The Bose distribution for a gas of nonrelativistic free bosons is derived in the framework of qp-deformed second quantization. Some thermodynamical functions for such a system in D dimensions are derived. Bose-Einstein condensation is discussed in terms of the parameters q and p as well as a parameter ν ′ 0 which characterizes the representation space of the oscillator algebra. The Bose distrib...

conclusions we found that ei and qp/qs ratio are significantly and positively associated and qp/qs ratio can be easily estimated by measuring ei in secundum type asd patients. background one of the inclusion criteria for applying atrial septal defect (asd) closing procedure is an increased pulmonary-to-systemic blood flow ratio (qp/qs). eccentricity index (ei) is associated with ventricular dys...

We study the Selmer variety associated to a canonical quotient of the Qp-pro-unipotent fundamental group of a smooth projective curve of genus at least two defined over Q whose Jacobian decomposes into a product of abelian varieties with complex multiplication. Elementary multivariable Iwasawa theory is used to prove dimension bounds, which, in turn, lead to a new proof of Diophantine finitenes...

In this lecture we will describe our recent joint work with SimonBrendle ([1], [2]) in which we give the differentiable classification ofcompact Riemannian manifolds with pointwise 1/4-pinched curvature.Our theorems are:Theorem 1. Let M be a compact Riemannian manifold with pointwise1/4-pinched curvature. Then M admits a metric of constant curvature,and therefore is ...

Let 1 < p, q < ∞ and s, r ∈ R. It is proved that any function in the amalgam space W (H p′(R ), l∞), where p ′ is the conjugate exponent to p and H p′(R ) is the Bessel potential space, defines a bounded pointwise multiplication operator in the modulation space M p,q(R ), whenever r > |s|+ d.

A topological space X is a ΣΣ∗-space provided for every sequence 〈fn〉n=0 of continuous functions from X to R, if the series ∑∞ n=0 |fn| converges pointwise then it converges pseudo-normally. We show that every regular Lindelöf ΣΣ∗-space has Rothberger property. We also construct, under the continuum hypothesis, a ΣΣ∗-subset of R of cardinality continuum.

We give a detailed proof, in the case of one space dimension, of a pointwise upper estimate for the space gradient of a temperature. The operators involved are a one-sided Hardy-Littlewood maximal in time and the Calderón sharp maximal operator in space.

Let p be a prime, and let N be a positive integer coprime to p. Let Mk(Γ1(N);Qp) denote the weight k modular forms of level Γ1(N) defined overQp. In recent years, work of Coleman and others (for example [5],[6],[7],[8],[9]) has shown that a very profitable way of studying this finite-dimensional Qp-vector space is to choose a small positive rational number r and then to embed Mk(Γ1(N);Qp) into ...

We prove a characterization result in the spirit of the Kinderlehrer–Pedregal Theorem for Young measures generated by gradients of Sobolev maps satisfying the orientation-preserving constraint, that is the pointwise Jacobian is positive almost everywhere. The argument to construct the appropriate generating sequences from such Young measures is based on a variant of convex integration in conjun...