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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。 | |
The theory is applied to the case of cubic hypersurfaces, which is the one most relevant to special geometry, obtaining the solution of the two classification problems and the description of the corresponding homogeneous special K?hler manifolds.
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Well known wonderfulG-varieties are those of rank zero, namely the generalized flag varietiesG/P, those of rank one, classified in [A], and certain complete symmetric varieties described in [DP] such as the famous space of complete conics.
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[M]) for the symplectic case and Berndt and Vanhecke [BV1] for the rank-one case.
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In the present article we propose a more detailed proof of this fact than the one given by Varagnolo and Vasserot.
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The first one is a conjecture of Ian Hughes which states that iff1, ..., fn are primary invariants of a finite linear groupG, then the least common multiple of the degrees of thefi is a multiple of the exponent ofG.
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The method applies to the standard arithmetic subgroups ofSO(n,1) (a case which was proved previously by Millson [Mi]), to the non-arithmetic lattices inSO(n,1) constructed by Gromov and Piatetski-Shapiro [GPS] and to groups generated by reflections.
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In all these cases we actually show that Γ=π1(M) has a finite index subgroup which is mapped onto a nonabelian free group.
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We consider some remarkable central elements of the universal enveloping algebraU(gl(n)) which we call quantum immanants.
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The aim of the paper is to describe all open subsets of a projective space with an action of a reductive group which admits a good quotient.
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As in the case of Mumford's geometric invariant theory (which concerns projective good quotients) the problem can be reduced to the case of an action of a torus.
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Recently one of the authors obtained a classification of simple infinite dimensional Lie superalgebras of vector fields which extends the well known classification of E.
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The proof of the results uses an extension of the Littlewood-Paley-Stein theory of square functions to the vector-valued case and inequalities previously proved by one of the authors in the context of the Riesz transforms of order one.
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For 0 ≤α >amp;lt; ∞ let Tαf denote one of the operators We characterize the pairs of weights (u, v) for which Tα is a bounded operator from Lp(v) to Lq(u), 0 >amp;lt;p ≤q >amp;lt; ∞.
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The Calderón Projector, is one of the most important tools in the study of boundary value problems for elliptic operators.
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The Density Theorem for Gabor Frames is one of the fundamental results of time-frequency analysis.
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It is known [7] that dualizing a form of the Poisson summation formula yields a pair of linear transformations which map a function ? of one variable into a function and its cosine transform in a generalized sense.
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In this article we develop the theory of one-sided versions of the g function of Littlewood and Paley, the area function S of Lusin and the that admit weighted norm estimates with weights belonging to the classes Ap+ of Sawyer.
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This criterion implies several results concerning the problem of integrable solutions of n-scale refinement equations and the problem of absolutely continuity of distribution function of one random series.
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We discuss the linear independence of systems ofmvectors in n-dimensional complex vector spaces where the m vectors are time-frequency shifts of one generating vector.
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The notions of localization and related approximation properties are a spectrum of ideas that quantify the degree to which elements of one frame can be approximated by elements of another frame.
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