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This is a review paper, concerning some extensions of the celebrated Merton's mutual fund theorem in infinite-dimensional financial models, in particular, the so-called Large Financial Markets (where a sequence of assets is taken into account) and Bond Markets Models (where there is a continuum of assets). In order to obtain these results, an infinite-dimensional stochastic integration theory is essential: the paper illustrates briefly a new theory introduced to this extent by M. De Donno and the author. [ABSTRACT FROM AUTHOR]

In a recent paper, Pan and Başar [19] have studied the H∞ control of large scale Jump Linear systems in which the transitions of the jump Markov chain can be separated into sets having strong and weak interactions. They obtained an approximating reduced-order aggregated problem which is the limit as the rate of transitions of the faster time scale (which is a multiple of some parameter 1/∈) goes to infinity. In this paper we further investigate the solution of that problem as a function of the parameter ϵ. We show that the related optimal feedback policy and the value admit a Taylor series in terms of ϵ, and we compute its coefficients. [ABSTRACT FROM AUTHOR]

This paper exposes in voluntarily simple terms the concept of S-adapted equilibrium introduced to represent and compute economic equilibria on stochastic markets. A model of the European gas market, that has been at the origin of the introduction of the concept, is recalled in this paper and the results obtained in 1987, when the contingent equilibrium has been computed for a time horizon extending until 2020, are compared with the observed trend in these markets over the last two decades. The information structure subsumed by this concept of S-adapted strategies is then analyzed, using different paradigms of dynamic games. The paper terminates with some open and intriguing questions related to the time consistency and subgame perfectness of the dynamic equilibrium thus introduced. [ABSTRACT FROM AUTHOR]

This set of notes was used to complement my short course on the convergence to equilibrium for the Boltzmann equation, given at Institut Henri Poincaré in November\2-December 2001, as part of the Hydrodynamic limits program organized by Stefano Olla and François Golse. The informal style is in accordance with the fact that this is neither a reference book nor a research paper. The reader can use my review paper, A review of mathematical topics in collisional kinetic theory, as a reference source to dissipate any ambiguity with respect to notation for instance. Apart from minor corrections here and there, the main changes with respect to the original version of the notes were the addition of a final section to present some more recent developments and open directions, and the change of the sign convention for the entropy, to agree with physical tradition. Irene Mazzella is warmly thanked for kindly typesetting a preliminary version of this manuscript. [ABSTRACT FROM AUTHOR]

The current industry standard is to optimize loan portfolios with respect to variance. In this paper we show that optimization with respect to expected shortfall and expected regret is fairly easy to implement. [ABSTRACT FROM AUTHOR]

We consider, in a Hilbert space U, a class of Gaussian processes defined by a linear filter with a cylindrical Wiener process as input process. This noise is used as an additive perturbation to a family of fractional order (in time) partial differential equations. We give conditions such that the stochastic convolution process is well defined, both in finite time horizon and in an infinite interval. An important example of noise that is contained in the paper is the fractional Brownian motion. [ABSTRACT FROM AUTHOR]

In this paper we apply the general framework introduced in [2] to two models with transaction costs: • a dynamic model with an infinite number of assets; • a model with European call options as basic assets. In particular, it is proved that a dynamic model with an infinite number of assets satisfies the No Generalized Arbitrage condition (this notion was introduced in [2]) if and only if there exist an equivalent measure and a martingale with respect to this measure that lies (componentwise) between the discounted ask and bid price processes. Furthermore, the set of fair prices of a contingent claim coincides with the set of expectations of the payoff with respect to these measures. Our approach to arbitrage pricing in models with transaction costs differs from the existing ones. Key words: Delta-martingale, Fair price, Fundamental theorem of asset pricing, General arbitrage pricing model, Generalized arbitrage, Risk-neutral measure, Set of attainable incomes, Transaction costs [ABSTRACT FROM AUTHOR]

The purpose of this paper is to present a unified approach to pricing contingent claims through a new concept of generalized arbitrage. First, we prove the fundamental theorem of asset pricing and establish the form of the fair price intervals within the framework of a general arbitrage pricing model. [ABSTRACT FROM AUTHOR]

