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61.
62.
63.
This paper attempts to develop a theory of sufficiency in the setting of non-commutative algebras parallel to the ideas in
classical mathematical statistics. Sufficiency of a coarse-graining means that all information is extracted about the mutual
relation of a given family of states. In the paper sufficient coarse-grainings are characterized in several equivalent ways
and the non-commutative analogue of the factorization theorem is obtained. As an application we discuss exponential families.
Our factorization theorem also implies two further important results, previously known only in finite Hilbert space dimension,
but proved here in generality: the Koashi-Imoto theorem on maps leaving a family of states invariant, and the characterization
of the general form of states in the equality case of strong subadditivity.
Supported by the EU Research Training Network Quantum Probability with Applications to Physics, Information Theory and Biology
and Center of Excellence SAS Physics of Information I/2/2005.
Supported by the Hungarian grant OTKA T032662 相似文献
64.
We present a new approach to study the convergence of Newton's method in Banach spaces, which relax the conditions appearing in the usual studies. The approach is based on the bound required for the second derivative of the operator involved. An application to a nonlinear integral equation is presented. 相似文献
65.
Balázs Szendröi 《Mathematische Zeitschrift》2002,240(2):233-241
This note shows that a certain toric quotient of the quintic Calabi-Yau threefold in provides a counterexample to a recent conjecture of Cox and Katz concerning nef cones of toric hypersurfaces.
Received: 8 February 2001; in final form: 17 September 2001 / Published online: 1 February 2002 相似文献
66.
67.
J. Kudrna I. Pelant J. Štěpánek F. Trojánek P. Malý 《Applied Physics A: Materials Science & Processing》2002,74(2):253-256
We have studied ultra-fast carrier dynamics of photo-excited carriers in hydrogenated microcrystalline silicon prepared by
a very high frequency glow-discharge technique. We report on direct observation of two types of dynamics using selective photo-excitation
in picosecond pump and probe measurements. One type of the observed dynamics has been found to be independent of the sample
preparation, while the other reflects the relative weights of crystalline and amorphous fractions. We propose a simple rate-equation
model that describes the carrier dynamics in microcrystalline silicon in terms of the composition of those in Si microcrystallites
and in the a-Si:H tissue which surrounds the microcrystallites. The model without any fitting parameters reproduces the experimental
data very well when the dynamics are scaled with relative volume fractions as obtained from Raman spectra.
Received: 23 November 2000 / Accepted: 17 March 2001 / Published online: 23 May 2001 相似文献
68.
T. Temesvári C. De Dominicis I.R. Pimentel 《The European Physical Journal B - Condensed Matter and Complex Systems》2002,25(3):361-372
Symmetry considerations and a direct, Hubbard-Stratonovich type, derivation are used to construct a replica field-theory relevant
to the study of the spin glass transition of short range models in a magnetic field. A mean-field treatment reveals that two
different types of transitions exist, whenever the replica number n is kept larger than zero. The Sherrington-Kirkpatrick critical point in zero magnetic field between the paramagnet and replica
magnet (a replica symmetric phase with a nonzero spin glass order parameter) separates from the de Almeida-Thouless line,
along which replica symmetry breaking occurs. We argue that for studying the de Almeida-Thouless transition around the upper
critical dimension d = 6, it is necessary to use the generic cubic model with all the three bare masses and eight cubic couplings. The critical
role n may play is also emphasized. To make perturbative calculations feasible, a new representation of the cubic interaction is
introduced. To illustrate the method, we compute the masses in one-loop order. Some technical details and a list of vertex
rules are presented to help future renormalisation-group calculations.
Received 9 October 2001 相似文献
69.
Lubomír Kubáček 《Applications of Mathematics》2006,51(6):565-582
Some remarks to problems of point and interval estimation, testing and problems of outliers are presented in the case of multivariate
regression model.
This work was supported by the Council of Czech Government J14/98:153100011. 相似文献
70.
Ricardo Celorrio Vı́ctor Domínguez Francisco-Javier Sayas 《Comptes Rendus Mathematique》2002,334(10):923-926
In this work we study the solution of Laplace's equation in a domain with holes by an iteration consisting of splitting the problem in an exterior one, around the holes, plus an interior problem in the unholed domain. We show the existence of a decomposition of the solution when the exterior problem is represented by means of a single-layer protential. Also, for the three-dimensional case and with some adjustments for the two-dimensional case, we prove convergence of the method by writing the iteration as a Jacobi iteration for an operator equation and studying the spectrum of the iteration operator. To cite this article: R. Celorrio et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 923–926. 相似文献