Convergence of optimal stochastic bin packing

Consider independent identically distributed random variables (X_i) valued in [0,1]. Let B(n) be the optimal (minimum) number of unit size bins needed to pack n items of size X₁, X₂,…,X_n. We prove that there exists a numerical constant C such that for t > 0,

$\text{Pr(∣B(n)?E(B(n))∣>t}\text{n}\text{)≤ C exp(? t).}$

The constant C does not depend on the distribution of X.     

Irreversible deformation of macromolecular networks

Based upon a thermodynamical approach, the generalized Onsager type of relaxation of van der Waals networks is presented. By linearly and identically coupling the set hidden variables to the network, the memory function of the system can be related to the equilibrium strain-energy function. The relaxation behavior of real networks on stretching can quantitatively be described by means of a distribution of relaxation times known from small strain experiments. Some new and interesting conclusions are discussed as to how the macroscopically non-linear visco-elastic response might be interpreted.     

水溶性聚合物和两亲聚合物:12.环氧乙烷-环氧丙烷无规共聚醚结构与性能的关系

来用连续加料法,以二元醇-KOH为引发剂合成一组不同组成的环氧乙烷-环氧丙烷无规共聚醚,并用核磁共振、红外光谱、示差扫描量热计和热失重等方法对其本体聚合物,用浊点和表面张力测定的方法对其水溶液,进行系统的表征。     

Effects of Amplitude of the Radiofrequency Electromagnetic Radiation on Aqueous Suspensions and Solutions

The effects of radiofrequency (RF) (1–4) and magnetic fields (5–9) on the behavior of aqueous solutions and suspensions have been a popular subject in recent years. The mechanism of the magnetic “water memory” effect, though, is still largely unknown (5). In this work, we present evidence that the primary “receptor” of the electromagnetic radiation is a gas/liquid interface. Gas can be either already present in water or produced by the effects of electromagnetic fields. Perturbed gas/liquid interfaces require hours to equilibrate. Certain RF and magnetic signals also produce reactive oxygen and hydrogen species (superoxide, hydrogen peroxide, hydrogen, atomic hydrogen). The perturbed gas/liquid interface modifies the hydrogen bonding networks in water and also the hydration of ions and interfaces. Careful outgassing removes all of the effects of the electromagnetic fields, including the magnetic memory effect. The amplitude of the applied field influences the observed effects. Different amplitudes of RF radiation perturb the interfacial water in different ways and consequently affect the behavior of colloids and ions in specific manners. For instance, the bulk and template precipitation of calcium carbonate, zeta potentials of suspended colloids, rate of dissolution of colloidal silica, and attachment of colloidal silica to metal surfaces are modified in specific ways with the low amplitude or high amplitude RF treatments described in this paper. The solubility/diffusivity of gas species is also modified in a different manner, and it is probably at the core of the specificity of the RF amplitude effects.     

Excess molar heat capacities of ((<Emphasis Type="Italic">R</Emphasis>)-(+)-α-pinene+(<Emphasis Type="Italic">S</Emphasis>)-(-)- α-pinene) at temperatures between 293.15-308.15 K

Summary {\rtf1\ansi\ansicpg1250\deff0\deflang1038\deflangfe1038\deftab708{\fonttbl{\f0\froman\fprq2\fcharset238{\*\fname Times New Roman;}Times New Roman CE;}} \viewkind4\uc1\pard\f0\fs20 New explanations are given for two types of irregular thermogravimetric (TG) data. A TG relationship between mass and temperature is derived on the basis of migration behavior of bubbles generated in bulk of sample system, and superposed on that derived on the basis of kinetics of the 4\super th\nosupersub order event, which is superposed on the experimental TG data obtained from three reference papers. This suggests that these TG data are reflecting migration of bubbles. A dependence of TG behavior on heating rate, which is contrary to usual that, is shown and is explained in terms of event-rate determination by boiling. \par }     

The spherical-model limit in a random field

The spherical-model limitn of then-vector model in a random field, with either a statistically independent distribution or with long-range correlated random fields, is studied to demonstrate the correctness of the replica method in which then and replica limits limits are interchanged, provided the replica and thermodynamic limits are taken in the right order, in the case of long-range correlated random fields. A scaling form for the two-point correlation function relevant to the first-order phase transition below the lower critical dimensionality of the random system is also obtained.     

Application of the essential work of fracture concept to nanostructured polymer materials

The first part of the paper deals with a critical discussion of the methodical basis of essential work of fracture (EWF) concept with respect to the specimen geometry (especially the notch depth) and application to polymers. In the second part, an in situ testing device, which combines a tensile testing machine with an optical strain-field measuring system, has successfully demonstrated possibility of characterization of fracture behaviour of polystyrene-polybutadiene block copolymers and block copolymer/homopolymer blends as examples of nanostructured polymer materials. It has been shown that knowledge of the time evolution of the strain field close to the crack tips leads to a simple verification of the basic precondition for the applicability of the EWF concept, the precondition “plastic zone coalescence-before-stable crack propagation”.     

Markov processes in single molecule fluorescence

This article examines the current status of Markov processes in single molecule fluorescence. For molecular dynamics to be described by a Markov process, the Markov process must include all states involved in the dynamics and the first-passage time (FPT) distributions out of those states must be describable by a simple exponential law. The observation of non-exponential FPT distributions or other evidence of non-Markovian dynamics is common in single molecule studies and offers an opportunity to expand the Markov model to include new dynamics or states that improve understanding of the system.     

Aldol condensations over reconstructed Mg-Al hydrotalcites: structure-activity relationships related to the rehydration method

Two different rehydration procedures in the liquid or gas phase have been applied to reconstruct mixed oxides derived from calcined hydrotalcite-like materials to be used as catalysts for aldol condensation reactions. The as-synthesized hydrotalcite, its decomposition product, as well as the reconstructed solids upon rehydration were characterized by XRD, N(2) adsorption, He pycnometry, FTIR, SEM, TEM, (27)Al MAS-NMR and CO(2)-TPD (TPD=temperature-programmed desorption). Compared to the Mg-Al mixed oxide rehydrated in the gas phase (HT-rg), that rehydrated in the liquid phase (HT-rl) exhibits a superior catalytic performance with respect to the aldol condensation of citral with ketones to yield pseudoionones and in the self-aldolization of acetone. The textural properties of HT-rl and HT-rg differ strongly and determine the catalytic behavior. A memory effect led to a higher degree of reconstruction of the lamellar structure when the mixed oxide was rehydrated in the gas phase rather than in the liquid phase, although liquid-phase rehydration under fast stirring produced a surface area that was 26 times greater. This contrasts to typical statements in the literature claiming a higher degree of reconstruction in the presence of large amounts of water in the medium. CO(2)-TPD shows that the number of OH(-) groups and their nature are very similar in HT-rg and HT-rl, and cannot explain the markedly different catalytic behavior. Accordingly, only a small fraction of the available basic sites in the rehydrated samples is active in liquid-phase aldol condensations. Our results support the model in which only basic sites near the edges of the hydrotalcite platelets are partaking in aldol reactions. Based on this, reconstructed materials with small crystallites (produced by exfoliation during mechanical stirring), that is, possessing a high external surface area, are beneficial in the reactions compared to larger crystals with a high degree of intraplatelet porosity.