In the original version of Parrondo's paradox, two losing sequences of games of chance are combined to form a winning sequence. The games in the first sequence depend on a single parameter p, while those in the second depend on two parameters p1 and p2. The paradox is said to occur because there exist choices of p, p1 and p2 such that the individual sequences of games are losing but a sequence constructed by choosing randomly between the games at each step is winning. At first sight, such behavior seems surprising. However, we contend in this paper that it should not be seen as surprising. On the contrary, we showthat such behaviour is typical in situations in which we randomly create a sequence from games whose winning regions can be defined on the same parameter space. Before we discuss this issue, we investigate in some detail the issue of when sequences of games, such as those proposed by Parrondo, should be considered to be winning, losing or fair. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to compare two ways of modelling exploitation of common renewable resource by a large group of players. [ABSTRACT FROM AUTHOR]

In this paper we analyse the robustness of the Hobson-Rogers model with respect to the offset function, which depends on the whole past of the risky asset and is thus not fully observable. We prove that, if the offset function is the realisation of a stationary process, then the error in pricing a derivative asset decreases exponentially with respect to the observation window. We present sufficient conditions on the volatility in order to characterise the invariant density and three examples. [ABSTRACT FROM AUTHOR]

Suppose that the trajectory of a particle x(t; x, k) is a solution of the Newton equation $$ \ddot x\left( {t;x{\text{,}}k} \right) = \delta ^{1/2} F\left( {x\left( {t;x{\text{,}}k} \right),\dot x\left( {t;x{\text{,}}k} \right)} \right),{\mathbf{ }}x\left( {\text{0}} \right) = x,\dot x\left( 0 \right) = k $$ , where F(x, k) is a spatially homogeneous random force field defined over a certain probability space (Ω,Σ, ℙ). It has been proved by Kesten and Papanicolaou in [2] that if d ≥ 3 and F(x, k) is sufficiently regular, nondegenerate and mixing in the spatial variable, then the process $$ \left( {\delta ^{1/2} x\left( {\delta ^{ - 1} t;x{\text{,}}k} \right),\ddot x\left( {\delta ^{ - 1} t;x,k} \right)} \right),t \geqslant 0 $$ , converges weakly to a hypoelliptic diffusion. In this paper we prove power-like bounds on the convergence rate for one-dimensional marginals of the process. [ABSTRACT FROM AUTHOR]

We consider a stochastic equation in ℝn with time-dependent coefficients assuming that it has a unique solution and denote by Ps,t, s < t the corresponding transition semigroup. Then we consider a family of measures (νt)t∈ℝ such that $$ \smallint _{\mathbb{R}^d } P_{s,t} \varphi \left( x \right)\nu _s \left( {dx} \right) = \smallint _{\mathbb{R}^d } \varphi \left( x \right)\nu _t \left( {dx} \right),s \leqslant t $$ , for all continuous and bounded functions ϕ. The family (νt)t∈ℝ is called an evolution system of measures indexed by ℝ. It plays the role of a probability invariant measure for autonomous systems. In this paper we generalize the Krylov-Bogoliubov criterion to prove the existence of an evolution system of measures. Moreover, we study some properties of the corresponding Kolmogorov operator proving in particular that it is dissipative with respect to the measure ν(dt, dx) = νt(dx)dt. [ABSTRACT FROM AUTHOR]

The aim of this paper is to approximate the solution of a stochastic differential equation driven by fractional Brownian motion (with Hurst index greater than 1/2 ) using a series expansion for the noise. We prove that the solution of the approximating equations converge in probability to the solution of the given equation. We illustrate the approximation through an example from mathematical finance. [ABSTRACT FROM AUTHOR]

