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.     

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。     

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”.     

Performance of SuSi: a method for generating atomistic models of amorphous polymers based on a random search of energy minima

The performance of a recently developed method to generate representative atomistic models of amorphous polymers has been investigated. This method, which is denoted SuSi, can be defined as a random generator of energy minima. The effects produced by different parameters used to define the size of the system and the characteristics of the generation algorithm have been examined. Calculations have been performed on poly(L,D-lactic) acid (rho = 1.25 g/cm3) and nylon 6 (rho = 1.084 g/cm(3)), which are important commercial polymers.     

Electron kinetics of collision dominated r.f. bulk plasma in CO: The role of second-kind collisions

Electron energy distribution functions (EEDF) and related properties in the bulk region of the rf CO plasma at the reduced rf field frequency /p₀=×10⁷ sec^–1 torr^–1 have been calculated by solving the time-dependent spatially homogeneous Boltzmann equation in the presence of second-kind collisions and have been interpreted on a microphysical basis. The results show that second-kind collisions (vibrational and electronic) strongly affect the temporal evolution of EEDF, of the mean energy, and of the mean collision frequencies for vibrational and electronic excitation processes, as well as for ionization. In particular, second-kind collisions in the CO rf bulk plasma strongly decrease the modulation of the mean ionization frequency during its periodical alteration in the rf field. Furthermore, the effect of second-kind collisions on an approximate determination of the time-averaged EEDF in the rf bulk plasma using the so-called effective-field appriximation has been estimated.     

Asymptotically independent topological indices on random trees

Topological indices are graph invariants used in computational chemistry to encode molecules. A frequent problem when performing structure-activity studies is that topological indices are inter-correlated. We consider a simple topological index and show asymptotic independence for a random tree model. This continues previous work on the correlation among topological indices. These findings suggest that a size-dependence in a certain class of distance-based topological indices can be eliminated.AMS subject classification: 05C80, 60E10, 92E10