Strong solutions for a 1D viscous bilayer shallow water model

In this paper, we consider a viscous bilayer shallow water model in one space dimension that represents two superposed immiscible fluids. For this model, we prove the existence of strong solutions in a periodic domain. The initial heights are required to be bounded above and below away from zero and we get the same bounds for every time. Our analysis is based on the construction of approximate systems which satisfy the BD entropy and on the method developed by A. Mellet and A. Vasseur to obtain the existence of global strong solutions for the one dimensional Navier–Stokes equations.     

Quasi static growth of brittle cracks in a linearly elastic flexural plate

In this paper we propose a variational model for the irreversible quasi static growth in brittle fractures for a linearly elastic homogeneous isotropic plate, subject to a time dependent vertical displacement on a part of its lateral surface. The model is based on the Griffith’s criterion for crack growth and is inspired to the model proposed in [11] by Francfort and Marigo in the case of 3-D elasticity. We give a precise mathematical formulation of the model and in this framework we prove an existence result. Mathematics Subject Classification (2000) 74K20, 35J35, 74G65, 35R35, 35A35, 74R10     

On the particular solutions of an integrable equation governing short waves in a long-wave model

In this paper, we study Lie symmetries and similarity reductions of an integrable equation governing short waves in a long-wave model, derived recently by Faquir et al [M.J. Faquir, M.A. Manna, A. Neveu, Proc. R. Soc. A 463 (2007) 1939]. We present explicit solutions for this model for the first time, for the different choices of the physical parameter $\gamma$.     

A parametric lifetime model for a multicomponents system with spatial interactions

In this paper, we consider a system made of n components displayed on a structure (eg, a steel plate). We define a parametric model for the hazard function, which includes covariates and spatial interaction between components. The state (nonfailed or failed) of each component is observed at some inspection times. From these data, we consider the problem of model parameter estimation. To achieve this, we suggest to use the SEM algorithm based on a pseudo‐likelihood function. A definition for the time‐to‐failure of the system is given, generalizing the classical cases. A study based on numerical simulations is provided to illustrate the proposed approach.     

Bayesian stratified random sampling using auxiliary information

Summary Smith (1976,J. R. Statist. Soc., A,139, 183–204) has argued that survey statisticians should attempt to model finite population structures in the same way that statisticians in other disciplines have to provide models of finite or infinite populations. Following this argument, we suggest in this paper that an obvious model for a stratified population when auxiliary information regarding variate values is available, is the one way analysis of covariance model with unequal variances and we consider the problem of estimating the finite population mean. Finally a possible extension of this result is discussed.     

Theoretical and numerical analysis for the quasi-continuum approximation of a material particle model

In many applications materials are modeled by a large number of particles (or atoms) where any one of particles interacts with all others. Near or nearest neighbor interaction is expected to be a good simplification of the full interaction in the engineering community. In this paper we shall analyze the approximate error between the solution of the simplified problem and that of the full-interaction problem so as to answer the question mathematically for a one-dimensional model. A few numerical methods have been designed in the engineering literature for the simplified model. Recently much attention has been paid to a finite-element-like quasicontinuum (QC) method which utilizes a mixed atomistic/continuum approximation model. No numerical analysis has been done yet. In the paper we shall estimate the error of the QC method for this one-dimensional model. Possible ill-posedness of the method and its modification are discussed as well.

     

Asymptotic stability of traveling waves in a discrete convolution model for phase transitions

In a recent paper [P. Bates, A. Chmaj, A discrete convolution model for phase transition, Arch. Rational Mech. Anal. 150 (1999) 281-305], a discrete convolution model for Ising-like phase transition has been derived, and the existence, uniqueness of traveling waves and stability of stationary solution have been studied. This nonlocal model describes l₂-gradient flow for a Helmholts free energy functional with general range interaction. In this paper, by using the comparison principle and the squeezing technique, we prove that the traveling wavefronts with nonzero speed is globally asymptotic stable with phase shift.     

Hopf bifurcations in a Ricardo-Malthus model

Brander and Taylor presented a simple and basic framework for discussing the problem on human population and renewable natural resources in the year 1998, and D’Alessandro recently extended this work mainly by introducing a nonlinear term into the model, if seeing from the mathematical point of view. A limit cycle in this new model was reported by the author via numerically simulated drawing. In this paper, we show that this limit cycle actually is a bifurcating limit cycle of a one-parameter Hopf bifurcation.     

