Related papers: A q-analogue of Wolstenholme's harmonic series con…
We analyse an analog of the entropy-power inequality for the weighted entropy.
We show that Genocchi and Bernoulli numbers are closely related to Fibonacci polynomials and derive some q-analogues.
We extend the definition of Lagrangian quantum homology to monotone Lagrangian cobordism and establish its general algebraic properties. In particular we develop a relative version of Lagrangian quantum homology associated to a cobordism…
We compute asymptotic series for Hofstadter's figure-figure sequences.
An technically interesting proof of a known theorem.
We provide several new $q$-congruences for truncated basic hypergeometric series, mostly of arbitrary order. Our results include congruences modulo the square or the cube of a cyclotomic polynomial, and in some instances, parametric…
In this paper, new inequalities connected with the celebrated Steffensen's integral inequality are proved.
In this paper we prove a compactness theorem for a sequence of harmonic maps which are defined on a converging sequence of Riemannian manifolds.
We study a class of q-analogues of multiple zeta values given by certain formal q-series with rational coefficients. After introducing a notion of weight and depth for these q-analogues of multiple zeta values we present dimension…
We introduce an L-series associated with harmonic Maass forms and prove their functional equations. We establish converse theorems for these L-series and, as an application, we formulate and prove a summation formula for the holomorphic…
In this article we give a result obtained of an experimental way for the Euler totient function.
We present full classification of Q-conditional symmetries for the two-dimensional nonlinear wave equation.
We evaluate binomial series with harmonic number coefficients, providing recursion relations, integral representations, and several examples. The results are of interest to analytic number theory, the analysis of algorithms, and…
An interplay between the sum of certain series related to Harmonic numbers and certain finite trigonometric sums is investigated. This allows us to express the sum of these series in terms of the considered trigonometric sums, and permits…
We present numerical evidence that a simple variational improvement of the ordinary perturbation theory of the quantum anharmonic oscillator can give a convergent sequence of approximations even in the extreme strong coupling limit, the…
In this paper we discuss an analogue of the Kac-Weisfeiler conjecture for a certain class of almost commutative algebras. In particular, we prove the Kac-Weisfeiler type statement for rational Cherednik algebras.
We define the $(q,\bar{\boldsymbol{\alpha}})$-Whitney numbers which are reduced to the $\bar{\boldsymbol{\alpha}}$-Whitney numbers when $q\rightarrow1$. Moreover, we obtain several properties of these numbers such as explicit formulas,…
We consider a $q$-analogue of abstract simplicial complexes, called $q$-complexes, and discuss the notion of shellability for such complexes. It is shown that $q$-complexes formed by independent subspaces of a $q$-matroid are shellable.…
In this paper, we study some symmetric identities of q-Euler numbers and polynomials. From these properties, we derive several identities of q-Euler numbers and polynomials.
In this paper, we describe a congruence property of solvable polynomials with coefficients in the Gaussian field Q(i).