Related papers: A q-analogue of Wolstenholme's harmonic series con…

In this short note a new proof of the monotone con- vergence theorem of Lebesgue integral on \sigma-class is given.

The geometric realizations of Lusztig's symmetries of symmetrizable quantum groups are given in this paper. This construction is a generalization of that in [19].

This paper can be considered as an extension to our paper [On symplectically harmonic forms on six-dimensional nilmanifolds, Comment. Math. Helv. 76 (2001), n 1, 89-109]. Also, it contains a brief survey of recent results on symplectically…

We make some observation on the logarithmic version of K-stability.

We give a simple and a more explicit proof of a mod $4$ congruence for a series involving the little $q$-Jacobi polynomials which arose in a recent study of a certain restricted overpartition function.

We study the relationships among the various forms of the $q$ oscillator algebra and consider the conditions under which it supports a Hopf structure. We also present a generalization of this algebra together with its corresponding Hopf…

We obtain sufficient conditions ensuring the topological equivalence of two perturbed difference linear systems whose linear part has a property of generalized exponential dichotomy. When the exponential dichotomy is verified, we obtain a…

In this short paper we review and extract some features of the Fredholm Alternative problem .

We provide a simple proof that conformally semi-symmetric spacetimes are actually semi-symmetric. We also present a complete refined classification of the semi-symmetric spacetimes.

The aim of this paper is to present a general algebraic identity. Applying this identity, we provide several formulas involving the q-binomial coefficients and the q-harmonic numbers. We also recover some known identities including an…

We show various supercongruences for truncated series which involve central binomial coefficients and harmonic numbers. The corresponding infinite series are also evaluated.

A system of q-Painlev\'e type equations with multi-time variables t_1,...,t_M is obtained as a similarity reduction of the N-reduced q-KP hierarchy. This system has affine Weyl group symmetry of type A^{(1)}_{M-1} \times A^{(1)}_{N-1}. Its…

A method of computation of its terms is presented together with some stabilization results. As an application a characterization of symplectic harmonic manifolds is given and a relationship with the C-spectral sequence is indicated.

The analog of the Schauder inequality for closed surfaces in Euclidean spaces is obtained in this article.

We introduce a Zariskian analogue of the theory of Huber's adic spaces.

A complete p-adic Khintchine type theorem for approximation by p-adic algebraic numbers is established.

We prove an analog of Gromov--Lawson type relative index theorems for K-homology classes.

In this letter, the (q,h)-analogue of Newton's binomial formula is obtained in the (q,h)-deformed quantum plane which reduces for h=0 to the q-analogue. For (q=1,h=0), this is just the usual one as it should be. Moreover, the h-analogue is…

We prove some integral inequalities related to Feng Qi's inequality (2000) and obtain a few corollaries.

We settle in the affirmative the Graham-Sloane conjecture.