Path integrals for continuous-time Markov chains

This note presents a method of evaluating the distribution of a path integral for Markov chains on a countable state space.

Set-valued Markov chains and negative semitrajectories of discretized dynamical systems

Computer simulation of dynamical systems involves a phase space which is the finite set of machine arithmetic. Rounding state values of the continuous system to this grid yields a spatially discrete dynamical system, often with different dynamical behaviour. Discretization of an invertible smooth system gives a system with set-valued negative semitrajectories. As the grid is refined, asymptotic behaviour of the semitrajectories follows probabilistic laws which correspond to a set-valued Markov chain, whose transition probabilities can be explicitly calculated. The results are illustrated for two-dimensional dynamical systems obtained by discretization of fractional linear transformations of the unit disc in the complex plane.

Integrals for continuous-time Markov chains

This paper presents a method of evaluating the expected value of a path integral for a general Markov chain on a countable state space. We illustrate the method with reference to several models, including birth-death processes and the birth, death and catastrophe process. (C) 2002 Elsevier Science Inc. All rights reserved.

Lexicographic decomposition of chains and the concept of a planar chain

In an earlier paper [Journal of Mathematical Economics, 37 (2002) 17-38], we proved that if a preference relation on a commodity space is non-representable by a real-valued function then that chain is necessarily a long chain, a planar chain, an Aronszajn-like chain or a Souslin chain. In this paper, we study the class of planar chains, the simplest example of which is the Debreu chain (R-2, <(l)). (C) 2002 Elsevier Science B.V. All rights reserved.

Segregation in binary and ternary liquid fluidized beds

The mechanism underlying segregation in liquid fluidized beds is investigated in this paper, A binary fluidized bed system not at a stable equilibrium condition. is modelled in the literature as forming a mixed part-corresponding to stable mixture-at the bottom of the bed and a pure layer of excess components always floating on the mixed part. On the basis of this model: (0 comprehensive criteria for binary particles of any type to mix/segregate, and (ii) mixing, segregation regime map in terms of size ratio and density ratio of the particles for a given fluidizing medium, are established in this work. Therefore, knowing the properties of given particles, a second type of particles can be chosen in order to avoid or to promote segregation according to the particular process requirements. The model is then advanced for multicomponent fluidized beds and validated against experimental results observed for ternary fluidized beds. (C) 2002 Elsevier Science B.V. All rights reserved.

Vacancy solution theory for binary adsorption equilibria in heterogeneous carbon

A heterogeneous modified vacancy solution model of adsorption developed is evaluated. The new model considers the adsorption process through a mass-action law and is thermodynamically consistent, while maintaining the simplicity in calculation of multicomponent adsorption equilibria, as in the original vacancy solution theory. It incorporates the adsorbent heterogeneity through a pore-width-related potential energy, represented by Steele's 10-4-3 potential expression. The experimental data of various hydrocarbons, CO2 and SO2 on four different activated carbons - Ajax, Norit, Nuxit, and BPL - at multiple temperatures over a wide range of pressures were studied by the heterogeneous modified VST model to obtain the isotherm parameters and micropore-size distribution of carbons. The model successfully correlates the single-component adsorption equilibrium data for all compounds studied on various carbons. The fitting results for the vacancy occupancy parameter are consistent with the pressure change on different carbons, and the effect of pore heterogeneity is important in adsorption at elevated pressure. It predicts binary adsorption equilibria better than the IAST scheme, reflecting the significance of molecular size nonideality.

Mixed gas equilibrium adsorption on zeolites and energetic heterogeneity of adsorption volume

A model for binary mixture adsorption accounting for energetic heterogeneity and intermolecular interactions is proposed in this paper. The model is based on statistical thermodynamics, and it is able to describe molecular rearrangement of a mixture in a nonuniform adsorption field inside a cavity. The Helmholtz free energy obtained in the framework of this approach has upper and lower limits, which define a permissible range in which all possible solutions will be found. One limit corresponds to a completely chaotic distribution of molecules within a cavity, while the other corresponds to a maximum ordered molecular structure. Comparison of the nearly ideal O-2-N-2-zeolite NaX system at ambient temperature with the system Of O-2-N-2-zeolite CaX at 144 K has shown that a decrease of temperature leads to a molecular rearrangement in the cavity volume, which results from the difference in the fluid-solid interactions. The model is able to describe this behavior and therefore allows predicting mixture adsorption more accurately compared to those assuming energetic uniformity of the adsorption volume. Another feature of the model is its ability to correctly describe the negative deviations from Raoult's law exhibited by the O-2-N-2-CaX system at 144 K. Analysis of the highly nonideal CO2-C2H6-zeolite NaX system has shown that the spatial molecular rearrangement in separate cavities is induced by not only the ion-quadrupole interaction of the CO2 molecule but also the significant difference in molecular size and the difference between the intermolecular interactions of molecules of the same species and those of molecules of different species. This leads to the highly ordered structure of this system.

Multiple ordered phases in Langmuir-Blodgett films of cadmium arachidate at elevated temperatures

Using synchrotron X-ray grazing incidence diffraction, superlattice structures have been observed to develop in Langmuir-Blodgett films of cadmium arachidate as the temperature is raised. The previously reported superstructure in the stacked lamellae at room temperature changes at about 70 degreesC and there are further changes at about 90 and 103 degreesC before the major phase transition from stacked lamellae to hexagonally packed rods occurs at 107 degreesC (Langmuir 1997, 13, 1602). Between 70 and 103 degreesC there is a 1 x 10 one-dimensional in-plane superstructure, which is commensurate with the local structure and has an interlayer shift along [01] by a distance of b (of the local structure) at lower temperatures, and a further shift at about 90 degreesC. At lower (

INTERNATIONALIZATION OF BRAZILIAN FRANCHISE CHAINS: A COMPARATIVE STUDY

The primary goal of this paper is to comprehend the fundamental organizational differences between Brazilian franchise chains that only operate in the home market and Brazilian franchise chains that operate internationally. The sample chosen for this study comprehends 96 Brazilian franchises operating in the home market and 67 franchises with international operations; logistic regression was used to analyze data obtained from these sources. Our findings suggest that the development of a brand in international operations can be strategic for certain Brazilian franchise chains; this seems to be, however, a scarce resource for many franchises and it could be developed through international operations. With regard to the fees charged, the outcomes demonstrate that Brazilian franchises with international operations tend to charge lower fees from its franchisees to install new units. Regarding the monitoring and control of franchises, there is evidence that the monitoring capability is one of the determining factors in the development of Brazilian franchises international operations.