Results 281 to 290 of about 391,352 (330)

Relative entropy of Z-numbers

Information Sciences, 2021
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Li, Yangxue, Pelusi, Danilo, Deng, Yong, Cheong, Kang Hao   +3 more
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Entropy Numbers of Compact Operators

Bulletin of the London Mathematical Society, 1986
In this paper it is shown that if T is a compact linear map of a Hilbert space to itself and \(| T|\) is the positive square root of \(T^*T\), then for all \(n\in {\mathbb{N}}\), \(e_ n(T)=e_ n(T^*)=e_ n(| T|)\), where \(e_ n(S)\) is the \(n^{th}\) entropy number of S.
Edmunds, D. E., Edmunds, R. M.
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Continuous Symmetry Numbers and Entropy

Journal of the American Chemical Society, 2003
Traditionally, entropy changes are corrected for rotational permutability only if the molecule is perfectly rotationally symmetric. By this approach, only a small fraction of all known molecules must be evaluated in terms of symmetry numbers, while all other molecules are totally exempt of these considerations.
Ernesto, Estrada, David, Avnir
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OnA-Compact Operators, Generalized Entropy Numbers and Entropy Ideals

Mathematische Nachrichten, 1984
Using the notion of precompact subset in a Banach space, the authors introduce what are called A-compact sets referring to a given operator ideal A. Based upon this concept, A-compact operators are defined between Banach spaces. It is established that both A compact sets and A compact operators admit similar characterizations as precompact sets and ...
Carl, Bernd, Stephani, Irmtraud
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Entropy Numbers and Approximation Numbers in Function Spaces, II

Proceedings of the London Mathematical Society, 1989
This paper continues the study of entropy and approximation numbers related to compact embeddings between scales of Besov type function spaces \(B^ s_{p,q}\). In a previous paper [Proc. London Math Soc., III. Ser. 58, No. 1, 137-152 (1989; Zbl 0629.46034)], the authors obtained estimates from above for the entropy numbers \(e_ k\) and approximation ...
Edmunds, D. E, Triebel, H.
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Entropy numbers and interpolation

Mathematische Annalen, 2010
This paper settles a long-standing question by showing that in certain circumstances the entropy numbers of a map do not behave well under real interpolation, that is, that an inequality of the form \[ e_{m+n-1}(T: (X_0,X_1)_{\theta,q} \to (Y_0,Y_1)_{\theta,q}) \leq C \, e_m(T:X_0 \to Y_0)^{1-\theta} e_n(T:X_1 \to Y_1)^\theta \] is not possible in ...
Edmunds, DE, Netrusov, Y
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Entropy Numbers of Some Ergodic Averages

Theory of Probability & Its Applications, 2000
If \(X\) is a seminormed linear space and \(U\) a bounded linear operator on \(X\), we may consider the moving averages \(A_n= n^{-1} \sum^{n-1}_{j=0} U^j\), \(n= 1,2,\dots\). Given \(x\in X\), does a subsequence \(S\) of the sequence \(\{A_n(x)\}^\infty_{n=1}\) converge or cluster in some sense? The main thrust of this paper, building upon a result of
Gamet, C., Weber, M.
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Uniform Entropy Numbers

1996
In Section 2.5.1 the empirical process was shown to converge weakly for indexing sets F satisfying a uniform entropy condition. In particular, if $$ s\mathop u\limits_Q p\log N\left( {\varepsilon \parallel F{\parallel _{Q,2}},F,\mathop L\nolimits_2 \left( Q \right)} \right) \leqslant K{\left( {\frac{1}{\varepsilon }} \right)^{2 - \delta ...
Aad W. van der Vaart, Jon A. Wellner
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Gaussian Approximation Numbers and Metric Entropy

Journal of Mathematical Sciences, 2019
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Kühn, T., Linde, W.
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