Related papers: The Minimal Euclidean Function on the Gaussian Int…

An algorithm for integration of polynomial functions with variable weight is considered. It provides extension of the Gaussian integration, with appropriate scaling of the abscissas and weights. Method is a good alternative to usually…

We obtain another proof of Hermite's integral for the Hurwitz zeta function.

This is a short note in which we show how to calculate the value of Perelman's nu-functional for a variety of metrics. In particular we complete the calculation of values for the known 4-dimensional Einstein and shrinking Ricci soliton…

We establish Bernstein Theorems for Lagrangian graphs which are Hamiltonian minimal or have conformal Maslov form. Some known results of minimal (Lagrangian) submanifolds are generalized.

In this paper the Gaussian integral is proven using contour integration on $\frac{1}{e^{x^2}+1}$ and linking it using a limit to said Gaussian integral. The limit is alsorelated to the Riemann Zeta function using a few manipulations. This…

A relationship between the Riemann zeta function and a density on integer sets is explored. Several properties of the examined density are derived.

A modified Gauss's algorithm for solving a system of linear equations in an integral ring is proposed, as well as an appropriate algorithm for calculating the elements of the adjoint matrix.

In this article we study certain properties of the image of Euler's totient function; we also consider the structure of the preimage of certain elements of the image of this function.

In this work, we study probability functions associated with Gaussian mixture models. Our primary focus is on extending the use of spherical radial decomposition for multivariate Gaussian random vectors to the context of Gaussian mixture…

This note provides an effective bound in the Gauss-Kuzmin-L\'evy problem for some Gauss type shifts associated with nearest integer continued fractions, acting on the interval $I_0=[0,\frac{1}{2}]$ or $I_0=[-\frac{1}{2},\frac{1}{2}]$. We…

We study the following fundamental hypothesis testing problem, which we term Gaussian mean testing. Given i.i.d. samples from a distribution $p$ on $\mathbb{R}^d$, the task is to distinguish, with high probability, between the following…

In this paper, the integral $\pmatrix{\lambda_1 &\lambda_2 &\lambda_3\cr 0 &0 &0\cr}\, \int_0^\infty \, r^{\lambda_3+2}\, \exp{(-\alpha r^2)}\, j_{\lambda_1}(k_1r) \,j_{\lambda_2}(k_2r) \,dr$, where $k_1$, $k_2$ and $\alpha$ are positive,…

We provide analytical functions approximating $\int e^{-x^2} dx$, the basis of which is the kink soliton and which are both accurate (error $< 0.2 %$) and simple. We demonstrate our results with some applications, particularly to the…

We prove Gaussian approximation theorems for specific $k$-dimensional marginals of convex bodies which possess certain symmetries. In particular, we treat bodies which possess a 1-unconditional basis, as well as simplices. Our results…

In this paper, we solve the longstanding Gaussian curvature conjecture of a minimal graph $S$ over the unit disk. The conjecture asserts that for any minimal graph above the unit disk, the Gaussian curvature at the point directly above the…

In this paper we prove a version of Gruss integral inequality for mappings with values in Hilbert C*-modules. Some applications for such functions are also given.

In this paper we study the mean values of some multiplicative functions connected with the divisor function on the short interval of summation. The asymptocic values for such mean values are proved.

In this paper we initiate a study on Gauss factorials of polynomials over finite fields, which are the analogues of Gauss factorials of positive integers.

Euclidean distance geometry is the study of Euclidean geometry based on the concept of distance. This is useful in several applications where the input data consists of an incomplete set of distances, and the output is a set of points in…

The Gaussian entire function is a random entire function, characterised by a certain invariance with respect to isometries of the plane. We study the fluctuations of the increment of the argument of the Gaussian entire function along planar…