共查询到20条相似文献,搜索用时 15 毫秒
1.
Yang Wang 《Advances in Computational Mathematics》2008,28(2):101-118
In transmission, storaging and coding of digital signals we frequently perform A/D conversion using quantization. In this
paper we study the maximal and mean square errors as a result of quantization. We focus on the sigma–delta modulation quantization
scheme in the finite frame expansion setting. We show that this problem is related to the classical Traveling Salesman Problem
(TSP) in the Euclidean space. It is known [Benedetto et al., Sigma–delta () quantization and finite frames, IEEE Trans. Inform. Theory 52, 1990–2005 (2006)] that the error bounds from the sigma–delta scheme depends on the ordering of the frame elements. By examining
a priori bounds for the Euclidean TSP we show that error bounds in the sigma–delta scheme is superior to those from the pulse code
modulation (PCM) scheme in general. We also give a recursive algorithm for finding an ordering of the frame elements that
will lead to good maximal error and mean square error.
Supported in part by the National Science Foundation grant DMS-0139261. 相似文献
2.
D. Sternheimer 《Journal of Mathematical Sciences》2007,141(4):1494-1505
We start with a short presentation of the difference in attitude between mathematicians and physicists even in their treatment
of physical reality, and look at the paradigm of quantization as an illustration. In particular, we stress the differences
in motivation and realization between the Berezin and deformation quantization approaches, exposing briefly Berezin’s view
of quantization as a functor. We continue with a schematic overview of deformation quantization and of its developments in
contrast with the latter and discuss related issues, in particular, the spectrality question. We end by a very short survey
of two main avatars of deformation quantization, quantum groups and quantum spaces (especially noncommutative geometry) presented
in that perspective. Bibliography: 74 titles.
This paper is dedicated to the memory of “Alik” Berezin
Published in Zapiski Nauchnykh Seminarov POMI, Vol. 331, 2006, pp. 199–220. 相似文献
3.
Evolution Equations for Markov Cocycles Obtained by Second Quantization in the Symplectic Fock Space
G. G. Amosov 《Theoretical and Mathematical Physics》2006,146(1):152-157
We derive a quantum stochastic differential equation satisfied by the unitary Markov cocycles obtained for a model situation
during second quantization in the symmetric Fock space.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 146, No. 1, pp. 186–192, January, 2006. 相似文献
4.
5.
A. G. Sergeev 《Theoretical and Mathematical Physics》2008,157(3):1745-1759
We consider the problem of twistor quantization for the loop space ΩTG of a compact Lie group G. We show that this problem is solvable in the critical dimension.
Dedicated to Vasilii Sergeevich Vladimirov for his 85th birthday
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 157, No. 3, pp. 450–467, December, 2008. 相似文献
6.
S. E. Konstein A. G. Smirnov I. V. Tyutin 《Theoretical and Mathematical Physics》2006,148(2):1011-1024
All continuous formal deformations of the Poisson algebra realized on Grassmann-valued compactly supported smooth functions
on ℝ2n with 2n ≥ 4 are found up to an equivalence transformation. We show that in the algebras considered, there exist additional
deformations that di.er from the Moyal bracket.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 148, No. 2, pp. 163–178, August, 2006. 相似文献
7.
Ziv Ran 《Geometric And Functional Analysis》2008,18(1):184-221
A Lie atom is essentially a pair of Lie algebras and its deformation theory is that of a deformation with respect to the first
algebra, endowed with a trivialization with respect to the second. Such deformations occur commonly in algebraic geometry,
for instance as deformations of subvarieties of a fixed ambient variety. Here we study some basic notions related to Lie atoms,
focussing especially on their deformation theory, in particular the universal deformation. We introduce Jacobi–Bernoulli cohomology,
which yields the deformation ring, and show that, under suitable hypotheses, infinitesimal deformations are classified by
certain Kodaira–Spencer data.
Received: May 2006 Revision: January 2007 Accepted: March 2007 相似文献
8.
Non-nilpotent, finitely generated, associative nil-algebras are studied as well as their adjoint groups and Golod groups.
