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|  | | 为了更好的帮助您理解掌握查询词或其译词在地道英语中的实际用法,我们为您准备了出自英文原文的大量英语例句,供您参考。 | |
This implies that a system is algebraically integrable (i.e., its eigenvalue problem is explicitly solvable in quadratures) if and only if the differential Galois group is commutative for generic eigenvalues.
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We apply this criterion of algebraic integrability to two examples: finite-zone potentials and the elliptic Calogero-Moser system.
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In the second example, we obtain a proof of the Chalyh-Veselov conjecture that the Calogero-Moser system with integer parameter is algebraically integrable, using the results of Felder and Varchenko.
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The least upper bound for the degrees of elements in a system of generators turns out to be independent of the number of vector variables.
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We consider 3-parametric polynomialsPμ*(x; q, t, s) which replace theAn-series interpolation Macdonald polynomialsPμ*(x; q, t) for theBCn-type root system.
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Quantum integrable systems and differential Galois theory
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This paper is devoted to a systematic study of quantum completely integrable systems (i.e., complete systems of commuting differential operators) from the point of view of algebraic geometry.
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We investigate the eigenvalue problem for such systems and the correspondingD-module when the eigenvalues are in generic position.
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We give explicit systems of generators of the algebras of invariant polynomials in arbitrary many vector variables for the classical reflection groups (including the dihedral groups).
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We show that manifolds which parameterize values of first integrals of integrable finite-dimensional bihamiltonian systems carry a geometric structure which we call aKronecker web.
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The least upper bound for the degrees of elements in a system of generators turns out to be independent of the number of vector variables.
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Fourier transforms related to a root system of rank 1
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Explicit bounds on the number of type V variables in a complete system of typical separating invariants are given for the binary polyhedral groups, and this is applied to the invariant theory of binary
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We extend to general finite groups a well-known relation used for checking the orthogonality of a system of vectors as well as for orthogonalizing a nonorthogonal one.
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We extend to general finite groups a well-known relation used for checking the orthogonality of a system of vectors as well as for orthogonalizing a nonorthogonal one.
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In our paper [KR] we began a systematic study of representations of the universal central extension[InlineEquation not available: see fulltext.] of the Lie algebra of differential operators on the circle.
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This paper is devoted to a systematic study of quantum completely integrable systems (i.e., complete systems of commuting differential operators) from the point of view of algebraic geometry.
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The present paper contains a systematic study of the structure of metric Lie algebras, i.e., finite-dimensional real Lie algebras equipped with a nondegenerate invariant
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The results indicate that the method is reliable, sensitive, systematic and is especially suitable for practical use.
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A systematic investigation was performed on the influence of several factors such as ageing of the reaction mixture, alkalinity, salt addition and temperature on the formation of a mordenite membrane on the seeded support.
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