A limit model for thermoelectric equations

We analyze the asymptotic behavior corresponding to the arbitrary high conductivity of the heat in the thermoelectric devices. This work deals with a steady-state multidimensional thermistor problem, considering the Joule effect and both spatial and temperature dependent transport coefficients under some real boundary conditions in accordance with the Seebeck–Peltier–Thomson cross-effects. Our first purpose is that the existence of a weak solution holds true under minimal assumptions on the data, as in particular nonsmooth domains. Two existence results are studied under different assumptions on the electrical conductivity. Their proofs are based on a fixed point argument, compactness methods, and existence and regularity theory for elliptic scalar equations. The second purpose is to show the existence of a limit model illustrating the asymptotic situation.     

A transformed random effects model with applications

This paper proposes a transformed random effects model for analyzing non-normal panel data where both the response and (some of) the covariates are subject to transformations for inducing flexible functional form, normality, homoscedasticity, and simple model structure. We develop a maximum likelihood procedure for model estimation and inference, along with a computational device which makes the estimation procedure feasible in cases of large panels. We provide model specification tests that take into account the fact that parameter values for error components cannot be negative. We illustrate the model and methods with two applications: state production and wage distribution. The empirical results strongly favor the new model to the standard ones where either linear or log-linear functional form is employed. Monte Carlo simulation shows that maximum likelihood inference is quite robust against mild departure from normality. Copyright © 2009 John Wiley & Sons, Ltd.     

A multivariate Markov chain model for categorical data sequences and its applications in demand predictions

Markov models are commonly used in modelling many practicalsystems such as telecommunication systems, manufacturing systemsand inventory systems. In this paper we propose a multivariateMarkov chain model for modelling multiple categorical data sequences.We develop efficient estimation methods for the model parameters.We then apply the model and method to demand predictions fora soft-drink company in Hong Kong.     

A model for martensitic microstructure,its geometry and interface effects

In line with our formerly presented continuum micromechanical model [4,5] of the laminate microstructure of martensite, we here modify and reformulate the model to further its simplicity and clarity. The basic postulates are slightly altered. However, the approach remains the same, namely the kinematic assumption of nearly-planar laminate geometry put into an energy minimization framework with proper ansatzes of twin-interface and boundary energies. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A practical exercise in simulation model validation

The validation of continuous system simulation models is a matter of great practical importance. Unfortunately, however, it often receives very little attention in university-level courses on modelling and simulation. The paper considers some possible reasons for the lack of emphasis given to model validation issues in education and describes an exercise which has been designed to introduce students to some practical aspects of internal verification and external validation of nonlinear dynamic models. The work involves a laboratory-scale system based on two inter-connected tanks of liquid and also demonstrates some important limitations of a widely-used nonlinear model. Features which make the chosen system particularly suitable for this teaching application include the relatively simple physical nature of the system and the fact that all the key variables of the model are accessible for measurement. Students are exposed to a range of practical issues, such as the selection of the sampling rate for data collection and the design of experiments to provide data sets appropriate for external validation purposes. Dealing successfully with such questions and carrying out validation tests exposes students to concepts of model credibility and the whole process of model development and application. They are also challenged in terms of their practical abilities to use computer simulation techniques and in their understanding of the mathematical model and the physics of the real system. It is argued that an exercise of this type can have very important educational benefits.     

A sharp inequality for martingales and its applications

In this paper, the best constant with respect to an inequality for martingales in Hall and Heyde (1980) is obtained. As a consequence, some large deviations with martingale difference and moving average process are established.     

Damage model for ferroelectric materials and its applications to multilayer actuators

In this paper a damage model for ferroelectric materials is presented. It is implemented in terms of a user element in the commercial FEM-code Abaqus. The model is based on micromechanical considerations of domain switching and its interaction with microcrack growth and coalescence. Finite element analysis of a multilayer actuator is performed, showing principal stresses leading to crack initiation and damage of the actuator. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A new stochastic Petri net model and its applications to logistics systems

This is a summary of the author’s PhD thesis supervised by Lionel Amodeo and Hoaxun Chen and defended on 29 November 2005 at the Université de Technologie de Troyes (France). The thesis is written in French and is available from the author upon request. This work deals with a new stochastic Petri net model and its applications for modeling and studying logistics systems and more generally discrete event dynamic systems.      