Starting from the modelling requirements of the early design phase of the product development, the paper will show a possible strategy to overcome some limitations of current CAS/CAD systems. In fact, the styling stage involves both technical knowledge and fuzzy and dynamic aspects, which have to be taken into account for a proper management. The paper focuses on high-level modelling tools developed to deform surfaces with semantic (aesthetic) constraints, i.e. the crucial design elements for the stylist. Furthermore, the communication among the other actors of the design process is consequently facilitated. [ABSTRACT FROM AUTHOR]

In finance, the strong convergence properties of discretisations of stochastic differential equations (SDEs) are very important for the hedging and valuation of exotic options. In this paper we show how the use of the Milstein scheme can improve the convergence of the multilevel Monte Carlo method, so that the computational cost to achieve an accuracy of O(e) is reduced to O(ϵ−2) for a Lipschitz payoff. The Milstein scheme gives first order strong convergence for all one-dimensional systems (one Wiener process). However, for processes with two or more Wiener processes, such as correlated portfolios and stochastic volatility models, there is no exact solution for the iterated integrals of second order (Lévy area) and the Milstein scheme neglecting the Lévy area gives the same order of convergence as the Euler-Maruyama scheme. The purpose of this paper is to show that if certain conditions are satisfied, we can avoid the calculation of the Lévy area and obtain first convergence order by applying an orthogonal transformation. We demonstrate when the conditions of the two-dimensional problem permit this and give an exact solution for the orthogonal transformation. We present examples of pricing exotic options to demonstrate that the use of both the orthogonal Milstein scheme and the multilevel Monte Carlo give a substantial reduction in the computation cost. [ABSTRACT FROM AUTHOR]

This paper is meant to be the continuation of the previous work [1] where a coupled ODE/PDE method for the simulation of semiconductor devices was introduced. From a strictly mathematical viewpoint, analytical results on coupled PDE/ODE systems (as arising in integrated circuit simulation) can be found in [2]. In particular, in the present paper, we investigate numerically new algorithms of Domain Decomposition type for the simulation of circuits containing distributed devices (Sect. 2) as well as semiconductors in which some part is modeled with lumped parameters (Sect. 3). The results presented here have been investigated in the seminal work [3], while a more extended analysis is ongoing [4]. [ABSTRACT FROM AUTHOR]

This paper studies the problem of optimal switching for a one-dimensional diffusion, which may be regarded as a sequential optimal stopping problem with changes of regimes. The resulting dynamic programming principle leads to a system of variational inequalities, and the state space is divided into continuation regions and switching regions. By a viscosity solutions approach, we prove the smooth-fit C1 property of the value functions. MSC Classification (2000): 60G40, 49L25, 60H30 Key words: Optimal switching, System of variational inequalities, Viscosity solutions, Smooth-fit principle [ABSTRACT FROM AUTHOR]

This paper first summarizes the foundations of stochastic calculus via regularization and constructs through this procedure Ito and Stratonovich integrals. In the second part, a survey and new results are presented in relation with finite quadratic variation processes, Dirichlet and weak Dirichlet processes. MSC 2000: 60H05, 60G44, 60G48 Key words: Integration via regularization, Weak Dirichlet processes, Covariation, Ito formula [ABSTRACT FROM AUTHOR]

In this paper the definition of cooperative game in characteristic function form is given. The notions of optimality principle and solution concepts based on it are introduced. The new concept of "imputation distribution procedure" (IDP) is defined and connected with the basic definitions of time-consistency and strong time-consistency. Sufficient conditions of the existence of time-consistent solutions are derived. For a large class of games where these conditions cannot be satisfied, the regularization procedure is developed and new c.f. constructed. The "regularized" core is defined and its strong time-consistency proved. [ABSTRACT FROM AUTHOR]

In this paper, we provide an introduction to quantum game theory through discussion of ways of converting classical games into the quantum regime. We illustrate how a quantum-based approach can simulate all possible classical game histories in parallel, for the example of Parrondo's games. [ABSTRACT FROM AUTHOR]

