Main theorems

We construct an exhaustive submeasure that is not equivalent to a measure. This solves problems of J. von Neumann (1937) and D. Maharam (1947). Contents 1. Introduction 2. Roberts 3. Farah 4. The construction 5. The main estimate 6. Exhaustivity 7. Proof of Theorems 1.2 to 1.4 References 1. Introduction Consider a Boolean algebra B of sets.

30p dontetvui 17-01-2013 77 11   Download

We prove that there are arbitrarily long arithmetic progressions of primes. There are three major ingredients. The first is Szemer´di’s theorem, which ase serts that any subset of the integers of positive density contains progressions of arbitrary length. The second, which is the main new ingredient of this paper, is a certain transference principle. This allows us to deduce from Szemer´di’s e theorem that any subset of a sufficiently pseudorandom set (or measure) of positive relative density contains progressions of arbitrary length. ...

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We establish new results and introduce new methods in the theory of measurable orbit equivalence, using bounded cohomology of group representations. Our rigidity statements hold for a wide (uncountable) class of groups arising from negative curvature geometry.

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Let X = G/H be a reductive symmetric space and K a maximal compact subgroup of G. The image under the Fourier transform of the space of K-finite compactly supported smooth functions on X is characterized. Contents 1. Introduction 2. Notation 3. The Paley-Wiener space. Main theorem 4. Pseudo wave packets 5. Generalized Eisenstein integrals 6. Induction of Arthur-Campoli relations 7. A property of the Arthur-Campoli relations 8. Proof of Theorem 4.4 9.

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We classify measures on the locally homogeneous space Γ\ SL(2, R) × L which are invariant and have positive entropy under the diagonal subgroup of SL(2, R) and recurrent under L. This classification can be used to show arithmetic quantum unique ergodicity for compact arithmetic surfaces, and a similar but slightly weaker result for the finite volume case. Other applications are also presented. In the appendix, joint with D. Rudolph, we present a maximal ergodic theorem, related to a theorem of Hurewicz, which is used in theproof of the main result. ...

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Let p be a prime number, F a totally real field such that [F (µp ) : F ] = 2 and [F : Q] is odd. For δ ∈ F × , let [ δ ] denote its class in F × /F ×p . In this paper, we show Main Theorem. There are infinitely many classes [ δ ] ∈ F × /F ×p such that the twisted affine Fermat curves Wδ : have no F -rational points. Remark. It is clear that if [ δ ] = [ δ ], then Wδ is isomorphic to Wδ over F . For any δ ∈ F × , Wδ /F has rational points locally everywhere.

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The main question studied in this article may be viewed as a nonlinear analogue of Dvoretzky’s theorem in Banach space theory or as part of Ramsey theory in combinatorics. Given a finite metric space on n points, we seek its subspace of largest cardinality which can be embedded with a given distortion in Hilbert space. We provide nearly tight upper and lower bounds on the cardinality of this subspace in terms of n and the desired distortion. Our main theorem states that for any 0, every n point metric space contains a subset of size at least n1−...

68p noel_noel 17-01-2013 37 5   Download

This paper is devoted to the proof of the orbifold theorem: If O is a compact connected orientable irreducible and topologically atoroidal 3-orbifold with nonempty ramification locus, then O is geometric (i.e. has a metric of constant curvature or is Seifert fibred). As a corollary, any smooth orientationpreserving nonfree finite group action on S 3 is conjugate to an orthogonal action. Contents 1. Introduction 2. 3-dimensional orbifolds 2.1. Basic definitions 2.2. Spherical and toric decompositions 2.3. Finite group actions on spheres with fixed points 2.4.

