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In 1991, one of the authors showed the existence of quadratic transformations between the Painlevé VI equations with local monodromy differences (1/2, a, b, ±1/2) and (a, a, b, b). In the present paper we give concise forms of these transformations. They are related to the quadratic transformations obtained by Manin and Ramani–Grammaticos–Tamizhmani via Okamoto transformations. To avoid cumbersome expressions with differentiation, we use contiguous relations instead of the Okamoto transformations. The 1991 transformation is particularly important as it can be realized as a quadratic‐pull back transformation of isomonodromic Fuchsian equations. The new formulas are illustrated by derivation of explicit expressions for several complicated algebraic Painlevé VI functions. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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Raimundas Vidūnas 《Journal of Mathematical Analysis and Applications》2010,365(1):135-141
It is tempting to evaluate F2(x,1) and similar univariate specializations of Appell's functions by evaluating the apparent power series at x=0 straight away using the Gauss formula for 2F1(1). But this kind of naive evaluation can lead to errors as the 2F1(1) coefficients might eventually diverge; then the actual power series at x=0 might involve branching terms. This paper demonstrates these complications by concrete examples. 相似文献
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Raimundas Vidunas Nico M. Temme 《Journal of Mathematical Analysis and Applications》2002,269(1):317-331
Computer algebra algorithms are developed for evaluating the coefficients in Airy-type asymptotic expansions that are obtained from integrals with a large parameter. The coefficients are defined from recursive schemes obtained from integration by parts. An application is given for the Weber parabolic cylinder function. 相似文献
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Motivated by a demand for explicit genus 1 Belyi maps from theoretical physics, we give an efficient method of explicitly computing genus one Belyi maps by (1) composing covering maps from elliptic curves to the Riemann sphere with simpler (univariate) genus zero Belyi maps, as well as by (2) composing further with isogenies between elliptic curves. The computed examples of genus 1 Belyi maps has doubly-periodic dessins d’enfant that are listed in the physics literature as so-called brane-tilings in the context of quiver gauge theories. 相似文献
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Algirdas Audzijonis Gediminas Gaigalas Leonardas Žigas Audrius Pauliukas Raimundas Žaltauskas Aurimas Čerškus Jurgis Narusis 《Central European Journal of Physics》2005,3(3):382-394
This paper presents the theoretical investigation of energy levels of valence bands (VB) and core levels (CL) of the ferroelectric
SbSl single crystals in antiferroelectric and ferroelectric phases. Since the best approximation for the deep VB levels is
a calculation by the Hartree-Fock method, the molecular model of a SbSI crystal was used for calculations. This model of the
crystal was also used for calculations of the total density of states. It was found that the VB and CL of this ferroelectric
semiconductor are sensitive to the small lattice distortion at the phase transition, and that an average of the total density
of states, when all atoms participate in oscillations of all normal modes, are more similar to the experimental X-ray photoelectron
spectra (XPS). The experimental splitting of CL obtained by XPS was compared with the theoretically calculated one by two
different methods. The cluster model calculations showed that the splitting of the CL in SbSI might be caused by photoelectron
emission from the atoms, which have different valence state, at the surface. 相似文献
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Raimundas Vidūnas 《Linear algebra and its applications》2007,422(1):39-57
Let V denote a vector space with finite positive dimension, and let (A, A∗) denote a Leonard pair on V. As is known, the linear transformations A, A∗ satisfy the Askey-Wilson relations
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Raimundas Vidūnas 《Discrete Mathematics》2008,308(4):479-495
It is known that if (A,A*) is a Leonard pair, then the linear transformations A, A* satisfy the Askey-Wilson relations
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The Ramanujan Journal - Algebraic hypergeometric functions can be compactly expressed as radical functions on pull-back curves where the monodromy group is simpler, say, a finite cyclic group.... 相似文献