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AbstractAbstract
[en] When f(z) is given by a known power series expansion, it is possible to construct the power series expansion for f(z; p) = e-pz f(z). We define popt to be the value of p for which the expansion for f(z; p) converges most rapidly. When f(z) is an entire function of order 1, we show that popt is uniquely defined and may be characterized in terms of the set of singularities zi = 1/sigmai of an associated function h(z). Specifically, it is the center of the smallest circle in the complex plane which contains all points sigmai
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Record Type
Journal Article
Journal
Mathematics of Computation; ISSN 0025-5718;
; v. 39(160); p. 587-597

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AbstractAbstract
[en] In this paper, nonlocal symmetries for the bilinear semi-discrete Kadomtsev-Petviashvili (KP) and bilinear semi-discrete B-type KP (BKP) equations are derived. By expanding these nonlocal symmetries in power series of each of two parameters, we have derived bilinear negative semi-discrete KP and BKP hierarchies. An interesting observation is that bilinear positive and negative semi-discrete KP hierarchies may be derived from the same nonlocal symmetry for the semi-discrete KP equation.
Primary Subject
Source
SIDE 8: International conference on symmetries and integrability of difference equations; Ste-Adele, PQ (Canada); 22-28 Jun 2008; S1751-8113(09)10908-3; Available from http://dx.doi.org/10.1088/1751-8113/42/45/454022; Country of input: International Atomic Energy Agency (IAEA)
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Journal Article
Literature Type
Conference
Journal
Journal of Physics. A, Mathematical and Theoretical (Online); ISSN 1751-8121;
; v. 42(45); [12 p.]

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Moodie, Jordan C; Long, M W, E-mail: jxm276@student.bham.ac.uk2021
AbstractAbstract
[en] An exact representation of the Baker–Campbell–Hausdorff formula as a power series in just one of the two variables is constructed. Closed form coefficients of this series are found in terms of hyperbolic functions, which contain all of the dependence on the second variable. It is argued that this exact series may then be truncated and be expected to give a good approximation to the full expansion if only the perturbative variable is small. This improves upon existing formulae, which require both to be small. Several different representations are provided and emphasis is given to the situation where one of the matrices is diagonal, where a particularly easy to use formula is obtained. (paper)
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Source
Available from http://dx.doi.org/10.1088/1751-8121/abcbae; Country of input: International Atomic Energy Agency (IAEA)
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Journal Article
Journal
Journal of Physics. A, Mathematical and Theoretical (Online); ISSN 1751-8121;
; v. 54(1); [30 p.]

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AbstractAbstract
[en] Von Neumann's method of generating random variables with the exponential distribution and Forsythe's method for obtaining distributions with densities of the form e/sup -G//sup( x/) are generalized to apply to certain power series representations. The flexibility of the power series methods is illustrated by algorithms for the Cauchy and geometric distributions
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Journal Article
Journal
Mathematics of Computation; ISSN 0025-5718;
; v. 33(147); p. 1065-1069

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AbstractAbstract
[en] We find order estimates for the modulus of variation and the averaged modulus of the sum of a lacunary trigonometric series in terms of its coefficients. These interesting global characteristics of a function and their applications have been studied in papers by Chanturiya, Dolzhenko, Sevast'yanov, Sendov, Popov, and others. Since the sum of a lacunary trigonometric series has frequently been used in the theory of functions to provide an example of a function having one property or another, it is useful to know as much as possible about such a function, especially such global characteristics as the modulus of variation and the averaged modulus. We also give necessary and sufficient conditions for the sum of a lacunary trigonometric series to belong to certain classes of functions defined in terms of these characteristics
Primary Subject
Source
Available from http://dx.doi.org/10.1070/SM1998v189n05ABEH000317; Country of input: International Atomic Energy Agency (IAEA)
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Journal Article
Journal
Sbornik. Mathematics; ISSN 1064-5616;
; v. 189(5); p. 639-656

