Projector formalism of generalized Brownian motion theory applied to dissipative and noisy systems

The projector formalism of Zwanzig-Mori type is extended to obtain generalized Fokker-Planck and generalized nonlinear Langevin equations for coarse-grained variables when the underlying microscopic dynamics is dissipative and noisy (stochastic).     

Synthesis,Properties, and Photopolymerization of Liquid‐Crystalline Oxetanes: Application in Transflective Liquid‐Crystal Displays

Mixtures of liquid‐crystalline di‐oxetanes and mono‐oxetanes are made for the purpose of making birefringent films by photopolymerization. The composition of a di‐oxetane mixture that forms spin‐coated films of planarly aligned nematic monomers is reported. These films are photopolymerized in air. The molecular order of the monomers can be changed on the microscale to form thin films with alternating birefringent and isotropic parts by using a combination of photopolymerization and heating. The interface observed between the birefringent and isotropic 10 μm × 10 μm domains is very sharp and the films show hardly any surface corrugation. In addition, the polymerized films are thermally stable, making them very suitable for use as patterned thin‐film retarders in high‐performance transflective liquid‐crystal displays (LCDs) which satisfy customer demand for displays that are brighter and thinner and that deliver better optical performance than conventional LCDs with an external non‐patterned retarder.     

Inexact Newton methods for the nonlinear complementarity problem

An exact Newton method for solving a nonlinear complementarity problem consists of solving a sequence of linear complementarity subproblems. For problems of large size, solving the subproblems exactly can be very expensive. In this paper we study inexact Newton methods for solving the nonlinear, complementarity problem. In such an inexact method, the subproblems are solved only up to a certain degree of accuracy. The necessary accuracies that are needed to preserve the nice features of the exact Newton method are established and analyzed. We also discuss some extensions as well as an application. This research was based on work supported by the National Science Foundation under grant ECS-8407240.     

Nonlinear multiple objective optimization: An algorithm and some theory

This paper presents an algorithm and the supporting theory for solving a class of nonlinear multiple criteria optimization problems using Zionts—Wallenius type of interaction. The Zionts—Wallenius method, as extended in this paper, can be used for solving multiple criteria problems with concave objective and (implicit) value functions and convex feasible regions. Modifications of the method to handle nonconvex feasible regions and general nonlinear objective functions are also discussed.This research was supported, in part, by a Faculty Research Development Award and by a Council of 100 Research Grant from Arizona State University (Roy), and by a grant from Y. Jahnsson Foundation, Finland (Wallenius). The research was performed while the second author was a Visiting Professor at Arizona State University.     

THE MODELING AND ESTIMATION OF THE SHORT-RUN SUPPLY OF ROUNDWOOD UNDER NONLINEAR INCOME TAXES

This paper deals with the theory and estimation of the short-run supply of roundwood under nonlinear (progressive) income taxation. The theoretical part of the paper uses the two-period consumption harvesting model to introduce nonlinear income taxes into the forest management problem and presents a simple method to determine the optimal supply of roundwood in this case. In the empirical part of the paper, the model is specified in a way suitable for econometric analysis. The estimation method is the maximum likelihood method, and the estimation results seem to support the theoretical model. Finally, some results from model simulation imply that income taxation may have a nonnegligible impact on the supply of roundwood.     

Irradiation Defects in Silicon Crystal

The application of irradiation in silicon crystal is introduced.The defects caused by irradiation are reviewed and some major ways of studying defects in irradiated silicon are summarized.Furthermore the problems in the investigation of irradiated silicon are discussed as well as its properties.     

Crystallographic report: Bis[bis(N,N‐dibenzyldithiocarbamato)cadmium(II)]

The centrosymmetric structure of {Cd[S₂CN(CH₂Ph)₂]₂}₂ features both bridging and chelating dithiocarbamate ligands so that a square pyramidal S₅ coordination geometry results. Copyright © 2004 John Wiley & Sons, Ltd.     

Crystallographic report: Bis{µ‐[O‐cyclopentyl(4‐methoxyphenyl)dithiophosphonato]1κ:S,2κ:S‐[O‐cyclopentyl(4‐methoxyphenyl)dithiophosphonato]‐1κ2S,S′}dicadmium(II)

The centrosymmetric title compound, [Cd₂{CH₃OC₆H₄P(OC₅H₉)S₂}₄], features an eight‐membered [? Cd? S? P? S? ]₂ ring owing to the presence of bridging dithiolate ligands. Tetrahedral coordination geometries for cadmium are completed by chelating ligands. Copyright © 2004 John Wiley & Sons, Ltd.     

Fluctuation Theory for a Three-Dimensional Model of Maxwellian Molecules

Under suitable assumptions, a functional central limit theorem is obtained for a three-dimensional model of Maxwellian molecules. This model is related to a nonlinear Boltzmann-type equation. It will be proved that the family of the distributions induced by fluctuation processes converges weakly.     

Formation of β‐iPP in isotactic polypropylene/ethylene–propylene rubber blends: Effects of preparation method,composition, and thermal condition

The effects of preparation method, composition, and thermal condition on formation of β‐iPP in isotactic polypropylene/ethylene–propylene rubber (iPP/EPR) blends were studied using modulated differential scanning calorimeter (MDSC), wide angle X‐ray diffraction (WAXD), and phase contrast microscopy (PCM). It was found that the α‐iPP and β‐iPP can simultaneity form in the melt‐blended samples, whereas only α‐iPP exists in the solution‐blended samples. The results show that the formation of β‐iPP in the melt‐blended samples is related to the crystallization temperature and the β‐iPP generally diminishes and finally vanishes when the crystallization temperature moves far from 125 °C. The phenomena that the lower critical temperature of β‐iPP in iPP/EPR obviously increases to 114 °C and the upper critical temperature decreases to 134 °C indicate the narrowing of temperature interval, facilitating the formation of β‐iPP in iPP/EPR. Furthermore, it was found that the amount of β‐iPP in melt‐blended iPP/EPR samples is dependent on the composition and the maximum amount of β‐iPP formed when the composition of iPP/EPR blends is 85:15 in weight. The results through examining the effect of annealing for iPP/EPR samples at melt state indicate that this annealing may eliminate the susceptibility to β‐crystallization of iPP. However, only α‐iPP can be observed in solution‐blended samples subjected to annealing for different time. The PCM images demonstrate that an obvious phase‐separation happens in both melt‐blended and solution‐blended iPP/EPR samples, implying that compared with the disperse degree of EPR in iPP, the preparation method plays a dominant role in formation of β‐iPP. It is suggested that the origin of formation of β‐iPP results from the thermomechanical history of the EPR component in iPP/EPR. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1704–1712, 2007