Search results for "Theorem"
showing 10 items of 1250 documents
Abelian varieties and theta functions associated to compact Riemannian manifolds; constructions inspired by superstring theory
2012
We look into a construction of principal abelian varieties attached to certain spin manifolds, due to Witten and Moore-Witten around 2000 and try to place it in a broader framework. This is related to Weil intermediate Jacobians but it also suggests to associate abelian varieties to polarized even weight Hodge structures. The latter construction can also be explained in terms of algebraic groups which might be useful from the point of view of Tannakian categories. The constructions depend on moduli much as in Teichm\"uller theory although the period maps in general are only real analytic. One of the nice features is how the index for certain differential operators canonically associated to …
Tensor Operators and the Wigner-Eckart Theorem
2007
In this chapter we pave the way to the use of the coupling methods of Chap. 1 for manipulating operators and their matrix elements. To enable smooth application of the angular momentum methods, we introduce so-called spherical tensor operators. Spherical tensors can be related to Cartesian tensors. A Cartesian tensor of a given Cartesian rank can be reduced to spherical tensors of several spherical ranks. There is a very convenient procedure, the so-called Wigner-Eckart theorem, to separate the part containing the projection quantum numbers from the rest of the matrix element of a spherical tensor operator. The remaining piece, called the reduced matrix element, is rotationally invariant an…
Distributed Consensus on Boolean Information
2009
Abstract In this paper we study the convergence towards consensus on information in a distributed system of agents communicating over a network. The particularity of this study is that the information on which the consensus is seeked is not represented by real numbers, rather by logical values or sets. Whereas the problems of allowing a network of agents to reach a consensus on logical functions of input events, and that of agreeing on set–valued information, have been separately addressed in previous work, in this paper we show that these problems can indeed be attacked in a unified way in the framework of Boolean distributed information systems. Based on a notion of contractivity for Bool…
Analog Multiple Description Joint Source-Channel Coding Based on Lattice Scaling
2015
Joint source-channel coding schemes based on analog mappings for point-to-point channels have recently gained attention for their simplicity and low delay. In this paper, these schemes are extended either to scenarios with or without side information at the decoders to transmit multiple descriptions of a Gaussian source over independent parallel channels. They are based on a lattice scaling approach together with bandwidth reduction analog mappings adapted for this multiple description scenario. The rationale behind lattice scaling is to improve performance through bandwidth expansion. Another important contribution of this paper is the proof of the separation theorem for the communication …
Kolmogorov superposition theorem for image compression
2012
International audience; The authors present a novel approach for image compression based on an unconventional representation of images. The proposed approach is different from most of the existing techniques in the literature because the compression is not directly performed on the image pixels, but is rather applied to an equivalent monovariate representation of the wavelet-transformed image. More precisely, the authors have considered an adaptation of Kolmogorov superposition theorem proposed by Igelnik and known as the Kolmogorov spline network (KSN), in which the image is approximated by sums and compositions of specific monovariate functions. Using this representation, the authors trad…
A Representation of Relational Systems
2003
In this paper elements of a theory of multistructures are formulated. The theory of multistructures is used to define a binary representation of relational systems.
New Representations for Multidimensional Functions Based on Kolmogorov Superposition Theorem. Applications on Image Processing
2012
Mastering the sorting of the data in signal (nD) can lead to multiple applications like new compression, transmission, watermarking, encryption methods and even new processing methods for image. Some authors in the past decades have proposed to use these approaches for image compression, indexing, median filtering, mathematical morphology, encryption. A mathematical rigorous way for doing such a study has been introduced by Andrei Nikolaievitch Kolmogorov (1903-1987) in 1957 and recent results have provided constructive ways and practical algorithms for implementing the Kolmogorov theorem. We propose in this paper to present those algorithms and some preliminary results obtained by our team…
Quantum Real - Time Turing Machine
2001
The principles of quantum computation differ from the principles of classical computation very much. Quantum analogues to the basic constructions of the classical computation theory, such as Turing machine or finite 1-way and 2-ways automata, do not generalize deterministic ones. Their capabilities are incomparable. The aim of this paper is to introduce a quantum counterpart for real - time Turing machine. The recognition of a special kind of language, that can't be recognized by a deterministic real - time Turing machine, is shown.
Space-Efficient 1.5-Way Quantum Turing Machine
2001
1.5QTM is a sort of QTM (Quantum Turing Machine) where the head cannot move left (it can stay where it is and move right). For computations is used other - work tape. In this paper will be studied possibilities to economize work tape space more than the same deterministic Turing Machine can do (for some of the languages). As an example language (0i1i|i ≥ 0) is chosen, and is proved that this language could be recognized by deterministic Turing machine using log(i) cells on work tape , and 1.5QTM can recognize it using constant cells quantity.
Convex semi-infinite games
1986
This paper introduces a generalization of semi-infinite games. The pure strategies for player I involve choosing one function from an infinite family of convex functions, while the set of mixed strategies for player II is a closed convex setC inRn. The minimax theorem applies under a condition which limits the directions of recession ofC. Player II always has optimal strategies. These are shown to exist for player I also if a certain infinite system verifies the property of Farkas-Minkowski. The paper also studies certain conditions that guarantee the finiteness of the value of the game and the existence of optimal pure strategies for player I.