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We present a so-called universal convergence theorem for inexact primal-dual penalty and augmented Lagrangian methods that can be applied to a large number of such methods and reduces their convergence analysis to verification of some…
Consider a mean-reverting equation, generalized in the sense it is driven by a 1-dimensional centered Gaussian process with H\"older continuous paths on $[0,T]$ ($T > 0$). Taking that equation in rough paths sense only gives local existence…
In this paper we present some observations about the well-known Goldbach conjecture. In particular we list and interpret some numerical results which allow us to formulate a relation between prime numbers and even integers. We can also…
The Dirichlet divisor problem is used as a model to give a conjecture concerning the conditional convergence of the Dirichlet series of an L-function.
The objective of this paper is, in the main, twofold: Firstly, to develop an algebraic setting for dealing with Bell polynomials and related extensions. Secondly, based on the author's previous work on multivariate Stirling polynomials…
The $p$-set, which is in a simple analytic form, is well distributed in unit cubes. The well-known Weil's exponential sum theorem presents an upper bound of the exponential sum over the $p$-set. Based on the result, one shows that the…
In a prime number decomposition of integers in a given set, the occurrence frequencies of prime numbers are shown to satisfy a general forms of Zipf's law.
We present inequalities and some applications to Kellers' limit and Carlemans' inequality.
An improved estimate is given for $|\theta(x) -x|$, where $\theta(x) = \sum_{p\leq x} \log p$. Three applications are given: the first to arithmetic progressions that have points in common, the second to primes in short intervals, and the…
In this paper we generalize the Deuring theorem on a reduction of elliptic curve with complex multiplication. More precisely, for an Abelian variety $A$, arising after reduction of an Abelian variety with complex multiplication by a CM…
We provide numerical procedures for possibly best evaluating the sum of positive series. Our procedures are based on the application of a generalized version of Kummer's test.
The symmetry group method is applied to a generalized Korteweg-de Vries equation and several classes of group invarint solution for it are obtained by means of this technique. Polynomial, trigonometric and elliptic function solutions can be…
We derive a generalized matrix version of Pellet's theorem, itself based on a generalized Rouch\'{e} theorem for matrix-valued functions, to generate upper, lower, and internal bounds on the eigenvalues of matrix polynomials. Variations of…
In the present note, we generalize the first part of the Borel-Cantelli lemma. By this generalization, we obtain some strong limit results.
We derive recursions for the probability distribution of random sums by computer algebra. Unlike the well-known Panjer-type recursions, they are of finite order and thus allow for computation in linear time. This efficiency is bought by the…
In this paper we prove a generalization of Montel's theorem for a class of first order elliptic equations with measurable coefficients involving Hodge-Dirac operators. We then apply this result to sequences of solutions of second order…
In this paper, we introduce a convergence notion for ordered selections. Our convergence notion is based on subpermutation densities and convergences of the marginal distributions. A particular case of this convergence is the well-known…
Gerth generalised Cohen-Lenstra heuristics to the prime $p=2$. He conjectured that for any positive integer $m$, the limit $$ \lim_{x \to \infty} \frac{\sum_{0 < D \le X, \atop{ \text{squarefree} }} |{\rm Cl}^2_{\Q(\sqrt{D})}/{\rm…
In the present article, real number representations, that are generalizations of classical positive and alternating representations of numbers, are introduced and investigated. The main metric relation, properties of cylinder sets are…
A generalization of the notion of surfaces of revolution in the spaces of General Relativity is presented. We apply this definition to the case of Carter's family [A] of solutions and we study the Kerr's metric with respect the above…