Related papers: The Schinzel-Szekeres function
We provide asymptotic results for the distribution of weighted nonlinear functionals of Gaussian field with long-range dependence. We also show that integral functionals and the corresponding additive functionals have same distributions…
We derive functional equations for distributions of six classical statistics (ascents, descents, left-to-right maxima, right-to-left maxima, left-to-right minima, and right-to-left minima) on separable and irreducible separable…
We investigate discretizations of the integrable discrete nonlinear Schr\"odinger dynamical system and related symplectic structures. We develop an effective scheme of invariant reducing the corresponding infinite system of ordinary…
We derive the joint asymptotic distribution of empirical quantiles and expected shortfalls under general conditions on the distribution of the underlying observations. In particular, we do not assume that the distribution function is…
We consider the scattering theory for the Schr\"odinger operator $-\Dc_x^2+V(x)$ on graphs made of one-dimensional wires connected to external leads. We derive two expressions for the scattering matrix on arbitrary graphs. One involves…
The focus of this work is on estimation of the in-degree distribution in directed networks from sampling network nodes or edges. A number of sampling schemes are considered, including random sampling with and without replacement, and…
We prove dispersive and Strichartz estimates for Schr\"{o}dinger equations on normal real form symmetric spaces. These estimates apply to the well-posedness and scattering for the nonlinear Schr\"{o}dinger equations.
Motivated by applications to prediction and forecasting, we suggest methods for approximating the conditional distribution function of a random variable Y given a dependent random d-vector X. The idea is to estimate not the distribution of…
The explicit form for the characteristic function of a stable distribution on the line is derived analytically by solving the associated functional equation and applying theory of regular variation, without appeal to the general…
We consider analytic functions of the Riemann zeta type, for which, if $s$ is a zero, so is $1-s$. We use infinite product representations of these functions, assuming their zeros to be of first order. We use exponential factors to…
We prove asymptotic estimates for the cross-ratio distortion with respect to a smooth or holomorphic function in terms of its Schwarz derivative.
This thesis deals with applications of experimental mathematics to a number of problems. The first problem is related to random graph statistics. We consider a certain class of Galton-Watson random trees and look at the total height…
We present a theorem on taking the repeated indefinite summation of a holomorphic function $\phi(z)$ in a vertical strip of $\mathbb{C}$ satisfying exponential bounds as the imaginary part grows. We arrive at this result using transforms…
The purpose of this note is to provide a summary of the recent work of the authors on two variations of the pointwise convergence problem for the solutions to the fractional Schr\"odinger equations; convergence along a tangential line and…
We derive a simple and precise approximation to probability density functions in sampling distributions based on the Fourier cosine series. After clarifying the required conditions, we illustrate the approximation on two examples: the…
We prove the well-posedness results of scattering data for the derivative nonlinear Schr\"odinger equation in $H^{s}(\mathbb{R})(s\geq\frac12)$. We show that the reciprocal of the transmission coefficient can be written as the sum of some…
Several general results for the spectral determinant of the Schr\"odinger operator on metric graphs are reviewed. Then, a simple derivation for the $\zeta$-regularised spectral determinant is proposed, based on the Roth trace formula. Two…
We show that if we start from a symmetric lower semi-bounded Schr\"odinger operator $\mathcal{H}$ on finitely supported functions on a discrete weighted graph (satisfying certain conditions), apply the Friedrichs construction to get a…
This paper gives some results for the logarithm of the Riemann zeta-function and its iterated integrals. We obtain a certain explicit approximation formula for these functions. The formula has some applications, which are related with the…
We consider the Schr\"{o}dinger equation $(i\partial_t+\Delta)u=0$ on an $n$-dimensional simplex with Dirichlet boundary conditions. We use a commutator argument along with integration by parts to obtain an observability asymptotic for any…