Spectrum of positive entropy multidimensional dynamical systems with a mixed time

It is shown that if an abelian countable group is such that is a finite group and every aperiodic positive entropy action of on a Lebesgue probability space has a countable Haar spectrum in the subspace , where denotes the Pinsker -
algebra of , then every aperiodic positive entropy action of on has the same property. A positive answer to the question of J.P. Thouvenot is obtained as a corollary.

     

HYPERFINITE TRANSVERSAL THEORY. II

We continue the investigation of validity of Hall's theorem in the case of the Loeb space of an internal, uniformly distributed, hyperfinite measure space initiated in1992 by the author. Some new classes of graphs are introduced for which the measure theoretic version of Hall's theorem still holds.

     

Carleson measure characterization of Bloch functions

We give several equivalences of Bloch functions and little Bloch functions. Using these results we obtain the generalized Carleson measure characterization of Bloch functions and the generalized vanishing Carleson measure characterization of little Bloch functions, that is,f B if and only if |D f(z)| ^p (1-|z|²)^p-1 dm(z) is a generalized Carleson measure;f B ₀ if and only if |D f(z)| ^p (1-|z|²)^p-1 dm(z) is a generalized vanishing Carleson measure, whereD f( > 0) is the fractional derivative of analytic functionf of order, m denotes the normalised Lebesgue measure.Supported partly by the Young Teacher Natural Science Foundation of Shandong Province.     

Volumetric study on the inclusion complex formation of α- and β-cyclodextrin with 1-alkanols at different temperatures

The partial molar volumes (V_a) of 1-alkanols (carbon number, m=5, 6, 7) in - and -cyclodextrin (CD) solutions at 5.00 mmol kg^–1 have been determined as a function of alkanol concentration (C_a) between 293.2 and 308.2 K by using a dilatometer. It has been observed that with an increase in C_a, V_a increased in -CD solution but decreased in -CD solution, asymptotically to a value of V_a in CD-free water. The dependence of V_a on C_a provided the binding constant (K) of 1:1 complex, the volume change in complex formation, and the partial molar volume of complex itself. The complex formation mechanism has been discussed on the basis of these values and their carbon number dependences in the respect of geometric behavior, hydrophobic interaction, and van der Waals interaction. It is concluded that the CD cavity in water is not rigid but flexible for fitting in nicely with guest molecule.     

Investigation of solution and solid-state properties of poly(R,R,4,4-cyclohexylidene diphenylene diphenyl-4,4-disulfonate)

Solution and solid-state properties of poly(R,R^′,4,4^′-cyclohexylidene diphenylene diphenyl-4,4^′-disulfonate) (PS-6: R=R^′=H; PS-7: R=CH₃, R^′=H; PS-8: R=R^′=Cl; PS-9: R=CH₃, R^′=Cl and PS-10: R=R^′=Br) have been determined and discussed in terms of nature of the substituents. Ultrasonic velocity (2 MHz) and acoustical parameters of PS-7 and PS-9 solutions in chloroform, 1,2-dichloroethane and tetrahydrofuran (THF) at 30, 35 and 40 °C have been evaluated to understand the effect of methyl and chlorine groups, concentration, and temperature on molecular interactions. The data are interpreted in light of solvent-polymer and polymer-polymer interactions. Predominant solvation is observed in THF system and the least in chloroform system at all three temperatures. The structural change is observed above 2%. Both the polymers possess structure-forming tendency and it is supported by positive values of S_n.The densities of PS-7 and PS-9 determined by floatation method are in excellent agreement with calculated values but those determined by specific volume method differ remarkably from calculated values due to solvation effect. PS-7 and PS-9 possess respectively tensile strength of 38.4 and 1.1 N/mm²; electric strength of 16.2 and 25.0 kV/mm and volume resistivity of 5.7×10¹⁶ and 1.0×1017Ωcm. The low tensile strength of PS-9 is due to low molecular weight, rigid and brittle nature of the polymer chains. PS-6 to PS-9 are thermally stable up to about 349-379 °C while PS-10 up to about 279 °C and involved two-step degradation. DTA thermograms indicated T_g at about 204-226 °C. High activation energy indicated rigid nature of the polymer chains and the positive magnitudes of ΔS* indicated less ordered transition state. The nature of the substituents (CH₃, Cl and Br) affected thermal, mechanical and electrical properties.     

Repleteness and regular lattice measures

Let X be an abstract set and L a lattice of subsets of X. To each lattice regular measure µ, we associate two induced measures and on suitable lattices of the Wallman space IR(L) and another measure µ on the spaceIR(L). We will investigate the reflection of smoothness properties of p onto , and µ; and try to set some new criterion for repleteness and measure repleteness.     

再论Pedoe不等式的高维推广及应用

本文对欧氏空间E~n中的两个n维单形,给出了著名的Pedoe不等式的一个实质性推广,并讨论了它的应用.     

Finitely maxitive T-conditional possibility theory: Coherence and extension

Starting from the axiomatic definition of finitely maxitive T-conditional possibility (where T is a continuous triangular norm), the paper aims at a comprehensive and self-contained treatment of coherence and extension of a possibilistic assessment defined on an arbitrary set of conditional events. Coherence (or consistence with a T-conditional possibility) is characterized either in terms of existence of a linearly ordered class of finitely maxitive possibility measures (T-nested class) agreeing with the assessment, or in terms of solvability of a finite sequence of nonlinear systems for every finite subfamily of conditional events. Coherence reveals to be a necessary and sufficient condition for the extendibility of an assessment to any superset of conditional events and, in the case of T equal to the minimum or a strict t-norm, the set of coherent values for the possibility of a new conditional event can be computed solving two optimization problems over a finite sequence of nonlinear systems for every finite subfamily of conditional events.     

Size-dependent electron chemical potential: Effect on particle charging

Electrostatic charging of particles of identical composition, but different sizes, is a poorly understood phenomenon that may be of importance in dust storms, generation of lightning, numerous technological applications involving solid particulates, and in the agglomeration of lunar dust and inter-stellar dust clouds. We show that under optical excitation, the relative magnitude of surface to volume de-excitation gives size-dependent electron and hole concentrations. The consequent differences in chemical potentials can lead to charge transfer between particles of different size. The direction of charge transfer, from large to small or vice versa, depends critically on the properties of the materials.     

Improved estimation of duality gap in binary quadratic programming using a weighted distance measure

We present in this paper an improved estimation of duality gap between binary quadratic program and its Lagrangian dual. More specifically, we obtain this improved estimation using a weighted distance measure between the binary set and certain affine subspace. We show that the optimal weights can be computed by solving a semidefinite programming problem. We further establish a necessary and sufficient condition under which the weighted distance measure gives a strictly tighter estimation of the duality gap than the existing estimations.