共查询到20条相似文献,搜索用时 15 毫秒
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Bilinear restriction estimates have appeared in work of Bourgain, Klainerman, and Machedon. In this paper we develop the theory of these estimates (together with the analogues for Kakeya estimates). As a consequence we improve the spherical restriction theorem of Wolff from to , and also obtain a sharp spherical restriction theorem for .
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We explore the interlacing between model category structures attained to classes of modules of finite $\mathcal {X}$‐dimension, for certain classes of modules $\mathcal {X}$. As an application we give a model structure approach to the finitistic dimension conjectures and present a new conceptual framework in which these conjectures can be studied. 相似文献
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Let G be a connected reductive linear algebraic group. We use geometric methods to investigate G-completely reducible subgroups of G, giving new criteria for G-complete reducibility. We show that a subgroup of G is G-completely reducible if and only if it is strongly reductive in G; this allows us to use ideas of R.W. Richardson and Hilbert–Mumford–Kempf from geometric invariant theory. We deduce that a normal subgroup of a G-completely reducible subgroup of G is again G-completely reducible, thereby providing an affirmative answer to a question posed by J.-P. Serre, and conversely we prove that the normalizer of a G-completely reducible subgroup of G is again G-completely reducible. Some rationality questions and applications to the spherical building of G are considered. Many of our results extend to the case of non-connected G. Mathematics Subject Classification (2000) 20G15, 14L24, 20E42 相似文献
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We prove some results on the geometry of the level sets of harmonic functions, particularly regarding their ‘oscillation’ and ‘pinching’ properties. These results allow us to tackle three recent conjectures due to De Carli and Hudson (Bull London Math Soc 42:83–95, 2010). Our approach hinges on a combination of local constructions, methods from differential topology and global extension arguments. 相似文献
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Lee A. Butler 《The Ramanujan Journal》2017,42(1):199-221
Some special cases of Wilkie’s conjecture are shown to be equivalent to real versions of the three and four exponentials conjectures. Wilkie’s conjecture is an open problem originating in model theory that concerns the density of algebraic points in sets defined using the exponential function; the latter conjectures concern the algebraic nature of values of the exponential function. 相似文献
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In 1969 Denniston [3] gave a construction of maximal arcs of degree d in Desarguesian projective planes of even order q, for all d dividing q. In 2002 Mathon [8] gave a construction method generalizing the one of Denniston. We will give a new geometric approach to these maximal arcs. This will allow us to count the number of isomorphism classes of Mathon maximal arcs of degree 8 in PG(2,h2), h prime. 相似文献
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《Comptes Rendus de l'Academie des Sciences Series IIA Earth and Planetary Science》2001,332(2):157-162
We introduce a new geometric approach for studying the Duality of Metric Entropy (of operators, or of convex sets). We demonstrate such duality, up to a logarithmic factor, in one important case, for the hitherto not-too-well understood low `levels of resolution'. 相似文献
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Most existing methods of global optimization for generalized geometric programming (GGP) actually compute an approximate optimal
solution of a linear or convex relaxation of the original problem. However, these approaches may sometimes provide an infeasible
solution, or far from the true optimum. To overcome these limitations, a robust solution algorithm is proposed for global
optimization of (GGP) problem. This algorithm guarantees adequately to obtain a robust optimal solution, which is feasible
and close to the actual optimal solution, and is also stable under small perturbations of the constraints. 相似文献
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Jeffrey Stewart Ely 《代数通讯》2013,41(12):1533-1544
A geometric viewpoint of much broader potential yields a unified proof of the quadratic reciprocity law based on counting points on quadratic surfaces over finite prime fields. 相似文献
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Kinematic analysis, in contrast to sophisticated molecular dynamics simulations, can provide high-level insights into conformational diversity of proteins and other biomolecules, with broad implications for human health. Here, we model a protein as a kinematic linkage and present a new geometric method to characterize molecular rigidity. While existing combinatorial constraint counting is limited to generic structures, our geometric approach is also valid for non-generic linkages. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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Václav Mácha 《Central European Journal of Mathematics》2011,9(4):874-887
We deal with a generalization of the Stokes system. Instead of the Laplace operator, we consider a general elliptic operator and a pressure gradient with small perturbations. We investigate the existence and uniqueness of a solution as well its regularity properties. Two types of regularity are provided. Aside from the classical Hilbert regularity, we also prove the Hölder regularity for coefficients in VMO space. 相似文献
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The paper concerns a posteriori estimates of functional type for the difference between exact and approximate solutions to
a generalized Stokes problem. The estimates are derived by transformations of the basic integral identity defining a generalized
solution to the problem using the method suggested by the first author. The estimates obtained can be classified into two
types. Estimates of the first type are valid only for solenoidal functions, while estimates of the second type are applicable
for any functions that belong to the energy space of the respective problem and satisfy the boundary conditions. In the second
case, the estimates include an additional penalty term with a multiplier defined by the constant in the Ladyzhenskaya-Babuška-Brezzi
condition. It is proved that a posteriori estimates for the velocity field yield computable estimates of the difference between
exact and approximate pressure functions in the L2-norm. It is shown that the estimates provide sharp upper and lower bounds of the error and their practical computation requires
to solve only finite-dimensional problems. Bibliography: 34 titles.
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Translated from Problemy Matematicheskogo Analiza, No. 34, 2006, pp. 89–101. 相似文献