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Let us consider two new perfect substitute durable products which are produced and sold in a market by two competing firms. [ABSTRACT FROM AUTHOR]

Several methods are currently available to simulate paths of the Brownian motion. In particular, paths of the BM can be simulated using the properties of the increments of the process like in the Euler scheme, or as the limit of a random walk or via L2 decomposition like the Kac-Siegert/Karnounen-Loeve series. In this paper we first propose a IFSM (Iterated Function Systems with Maps) operator whose fixed point is the trajectory of the BM. We then use this representation of the process to simulate its trajectories. The resulting simulated trajectories are self-affine, continuous and fractal by construction. This fact produces more realistic trajectories than other schemes in the sense that their geometry is closer to the one of the true BM's trajectories. The IFSM trajectory of the BM can then be used to generate more realistic solutions of stochastic differential equations. [ABSTRACT FROM AUTHOR]

This paper deals with the process of crystallization.We first present two major models that describe this phenomenon either as a birth-and-growth process or in terms of a Johnson-Mehl random tessellation. Then, we estimate the parameters of these models and we establish the asymptotic law of the estimators for the geometrical aspect of this phenomenon. Simulations of these laws are also provided in some cases. [ABSTRACT FROM AUTHOR]

It has been shown by a substantial body of literature that the hazard function plays an important role in the derivation of evolution equations of volume and n-facet densities of Johnson-Mehl tessellations generated by germ-grain models associated with spatially homogeneous birth-and-growth processes. [ABSTRACT FROM AUTHOR]

The paper investigates the problem of tracking a desired level of plasma glucose concentration. The model for the glucose-insulin system considered here, and recently published, belongs to the class of single-distributed delay models. The control law is obtained according to the feedback linearization theory. Both the cases of hyperglycemic and hypoglycemic patients have been considered. Simulations support theoretical results and show the physical reliability of the approach proposed. [ABSTRACT FROM AUTHOR]

Discrete kinetic equations describe homogeneous nucleation and many other processes such as the formation and growth of helium bubbles due to selfirradiation in plutonium. A key ingredient in the analysis of these equations is a wave front expansion which is the equivalent of boundary layer theory for discrete equations. This expansion solves approximately the nucleation problem, but it needs to be patched to an outer solution describing sizes not too close to the maximum size for the helium bubble problem. The composite theory yields an integrodifferential equation for the monomer concentration of single helium atoms which compares well with numerical solution of the full discrete model. [ABSTRACT FROM AUTHOR]

In this paper we investigate two different models for minimizing the makespan of batch processes by mixed-integer linear programming models. Special emphasis is laid on a small number of binary variables and on valid constraints. After a reformulation of the objective function, it is for the first time possible to find optimal solutions for medium-sized benchmark problems. Furthermore, a powerful iterative construction heuristic for larger-sized problems is developed. [ABSTRACT FROM AUTHOR]

A subsoil cleanup technology is called bioventing: bacteria are used to biodegrade pollutants and air is injected to enhance their activity. In this paper a general mathematical model describing the physical phenomenon is presented. The model is based on the theory of fluid dynamics in porous media. A multi-component and multi-phase fluid is considered and the system of partial differential equations is coupled with a population bacteria equation. [ABSTRACT FROM AUTHOR]

A new mathematical model for an algal allelopathic competition is analyzed. The competition takes place in a chemostat-like environment, in the presence of a further concentration input of the same allelochemical compound produced by one of the two species. Steady-states and their asymptotic stability properties are investigated in the two different cases: in the case of an instantaneous constant internal production of allelochemicals and in the case of an instantaneous production linearly increasing with the concentration of the producing species. Some numerical simulations, obtained by means of Mathematica and performed by using recent experimental data are presented, which confirm the allelopathic nature of the competition. [ABSTRACT FROM AUTHOR]