In this paper we develop two new parallel algorithms for differential games based on the principle of "data replication". This technique is efficient on distributed memory architectures such as IBM/PS2 or Digital Alpha and is coupled with a domain decomposition techniques to construct an approximation scheme for the Isaacs equation in ℝn. The algorithms are presented for a 2-domain decomposition and some hints are given for the case of d subdomains having crossing points. The above parallel algorithms have the same fixed point as the serial algorithm so that convergence to the viscosity solution of the Isaacs equation is guaranteed by previous results. The efficiency of the above algorithms is discussed analyzing some numerical tests which include the homicidal chauffeur game. [ABSTRACT FROM AUTHOR]

This paper models adaptive learning behavior in a simple coordination game that Van Huyck, Cook and Battalio (1994) have investigated in a controlled laboratory setting with human subjects. We consider how populations of arti- ficially intelligent players behave when playing the same game. We use the genetic programming paradigm, as developed by Koza (1992, 1994), to model how a population of players might learn over time. In genetic programming one seeks to breed and evolve highly fit computer programs that are capable of solving a given problem. In our application, each computer program in the population can be viewed as an individual agent's forecast rule. The various forecast rules (programs) then repeatedly take part in the coordination game evolving and adapting over time according to principles of natural selection and population genetics.We argue that the genetic programming paradigm that we use has certain advantages over other models of adaptive learning behavior in the context of the coordination game that we consider. We find that the pattern of behavior generated by our population of artificially intelligent players is remarkably similar to that followed by the human subjects who played the same game. In particular, we find that a steady state that is theoretically unstable under a myopic, best-response learning dynamic turns out to be stable under our genetic-programming-based learning system, in accordance with Van Huyck et al.'s (1994) finding using human subjects. We conclude that genetic programming techniques may serve as a plausible mechanism for modeling human behavior, and may also serve as a useful selection criterion in environments with multiple equilibria. [ABSTRACT FROM AUTHOR]

In this paper, we study the linear quadratic Nash games for infinite horizon singularly perturbed systems (SPS). In order to solve the generalized algebraic Lyapunov equation (GALE) corresponding to the generalized Lyapunov iterations, we propose a new algorithm which is based on the fixed point iterations. Furthermore, we also propose a new algorithm which is based on the Kleinman algorithm for solving the generalized cross-coupled algebraic Riccati equations (GCARE). It is shown that the resulting algorithm guarantees the quadratic convergence. [ABSTRACT FROM AUTHOR]

We develop a mathematical model within a game theoretical framework to capture the flow control problem for variable rate traffic at a bottleneck node. In this context, we also address various issues such as pricing and allocation of a single resource among a given number of users. We obtain a distributed, end-to-end flow control using cost functions defined as the difference between particular pricing and utility functions. We prove the existence and uniqueness of a Nash equilibrium for two different utility functions. The paper also discusses three distributed update algorithms, parallel, random and gradient update, which are shown to be globally stable under explicitly derived conditions. The convergence properties and robustness of each algorithm are studied through extensive simulations. [ABSTRACT FROM AUTHOR]

We adopt the robust control, or game theoretic, approach of [5] to option pricing. In this approach, uncertainty is described by a restricted set of possible price trajectories, without endowing this set with any probability measure. We seek a hedge against every possible price trajectory. In the absence of transaction costs, the continuous trading theory leads to a very simple differential game, but to an uninteresting financial result, as the hedging strategy obtained lacks robustness to the unmodeled transaction costs. (A feature avoided by the classical Black and Scholes theory through the use of unbounded variation cost trajectories. See [5].) We therefore introduce transaction costs into the model. We examine first the continuous time model. Its mathematical complexity makes it beyond a complete solution at this time, but the partial results obtained do point to a robust strategy, and as a matter of fact justify the second part of the paper. In that second part, we examine the discrete time theory, deemed closer to a realistic trading strategy. We introduce transaction costs into the model from the outset and derive a pricing equation, which can be seen as a discretization of the quasi variational inequality of the continuous time theory. The discrete time theory is well suited to a numerical solution. We give some numerical results. In the particular case where the transaction costs are null, we recover our theory of [5], and in particular the Cox, Ross and Rubinstein formula when the contingent claim is a convex function of the terminal price of the underlying security. [ABSTRACT FROM AUTHOR]

