Related papers: Examples Concerning Abelian and Cesaro Limits

We formulate uncertainty relations for arbitrary $N$ observables. Two uncertainty inequalities are presented in terms of the sum of variances and standard deviations, respectively. The lower bounds of the corresponding sum uncertainty…

In this paper we develop a technique to extend any bound for cyclic codes constructed from its defining sets (ds-bounds) to abelian (or multivariate) codes. We use this technique to improve the searching of new bounds for abelian codes.

We present upper bounds on certain sums which are related to Artin's primitive root conjecture and are also used in counting ray class characters.

We shall study the existence of almost split sequences in tri-exact categories, that is, extension-closed subcategories of triangulated categories. Our results unify and extend the existence theorems for almost split sequences in abelian…

In this paper we present many congruences for several Ap\'ery-like sequences.

Easily computable lower and upper bounds are found for the sum of Catalan numbers. The lower bound is proven to be tighter than the upper bound, which previously was declared to be only an asymptotic. The average of these bounds is proven…

In this talk I first review at an elementary level a selection of central limit theorems, including some lesser known cases, for sums and maxima of uncorrelated and correlated random variables. I recall why several of them appear in…

We obtain large and moderate deviation estimates, as well as concentration inequalities, for a class of nonuniformly expanding maps with stretched exponential decay of correlations. In the large deviation regime, we also exhibit examples…

We give optimal estimates on the variation of the differential and modular heights within an isogeny class of abelian varieties defined over the function field of a curve (in any characteristic). We also prove a parallelogram inequality for…

The aim of this paper is first to give necessary and sufficient condition of existence (of free boundaries) for both Laplacian and bi-Laplacian operators in the case where the overdetermined condition is not constant. second, by using some…

We describe a large-scale computational experiment to study structure in the numbers of real solutions to osculating instances of Schubert problems. This investigation uncovered Schubert problems whose computed numbers of real solutions…

We derive upper and lower bounds on the determinant of an exponential matrix. They can be transformed into corresponding bounds for the determinant of a univariate Gaussian matrix.

Bayesian model comparison requires the specification of a prior distribution on the parameter space of each candidate model. In this connection two concerns arise: on the one hand the elicitation task rapidly becomes prohibitive as the…

For a general family of non-negative functions matching upper and lower bounds are established for their average over the values of any equidistributed sequence.

The limit of a sequence by the definition with $\varepsilon$ is introduced by the notion of checkmate in two moves. The idea is also extended to define the limit of a function with $\varepsilon$ and $\delta$.

There are versions of "calculus" in many settings, with various mixtures of algebra and analysis. In these informal notes we consider a few examples that suggest a lot of interesting questions.

Asymptotic behavior of the point process of high and medium values of a Gaussian stationary process with discrete time is considered. An approximation by a Poisson cluster point process is given for the point process.

We to a large extent sort out when does a (first order complete theory) T have a superlimit model in a cardinal lambda . Also we deal with relation notions of being limit.

In this article we introduce the concept of almost $\mathcal{P}$-numbers. We survey the existing results in literature for almost cyclic numbers and give characterizations for almost abelian and almost nilpotent numbers proving these two…

Objective priors for sequential experiments are considered. Common priors, such as the Jeffreys prior and the reference prior, will typically depend on the stopping rule used for the sequential experiment. New expressions for reference…