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AbstractAbstract
[en] Certain special classes of division algebras over the field of Laurent power series with arbitrary residue field are studied. We call algebras in these classes split and well-split algebras. These classes are shown to contain the group of tame division algebras. For the class of well-split division algebras we prove a decomposition theorem which is a generalization of the well-known decomposition theorems of Jacob and Wadsworth for tame division algebras. For both classes we introduce the notion of a δ-map and develop the technique of δ-maps for division algebras in these classes. Using this technique we prove decomposition theorems, reprove several old well-known results of Saltman, and prove Artin's conjecture on the period and index in the local case: the exponent of a division algebra A over a C2-field F is equal to the index of A if F=F1((t)), where F1 is a C1-field. In addition we obtain several results on split division algebras, which, we hope, will help in further research of wild division algebras.
Primary Subject
Source
Available from http://dx.doi.org/10.1070/SM2004v195n06ABEH000825; Country of input: International Atomic Energy Agency (IAEA)
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Journal Article
Journal
Sbornik. Mathematics; ISSN 1064-5616;
; v. 195(6); p. 783-817

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Shigyo, Yoko, E-mail: yoko.shigyo@gmail.com2016
AbstractAbstract
[en] We study the series expansion of the tau function of the BKP hierarchy applying the addition formulae of the BKP hierarchy. Any formal power series can be expanded in terms of Schur functions. It is known that, under the condition , a formal power series is a solution of the KP hierarchy if and only if its coefficients of Schur function expansion are given by the so called Giambelli type formula. A similar result is known for the BKP hierarchy with respect to Schur’s Q-function expansion under a similar condition. In this paper we generalize this result to the case of . (paper)
Primary Subject
Source
Available from http://dx.doi.org/10.1088/1751-8113/49/29/295201; Country of input: International Atomic Energy Agency (IAEA)
Record Type
Journal Article
Journal
Journal of Physics. A, Mathematical and Theoretical (Online); ISSN 1751-8121;
; v. 49(29); [17 p.]

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Lutovac, Tatjana; Malešević, Branko; Rašajski, Marija, E-mail: tatjana.lutovac@etf.bg.ac.rs, E-mail: branko.malesevic@etf.bg.ac.rs, E-mail: marija.rasajski@etf.bg.ac.rs2018
AbstractAbstract
[en] In this paper we present a new approach to proving some exponential inequalities involving the sinc function. Power series expansions are used to generate new polynomial inequalities that are sufficient to prove the given exponential inequalities.
Primary Subject
Source
Copyright (c) 2018 Springer Nature Switzerland AG; Article Copyright (c) 2018 Springer International Publishing AG, part of Springer Nature; Country of input: International Atomic Energy Agency (IAEA)
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Journal Article
Journal
Results in Mathematics; ISSN 1422-6383;
; v. 73(3); p. 1-15

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AbstractAbstract
[en] We study the behaviour of the quantities an(q) and bn(q), that is, the number of nth power residues in the reduced and complete residue systems modulo a composite number q, respectively, where n≥2 is an arbitrary fixed number. In particular, we prove asymptotic formulae for the sum functions An(x) and Bn(x) of these quantities.
Primary Subject
Source
Available from http://dx.doi.org/10.1070/IM2010v074n06ABEH002522; Country of input: International Atomic Energy Agency (IAEA)
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Journal Article
Journal
Izvestiya. Mathematics; ISSN 1064-5632;
; v. 74(6); p. 1225-1254

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Noonan, William A.
Korean Nuclear Society - KNS, Nutopia Building, Jangdae-dong, 794, Yuseongdaero, Yuseong-gu, Daejeon 34166 (Korea, Republic of)2017
Korean Nuclear Society - KNS, Nutopia Building, Jangdae-dong, 794, Yuseongdaero, Yuseong-gu, Daejeon 34166 (Korea, Republic of)2017
AbstractAbstract
[en] This paper derives integral representations for the multiplicity distribution of neutrons leaked from a multiplying assembly and the multiplicity distribution for those leaked neutrons that are then detected by a measurement system. The probability generating function (PGF) of the leaked neutron distribution is governed by Boehnel's equations, and an equivalent set of equations for the PGF of the detected neutron distribution is also given. This paper presents a method that utilizes functional power series for solving these two sets of equations for the respective PGFs and inverting those PGFs to arrive at the underlying multiplicity distributions. (authors)
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Apr 2017; 5 p; Korean Nuclear Society - KNS; Daejeon (Korea, Republic of); M and C 2017: International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering 2017; Jeju (Korea, Republic of); 16-20 Apr 2017; Country of input: France; 13 refs.; Available from the INIS Liaison Officer for France, see the INIS website for current contact and E-mail addresses
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Book
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Conference
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