113 research outputs found
An in-silico look at alternative battery materials : using combined quantum chemical and molecular dynamics approaches to determine physicochemical properties of novel battery materials
No full textauthor: Sabine U. Lerch, BScMasterarbeit University of Innsbruck 202
An in-silico look at alternative battery materials : using combined quantum chemical and molecular dynamics approaches to determine physicochemical properties of novel battery materials
No full textauthor: Sabine U. Lerch, BScMasterarbeit University of Innsbruck 202
An in-silico look at alternative battery materials : using combined quantum chemical and molecular dynamics approaches to determine physicochemical properties of novel battery materials
No full textauthor: Sabine U. Lerch, BScMasterarbeit University of Innsbruck 202
The Lerch zeta-function
No full textThe Lerch zeta-function is the first monograph on this topic, which is a generalization of the classic Riemann, and Hurwitz zeta-functions. Although analytic results have been presented previously in various monographs on zeta-functions, this is the first book containing both analytic and probability theory of Lerch zeta-functions. The book starts with classical analytical theory (Euler gamma-functions, functional equation, mean square). The majority of the presented results are new: on approximate functional equations and its applications and on zero distribution (zero-free regions, number of nontrivial zeros etc). Special attention is given to limit theorems in the sense of the weak convergence of probability measures for the Lerch zeta-function. From limit theorems in the space of analytic functions the universitality and functional independence is derived. In this respect the book continues the research of the first author presented in the monograph Limit Theorems for the Riemann zeta-function. This book will be useful to researchers and graduate students working in analytic and probabilistic number theory, and can also be used as a textbook for postgraduate students
Rational approximation of the Hurwitz-Lerch Zeta function
No full textThe main result of this paper is the construction of new sequences of rational approximations to the Lerch function. This construction is based on a generalization of the "remainder Padé approximants" method introduced by the author in 1996. More recently, this method has been applied, in the form of remainder Padé-type approximants, to the approximation of Stieltjes' constants
A Study of a Certain Subclass of Hurwitz-Lerch-Zeta Function Related to a Linear Operator
No full textBy using a linear operator with Hurwitz-Lerch-Zeta function, which is defined
here by means of the Hadamard product (or convolution), the author investigates
interesting properties of certain subclasses of meromorphically univalent functions in the
punctured unit disk
On the dual nature of partial theta functions and Appell-Lerch sums
No full textIn recent work, Hickerson and the author demonstrated that it is useful to think of Appell-Lerch sums as partial theta functions. This notion can be used to relate identities involving partial theta functions with identities involving Appell-Lerch sums. In this sense, Appell-Lerch sums and partial theta functions appear to be dual to each other. This duality theory is not unlike that found by Andrews between various sets of identities of Rogers-Ramanujan type with respect to Baxter's solution to the hard hexagon model of statistical mechanics. As an application we construct bilateral q-series with mixed mock modular behaviour. In subsequent work we see that our bilateral series are well-suited for computing radial limits of Ramanujan's mock theta functions
Das Leben des Abbé de Rancé Hrsg. u. aus d. Franz. übers. von Emil Lerch. Mit e. Vorw. von Roland Barthes
No full textA Novel Study Based on Lerch Polynomials for Approximate Solutions of Pure Neumann Problem
No full textThe Neumann problem is used to model many linear and nonlinear phenomena such as electrostatic problems, acoustic problems, vibrations of a string, fluid flow problems, the evolution of an isolated population, etc. This paper proposes a numerical technique to solve second-order linear partial differential equations with variable coefficients subject to the Neumann boundary condition (i.e., the boundary condition of the second kind). Our technique uses the operational matrix method and standard collocation points and approximates the solution using Lerch polynomials bases. Also, we enhance the method's effectiveness by utilizing an error analysis technique based on residual function. The implementation of our method to any computer program is more straightforward than many other numerical methods. The results of numerical experiments are illustrated with tables and figures and are compared with analytical solutions to confirm the good accuracy of the presented technique. © 2021, The Author(s), under exclusive licence to Springer Nature India Private Limited
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