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Given a permutation w ∈ Sn , we consider a determinantal ideal Iw whose generators are certain minors in the generic n × n matrix (filled with independent variables). Using ‘multidegrees’ as simple algebraic substitutes for torus-equivariant cohomology classes on vector spaces, our main theorems describe, for each ideal Iw : • variously graded multidegrees and Hilbert series in terms of ordinary and double Schubert and Grothendieck polynomials;

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This paper is the fourth in a series where we describe the space of all embedded minimal surfaces of fixed genus in a fixed (but arbitrary) closed 3manifold. The key is to understand the structure of an embedded minimal disk in a ball in R3 . This was undertaken in [CM3], [CM4] and the global version of it will be completed here; see the discussion around Figure 12 for the local case and [CM15] for some more details. Our main results are Theorem 0.1 (the lamination theorem) and Theorem 0.2 (the one-sided curvature estimate). ...

44p tuanloccuoi 04-01-2013 64 7   Download

The usual index theorems for holomorphic self-maps, like for instance the classical holomorphic Lefschetz theorem (see, e.g., [GH]), assume that the fixed-points set contains only isolated points. The aim of this paper, on the contrary, is to prove index theorems for holomorphic self-maps having a positive dimensional fixed-points set. The origin of our interest in this problem lies in holomorphic dynamics.

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The induction hypotheses Application to endoscopic and stable expansions Cancellation of p-adic singularities Separation by infinitesimal character Elimination of restrictions on f Local trace formulas Local Theorem 1 Weak approximation Global Theorems 1 and 2 10. Concluding remarks Introduction This paper is the last of three articles designed to stabilize the trace formula. Our goal is to stabilize the global trace formula for a general connected group, subject to a condition on the fundamental lemma that has been established in some special cases.

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MULTIPLE SOLUTIONS FOR QUASILINEAR ELLIPTIC NEUMANN PROBLEMS IN ORLICZ-SOBOLEV SPACES NIKOLAOS HALIDIAS AND VY K. LE Received 15 October 2004 and in revised form 21 January 2005 We investigate the existence of multiple solutions to quasilinear elliptic problems containing Laplace like operators (φ-Laplacians). We are interested in Neumann boundary value problems and our main tool is Br´ zis-Nirenberg’s local linking theorem. e 1. Introduction In this paper, we consider the following elliptic problem with Neumann boundary condition, −div α ∇u(x) ∇u(x) = g(x,u) a.e. on Ω (1.1) ∂u = 0 a.e.

8p sting12 10-03-2012 27 2   Download

OF INVARIANT FIBER BUNDLES FOR DYNAMIC EQUATIONS ON MEASURE CHAINS ¨ CHRISTIAN POTZSCHE AND STEFAN SIEGMUND Received 8 August 2003 m -SMOOTHNESS We present a new self-contained and rigorous proof of the smoothness of invariant fiber bundles for dynamic equations on measure chains or time scales. Here, an invariant fiber bundle is the generalization of an invariant manifold to the nonautonomous case.

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FINITE DIFFERENCE SCHEMES WITH MONOTONE OPERATORS N. C. APREUTESEI Received 13 October 2003 and in revised form 10 December 2003 To the memory of my mother, Liliana Several existence theorems are given for some second-order difference equations associated with maximal monotone operators in Hilbert spaces. Boundary conditions of monotone type are attached. The main tool used here is the theory of maximal monotone operators. 1. Introduction In [1, 2], the authors proved the existence of the solution of the boundary value problem p(t)u (t) + r(t)u (t) ∈ Au(t) + f (t), u (0) ∈ α u(0) − a , a.e.

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What makes work with rational numbers and integers comfortable are the essential properties they have, especially the unique factorization property (the Main Theorem of Arithmetic). However, the might of the arithmetic in Q is bounded. Thus, some polynomials, although they have zeros, cannot be factorized into polynomials with rational coefficients.

7p phuctran399 14-11-2010 73 6   Download

Stability Issues in RNN Architectures Perspective The focus of this chapter is on stability and convergence of relaxation realised through NARMA recurrent neural networks. Unlike other commonly used approaches, which mostly exploit Lyapunov stability theory, the main mathematical tool employed in this analysis is the contraction mapping theorem (CMT), together with the fixed point iteration (FPI) technique. This enables derivation of the asymptotic stability (AS) and global asymptotic stability (GAS) criteria for neural relaxive systems.

19p doroxon 12-08-2010 105 9   Download