Solutions are given to some problems in residually finite group theory, questions posed in the Kourovka Notebook included.
Supported by RFBR grant No. 03-01-00356.
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Translated from Algebra i Logika, Vol. 45, No. 2, pp. 231–238, March–April, 2006. 相似文献
9.
Centers of universal envelopes for Mal’tsev algebras are explored. It is proved that the center of the universal envelope
for a finite-dimensional semisimple Mal’tsev algebra over a field of characteristic 0 is a ring of polynomials in a finite
number of variables equal to the dimension of its Cartan subalgebra, and that universal enveloping algebra is a free module
over its center. Centers of universal enveloping algebras are computed for some Mal’tsev algebras of small dimensions.
Supported by FAPESP grant No. 04/08537-4 and by SO RAN grant No. 1.9.
Supported by FAPESP grant Nos. 05/60142-7, 05/60337-2 and by CNPq grant No. 304991/2006-6.
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Translated from Algebra i Logika, Vol. 46, No. 5, pp. 560–584, September–October, 2007. 相似文献
10.
For a quasi-Hopf algebra H, an H-bicomodule algebra and an H-bimodule coalgebra C we will show that the category of two-sided two-cosided Hopf modules is equivalent to the category of right–left generalized Yetter–Drinfeld modules . Using alternative versions of this result we will recover the category isomorphism between the categories of left–left and
left–right Yetter–Drinfeld modules over a quasi-Hopf algebra.
相似文献
11.
We study the baker’s map and its Walsh quantization, as a toy model of a quantized chaotic system. We focus on localization
properties of eigenstates, in the semiclassical régime. Simple counterexamples show that quantum unique ergodicity fails for
this model. We obtain, however, lower bounds on the entropies associated with semiclassical measures, as well as on the Wehrl
entropies of eigenstates. The central tool of the proofs is an “entropic uncertainty principle”.
Submitted: December 21, 2005; Accepted: March 1, 2006 相似文献
12.
This paper examines the process through which students learn to make functional use of computer algebra systems (CAS), and
the interaction between that process and the wider mathematical development of students. The result of ‘instrumentalising‘
a device to become a mathematical tool and correspondingly ‘instrumenting’ mathematical activity through use of that tool
is not only to extend students' mathematical technique but to shape their sense of the mathematical entities involved. These
ideas have been developed within a French programme of research – as reported by Artigue in this issue of the journal – which
has explored the integration of CAS – typically in the form of symbolic calculators – into the everyday practice of mathematics
classrooms. The French research –influenced by socio-psychological theorisation of the development of conceptual systems-
seeks to take account of the cultural and cognitive facets of these issues, noting how mathematical norms – or their absence
– shape the mental schemes which students form as they appropriate CAS as tools. Instrumenting graphic and symbolic reasoning
through using CAS influences the range and form of the tasks and techniques experienced by students, and so the resources
available for more explicit codification and theorisation of such reasoning. This illuminates an influential North American
study– conducted by Heid – which French researchers have seen as taking a contrasting view of the part played by technical
activity in developing conceptual understanding. Reconsidered from this perspective, it appears that while teaching approaches
which ‘resequence skills and concepts’ indeed defer – and diminish –attention to routinised skills, the tasks introduced in
their place depend on another –albeit less strongly codified – system of techniques, supporting more extensive and active
theorisation. The French research high lights important challenges which arise in instrumenting classroom mathematical activity
and correspondingly instrumentalising CAS. In particular, it reveals fundamental constraints on human-machine interaction
which may limit the capacity of the present generation of CAS to scaffold the mathematical thinking and learning of students.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
13.
E. S. Chibrikov 《Algebra and Logic》2006,45(4):261-276
We construct a basis for a free Lie superalgebra consisting of right-normed words
, where
are free generators.
Supported By RFBR Grant No. 05-01-00230.
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Translated from Algebra i Logika, Vol. 45, No. 4, pp. 458–483, July–August, 2006. 相似文献
14.