A criterion for differentiability in the sense of Belinskii and its consequences

There are obtained necessary and sufficient conditions for differentiability in the sense of Belinskii of quasiconformal mappings at a point.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 2, pp. 289–294, February, 1992.     

A graph based model for survivability applications

Many problems found in standard security and survivability applications can be transformed into graph and scheduling problems, thereby opening up the problems to a wealth of potential solutions or knowledge of limitations, infeasibility, scalability or intractability. This paper introduces a model to aid in the design, analysis, or operations of applications with security and survivability concerns. Specifically, a five step model is presented that transforms such applications into a parameterized graph model that, together with model abstraction and representations, can be the basis for solutions derived from graph and scheduling algorithms. A reverse transformation translates the solutions back to the application domain. The model is demonstrated using migratory agent security and fault-tolerant agreement and their transformation into chain constrained and group scheduling problems, respectively.     

Decomposition of a Schur-constant model and its applications

In this paper, the dependence structure of a Schur-constant model is investigated. A necessary and sufficient condition for a random vector to be Schur-constant is given, and some properties of the Schur-constant model are presented as well. Several applications of the Schur-constant model in insurance and finance are discussed.     

A local model for the trianguline variety and applications

Publications mathématiques de l'IHÉS - We describe the completed local rings of the trianguline variety at certain points of integral weights in terms of completed local rings of...     

A Kolmogorov-type competition model with multiple coexistence states and its applications to plant competition for sunlight

It is demonstrated that a Kolmogorov-type competition model featuring species allocation and gain functions can possess multiple coexistence states. Two examples are constructed: one in which the two competing species possess rectangular allocation functions but distinct gain functions, and the other in which one species has a rectangular allocation function, the second species has a bi-rectangular allocation function, and the two species share a common gain function. In both examples, it is shown that the species nullclines may intersect multiple times within the interior of the first quadrant, thus creating both locally stable and unstable equilibrium points. These results have important applications in the study of plant competition for sunlight, in which the allocation functions describe the vertical placement of leaves for two competing species, and the gain functions represent rates of photosynthesis performed by leaves at different heights when shaded by overlying leaves belonging to either species.     

A geometric property in and its applications

In this work, we initiate the study of the geometry of the variable exponent sequence space when . In 1931 Orlicz introduced the variable exponent sequence spaces while studying lacunary Fourier series. Since then, much progress has been made in the understanding of these spaces and of their continuous counterpart. In particular, it is well known that is uniformly convex if and only if the exponent is bounded away from 1 and infinity. The geometry of when either or remains largely ill‐understood. We state and prove a modular version of the geometric property of when , known as uniform convexity in every direction. We present specific applications to fixed point theory. In particular we obtain an analogue to the classical Kirk's fixed point theorem in when .     

A practical but rigorous approach to sum-of-ratios optimization in geometric applications

In this paper, we develop an algorithm for minimizing the L _q norm of a vector whose components are linear fractional functions, where q is an arbitrary positive integer. The problem is a kind of sum-of-ratios optimization problem, and often occurs in computer vision. In that case, it is characterized by a large number of ratios and a small number of variables. The algorithm we propose here exploits this feature and generates a globally optimal solution in a practical amount of computational time.     

A substitution theorem for graceful trees and its applications

A graceful labeling of a graph G=(V,E) assigns |V| distinct integers from the set {0,…,|E|} to the vertices of G so that the absolute values of their differences on the |E| edges of G constitute the set {1,…,|E|}. A graph is graceful if it admits a graceful labeling. The forty-year old Graceful Tree Conjecture, due to Ringel and Kotzig, states that every tree is graceful.We prove a Substitution Theorem for graceful trees, which enables the construction of a larger graceful tree through combining smaller and not necessarily identical graceful trees. We present applications of the Substitution Theorem, which generalize earlier constructions combining smaller trees.