A note on “Two-warehouse inventory model with deterioration under FIFO dispatch policy”

A recently published paper by Lee [C.C. Lee, Two-warehouse inventory model with deterioration under FIFO dispatching policy, European Journal of Operational Research 174 (2006) 861–873] considers different dispatching models for the two-warehouse inventory system with deteriorating items, in which Pakkala and Achary’s LIFO (last-in–first-out) model [T.P.M. Pakkala, K.K. Achary, A deterministic inventory model for deteriorating items with two warehouses and finite replenishment rate, European Journal of Operational Research 57 (1992) 71–76] is first modified, and then the author concludes that the modified LIFO model always has a lower cost than Pakkala and Achary’s LIFO model under a particular condition specified by him. The present note points out that this conclusion is incorrect and misleading. Alternatively, we provide a new sufficient condition such that the modified LIFO model always has a lower cost than Pakkala and Achary’s model. Besides, we also compare Pakkala and Achary’s original LIFO model with Lee’s FIFO (first-in–first-out) model for the special case where the two warehouses have the same deteriorating rates. Finally, numerical examples are provided to investigate and examine the impact of corresponding parameters on policy choice. The results in this note give a much clearer picture than those at Lee’s paper about the relationships between the different dispatching policies for the two-warehouse inventory system with deterioration items.     

并购后企业知识资本演化的数学模型

知识资本是企业价值系统的参变量 ,其存量和水平支配着并购企业的命运 .从知识和能力整合的角度出发 ,根据并购双方知识资本系统整合的机理和特点 ,建立了知识资本演化的数学模型 ,并且通过模型的数值分析模拟了并购后知识资本存量变化的过程和发展趋势 .     

Stability of spiky solution of Keller–Segel's minimal chemotaxis model

A huge volume of research has been done for the simplest chemotaxis model (Keller–Segel's minimal model) and its variants, yet, some of the basic issues remain unresolved until now. For example, it is known that the minimal model has spiky steady states that can be used to model the important cell aggregation phenomenon, but the stability of monotone spiky steady states was not shown. In this paper, we derive, first formally and then rigorously, the asymptotic expansion of these monotone steady states, and then we use this fine information on the spike to prove its local asymptotic stability. Moreover, we obtain the uniqueness of such steady states. We expect that the new ideas and techniques for rigorous asymptotic expansion and spectrum analysis presented in this paper will be useful in attacking and hence stimulating research on other more sophisticated chemotaxis models.     

Qualitative analysis of a stochastic ratio-dependent predator-prey system

A stochastic ratio-dependent predator-prey model is investigated in this paper. By the comparison theorem of stochastic equations and Itô’s formula, we obtain the global existence of a positive unique solution of the ratio-dependent model. Besides, a condition for species to be extinct is given and a persistent condition is established. We also conclude that both the prey population and the ratio-dependent function are stable in time average. In the end, numerical simulations are carried out to confirm our findings.     

A cost allocation problem in urban solid wastes collection and disposal

In this paper we consider a cost allocation problem arising in a consortium for urban solid wastes collection and disposal. A classical allocation rule is the proportional division according to the volume of wastes collected; here we propose a different allocation method, rooted in game theory, based on a model developed by Fragnelli et al. [3], using the Shapley Value and the Owen Value as allocation rules. The model was applied to the data of the consortium Ovadese – Valle Scrivia, comparing our results and the actual ones.     

An orthotropic plate model for decks of suspension bridges

The main purpose of the present paper is to compare two different kinds of approaches in modeling the deck of a suspension bridge: in the first approach we look at the deck as a rectangular plate and in the second one we look at the deck as a beam for vertical deflections and as a rod for torsional deformations. Throughout this paper we will refer to the model corresponding to the second approach as the beam-rod model. In our discussion, we observe that the beam-rod model contains a larger number of elastic parameters if compared with the isotropic plate model. For this reason the beam-rod model is supposed to be more appropriate to describe the behavior of the deck of a real suspension bridge. A possible strategy to make the plate model more efficient could be to relax the isotropy condition with a more general condition of orthotropy, which is expected to increase the number of elastic parameters. In this new setting, a comparison between the two approaches becomes now possible.Basic results are proved for the suggested problem, from existence and uniqueness of solutions to spectral properties. We suggest realistic values for the elastic parameters thus obtaining with both approaches similar responses in the static and dynamic behavior of the deck. This can be considered as a preliminary article since many work has still to be done with the perspective of formulating models for a complete suspension bridge which take into account not only the deck but also the action on it of cables and hangers. With this perspective, a section is devoted to possible future developments.     

