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41.
《Journal of Complexity》2006,22(3):371-381
We discuss adaptive strategies for choosing regularization parameters in Tikhonov–Phillips regularization of discretized linear operator equations. Two rules turn out to be based entirely on data from the underlying regularization scheme. Among them, only the discrepancy principle allows us to search for the optimal regularization parameter from the easiest problem. This potential advantage cannot be achieved by the standard projection scheme. We present a modified scheme, in which the discretization level varies with the successive regularization parameters, which has the advantage, mentioned before. 相似文献
42.
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
43.
Necessary conditions for the Gâteaux differentiability of the distance function to a set are considered. A series of characterizing results is obtained. 相似文献
44.
Natural populations, whose generations are non-overlapping, can be modelled by difference equations that describe how the populations evolve in discrete time-steps. In the 1970s ecological research detected chaos and other forms of complex dynamics in simple population dynamics models, initiating a new research tradition in ecology. However, in former studies most of the investigations of complex population dynamics were mainly concentrated on single populations instead of higher dimensional ecological systems. This paper reports a recent study on the complicated dynamics occurring in a class of discrete-time models of predator–prey interaction based on age-structure of predator. The complexities include (a) non-unique dynamics, meaning that several attractors coexist; (b) antimonotonicity; (c) basins of attraction (defined as the set of the initial conditions leading to a certain type of an attractor) with fractal properties, consisting of pattern of self-similarity and fractal basin boundaries; (d) intermittency; (e) supertransients; and (f) chaotic attractors. 相似文献
45.
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49.
We establish soliton-like asymptotics for finite energy solutions to the Schrödinger equation coupled to a nonrelativistic classical particle. Any solution with initial state close to the solitary manifold converges to a sum of a travelling wave and an outgoing free wave. The convergence holds in global energy norm. The proof uses spectral theory and the symplectic projection onto the solitary manifold in the Hilbert phase space. 相似文献
50.
We demonstrate a method that permits to obtain generalized solutions for some quasilinear equations and systems of hyperbolic
type. The corresponding variational principle is constructed using the theory of equilibrium of a potential in an external
field.
Dedicated to the memory of B. M. Levitan
Supported by RFBR grants Nos. 05-01-00522 and NSh-1551.2003.1, by Program No. 1 of the Branch of Mathematics, Russian Academy
of Sciences, and by INTAS project No. 03-51-6637. 相似文献