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Universality Theorem for the Iterated Integrals of the Logarithm of the Riemann Zeta-Function
In this paper, we prove the universality theorem for the iterated integrals of the logarithm of the Riemann zeta-function on a line parallel to the...
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Logarithmic Expansion, Entropy, and Dimension for Set-Valued Maps
We obtain a lower bound for the entropy of a Borel probability measure (not necessarily invariant) with respect to an upper semicontinuous set-valued...
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Law of iterated logarithm and model selection consistency for generalized linear models with independent and dependent responses
We study the law of the iterated logarithm (LIL) for the maximum likelihood estimation of the parameters (as a convex optimization problem) in the...
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On the Stochastic Magnus Expansion and Its Application to SPDEs
We derive the stochastic version of the Magnus expansion for linear systems of stochastic differential equations (SDEs). The main novelty with...
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Generalized Glaisher-Kinkelin constants and Ramanujan summation of series
We study a sequence of constants known as the Bendersky-Adamchik constants which appear quite naturally in number theory and generalize the classical...
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Expansion by Regions: An Overview
A short review of expansion by regions is presented. It is a well-known strategy to obtain an expansion of a given multiloop Feynman integral in a...
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New Approximations for the Higher Order Coefficients in an Asymptotic Expansion for the Barnes G-Function
In this paper, we provide new formulas for determining the coefficients appearing in the asymptotic expansion for the Barnes G -function as n tends to...
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A boundary expansion of solutions to nonlinear singular elliptic equations
In this paper we establish an asymptotic expansion near the boundary for solutions to the Dirichlet problem of elliptic equations with singularities...
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An Integrative Approach for Analysis of Nonlinear Electrical Circuits Using-Polynomial B-Spline Expansion and B-Spline Krawczyk Operator
This paper addresses the problem of finding a set of all direct current (DC) operating points of a nonlinear circuit, which is a crucial step in its...
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A series expansion for generalized harmonic functions
We consider a class of generalized harmonic functions in the open unit disc in the complex plane. Our main results concern a canonical series...
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Cumulant–Cumulant Relations in Free Probability Theory from Magnus’ Expansion
Relations between moments and cumulants play a central role in both classical and non-commutative probability theory. The latter allows for several...
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Basics
This chapter contains a summary of standard material from an introductory complex variables course, including the Cauchy integral formula, maximum...
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The law of iterated logarithm for the estimations of diffusion-type processes
This paper mainly discusses the asymptotic behaviours on the lasso-type estimators for diffusion-type processes with a small noise. By constructing...
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Pointwise Expansion of Degenerating Immersions of Finite Total Curvature
Generalising classical result of Müller and Šverák (J. Differ. Geom. 42(2), 229-258, 1995), we obtain a pointwise estimate of the conformal factor of...
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Solution of option pricing equations using orthogonal polynomial expansion
We study both analytic and numerical solutions of option pricing equations using systems of orthogonal polynomials. Using a Galerkin-based method, we...
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Complements in Real and Complex Analysis
Among the tools from real analysis to be mastered by a student of machine learning, statistical physics, and thermodynamics, we mention in particular...
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Objective Finite-Time Flow Topology from Flowmap Expansion and Contraction
We extend the definition of the classic instantaneous vector field saddles, sinks, and sources to the finite-time setting by categorizing the domain...
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Asymptotic Behaviors for Random Geometric Series
In this paper, we consider asymptotic behaviors for random geometric series. We first study the convergence rates in the central limit theorem, i.e.,...