Related papers: Existence of limit of multivariable function

We prove a law of large numbers and functional central limit theorem for a class of multivariate Hawkes processes with time-dependent reproduction rate. We address the difficulties induced by the use of non-convolutive Volterra processes by…

A short note on bounds on distance to variety of a point in terms of the Taylor coefficients at the point.

We extend Painlev\'e's determinateness theorem to the case of first order ordinary differential equations in the complex domain with known terms allowed be multivalued in the dependent variable as well; multivaluedness is supposed to be…

It is shown that the previous [1-3] generalization of the final-value theorem to the average (not necessarily limiting) values, can be extended to the higher-order running averages $(<>_{t}), lim_{s\rightarrow0}[sF(s)] =…

A non-classical formulation of the central limit theorem is given for sequences of independent random variables with finite second moments. Singular sequences whose members all have a degenerate or normal distribution are excluded from…

We establish a functional limit law of the logarithm for the increments of the normed quantile process based upon a random sample of size $n\to\infty$. We extend a limit law obtained by Deheuvels and Mason (12), showing that their results…

A criterion is established for the transitivity of connectedness in a transfinite graph. Its proof is much shorter than a prior argument published previously for that criterion.

In the paper, the occurrence of zeros and ones in the binary expansion of the primes is studied. In particular the statement in the title is established. The proof is unconditional.

We establish variational estimates related to the problem of restricting the Fourier transform of a three-dimensional function to the two-dimensional Euclidean sphere. At the same time, we give a short survey of the recent field of maximal…

We give examples of sequences of smooth non-isotrivial curves for every genus at least two, defined over a rational function field of positive characteristic, such that the (finite) number of rational points of the curves in the sequence…

We extend first-order logic to include variadic function symbols, and prove a substitution lemma. Two applications are given: one to bounded quantifier elimination and one to the definability of certain Borel sets.

This paper gives the existence and uniqueness results for solution of fractional differential equations with Hilfer derivative. Using some new techniques and generalizing the restrictive conditions imposed on considered function, the…

We find a nontrivial upper bound on the average value of the function M(n) which associates to every positive integer n the minimal Hamming weight of a multiple of n. Some new results about the equation M(n)=M(n') are given.

This is an extended version of a series of talks I held at the University of Bochum in 2017 about limit theorems for non-linear functionals of stationary Gaussian random fields. The goal of these talks was to give a fairly detailed…

Much work has been done attempting to understand the dynamic behaviour of the so-called "3x+1" function. It is known that finite sequences of iterations with a given length and a given number of odd terms have some combinatorial properties…

We establish some upper and lower bounds for the number of rational points of Prym varieties over finite fields.

In this short note we resort to the well known Hellmann-Feynman theorem to prove that some non-relativistic Hamiltonian operators support an infinite number of bound states.

Let H(f)(x)=\int_{(0,infty)^d} f(v) E_{x}(v) d\nu(v), be the multivariable Hankel transform, where E_{x}(v)=\prod_{k=1}^d (x_k v_k)^{-a_k+1/2} J_{a_k-1/2}(x_k v_k), d\nu(v)=v^a dv, a=(a_1,...,a_d). We give sufficient conditions on a bounded…

This paper investigates asymptotic properties of multifractal products of random fields. The obtained limit theorems provide sufficient conditions for the convergence of cumulative fields in the spaces $L_q.$ New results on the rate of…

The purpose of this article is to formulate a number of probabilistic hidden-variable theorems, to provide proofs in some cases, and counterexamples to some conjectured relationships. The first theorem is the fundamental one. It asserts the…