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Displaying 41 –
60 of
109
Dorsey, Di Bartolo and Dolgert (Di Bartolo et al., 1996; 1997) have constructed asymptotic matched solutions at order two for the half-space Ginzburg-Landau model, in the weak- limit. These authors deduced a formal expansion for the superheating field in powers of up to order four, extending the formula by De Gennes (De Gennes, 1966) and the two terms in Parr’s formula (Parr, 1976). In this paper, we construct asymptotic matched solutions at all orders leading to a complete expansion in powers...
Dorsey, Di Bartolo and Dolgert (Di Bartolo et al., 1996; 1997) have constructed
asymptotic matched solutions at order two for the half-space Ginzburg-Landau model,
in the weak-κ limit.
These authors deduced
a formal expansion for the superheating field in powers of up to
order four, extending the formula by De Gennes (De Gennes, 1966) and the two terms in
Parr's formula (Parr, 1976). In this paper, we construct asymptotic matched solutions
at all orders
leading to a complete expansion...
A two species non-autonomous competitive phytoplankton system with Beddington-DeAngelis functional response and the effect of toxic substances is proposed and studied in this paper. Sufficient conditions which guarantee the extinction of a species and global attractivity of the other one are obtained. The results obtained here generalize the main results of Li and Chen [Extinction in two dimensional nonautonomous Lotka-Volterra systems with the effect of toxic substances, Appl. Math. Comput. 182(2006)684-690]....
This paper is concerned with an SIR model with periodic incidence rate and saturated treatment function. Under proper conditions, we employ a novel argument to establish a criterion on the global exponential stability of positive periodic solutions for this model. The result obtained improves and supplements existing ones. We also use numerical simulations to illustrate our theoretical results.
When invading the tissue, malignant tumour cells (i.e. cancer cells) need to detach from
neighbouring cells, degrade the basement membrane, and migrate through the extracellular
matrix. These processes require loss of cell-cell adhesion and enhancement of cell-matrix
adhesion. In this paper we present a mathematical model of an intracellular pathway for
the interactions between a cancer cell and the extracellular matrix. Cancer cells use
similar...
This paper proposes a deterministic model for the spread of an epidemic. We extend the classical Kermack–McKendrick model, so that a more general contact rate is chosen and a vaccination added. The model is governed by a differential equation (DE) for the time dynamics of the susceptibles, infectives and removals subpopulation. We present some conditions on the existence and uniqueness of a solution to the nonlinear DE. The existence of limits and uniqueness of maximum of infected individuals are...
This paper is partially supported by the Bulgarian Science Fund under grant Nr. DO 02–
359/2008.We consider a nonlinear model of a continuously stirred bioreactor
and study the stability of the equilibrium points with respect to practically
important model parameters. We determine regions in the parameter
space where the steady states undergo transcritical and Hopf bifurcations.
In the latter case, the stability of the emerged limit cycles is also studied.
Numerical simulations in the computer algebra...
In this paper, by applying a simple mathematical model imitating the equation of state, behaviour of the phase transition curve near the critical point is investigated. The problem of finding the unique vapour-liquid equilibrium curve passing through the critical point is reduced to solving a nonlinear system of differential equations.
In this paper, we propose a mathematical model for flow and transport processes of diluted solutions in domains separated by a leaky semipermeable membrane. We formulate transmission conditions for the flow and the solute concentration across the membrane which take into account the property of the membrane to partly reject the solute, the accumulation of rejected solute at the membrane, and the influence of the solute concentration on the volume flow, known as osmotic effect. The model is solved...
This contribution is devoted to a new model of HIV multiplication motivated by the patent of one of the authors. We take into account the antigenic diversity through what we define “antigenicity”, whether of the virus or of the adapted lymphocytes. We model the interaction of the immune system and the viral strains by two processes. On the one hand, the presence of a given viral quasi-species generates antigenically adapted lymphocytes. On the other hand, the lymphocytes kill only viruses for which...
The cancer stem cell hypothesis has evolved to one of the most important paradigms in
biomedical research. During recent years evidence has been accumulating for the existence
of stem cell-like populations in different cancers, especially in leukemias. In the
current work we propose a mathematical model of cancer stem cell dynamics in leukemias. We
apply the model to compare cellular properties of leukemic stem cells to those of their
benign counterparts....
Recent discovery of cancer stem cells in tumorigenic tissues has raised many questions
about their nature, origin, function and their behavior in cell culture. Most of current
experiments reporting a dynamics of cancer stem cell populations in culture show the
eventual stability of the percentages of these cell populations in the whole population of
cancer cells, independently of the starting conditions. In this paper we propose a
mathematical model...
Currently displaying 41 –
60 of
109