The paper is concerned with two-person nonzero-sum stopping games in which pairs of randomized stopping times are game strategies. For a general form of reward functions, existence of Nash equilibrium strategies is proved under some restrictions for three types of games: quasi-finite-horizon, random-horizon and infinite-horizon games. [ABSTRACT FROM AUTHOR]

In this paper we investigate the existence and turnpike properties of overtaking Nash equilibria for an infinite horizon dynamic game in which the dynamic constraints are described by linear evolution equations in a Hilbert space. [ABSTRACT FROM AUTHOR]

We use in this paper the viability/capturability approach for studying the problem of characterizing the dynamic core of a dynamic cooperative game defined in a characteristic function form. In order to allow coalitions to evolve, we embed them in the set of fuzzy coalitions. Hence, we define the dynamic core as a set-valued map associating with each fuzzy coalition and each time the set of allotments is such that their payoffs at that time to the fuzzy coalition are larger than or equal to the one assigned by the characteristic function of the game. We shall characterize this core through the (generalized) derivatives of a valuation function associated with the game. We shall provide its explicit formula, characterize its epigraph as a viable-capture basin of the epigraph of the characteristic function of the fuzzy dynamical cooperative game, use the tangential properties of such basins for proving that the valuation function is a solution to a Hamilton-Jacobi-Isaacs partial differential equation and use this function and its derivatives for characterizing the dynamic core. [ABSTRACT FROM AUTHOR]

Consider the ID lattice Schrödinger operator (1) $$H = \lambda \cos (2\pi n^\rho \omega + \theta )\delta _{nn'} + \Delta$$ with 1 < ρ < 2 and define $$\gamma (E,\lambda )\mathop {\underline {\lim } }\limits_{N \to \infty } \frac{1}{N}\int_\mathbb{T} {\log } \left\ {\prod\limits_N^0 {\left( {\begin{array}{*{20}c}{E - \lambda cos(2\pi n^\rho \omega + \theta ) - 1} \\{10} \\\end{array} } \right)} } \right\d\theta$$ . If λ > 2, M. Herman's [H] argument implies that γ(E,λ)≥log λ/2 >0, for all E. We are interested here in small λ and show that for all E∈Eλ⊂[−2,2] (2) $$mes([ - 2,2]\backslash \mathcal{E}_\lambda )\xrightarrow{{\lambda \to 0}}0$$ we have that γ(E, λ) > 0. See Proposition 4. Considering the skew shift on $$\mathbb{T}^2$$ (3) $$T(x,y) = (x + y,y + \omega )$$ and the Hamiltonian (4) $$H = \lambda \cos (\pi _1 T^m (x,y))\delta _{nn'} + \Delta$$ where $$\pi _1 T^m (x,y) = x + ny + \frac{{n(n - 1)}}{2}\omega$$ we show that the Lyapounov exponent $$\gamma (E,\lambda )^{\underline{\underline {a.e.}} } \mathop {\underline {\lim } }\limits_{N \to \infty } \frac{1}{N}\log \left\ {\prod\limits_N^0 {\left( {\begin{array}{*{20}c}{E - \lambda \cos \pi _1 T^n (x,y) - 1} \\{10} \\\end{array} } \right)} } \right\$$ is strictly positive for E∈Eλ⊂[−2,2] satisfying (2), provided we assume in (3) that $$\left \omega \right < \varepsilon (\lambda )$$ . See Proposition 5. The method is based on a local approximation of (1), (4) by the almost Mathieu model (5) $$H_{\alpha ,\lambda ,\theta } = \lambda \cos (2\pi \alpha + \theta )\delta _{nn'} + \Delta$$ and uses the fact (see Corollary 3) that for λ small and E∈Eλ⊂[−2,2] satisfying (2), (6) $$\int_\mathbb{T} {\gamma (\alpha ,\lambda ,E)d\alpha > 0}$$ where γ(α, λ, E) refers to the Lyapounov exponents of (5). The proof of (6) does rely on the Aubry duality, [A-A], [La]). Added in Proof. Concerning lattice Schrödinger operators of the form (1), related references were pointed out to the author by Y. Last. First, it is shown in the paper [L-S] that H=λcos(mρ)+Δ on ℤ has no absolutely continuous spectrum for λ > 2, ρ > 1. In fact, Theorem 1.4 from [L-S] provides an alternative proof of Proposition 4 in this paper. Other numerical and heuristic studies appear in [G-F],[B-F]. The particular case 1 < ρ < 2 was studied in [Th]. See [L-S] for further details. [ABSTRACT FROM AUTHOR]

