Related papers: The Minimal Euclidean Function on the Gaussian Int…
The convergence of double Fourier series of functions of bounded partial $\Lambda$-variation is investigated. The sufficient and necessary conditions on the sequence $\Lambda=\{\lambda_n\}$ are found for the convergence of Fourier series of…
We prove a formula for the Mangoldt function which relates it to a sum over all the non-trivial zeros of the Riemann zeta function, in addition we analize a truncated version of it.
The Euclidean algorithm makes possible a simple but powerful generalization of Taylor's theorem. Instead of expanding a function in a series around a single point, one spreads out the spectrum to include any number of points with given…
An Eulerian-minor of an Eulerian graph is obtained from an Eulerian subgraph of the Eulerian graph by contraction. The Eulerian-minor operation preserves Eulerian properties of graphs and moreover Eulerian graphs are well-quasi-ordered…
In this paper we discuss three types of the mean values of the Euler double zeta function. In order to get results we introduce three approximate formulas for this function.
A simplified direct method is described for obtaining massless scalar functional determinants on the Euclidean ball. The case of odd dimensions is explicitly discussed.
This note contains a short proof of the functional equation for the zeta function.
In this paper, we derive tail approximations of integrals of exponential functions of Gaussian random fields with varying mean functions and approximations of the associated point processes. This study is motivated naturally by multiple…
We present some formulas for the computation of the zeros of the integral-degree associated Legendre functions with respect to the order.
We study the generalized continued fraction expansions of complex numbers in term of elements from Euclidean subrings, especially Gaussian or Eisenstein integers, in a general framework as pursued in [3] and [1]. We introduce a common…
This paper presents the Gaussian subordination framework to generate optimal one-sided approximations to multidimensional real-valued functions by functions of prescribed exponential type. Such extremal problems date back to the works of…
Under suitable conditions on the range of the Gauss map of a complete submanifold of Euclidean space with parallel mean curvature, we construct a strongly subharmonic function and derive a-priori estimates for the harmonic Gauss map. The…
We derive and prove the connection formulas for the lambda generalized diagonal Ising model correlation functions.
We introduce a new factorial function which agrees with the usual Euler gamma function at both the positive integers and at all half-integers, but which is also entire. We describe the basic features of this function.
When $k>1$ and $n$ is the product of the smallest $k$ primes, the $(k+1)$-st smallest prime is the least divisor exceeding $1$ of $n^{n^n}-1$. This variant of Euclid's prime generator is discussed with some of its cousins.
The Gaussian kernel plays a central role in machine learning, uncertainty quantification and scattered data approximation, but has received relatively little attention from a numerical analysis standpoint. The basic problem of finding an…
The present article is devoted to the description of further investigations of the author of this article. These investigations (in terms of various representations of real numbers) include the generalized Salem functions and…
The paper is devoted to the classical variational problem with a nonsmooth integrand of the functional to be minimized. The integrand is supposed to be subdifferentiable. Under some natural conditions the subdifferentiability of the…
The classical result of Nevanlinna states that two nonconstant meromorphic functions on the complex plane having the same images for five distinct values must be identically equal to each other. In this paper, we give a similar uniqueness…
Minimal length of a two-dimensional Klein-Gordon oscillator is investigated and illustrates the wave functions in the momentum space. The energy eigenvalues are found and the corresponding wave functions are calculated in terms of…