We study the behavior of the Etingof–Kazhdan quantization functors under the natural duality operations of Lie bialgebras
and Hopf algebras. In particular, we prove that these functors are “compatible with duality”, i.e., they commute with the
operation of duality followed by replacing the coproduct by its opposite. We then show that any quantization functor with
this property also commutes with the operation of taking doubles. As an application, we show that the Etingof–Kazhdan quantizations
of some affine Lie superalgebras coincide with their Drinfeld–Jimbo-type quantizations.
To the memory of Paulette Libermann (1919–2007) 相似文献
15.
Jin Yun GUO Bing Jun LI Qiu Xian WU 《数学学报(英文版)》2006,22(3):849-854
In this paper, we prove that there is a natural equivalence between the category F1(x) of Koszul modules of complexity 1 with filtration of given cyclic modules as the factor modules of an exterior algebra A = ∧V of an m-dimensional vector space, and the category of the finite-dimensional locally nilpotent modules of the polynomial algebra of m - 1 variables. 相似文献
16.
17.
The Maximal Graded Left Quotient Algebra of a Graded Algebra1) 总被引:1,自引:0,他引:1
Gonzalo ARANDA PINO Mercedes SILES MOLINA 《数学学报(英文版)》2006,22(1):261-270
We construct the maximal graded left quotient algebra of every graded algebra A without homogeneous total right zero divisors as the direct limit of graded homomorphisms (of left A-modules) from graded dense left ideals of A into a graded left quotient algebra of A. In the case of a superalgebra, and with some extra hypothesis, we prove that the component in the neutral element of the group of the maximal graded left quotient algebra coincides with the maximal left quotient algebra of the component in the neutral element of the group of the superalgebra. 相似文献
18.
A. I. Budkin 《Algebra and Logic》2008,47(5):304-313
Let A be a universal algebra and H its subalgebra. The dominion of H in A (in a class {ie304-01}) is the set of all elements
a ∈ A such that every pair of homomorphisms f, g: A → ∈ {ie304-02} satisfies the following: if f and g coincide on H, then
f(a) = g(a). A dominion is a closure operator on a set of subalgebras of a given algebra. The present account treats of closed
subalgebras, i.e., those subalgebras H whose dominions coincide with H. We introduce projective properties of quasivarieties
which are similar to the projective Beth properties dealt with in nonclassical logics, and provide a characterization of closed
algebras in the language of the new properties. It is also proved that in every quasivariety of torsion-free nilpotent groups
of class at most 2, a divisible Abelian subgroup H is closed in each group 〈H, a〉 generated by one element modulo H.
Translated from Algebra i Logika, Vol. 47, No. 5, pp. 541–557, September–October, 2008. 相似文献
19.
A. T. Gainov 《Algebra and Logic》2007,46(4):231-243
The concept of a composition algebra of the second kind is introduced. We prove that such algebras are non-degenerate monocomposition
algebras without unity. A big number of these algebras in any finite dimension are constructed, as well as two algebras in
a countable dimension. The constructed algebras each contains a non-isotropic idempotent e2 = e. We describe all orthogonally non-isomorphic composition algebras of the second kind in the following forms: (1) a two-dimensional
algebra (which has turned out to be unique); (2) three-dimensional algebras in the constructed series. For every algebra A,
the group Ortaut A of orthogonal automorphisms is specified.
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Translated from Algebra i Logika, Vol. 46, No. 4, pp. 428–447, July–August, 2007. 相似文献
20.
Veronika Valenčáková 《Mathematica Slovaca》2009,59(2):251-260
We formulate a version of the conditional probability of an IF-event considering the Łukasiewicz operations with IF-sets. Also some properties of conditional probability are proved. The results are strengthenings of preceding ones published
in [LENDELOVá, K.: Conditional IF-probability. In: Soft Methods for Integrated Uncertainty Modelling. Proceedings of the 2006 InternationalWorkshop on Soft Methods in
Probability and Statistics (SMPS 2006), Bristol, UK, September 5–7, 2006. Adv. Soft Comput., Springer-Verlag, Berlin, 2006,
pp. 275–283].
The paper was supported by Grant VEGA 1/0539/08. 相似文献