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Complete Minimal Logarithmic Energy Asymptotics for Points in a Compact Interval: A Consequence of the Discriminant of Jacobi Polynomials
The electrostatic interpretation of zeros of Jacobi polynomials, due to Stieltjes and Schur, enables us to obtain the complete asymptotic expansion...
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A closed-form expression for the Euler–Kronecker constant of a quadratic field
Given a number field, the Euler–Kronecker constant is defined as the constant term in the Laurent series expansion of the logarithmic derivative of...
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Four Classes of Definite Integrals about Hyperbolic and Trigonometric Functions
AbstractBy establishing recurrence relations and then determining boundary values, we examine four classes of definite integrals of
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Public-Key Ciphers
But how is it possible that you can encrypt, but you cannot decrypt even with the help of the largest and most modern computers? The keyword we want...
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Limit Theorems for Deviation Means of Independent and Identically Distributed Random Variables
We derive a strong law of large numbers, a central limit theorem, a law of the iterated logarithm and a large deviation theorem for so-called...
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Boundary Effect Under 2D Newtonian Gravity Potential in the Phase Space
We study linear two-and-a-half-dimensional Vlasov equations under the logarithmic gravity potential in the half-space of diffuse reflection boundary....
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Low-Parametrical Approximation of Solar Radiation’s Brightness Coefficient in a Gas Absorption Band
AbstractThe problem of the sunlight transfer equation in the atmosphere in a gas absorption band is considered. The structure of the spectral...
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An Asymptotic Expansion of the Trace of the Heat Kernel of a Singular Two-particle Contact Interaction in One-dimension
The regularized trace of the heat kernel of a one-dimensional Schrödinger operator with a singular two-particle contact interaction being of...
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Painlevé Analysis, Bäcklund Transformation, Lax Pair, Periodic- and Travelling-Wave Solutions for a Generalized (2+1)-Dimensional Hirota–Satsuma–Ito Equation in Fluid Mechanics
In this paper, under investigation is a generalized (2+1)-dimensional Hirota–Satsuma–Ito (HSI) equation in fluid mechanics. Motivated by its...
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Functional Summation of Series
AbstractWe consider a summation technique which reduces summation of a series to the solution of some linear functional equations. Partial sums of a...
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The Distribution of the Number of Automorphisms of Random Trees
We study the size of the automorphism group of two different types of random trees: Galton–Watson trees and rooted Pólya trees. In both cases, we...
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A CLT for the characteristic polynomial of random Jacobi matrices, and the G\(\beta \)E
We prove a central limit theorem for the real part of the logarithm of the characteristic polynomial of random Jacobi matrices. Our results cover the...
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Fractal zeta functions of orbits of parabolic diffeomorphisms
In this paper, we prove that fractal zeta functions of orbits of parabolic germs of diffeomorphisms can be meromorphically extended to the whole...
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An Adaptive Generalized Multiscale Finite Element Method Based Two-Grid Preconditioner for Large Scale High-Contrast Linear Elasticity Problems
In this paper, we propose an efficient and robust two-grid preconditioner for the linear elasticity equation with high contrasts. To tackle the...
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Lochs-type theorems beyond positive entropy
Lochs’ theorem and its generalizations are conversion theorems that relate the number of digits determined in one expansion of a real number as a...
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On periodicity of p-adic Browkin continued fractions
The classical theory of continued fractions has been widely studied for centuries for its important properties of good approximation, and more...
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Global linear convergence of evolution strategies with recombination on scaling-invariant functions
Evolution Strategies (ESs) are stochastic derivative-free optimization algorithms whose most prominent representative, the CMA-ES algorithm, is...
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Quasi-shuffle Algebras in Non-commutative Stochastic Calculus
This chapter is divided into two parts. The first is largely expository and builds on Karandikar’s axiomatisation of Itô calculus for matrix-valued...
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Fast Simulation of Collisions in the Particle-in-cell Method for Ions of Different Types
AbstractThe full computation of 3D-collisions in the modeling of plasma confinement systems is the difficult task. The current paper deals with the...
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Ramanujan’s approximation to the exponential function and generalizations
Ramanujan’s approximation to the exponential function is reexamined with the help of Perron’s saddle-point method. This allows for a wide...
