Related papers: Averages of multiplicative functions along equidis…
First we define a new kind of function over $\mathbb{N}$. For each $i\in\mathbb{N}$ we have an associated function, which will be called $S_i$ . Then we define a new kind of sequence, to be made from the functions $S_i$ . Finally, we will…
Starting from a description of various generalized function algebras based on sequence spaces, we develop the general framework for considering linear problems with singular coefficients or non linear problems. Therefore, we prove…
In this paper, we prove two normality criteria for families of some functions concerning shared values, the results generalize those given by Hu and Meng. Some examples are given to show the sharpness of our results.
Let $G$ be a simple undirected graph. The regular number of $G$ is defined to be the minimum number of subsets into which the edge set of $G$ can be partitioned so that the subgraph induced by each subset is regular. In this work, we obtain…
In this work, we deal with approximations for distribution functions of non-negative random variables. More specifically, we construct continuous approximants using an acceleration technique over a well-know inversion formula for Laplace…
The paper considers estimates for the asymptotics of summation functions of bounded multiplicative arithmetic functions. Several assertions on this subject are proved and examples are considered.
This paper proposes a general family of estimators for estimating the population mean in systematic sampling in the presence of non-response adapting the family of estimators proposed by Khoshnevisan et al. (2007). In this paper we have…
We consider weighted averages of the number of representations of an even integer as a sum of two prime numbers, where each summand lies in a given arithmetic progression modulo a common integer $q$. Our result is uniform in a suitable…
We present a general new method for constructing pointwise ergodic sequences on countable groups, which is applicable to amenable as well as to non-amenable groups and treats both cases on an equal footing. The principle underlying the…
This work gives a general approach to the determination of the asymptotic behavior of the sums of functions of primes based on the distribution of primes. It refines the estimate of the remainder term of the asymptotic expansion of the sums…
We study certain step functions whose nonnegativity is related to the integrality of sequences of ratios of factorial products. In particular, we obtain a lower bound for the mean square of such step functions which allows us to give a…
This is the first of two coupled papers estimating the mean values of multiplicative functions, of unknown support, on arithmetic progressions with large differences. Applications are made to the study of primes in arithmetic progression…
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…
Parametric distributions are an important part of statistics. There is now a voluminous literature on different fascinating formulations of flexible distributions. We present a selective and brief overview of a small subset of these…
We investigate the limiting behavior of multiple ergodic averages along sparse sequences evaluated at prime numbers. Our sequences arise from smooth and well-behaved functions that have polynomial growth. Central to this topic is a…
We define a new average - termed the resolvent average - for positive semidefinite matrices. For positive definite matrices, the resolvent average enjoys self-duality and it interpolates between the harmonic and the arithmetic averages,…
Asymptotic expansions for a wide class of distribution are studied. A simple method for computation of the series coefficients is suggested. The case when regularization parameter of the distribution depends on the asymptotic parameter is…
We consider the class of all non-negative on $\mathbb{R_+}$ functions such that each of them satisfies the Reverse H\"older Inequality uniformly over all intervals with some constant the minimum value of which can be regarded as the…
A common measure of a function's complexity is the count of its stationary points. For complicated functions, this count grows exponentially with the volume and dimension of their domain. In practice, the count is averaged over a class of…
Numerical functions, which characterize Dynkin schemes, Coxeter graphs and tame marked quivers, are considered.