In recent literature the authors have introduced a Delta formalism, á la Dirac, for the description of random closed sets of lower dimension with respect to the environment space ℝd. Mean densities can be introduced for expected measures associated with such sets, with respect to the usual Lebesgue measure. In this paper we offer a review of the main results; in particular approximating sequences for the quoted mean densities are provided, that are of interest in the concrete estimation of mean densities of fibre processes, surface processes, etc. For time dependent random closed sets, as the ones describing the evolution of birth-and-growth processes (of interest for many models in material science and in biomedicine), the Delta formalism provides a natural framework for deriving evolution equations for mean densities at any (integer) Hausdorff dimension, in terms of the relevant kinetic parameters. In this context connections with the concepts of hazard functions, and spherical contact functions are presented. [ABSTRACT FROM AUTHOR]

Standard models for the dynamics of infection disease are based on the assumption of homogeneous mixing among individuals. However, individuals are generally aggregated in patches (pieces of woodland, farms, households, villages…) and transmission of infection is much easier within patches than from one patch to the other. [ABSTRACT FROM AUTHOR]

The internal stabilization for a spatially structured epidemic system describing the spatial spread of epidemic diseases mediated by environmental pollution is investigated. The control acts on the pollutant in a subdomain. We provide in the affirmative case a simple stabilizing feedback control. [ABSTRACT FROM AUTHOR]

Butterfly wings are covered with a large number of colored scale cells. It is well known that there exist two different kinds of patterns in butterfly wings - the spacing pattern of scale cells and color pattern. The spacing pattern is cellular pattern in which scale cells form nearly parallel rows along the anteroposterior axis of the wing. On the other hand, the color pattern is mainly pigmentation pattern which is constructed as a finely-tiled mosaic of colored scale cells. In this paper, I present mathematical models together with numerical simulations for both the cellular spacing pattern and color pattern with experimental evidences. The relationship between color patterns of fore- and hind-wing are also discussed within the framework of the model. [ABSTRACT FROM AUTHOR]

We study the flow of a viscous incompressible fluid through a long and narrow elastic tube whose walls are modeled by the Navier equations for a curved, linearly elastic membrane. [ABSTRACT FROM AUTHOR]

Cell migration plays a central role in a wide variety of biological phenomena. In the case of chemotaxis, cells (or an organism) move in response to a chemical gradient. Chemotaxis underlies many events during embryo development and in the adult body. An understanding of chemotaxis is not only gained through laboratory experiments but also through the analysis of model systems, which often are more amenable to manipulation. This work is concerned with the relaxation schemes for the numerical approximation of a 2D and 3D model for cell movement driven by chemotaxis. More precisely, we consider models arising in the description of blood vessels formation and network formation starting from a random cell distribution. [ABSTRACT FROM AUTHOR]

The dynamics of cancerous tissue growth involves the complex interaction of a number of phenomena interacting over a range of temporal and spatial scales. While several processes involved have been studied, the adaptation of the vasculature within a growing tumour has thus far received little attention. We consider a hybrid cellular automaton model which analyses the interaction between the tumour vascular network and tissue growth. We compute the temporal behaviour of the cancerous cell population under different hypotheses of structural adaptation in the vasculature. This may provide a possible method of determining experimentally which adaptation mechanisms are at work. [ABSTRACT FROM AUTHOR]

Blood flow in tumour vasculature carries oxygen and nutrients necessary for cell life and proliferation, and allows delivery of therapeutic agents within the tumour. To reach their target cells, these agents must extravasate and be transported by diffusion and by the convection associated to the movement of extracellular fluid. Convective transport may become important for therapeutic agents with large molecular weight or size, such as the monoclonal antibodies or the viruses used as vectors in gene therapy [11]. The high interstitial fluid pressure, exhibited by most solid tumors, is thought to be a barrier for fluid extravasation and efficient convective transport. [ABSTRACT FROM AUTHOR]

