Entropy numbers in sequence spaces with an application to weighted function spaces

We determine the exact asymptotic behaviour of entropy numbers of diagonal operators from ℓ_p to ℓ_q, 0<q<p∞, under mild regularity conditions on the generating diagonal sequence. On one hand, this is a quantitative version of Pitt's theorem for diagonal operators, and on the other hand it is a limiting case of results by Carl. An application to embeddings of weighted Besov and Triebel–Lizorkin spaces is also given.     

<Emphasis Type="Italic">L</Emphasis><Superscript><Emphasis Type="Italic">q</Emphasis></Superscript>-Functional Inequalities and Weighted Porous Media Equations

Using measure-capacity inequalities we study new functional inequalities, namely L ^q -Poincaré inequalities

Entropy formula and continuity of entropy for piecewise expanding maps

We consider some classes of piecewise expanding maps in finite dimensional spaces having invariant probability measures which are absolutely continuous with respect to Lebesgue measure. We derive an entropy formula for such measures and, using this entropy formula, we present sufficient conditions for the continuity of that entropy with respect to the parameter in some parametrized families of maps. We apply our results to a classical one-dimensional family of tent maps and a family of two-dimensional maps which arises as the limit of return maps when a homoclinic tangency is unfolded by a family of three dimensional diffeomorphisms.     

Moment information and entropy evaluation for probability densities

How much information does the sequence of integer moments carry about the corresponding unknown absolutely continuous distribution? We prove that a reliable evaluation of the corresponding Shannon entropy can be done by exploiting some known theoretical results on the entropy convergence, uniquely involving exact moments without solving the underlying moment problem. All the procedure essentially rests on the solution of linear systems, with nearly singular matrices, and hence it requires both calculations in high precision and a pre-conditioning technique. Numerical examples are provided to support the theoretical results.     

Information Content of Fluorescence Polarization and Anisotropy

The equality of information content in fluorescence polarization and emission anisotropy is a common assumption and the two quantities are used according to practical considerations. However, an information-theoretic analysis presented here reveals that their information content is substantially different. A scaling relation exists between polarization and anisotropy, and normalization allows their direct comparison. Various measures of information such as the absolute, relative, differential, and potential entropies all appear larger for anisotropy over part or all of its normalized overlap with the polarization function. The larger information content coincides with the signal range where the emitted light is polarized mostly in the parallel direction. Polarization takes on larger absolute entropy only when the emission is about perpendicular to the incident light and when the differential entropy is considered over the entire physical domain. The additional information locally afforded by polarization appears to be related to its larger signal range whereas the extra information in anisotropy may be attributed to a second perpendicular emission plane in its definition, which is oriented along the axis of propagation of light and takes the contribution of all degrees of rotational freedom into account. Thus anisotropy may be considered as a more accurate and more informative representation of the underlying physical phenomena. Some practical aspects relevant to studies of protein–ligand interactions are also discussed.     

Quasilinear parabolic P.D.E.s with discontinuous hysteresis

This work deals with an initial- and boundary-value problem for a quasilinear parabolic equation that includes a possibly discontinuous hysteresis operator, :

水杨酸型螯合树脂对Fe(III)离子的螯合吸附行为

以5-氨基水杨酸(ASA)为胺化试剂, 使氯甲基化的交联聚苯乙烯(CMCPS)微球表面的苄氯基团发生亲核取代反应, 制得了水杨酸型螯合树脂ASA-CPS. 研究了该螯合树脂对金属离子的螯合吸附行为, 探讨了其吸附热力学与吸附机理, 考察了介质pH值对树脂螯合吸附性能的影响以及树脂对不同金属离子的螯合吸附能力. 实验结果表明, 水杨酸型螯合树脂ASA-CPS 对重金属离子具有强螯合吸附性能, 尤其对Fe3+离子表现出很强的螯合吸附能力, 常温下吸附容量可达21 g/100 g. 吸附过程属熵驱动的化学吸附过程, 升高温度, 吸附容量增高; 在可抑制金属离子水解的pH范围内, 介质的pH值越高, 螯合吸附能力越强; 对于性质不同的金属离子, ASA-CPS的吸附性能是有差别的, 吸附容量的顺序为Fe3+>Ni2+>Cu2+>Zn2+.     

Entropy, invertibility and variational calculus of adapted shifts on Wiener space

In this work we study the necessary and sufficient conditions for a positive random variable whose expectation under the Wiener measure is one, to be represented as the Radon-Nikodym derivative of the image of the Wiener measure under an adapted perturbation of identity with the help of the associated innovation process. We prove that the innovation conjecture holds if and only if the original process is almost surely invertible. We also give variational characterizations of the invertibility of the perturbations of identity and the representability of a positive random variable whose total mass is equal to unity. We prove in particular that an adapted perturbation of identity U=IW+u satisfying the Girsanov theorem, is invertible if and only if the kinetic energy of u is equal to the entropy of the measure induced with the action of U on the Wiener measure μ, in other words U is invertible iff

     

Entropy of formulas

A probability distribution can be given to the set of isomorphism classes of models with universe {1, ..., n} of a sentence in first-order logic. We study the entropy of this distribution and derive a result from the 0–1 law for first-order sentences.      

二维模糊向量可信性分布的联合熵及其性质

基于可信性测度, 定义了二维离散型模糊向量和二维连续型模糊向量的联合熵, 并研究了它们的极小性、极大性、单调性, 以及二维简单模糊向量的扩展性和严格凹性.