In this paper we extend the derivation of mezoscopic partial differential equations (or stochastic partial differential equations (SPDE's)) from particle systems with finite conserved mass to infinite conserved mass. We also sketch the history of stochastic and deterministic (i.e., mezoscopic and macroscopic) reaction-diffusion models initiated by Arnold's work as well as some results of Dawson's measure processes approach to SPDE's. At the end of the paper we show how to include creation and annihilation through a fractional step method into the mezoscopic PDE's. [ABSTRACT FROM AUTHOR]

In this paper, we examine the stochastic version of the Duffing-van der Pol equation. As in [2], [8], [19], [16], we introduce both multiplicative and additive stochastic excitations to the original Duffingvan der Pol equation, i.e. $$ \ddot x = \left( {\alpha + \sigma _1 \xi _1 } \right)x + \beta x + a\dot x^3 + bx^2 \dot x + \sigma _2 \xi _2 , $$ where, α and α are the bifurcation parameters, ξ1 and ξ2 are white noise processes with intensities σ1 and σ2, respectively. The existence of the extrema of the probability density function is presented for the stochastic system. The method used in this paper is essentially the same as that which was used in [19]. We first reduce the above system to a weakly perturbed conservative system by introducing an appropriate scaling. The corresponding unperturbed system is then studied. Subsequently, by transforming the variables and performing stochastic averaging, we obtain a one-dimensional Itô equation for the Hamiltonian H. The probability density function is found by solving the Fokker-Planck equation. The extrema of the probability density function are then calculated in order to study the so-called P-Bifurcation. The bifurcation diagrams for the stochastic version of the Duffing-van der Pol oscillator with a=−1.0, b=−1.0 over the whole (α, β)-plane are given. The related mean exit time problem is also studied. [ABSTRACT FROM AUTHOR]

In this chapter, we shall apply evolution algebra theory to non-Mendelian genetics. In the first section, we give a brief reflection of how non-Mendelian genetics motivated the development evolution algebras. In section 2, we review the basic biological components of non-Mendelian genetics and the inheritance of organelle genes; we also give a general algebraic formulation of non-Mendelian genetics. In section 3, we use evolution algebras to study the heteroplasmy and homoplasmy of organelle populations, and show that concepts of algebraic transiency and algebraic persistency relate to biological transitory and stability, respectively. Coexistence of triplasmy in tissues of patients with sporadic mitochondrial disorders is studied as well. In section 4, we apply evolution algebra theory to the study of asexual progenies of Phytophthora infestans, an important agricultural pathogen. [ABSTRACT FROM AUTHOR]

In the final chapter, we list some further related results that we have obtained. Because of the limitation of time and space, we do not give the detailed proofs for most of the results, although some explanations or brief proofs are given. To promote further study and better understanding of the significance of evolution algebras, we also put forward some interesting open problems and related research topics. [ABSTRACT FROM AUTHOR]

In this chapter, we provide several examples from biology, physics, and mathematics including topology and stochastic processes, which have motivated the development of the theory of evolution algebras. [ABSTRACT FROM AUTHOR]

This paper deals with a coupled system of non-linear elliptic differential equations arising in electrodeposition modelling process. We show the existence and uniqueness of the solution. A numerical algorithm to compute an approximation of the weak solution is described. We introduce a domain decomposition method to take in account the anisotropy of the solution. We show the domain decomposition method convergence. A numerical example is presented and commented. [ABSTRACT FROM AUTHOR]