A team of researchers demonstrated at the National Institute of Standards and Technology Cold Neutron Research Facility for the first time that ultra cold neutrons can be confined in a magnetic trap filled with liquid helium, see [6]. This technical breakthrough allows a more accurate measurement of the neutron lifetime and helps to answer questions fundamental to physics and astrophysics. Since the demonstration, an experimental protocol for data collection and statistical analysis has been under development. [ABSTRACT FROM AUTHOR]

We introduce a method of iterated function systems (IFS) over the space of set-valued mappings (multifunctions). This is done by first considering a couple of useful metrics over the space of multifunctions F(X, Y). [ABSTRACT FROM AUTHOR]

Stopping times and related random sets play a fundamental role in the analysis of stochastic processes on ℝ+. [ABSTRACT FROM AUTHOR]

We define and study the multiparameter fractional Brownian motion. This process is a generalization of both the classical fractional Brownian motion and the multiparameter Brownian motion, when the condition of independence is relaxed. Relations with the Lévy fractional Brownian motion and with the fractional Brownian sheet are discussed. Different notions of stationarity of the increments for a multiparameter process are studied and applied to the fractional property. Using self-similarity we present a characterization for such processes. Finally, behavior of the multiparameter fractional Brownian motion along increasing paths is analysed. [ABSTRACT FROM AUTHOR]

In many biological settings it is possible to observe phenomena of pattern formation and clustering by cooperative individuals of a population. In biology and medicine there is a wide spectrum of examples which exhibit collective behavior, leading to self organization, with pattern formation. Aggregation patterns are usually explained in terms of forces, external and/or internal, acting upon individuals. Over the past couple of decades, a large amount of literature has been devoted to the mathematical modelling of self-organizing populations, based on the concepts of short-range/long-range "social interaction" at the individual level. The main interest has been in catching the main features of the interaction at the lower scale of single individuals that are responsible, at a larger scale, for a more complex behavior that leads to the formation of aggregating patterns. [ABSTRACT FROM AUTHOR]

We consider a partially observed dynamic germ-grain model Θ = {Θ(t) : t ≥ 0} whose grains drop on the plane ℝ2 at times of a renewal process. The first contact distribution at time t is the distribution function of the distance from a fixed point 0 to the nearest point of Θ(t), where the distance is measured using scalar dilations of a fixed test set B. Due to partial observation of the model, an estimation problem arises for the first contact distribution function. We propose a product integral type estimator. Its asymptotic properties are studied. [ABSTRACT FROM AUTHOR]

We consider an ℝd dimensional homogeneous diffusion process with a unique invariant density f. We construct a kernel type estimator for the invariant density and study its mean-square convergence. We find that this estimator reaches in a specific minimax sense a rate that is slower than parametric but faster than in classical d-dimensional estimation problems. Finally we examine the almost sure (pointwise and uniform) behavior of the estimator and we give examples. [ABSTRACT FROM AUTHOR]

We analyze diffusively coupled dynamical systems, which are constructed from two dynamical systems in continuous time by switching between the two dynamics. If one of the vector fields is zero we call it a quiescent phase. We present a detailed analysis of coupled systems and of systems with quiescent phase and we prove results on scaling limits, singular perturbations, attractors, gradient fields, stability of stationary points and amplitudes of periodic orbits. In particular we show that introducing a quiescent phase is always stabilizing. [ABSTRACT FROM AUTHOR]

"Math Everywhere": this title of the conference dedicated to the sixtieth birthday of Vincenzo Capasso just summarizes an evaluation of the role of mathematics in science and society. Mathematics has always been an important part of culture and is respected as a basic discipline for natural sciences, medicine, engineering, economics and social sciences. The rapid progress of computer systems as well as new concepts and methods in mathematical modelling and simulation have strengthened the position of Mathematics. They offer a large potential and new perspectives for solving complex problems and for tackling important technological, medical, environmental, social, economical, and political challenges. [ABSTRACT FROM AUTHOR]