity half-lives based on a modified Gamow-like model

In this study, taking into account of the contribution of the centrifugal potential on half-life and the effect of electrostatic shielding, we modify the Gamow-like model proposed by Zdeb et al. [Phys. Rev. C 87, 024308 (2013)] to systematically investigate the cluster radioactivity half-lives of nuclei ranging from 221Fr to 238U. The calculated results can reproduce the experimental data well. Additionally, this modified Gamow-like model is applied to predict the half-lives of cluster radioactivity nuclei whose experimental half-lives have the lower limit. It is found that the predicted results are in good agreement with the ones obtained by using the Gamow-like model and a Viola-Seaborg type formula.

Some BBP-type series for polylog integrals

An investigation into a family of definite integrals containing log-polylog functions will be undertaken in this paper. It will be shown that Euler sums play an important part in the solution of these integrals and may be represented as a BBP-type formula. In a special case we prove that the corresponding log integral can be represented as a linear combination of the product of zeta functions and the Dirichlet beta function.

Some Kazhdan–Lusztig Coefficients of Affine Weyl Group of Type B~ 2

Let [Formula: see text] be the affine Weyl group of type [Formula: see text], on which we consider the length function [Formula: see text] from [Formula: see text] to [Formula: see text] and the Bruhat order [Formula: see text]. For [Formula: see text] in [Formula: see text], let [Formula: see text] be the coefficient of [Formula: see text] in Kazhdan–Lusztig polynomial [Formula: see text]. We determine some [Formula: see text] for [Formula: see text] and [Formula: see text], where [Formula: see text] is the lowest two-sided cell of [Formula: see text] and [Formula: see text] is the higher one. Furthermore, we get some consequences using left or right strings and some properties of leading coefficients.

A Riemann–von Mangoldt-Type Formula for the Distribution of Beurling Primes

In this paper we work out a Riemann–von Mangoldt type formula for the summatory function := , where is an arithmetical semigroup (a Beurling generalized system of integers) and is the corresponding von Mangoldt function attaining with a prime element and zero otherwise. On the way towards this formula, we prove explicit estimates on the Beurling zeta function , belonging to , to the number of zeroes of in various regions, in particular within the critical strip where the analytic continuation exists, and to the magnitude of the logarithmic derivative of , under the sole additional assumption that Knopfmacher’s Axiom A is satisfied. We also construct a technically useful broken line contour to which the technic of integral transformation can be well applied. The whole work serves as a first step towards a further study of the distribution of zeros of the Beurling zeta function, providing appropriate zero density and zero clustering estimates, to be presented in the continuation of this paper.

A note on degenerate generalized Laguerre polynomials and Lah numbers

The aim of this paper is to introduce the degenerate generalized Laguerre polynomials as the degenerate version of the generalized Laguerre polynomials and to derive some properties related to those polynomials and Lah numbers, including an explicit expression, a Rodrigues type formula, and expressions for the derivatives. The novelty of the present paper is that it is the first paper on degenerate versions of orthogonal polynomials.

Approximation by Bézier Variant of Baskakov-Durrmeyer-Type Hybrid Operators

We give a Bézier variant of Baskakov-Durrmeyer-type hybrid operators in the present article. First, we obtain the rate of convergence by using Ditzian-Totik modulus of smoothness and also for a class of Lipschitz function. Then, weighted modulus of continuity is investigated too. We study the rate of point-wise convergence for the functions having a derivative of bounded variation. Furthermore, we establish the quantitative Voronovskaja-type formula in terms of Ditzian-Totik modulus of smoothness at the end.

Singular nonsymmetric Jack polynomials for some trapeziform tableaux

Let [Formula: see text] be symmetric group of degree [Formula: see text]. In the representation of [Formula: see text] corresponding to trapeziform partition (precisely [Formula: see text], [Formula: see text]), we propose nonsymmetric Jack polynomials in [Formula: see text] variables which are singular at [Formula: see text]. Moreover those nonsymmetric Jack polynomials span a module of [Formula: see text] which is isomorphic to the representation of type [Formula: see text].