Related papers: On the sum of ordered spacings
This paper gives new explicit formulas for sums of powers of integers and their reciprocals.
In this paper we introduce the notion of the $P$-sequences and apply their properties in studying representability of real numbers. Another application of $P$-sequences we find in generating the Prouhet-Tarry-Escott pairs.
Distributions, i.e., subsets of tangent bundles formed by piecing together subspaces of tangent spaces, are commonly encountered in the theory and application of differential geometry. Indeed, the theory of distributions is a fundamental…
The generalized Poisson distribution is well known to be a compound Poisson distribution with Borel summands. As a generalization we present closed formulas for compound Bartlett and Delaporte distributions with Borel summands and a…
Smoothed analysis of complexity bounds and condition numbers has been done, so far, on a case by case basis. In this paper we consider a reasonably large class of condition numbers for problems over the complex numbers and we obtain…
Under certain circumstances, some of which are made explicit here, one can deduce bounds on the full sum of a perturbation series of a physical quantity by using a variational Borel map on the partial series. The method is illustrated by…
We study random points on the real line generated by the eigenvalues in unitary invariant random matrix ensembles or by more general repulsive particle systems. As the number of points tends to infinity, we prove convergence of the…
We construct a non - improved exponential bounds for distribution of normed sums of i.,i.d. random variables with random numbers of summand.
We present new mixture representations for the generalized Linnik distribution in terms of normal, Laplace, exponential and stable laws and establish the relationship between the mixing distributions in these representations. Based on these…
We investigate properties of an ordinal sum of uninorms introduced in [8] in the case that the summands are proper representable uninorms. We show sufficient and necessary conditions for a uninorm to be an ordinal sum of representable…
The purpose of this note is to extend the results on uniform smoothed analysis of condition numbers from \cite{BuCuLo:07} to the case where the perturbation follows a radially symmetric probability distribution. In particular, we will show…
Exact formulas are derived for the probability density functions of the sum and difference of two independent non-central gamma distributed random variables, with both series and integral representations of the density presented. These…
We take some first steps in providing a synthetic theory of distributions. In particular, we are interested in the use of distribution theory as foundation, not just as tool, in the study of the wave equation.
We study sums of arithmetic functions, defined on Gaussian integers and taken over those pairs of integers whose coordinates give rise to a singular system.
In this paper we study the distribution of orders of bounded discriminants in number fields. We give an asymptotic formula for the number of orders contained in the ring of integers of a quintic number field.
In this paper some new ways of generalizing perfect numbers are investigated, numerical results are presented and some conjectures are established.
In this note, an upper bound for the sum of fractional parts of certain smooth functions is established. Such sums arise naturally in numerous problems of analytic number theory. The main feature is here an improvement of the main term due…
A systematic study of the probability distribution of superimposed random codes is presented through the use of generating functions. Special attention is paid to the cases of either uniformly distributed but not necessarily independent or…
When approximating the joint distribution of the component counts of a decomposable combinatorial structure that is `almost' in the logarithmic class, but nonetheless has irregular structure, it is useful to be able first to establish that…
Nearest neighbor cells in $R^d,d\in\mathbb{N}$, are used to define coefficients of divergence ($\phi$-divergences) between continuous multivariate samples. For large sample sizes, such distances are shown to be asymptotically normal with a…