State estimation is necessary in diagnosing anomalies inWater Demand Systems (WDS). In this paper we present a neural network performing such a task. State estimation is performed by using optimization, which tries to reconcile all the available information. Quantification of the uncertainty of the input data (telemetry measures and demand predictions) can be achieved by means of robust estate estimation. Using a mathematical model of the network, fuzzy estimated states for anomalous states of the network can be obtained. They are used to train a neural network capable of assessing WDS anomalies associated with particular sets of measurements. [ABSTRACT FROM AUTHOR]

Thin-film flows occur in a variety of physical contexts including, for example, industry, biology and nature, and have been the subject of considerable theoretical research. (See, for example, the review by Oron, Davis and Bankoff [4].) In particular, there are several practically important situations in which an external airflow has a significant effect on the behaviour of a film of fluid, and consequently there has been considerable theoretical and numerical work done to try to understand better the various flows that can occur. (See, for example, the studies by King and Tuck [2] and Villegas-Díaz, Power and Riley [6].) The flow of a rivulet on a planar substrate subject to a shear stress at its free surface has been investigated by several authors, notably Myers, Liang and Wetton [3], Saber and El-Genk [5], and Wilson and Duffy [9]. All of these works concern a non-perfectly wetting fluid; the flow of a rivulet of a perfectly wetting fluid in the absence of a shear stress at its free surface has been treated by Alekseenko, Geshev and Kuibin [1], and by Wilson and Duffy [7,8]. In the present short paper we use the lubrication approximation to obtain a complete description of the steady unidirectional flow of a thin rivulet of a perfectly wetting fluid on an inclined substrate subject to a prescribed uniform longitudinal shear stress at its free surface. [ABSTRACT FROM AUTHOR]

The evaporation of liquid droplets is of fundamental importance to industry, with a vast number of applications including ink-jet printing, spray cooling and DNA mapping, and has been the subject of considerable theoretical and experimental research in recent years. Significant recent papers include those by Deegan [1], Deegan et al. [2], Hu and Larson [3], Poulard et al. [4], Sultan et al. [5], and Shahidzadeh-Bonn et al. [6]. [ABSTRACT FROM AUTHOR]

This paper introduces the principles of creating the web-tool on differential equations. It can be used to support European Master Program for Mathematics in Industry. Such a Program is working already on the leading partner universities of ECMI and now the use of e-study as an innovational step is being discussed. [ABSTRACT FROM AUTHOR]

In this paper we will show an industrial application of a new framework, called LaTEX2WeB, which translates LaTEX material into an interactive Web-based document. The more important characteristic of LaTEX2WeB is the possibility of integrating, in the Web-based document, external programs produced in every languages. We exploited LaTEX2WeB to create an interactive Web-based manual, which illustrates a new software for the multiobjective optimization applied to the parameter extraction in circuit design. Thanks to LaTEX2WeB it was possible to simulate the algorithms written in C, C++, and FORTRAN, used in the multiobjective optimization software. [ABSTRACT FROM AUTHOR]

In this paper we consider the recovery of ellipsoidal 3D shapes with piecewise constant coefficients in Diffuse Optical Tomography (DOT). We use an adjoint scheme for calculating gradients for the shape parameters defining the unknown ellipsoids, and a Newton-type optimisation process for the minimization of a least squares data misfit functional. A boundary integral formulation is used for the forward modelling. An advantage of the proposed method is the implicit regularisation effect arising from the reduced dimensionality of the inverse problem. Results of a numerical experiment in 3D are shown which demonstrate the performance of the method. [ABSTRACT FROM AUTHOR]

In this paper we demonstrate model order reduction of a nonlinear academic model of a diode chain. Two reduction methods, which are suitable for nonlinear differential algebraic equation systems are used, the trajectory piecewise linear approach and the proper orthogonal decomposition with missing point estimation. [ABSTRACT FROM AUTHOR]

