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Asymptotic expansions for ordinary differential equations
TLDR
Asymptotic expansions for ordinary differential equations as discussed by the authors, asymptotics expansions for ODEs, Asymptotically expansion for ordinary DDEs and their derivatives.Abstract:
Asymptotic expansions for ordinary differential equations , Asymptotic expansions for ordinary differential equations , مرکز فناوری اطلاعات و اطلاع رسانی کشاورزیread more
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NOTES ON THE KAZHDAN-LUSZTIG THEOREM ON EQUIVALENCE OF THE DRINFELD CATEGORY AND THE CATEGORY OF Uqg-MODULES
Sergey Neshveyev,Lars Tuset +1 more
TL;DR: In this article, Kazhdan and Lusztig showed the equivalence of the Drinfeld cate-goryD(g;~) of g-modules and the category of nite dimensional Uqg-modules, q = e i ~, for 2 CnQ.
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A density theorem for parameterized differential Galois theory
Abstract: We study parameterized linear differential equations with coefficients depending meromorphically upon the parameters As a main result, analogously to the unparameterized density theorem of Ramis, we show that the parameterized monodromy, the parameterized exponential torus and the parameterized Stokes operators are topological generators in Kolchin topology, for the parameterized differential Galois group introduced by Cassidy and Singer We prove an analogous result for the global parameterized differential Galois group, which generalizes a result by Mitschi and Singer These authors give also a necessary condition on a group for being a global parameterized differential Galois group; as a corollary of the density theorem, we prove that their condition is also sufficient As an application, we give a characterization of completely integrable equations, and we give a partial answer to a question of Sibuya about the transcendence properties of a given Stokes matrix Moreover, using a parameterized Hukuhara-Turrittin theorem, we show that the Galois group descends to a smaller field, whose field of constants is not differentially closed
Proceedings ArticleDOI
Gamma conjecture via mirror symmetry
Sergey Galkin,Hiroshi Iritani +1 more
TL;DR: The Gamma conjecture of Vasily Golyshev and the present authors of as discussed by the authors implies that the principal asymptotic class A_F equals the Gamma class G_F associated to Euler's $\Gamma$-function.
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A semi-analytical solution method for two dimensional Helmholtz Equation
TL;DR: A semi-analytical solution method, the scaled boundary finite element method (SBFEM), was developed for the two-dimensional Helmholtz equation in this article, which is applicable to 2D computational domains of any shape including unbounded domains.
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An exactly solvable system from quantum optics
TL;DR: In this article, a generalisation of the Rabi system in the Bargmann-Fock representation is proposed, in which the eigenproblem of the considered quantum model is described by a system of two linear differential equations with one independent variable, and an interpretation of the obtained results in terms of differential Galois group of the system is also given.