Related papers: Variations on theorems of Mertens
Assuming the Generalized Riemann Hypothesis we obtain uniform, effective number-field analogues of Mertens' theorems.
We study content ideals of polynomials and their behavior under multiplication. We give a generalization of the Lemma of Dedekind-Mertens and prove the converse under suitable dimensionality restrictions.
Kernel density estimation is a popular method for estimating unseen probability distributions. However, the convergence of these classical estimators to the true density slows down in high dimensions. Moreover, they do not define meaningful…
A connection between fractional calculus and statistical distribution theory has been established by the authors recently. Some extensions of the results to matrix-variate functions were also considered. In the present article, more results…
In this article, we consider limit theorems for some weighted type random sums (or discrete rough integrals). We introduce a general transfer principle from limit theorems for unweighted sums to limit theorems for weighted sums via rough…
We study the relationship between the discrete and the continuous versions of the Kronecker--Weyl equidistribution theorem, as well as their possible extension to manifolds in higher dimensions. We also investigate a way to deduce in some…
Invariance of the counted number of photons and the Lorentz-Einstein transformations enable us to derive transformation equations for the physical quantities introduced in order to characterize energy emission and transport in a plane and…
In this article we generalize packing density problems from permutations to patterns with repeated letters and generalized patterns. We are able to find the packing density for some classes of patterns and several other short patterns.
We prove an extension of the Regularity Lemma with vertex and edge weights which can be applied for a large class of graphs. The applications involve random graphs and a weighted version of the Erd\H{o}s-Stone theorem. We also provide means…
We introduce a new, elementary method for studying random differences in arithmetic progressions and convergence phenomena along random sequences of integers. We apply our method to obtain significant improvements on previously known…
We study how measures with finite lower density are distributed around $(n-m)$-planes in small balls in $\mathbb{R}^n$. We also discuss relations between conical upper density theorems and porosity. Our results may be applied to a large…
We prove variational forms of the Barban-Davenport-Halberstam Theorem and the large sieve inequality. We apply our result to prove an estimate for the sum of the squares of prime differences, averaged over arithmetic progressions.
A masses of a leptons deduced from a representation of a probability density vector by a spinors. A massive W and Z bosons and a massless A boson are obtained from a transformations for which a density vector is invariant.
We establish a link between the phenomenon of Taylor dispersion and the theory of empirical distributions. Using this connection, we derive, upon applying the theory of large deviations, an alternative and much more precise description of…
The variational theory of the perfect fluid with an intrinsic hypermomentum is developed. The Lagrangian density of such fluid is stated and the equations of motion of the fluid and the evolution equation of the hypermomentum tensor are…
In the first part of the paper a general notion of sampling expansions for locally compact groups is introduced, and its close relationship to the discretisation problem for generalised wavelet transforms is established. In the second part,…
We present some new nonparametric estimators of entropies and we establish almost sure consistency and central limit Theorems for some of the most important entropies in the discrete case. Our theorical results are validated by simulations.
Using a perturbation result established by Galatolo and Lucena, we obtain quantitative estimates on the continuity of the invariant densities and entropies of the physical measures for some families of piecewise expanding maps. We apply…
In this article we have studied bicomplex valued measurable functions on an arbitrary measurable space. We have established the bicomplex version of Lebesgue's dominated convergence theorem and some other results related to this theorem.…
We revisit a shape inversion formula derived by Panaretos in the context of a particle density estimation problem with unknown rotation of the particle. A distribution is presented which imitates, or 'fakes', the uniformity or Haar…