Conservative linear equations arise in many areas of application, including continuum mechanics or high-frequency geometrical optics approximations. This kind of equations admits most of the time solutions which are only bounded measures in the space variable known as duality solutions. In this paper, we study the convergence of a class of finite-differences numerical schemes and introduce an appropriate concept of consistency with the continuous problem. Some basic examples including computational results are also supplied.

This paper is devoted to a numerical simulation of the classical WKB system arising in geometric optics expansions. It contains the nonlinear eikonal equation and a linear conservation law whose coefficient can be discontinuous. We address the problem of treating it in such a way superimposed signals can be reproduced by means of the kinetic formulation of ``multibranch solutions'' originally due to Brenier and Corrias. Some existence and uniqueness results are given together with computational test-cases of increasing difficulty displaying up to five multivaluations.

We propose here a well-balanced numerical scheme for the one-dimensional Goldstein-Taylor system which is endowed with all the stability properties inherent to the continuous problem and works in both rarefied and diffusive regimes.

This paper investigates the behavior of numerical schemes for nonlinear conservation laws with source terms. We concentrate on two significant examples: relaxation approximations and genuinely nonhomogeneous scalar laws. The main tool in our analysis is the extensive use of weak limits and nonconservative products which allow us to describe accurately the operations achieved in practice when using Riemann-based numerical schemes. Some illustrative and relevant computational results are provided.

We consider the Cauchy problem for $n\times n$ strictly hyperbolic systems of nonresonant balance laws $$ \left\{\begin{array}{c} u_t+f(u)_x=g(x,u), \qquad x \in \reali, t>0\\ u(0,.)=u_o \in \L1 \cap \BV(\reali; \reali^n), \\ | \la_i(u)| \geq c > 0 \mbox{ for all } i\in \{1,\ldots,n\}, \\ |g(.,u)|+\norma{\nabla_u g(.,u)}\leq \om \in \L1\cap\L\infty(\reali), \\ \end{array}\right. $$ each characteristic field being genuinely nonlinear or linearly degenerate. Assuming that $\|\om\|_{\L1(\reali)}$ and $\|u_o\|_{\BV(\reali)}$ are small enough, we prove the existence and uniqueness of global entropy solutions of bounded total variation as limits of special wave-front tracking approximations for which the source term is localized by means of Dirac masses. Moreover, we give a characterization of the resulting semigroup trajectories in terms of integral estimates.

This paper focuses on a new method to compute fitness function (ff) values in genetic algorithms for bus network optimization. In the proposed methodology, a genetic algorithm is used to generate iteratively new populations (sets of bus networks). Each member of the population is evaluated by computing a number of performance indicators obtained by the analysis of the assignment of the O/D demand associated to the considered networks. Thus, ff values are computed by means of a multicriteria analysis executed on the performance indicators so found. The goal is to design a heuristic algorithm that allows to achieve the best bus network satisfying both the transport demand and supply.

Recently algebraic polynomials have been considered as wavelets and handled by wavelet techniques. In the unified approach for the construction of polynomial wavelets by Fischer and Prestin, the actual implementation of decomposition, reconstruction and/or compression schemes required at each level the inversion of generalized Grammian matrices, in general not orthogonal. In this context the present paper works out necessary and sufficient conditions for the polynomial wavelets to be orthogonal to each other. Furthermore it shows how these computable characterizations lead to attractive decomposition and reconstruction algorithms based on orthogonal matrices. Finally the special case of Bernstein--Szego weight functions is studied in detail.

This paper describes a new fast line-by-line radiative transfer scheme which computes top of the atmosphere spectral radiance and its Jacobians with respect to any set of geophysical parameters both for clear and cloudy sky, and presents the software which implements the procedure. The performance of the code has been evaluated with respect to accuracy and speediness through a comparison with a state-of-art line-by-line radiative transfer model. The new code is well suited for nadir viewing satellite and airplane infrared sensors with a sampling rate in the range 0.1-2 cm-1.

The mapping properties of the Cauchy singular integral operator with constant coefficients are studied in couples of spaces equipped with weighted uniform norms. Recently weighted Besov type spaces got more and more interest in approximation theory and, in particular, in the numerical analysis of polynomial approximation methods for Cauchy singular integral equations on an interval. In a scale of pairs of weighted Besov spaces the authors state the boundedness and the invertibility of the Cauchy singular integral operator. Such result was not expected for a long time and it will affect further investigations essentially. The technique of the paper is based on properties of the de la Vallee Poussin operator constructed with respect to some Jacobi polynomials.

We present computer simulations of the HIV infection based on a sophisticated cellular automata model of the immune response. The infection progresses following the well known three-phases dynamics observed in patients, that is, acute, silent and acquired immunodeficiency. Antigenic shift and selection of escape viral mutants with low transcription rate explain the long-term course of the asymptomatic phase, while the immunodeficiency status appears to be the consequence of a drastic reduction in T helper cell repertoire

Optimal management of flows arising in the bioventing techniques (BV) for soil remediation problems is considered. The aim is to determine optimal locations and flow rates of injection and extraction wells, in order to cover the contaminated region by a uniform air velocity flow field. An air flow optimization criterion is considered leading to a mathematical programming problem. Several numerical experiences have been employed: in all tests we show that wells are placed outside the contaminated zone and they surround it.

In this article we obtain rates of convergence to equilibrium of marked Hawkes processes in two situations. Firstly, the stationary process is the empty process, in which case we speak of the rate of extinction. Secondly, the stationary process is the unique stationary and non trivial marked Hawkes process, in which case we speak of the rate of installation. The first situation models small epidemics, whereas the results in the second case are useful in deriving stopping rules for simulation algorithms of Hawkes processes with random marks.

The dynamics of a system quenched into a state with lamellar order and subject to an uniform shear flow is solved in the large-N limit. The description is based on the Brazovskii free energy and the evolution follows a convection-diffusion equation. Lamellas order preferentially with the normal along the vorticity direction. Typical lengths grow as gammat(5/4) (with logarithmic corrections) in the flow direction and logarithmically in the shear direction. Dynamical scaling holds in the two-dimensional case while it is violated in D=3.

The numerical construction of a symmetric Toeplitz matrix having prescribed eigenvalues is faced by a two-step method using the continuation idea. The Cayley transform is exploited in order to integrate flows in the linear subspace of skew-symmetric and centro-symmetric matrices.

Si discutono le definizione di soluzioni ad ODE discontinue in relazione al problema della ricostruzione delle traiettorie ottime da un feedback. In particolare si danno condizioni su feedback stratificati alla Boltianskii-Brunovsky per avere l'uguaglianza fra soluzioni alla Krasowskii e treiettorie ottime.

In this paper we obtain the rate of convergence to equilibrium of a class of interacting marked point processes, introduced by Kerstan, in two different situations. Indeed, we prove the exponential and subexponential ergodicity of such a class of stochastic processes. Our results are an extension of the corresponding results in a paper by Bremaud, Nappo and Torrisi (JAP, 2002). The generality of the dynamics which we take into account allows the application to the so-called loss networks, and multivariate birth-and-death processes.