Related papers: Some symmetric $q$-congruences
Using Eulerian and Euler numbers, we establish congruences concerning sums involving harmonic numbers, tangent numbers and Genocchi numbers.
Comments are made on some recently published papers on matter collineations of plane symmetric, cylindrically symmetric and spherically symmetric spacetimes.
We give an explicit formulae for obtaining the translation symmetries in the cartesian product $X^N$, where $N$ is some positive integer and $X$ is some finite set. Moreover, we obtain some fundamental results from elementary number theory.
We show that a proof in multiplicative linear logic can be represented as a decorated surface, such that two proofs are logically equivalent just when their surfaces are geometrically equivalent. This is an extended abstract for…
We treat interpolation for various logics.
According to the $q$-series method, a short proof for Hou and Sun's identity, which is the $q$-analogue of a known $\pi$-formula, is offered. Furthermore, $q$-analogues of several other $\pi$-formulas are also established in terms of the…
We present a new and useful congruence identity satisfied by m-permutable varieties.
We examine $q-$series related to higher forms. These forms are cubics, quartics, etc. In some points, in the article we add parts from previous works, in such a way, the article be more complete and readable.
This proves Kontsevich's mirror conjecture for (on the symplectic side) a quartic surface in P^3.
We prove a stability theorem for families of holomorphically-parallelizable manifolds in the category of Hermitian manifolds.
We prove some isomorphisms between exceptional W-algebras associated with exceptional simple Lie algebras.
We prove two single-parameter q-supercongruences which were recently conjectured by Guo, and establish their further extensions with one more parameter. Crucial ingredients in the proof are the terminating form of q-binomial theorem and a…
Proofs that a smooth morphism is flat available in the literature are long and difficult. We give a short proof of this fact.
We obtain a presentation of certain affine q-Schur algebras in terms of generators and relations. The presentation is obtained by adding more relations to the usual presentation of the quantized enveloping algebra of type affine gl_n. Our…
The method of numerical symmetrization of state of identical particles proposed by us before is clarified and discussed.
We prove a result on the existence of linear forms of a given Diophantine type.
We review some convexity inequalities for Hermitian matrices an add one more to the list.
We give the q-analogue of the sums of the n-th powers of positive integers up to k-1.
We compare the geometrical and physical properties of the maths-type coherent states for $q>1$ with those of the same for $0 < q < 1$.
We give a rigorous proof for the linear stability of the Skyrmion. In addition, we provide new proofs for the existence of the Skyrmion and the GGMT bound.