The general question which will make the object of this paper is the homogenization of some nonlinear problems arising in the modelling of thermal diffusion in a two-component composite. We shall consider, at the microscale, a periodic structure formed by two materials with different thermal properties. We shall deal with two situations: in the first one, we assume that we have some nonlinear sources acting in both components and that at the interface between our two materials the temperature and the flux are continuous, while in the second problem we shall address here, we assume that the flux is still continuous, but depends in a nonlinear way on the jump of the temperature field. In both cases, since the characteristic sizes of these two components are small compared with the macroscopic length-scale of the flow domain, we can apply an homogenization procedure. [ABSTRACT FROM AUTHOR]

The correct simulation of industrial plants firing pulverized fuels (pf: coal, biomass, etc.) by means of commercial CFD codes relies on a number of submodels for the various processes, including, e.g. heat transfer (radiation, conduction through deposits, etc.) and particle combustion. The latter is of major importance in the design of the combustion chamber and the selection of the mills or, conversely, regarding the feasibility of burning a new fuel in an existing boiler. In the last decade, the introduction of new, internationally traded coals and alternative fuels into the power market has motivated renewed interest in the experimental and theoretical characterization of the combustion of these fuels. Regarding experimentation, it is generally accepted that the ‘reactivity' of a fuel can not be determined in desktop analytical instruments; instead, drop tube furnaces or entrained flow reactors (EFR) must be used in order to reproduce the high temperature, high heating rate conditions found in a real pf combustion chamber [1]. Several alternative experimental procedures have been developed in the past and are still used (see, e.g. [2, 3]). On the other hand, two general approaches are used in the literature to model pulverized coal/biomass char combustion: one intends to characterize the evolution of the pores inside the burning particle, and considers both internal and external diffusion, whereas the kinetics for the basic homogeneous and heterogeneous reactions are taken from low temperature analysis or fundamental knowledge of the chemistry involved (e.g. [4]); the other one, followed here, makes use of an apparent kinetics based on the outer particle surface, and includes external diffusion [5]. In the latter case, two parameters governing an Arrhenius-like kinetics are the main unknowns to be determined from the experiments performed in an EFR. The aim of this paper is to discuss some aspects of the mathematical procedure for the determination of those parameters. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to contribute to the mathematical modelling of the combustion of coal particles in pulverised coal furnaces, and also to propose an algorithm for its numerical solution. The mathematical model includes two coupled phases: the solid phase, for the coal particles, where a Lagrangian description is used and an Eulerian description for the gas phase, where the effects of the combustion of coal particles are homogenised. [ABSTRACT FROM AUTHOR]

This paper is concerned with a fascinating phenomenon in boundary layer transition, namely, three-dimensional disturbances undergo rapid amplification despite that they have smaller linear growth rates than two-dimensional ones. Physical mechanisms are sought by considering two types of nonlinear interactions between oblique and planar instability modes. The first is the well-known subharmonic resonance. The relevant mathematical theory and its main predictions are briefly summarised. This mechanism, however, operates only among a very restrictive set of modes, and hence is unable to explain the broadband nature of the amplifying disturbances observed in experiments. The second mechanism involves the interaction between a planar and a pair of oblique Tollmien—Schlichting (T—S) waves which are phase-locked in that they travel with (nearly) the same phase speed. It is a more general type of interaction than subharmonic resonance since no further restriction is imposed on the frequencies. Yet similar to subharmonic resonance, this interaction also leads to super-exponential growth of the oblique modes, while the planar mode remains to follow linear stability theory. The dominant planar mode therefore plays the role of a catalyst, the implications of which for the eN-method and for transition control are discussed. [ABSTRACT FROM AUTHOR]

This paper deals with mathematical modelling and numerical simulation of induction heating furnaces for axisymmetric geometries. The mathematical model presented consists in a coupled thermo-magneto-hydrodynamic problem with phase change. We propose a finite element method and an iterative algorithm to solve the equations. Some numerical results for an industrial furnace used for silicon purification are shown. [ABSTRACT FROM AUTHOR]