Results 11 to 20 of about 2,569 (239)
The Equivalence of the Charge Interaction Sum and the Ionic Strength
Chemical Thermodynamics and Thermal Analysis, 2022 The electrostatic interaction among a neutral and finite set of point charges is based on the sum of their pairwise charge products, zizj, yet many analyses yield terms which simply contain a sum of the squares of the separate charges, corresponding to ...
Leslie Glasser
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The Sum and Product of Finite Sequences of Complex Numbers [PDF]
Formalized Mathematics, 2010 The Sum and Product of Finite Sequences of Complex Numbers This article extends the [10]. We define the sum and the product of the sequence of complex numbers, and formalize these theorems. Our method refers to the [11].
Miyajima, Keiichi, Kato, Takahiro
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Bounds on Moments of Weighted Sums of Finite Riesz Products [PDF]
Journal of Fourier Analysis and Applications, 2020 Let $n_j$ be a lacunary sequence of integers, such that $n_{j+1}/n_j\geq r$. We are interested in linear combinations of the sequence of finite Riesz products $\prod_{j=1}^N(1+\cos(n_j t))$. We prove that, whenever the Riesz products are normalized in $L^p$ norm ($p\geq 1$) and when $r$ is large enough, the $L^p$ norm of such a linear combination is ...
Bonami, Aline +3 more
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Axioms, 2023 In this paper, first derivatives of the Whittaker function Mκ,μx are calculated with respect to the parameters. Using the confluent hypergeometric function, these derivarives can be expressed as infinite sums of quotients of the digamma and gamma ...
Alexander Apelblat +1 more
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Theory and Applications of Categories, 2001 Summary: In this paper we describe a deductive system for categories with finite products and coproducts, prove decidability of equality of morphisms via cut elimination, and prove a ``Whitman theorem'' for the free such categories over arbitrary base categories.
Cockett, J. R. B., Seely, R. A. G.
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Mathematics, 2018 In this paper, we derive Fourier series expansions for functions related to sums of finite products of Chebyshev polynomials of the first kind and of Lucas polynomials. From the Fourier series expansions, we are able to express those two kinds of sums of
Taekyun Kim +3 more
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Julius Kruopis – the pioneer of applied statistics in Lithuania
Lithuanian Journal of Statistics, 2023 Julius Kruopis was born on 21.02.1941 in Utena district. In 1963 he graduated from Vilnius University, Faculty of Physics and Mathematics. In 1964–1966 he worked as a trainee lecturer at the Department of Probability Theory and Number Theory of the ...
Vilijandas Bagdonavičius +3 more
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Demonstratio Mathematica, 2022 In this article, by virtue of expansions of two finite products of finitely many square sums, with the aid of series expansions of composite functions of (hyperbolic) sine and cosine functions with inverse sine and cosine functions, and in the light of ...
Qi Feng
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On Some Formulas for the Lauricella Function
Mathematics, 2023 Lauricella, G. in 1893 defined four multidimensional hypergeometric functions FA, FB, FC and FD. These functions depended on three variables but were later generalized to many variables.
Ainur Ryskan, Tuhtasin Ergashev
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THE FINITE SUM OF THE PRODUCTS OF TWO TOEPLITZ OPERATORS [PDF]
Journal of the Australian Mathematical Society, 2009 AbstractWe consider in this paper the question of when the finite sum of products of two Toeplitz operators is a finite-rank perturbation of a single Toeplitz operator on the Hardy space over the unit disk. A necessary condition is found. As a consequence we obtain a necessary and sufficient condition for the product of three Toeplitz operators to be a
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