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21.
Quantization consists in studying the L
r
-error induced by the approximation of a random vector X by a vector (quantized version) taking a finite number n of values. We investigate this problem for Gaussian random vectors in an infinite dimensional Banach space and in particular, for Gaussian processes. A precise link proved by Fehringer(4) and Dereich et al.
(3) relates lower and upper bounds for small ball probabilities with upper and lower bounds for the quantization error, respectively. We establish a complete relationship by showing that the same holds for the direction from the quantization error to small ball probabilities. This allows us to compute the exact rate of convergence to zero of the minimal L
r
-quantization error from logarithmic small ball asymptotics and vice versa. 相似文献
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E. Manova C. Estournès D. Paneva J.-L. Rehspringer T. Tsoncheva B. Kunev I. Mitov 《Hyperfine Interactions》2005,165(1-4):215-220
Iron–nickel spinel oxide NiFe2O4 nanoparticles have been prepared by the combination of chemical precipitation and subsequent mechanical milling. For comparison, their analogue obtained by thermal synthesis is also studied. Phase composition and structural properties of iron–nickel oxides are investigated by X-ray diffraction and Mössbauer spectroscopy. Their catalytic behavior in methanol decomposition to CO and methane is tested. An influence of the preparation method on the reduction and catalytic properties of iron–nickel samples is established. 相似文献
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Francisco-Javier Muñoz-Delgado Victoriano Ramirez-González Paul Sablonnière 《分析论及其应用》1995,11(1):62-71
In this work we study linear polynomial operators preserving some consecutive i-convexities and leaving invariant the polynomials
up to a certain degree. First, we study the existence of an incom patibility between the conservation of certain i-convexities
and the invariance of a space of polynomials. Interpolation properties are obtained and a theorem by Berens and DeVore about
the Bernstein's operator is extended. Finally, from these results a generalized Bernstein's operator is obtained.
This work was supported by Junta de Andalucia. Grupo de investigación: Matemática Aplicada. Código: 1107 相似文献
27.
Roland Omnès 《Foundations of Physics》1995,25(4):605-629
A rather recent interpretation of quantum mechanics, known under the various names of consistent histories, decohering histories, or logical interpretation, has brought interpretation into a standard deductive theory and is now investigated in many places. A key difference with the Copenhagen interpretation is the status of classical physics, now derived completely from quantum principles in both its dynamical and logical aspects. After describing briefly this new interpretation in its essentials, leaving aside technical details, it is shown how its consequences in epistemology differ drastically from the familiar outcomes of the Copenhagen interpretation, leading in particular to a well-defined theory of knowledge. Some more speculative philosophical consequences associated with the unsolved problem of actuality are also mentioned. 相似文献
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