1,205 research outputs found

    Hancock - July 13 - W. S. Lerch

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    W. S. Lerch is the name of the new condutor who runs on the South Shore to this place

    Leaf-to-leaf distances and their moments in finite and infinite m-ary tree graphs

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    We study the leaf-to-leaf distances on full and complete m-ary graphs using a recursive approach. In our formulation, leaves are ordered along a line. We find explicit analytical formulae for the sum of all paths for arbitrary leaf-to-leaf distance r as well as the average path lengths and the moments thereof. We show that the resulting explicit expressions can be recast in terms of Hurwitz-Lerch transcendants. Results for periodic trees are also given. For incomplete random binary trees, we provide first results by numerical techniques; we find a rapid drop of leaf-to-leaf distances for large r

    ELECTRONIC-STRUCTURE OF TETRAPHOSPHABICYCLO[1.1.0]BUTANE

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    Schoeller W, LERCH C. ELECTRONIC-STRUCTURE OF TETRAPHOSPHABICYCLO[1.1.0]BUTANE. INORGANIC CHEMISTRY. 1983;22(21):2992-2998

    The Lerch zeta-function

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    The 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

    ON THE ELECTRONIC-STRUCTURE OF BICYCLOTETRAPHOSPHABUTANE

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    Schoeller W, LERCH C. ON THE ELECTRONIC-STRUCTURE OF BICYCLOTETRAPHOSPHABUTANE. PHOSPHORUS SULFUR AND SILICON AND THE RELATED ELEMENTS. 1983;18(1-3):450

    DICOORDINATION AND TRICOORDINATION AT PHOSPHORUS - ABINITIO STUDY OF BONDING IN BIS(IMINO)PHOSPHORANES AND RELATED-COMPOUNDS

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    Schoeller W, LERCH C. DICOORDINATION AND TRICOORDINATION AT PHOSPHORUS - ABINITIO STUDY OF BONDING IN BIS(IMINO)PHOSPHORANES AND RELATED-COMPOUNDS. INORGANIC CHEMISTRY. 1986;25(4):576-580
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