On Huber's contaminated model

Huber's contaminated model is a basic model for data with outliers. This paper aims at addressing several fundamental problems about this model. We first study its identifiability properties. Several theorems are presented to determine whether the model is identifiable for various situations. Based on these results, we discuss the problem of estimating the parameters with observations drawn from Huber's contaminated model. A definition of estimation consistency is introduced to handle the general case where the model may be unidentifiable. This consistency is a strong robustness property. After showing that existing estimators cannot be consistent in this sense, we propose a new estimator that possesses the consistency property under mild conditions. Its adaptive version, which can simultaneously possess this consistency property and optimal asymptotic efficiency, is also provided. Numerical examples show that our estimators have better overall performance than existing estimators no matter how many outliers in the data.     

Discrete-time analysis of the GI/G/1 system with Bernoulli retrials: An algorithmic approach

In this paper, we show that the discrete GI/G/1 system with Bernoulli retrials can be analyzed as a level-dependent QBD process with infinite blocks; these blocks are finite when both the inter-arrival and service times have finite supports. The resulting QBD has a special structure which makes it convenient to analyze by the Matrix-analytic method (MAM). By representing both the inter-arrival and service times using a Markov chain based approach we are able to use the tools for phase type distributions in our model. Secondly, the resulting phase type distributions have additional structures which we exploit in the development of the algorithmic approach. The final working model approximates the level-dependent Markov chain with a level independent Markov chain that has a large set of boundaries. This allows us to use the modified matrix-geometric method to analyze the problem. A key task is selecting the level at which this level independence should begin. A procedure for this selection process is presented and then the distribution of the number of jobs in the orbit is obtained. Numerical examples are presented to demonstrate how this method works.     

Steady-state solutions in a three-dimensional nonlinear pool-boiling heat-transfer model

We consider a relatively simple model for pool-boiling processes. This model involves only the temperature distribution within the heater and describes the heat exchange with the boiling medium via a nonlinear boundary condition imposed on the fluid-heater interface. This results in a standard heat-transfer problem with a nonlinear Neumann boundary condition on part of the boundary. In a recent paper [Speetjens M, Reusken A, Marquardt W. Steady-state solutions in a nonlinear pool-boiling model. IGPM report 256, RWTH Aachen. Commun Nonlinear Sci Numer Simul, in press, doi:10.1016/j.cnsns.2006.11.002] we analysed this nonlinear heat-transfer problem for the case of two space dimensions and in particular studied the qualitative structure of steady-state solutions. The study revealed that, depending on system parameters, the model allows both multiple homogeneous and multiple heterogeneous temperature distributions on the fluid-heater interface. In the present paper we show that the analysis from Speetjens et al. (doi:10.1016/j.cnsns.2006.11.002) can be generalised to the physically more realistic case of three space dimensions. A fundamental shift-invariance property is derived that implies multiplicity of heterogeneous solutions. We present a numerical bifurcation analysis that demonstrates the multiple solution structure in this mathematical model by way of a representative case study.     

On the pebbling threshold of paths and the pebbling threshold spectrum

A configuration of pebbles on the vertices of a graph is solvable if one can place a pebble on any given root vertex via a sequence of pebbling steps. A function is a pebbling threshold for a sequence of graphs if a randomly chosen configuration of asymptotically more pebbles is almost surely solvable, while one of asymptotically fewer pebbles is almost surely not. In this paper we tighten the gap between the upper and lower bounds for the pebbling threshold for the sequence of paths in the multiset model. We also find the pebbling threshold for the sequence of paths in the binomial model. Finally, we show that the spectrum of pebbling thresholds for graph sequences in the multiset model spans the entire range from n^1/2 to n, answering a question of Czygrinow, Eaton, Hurlbert and Kayll. What the spectrum looks like above n remains unknown.     

Nonadaptive algorithms for threshold group testing

Threshold group testing first proposed by Damaschke is a generalization of classic group testing. Specifically, a group test is positive (negative) if it contains at least u (at most l) positives, and if the number of positives is between l and u, the test outcome is arbitrary. Although sequential group testing algorithms have been proposed, it is unknown whether an efficient nonadaptive algorithm exists. In this paper, we give an affirmative answer to this problem by providing efficient nonadaptive algorithms for the threshold model. The key observation is that disjunct matrices, a standard tool for group testing designs, also work in this threshold model. This paper improves and extends previous results in three ways:1. The algorithms we propose work in one stage, which saves time for testing.2. The test complexity is lower than previous results, at least for the number of elements which need to be tested is sufficiently large.3. A limited number of erroneous test outcomes are allowed.