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作者：Hiary, Ghaith Ayesh
摘要：A poly-log time method to compute the truncated theta function, its derivatives, and integrals is presented. The method is elementary, rigorous, explicit, and suited for computer implementation. We repeatedly apply the Poisson summation formula to the truncated theta function while suitably normalizing the linear and quadratic arguments after each repetition. The method relies on the periodicity of the complex exponential, which enables the suitable normalization of the arguments, and on the s...
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作者：Wang, Xu-Jia
摘要：In this paper we study the classification of ancient convex solutions to the mean curvature flow in Rn+1. An open problem related to the classification of type II singularities is whether a convex translating solution is k-rotationally symmetric for some integer 2 <= k <= n, namely whether its level set is a sphere or cylinder Sk-1 x Rn-k. In this paper we give an affirmative answer for entire solutions in dimension 2. In high dimensions we prove that there exist nonrotationally symmetric, ent...
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作者：Chemin, Jean-Yves; Gallagher, Isabelle; Paicu, Marius
摘要：In previous works by the first two authors, classes of initial data to the three-dimensional, incompressible Navier-Stokes equations were presented, generating a global smooth solution although the norm of the initial data may be chosen arbitrarily large. The main feature of the initial data considered in one of those studies is that it varies slowly in one direction, though in some sense it is well-prepared (its norm is large but does not depend on the slow parameter). The aim of this article...
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作者：Haydon, Richard; Odell, Edward; Schlumprecht, Thomas
摘要：We prove that if X is a subspace of L-p (2 < p < infinity), then either X embeds isomorphically into l(p) circle plus l(2) or X contains a subspace Y, which is isomorphic to l(p)(l(2)). We also give an intrinsic characterization of when X embeds into fp e 2 in terms of weakly null trees in X or, equivalently, in terms of the infinite asymptotic game played in X. This solves problems concerning small subspaces of L-p originating in the 1970's. The techniques used were developed over several dec...
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作者：Shapira, Uri
摘要：We prove that almost any pair of real numbers alpha, beta, satisfies the following inhomogeneous uniform version of Littlewood's conjecture: (C1) for all gamma, delta is an element of R, liminf(vertical bar n vertical bar -> infinity)vertical bar n vertical bar < n alpha - gamma > < n beta - delta > = 0, where <.> denotes the distance from the nearest integer. The existence of even a single pair that satisfies statement (C1), solves a problem of Cassels from the 50's. We then prove that if 1, ...
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作者：Freed, Daniel S.; Hopkins, Michael J.; Teleman, Constantin
摘要：In this paper, we identify the Ad-equivariant twisted K-theory of a compact Lie group G with the Verlinde group of isomorphism classes of admissible representations of its loop groups. Our identification preserves natural module structures over the representation ring R(G) and a natural duality pairing. Two earlier papers in the series covered foundations of twisted equivariant K-theory, introduced distinguished families of Dirac operators and discussed the special case of connected groups wit...
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作者：Hadani, Ronny; Singer, Amit
摘要：In this paper, we reveal the formal algebraic structure underlying the intrinsic reconstitution algorithm, introduced by Singer and Shkolnisky in [9], for determining three dimensional macromolecular structures from images obtained by an electron microscope. Inspecting this algebraic structure, we obtain a conceptual explanation for the admissibility (correctness) of the algorithm and a proof of its numerical stability. In addition, we explain how the various numerical observations reported in...
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作者：Galatius, Soren
摘要：Homology of the group Aut(F-n) of automorphisms of a free group on n generators is known to be independent of n in a certain stable range. Using tools from homotopy theory, we prove that in this range it agrees with homology of symmetric groups. In particular we confirm the conjecture that stable rational homology of Aut(F-n) vanishes.
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作者：Constantin, Adrian; Escher, Joachim
摘要：We prove that the profile of a periodic traveling wave propagating at the surface of water above a flat bed in a flow with a real analytic vorticity must be real analytic, provided the wave speed exceeds the horizontal fluid velocity throughout the flow. The real analyticity of each streamline beneath the free surface holds even if the vorticity is only Holder continuously differentiable.
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作者：Guralnick, Robert M.; Pham Huu Tiep
摘要：Let G be a simple Chevalley group defined over F-q. We show that if r does not divide q and k is an algebraically closed field of characteristic r, then very few irreducible kG-modules have nonzero H-1(G, V). We also give an explicit upper bound for dim H-1(G, V) for V an irreducible kG-module that does not depend on q, but only on the rank of the group. Cline, Parshall and Scott showed that such a bound exists when r vertical bar q. We obtain extremely strong bounds in the case that a Borel s...
