On food chain in a chemostat with distinct removal rates.
On geodesics of phyllotaxis
Seeds of sunflowers are often modelled by leading to a roughly uniform repartition with seeds indexed by consecutive integers at angular distance for the golden ratio. We associate to such a map a geodesic path of the modular curve and use it for local descriptions of the image of the phyllotactic map .
On geometry of binary symmetric models of phylogenetic trees
We investigate projective varieties which are binary symmetric models of trivalent phylogenetic trees. We prove that they have Gorenstein terminal singularities and are Fano varieties of index 4 and dimension equal to the number of edges of the tree in question. Moreover any two such varieties which are of the same dimension are deformation equivalent, that is, they are in the same connected component of the Hilbert scheme of the projective space. As an application we provide a simple formula for...
On global exponential stability of discrete-time Hopfield neural networks with variable delays.
On linearizing systems of diffusion equations.
On mixing processes and the lost-games distribution
On monotone and Schwarz alternating methods for nonlinear elliptic PDEs
The Schwarz alternating method can be used to solve elliptic boundary value problems on domains which consist of two or more overlapping subdomains. The solution is approximated by an infinite sequence of functions which results from solving a sequence of elliptic boundary value problems in each of the subdomains. In this paper, proofs of convergence of some Schwarz alternating methods for nonlinear elliptic problems which are known to have solutions by the monotone method (also known as the method...
On Monotone and Schwarz Alternating Methods for Nonlinear Elliptic PDEs
The Schwarz alternating method can be used to solve elliptic boundary value problems on domains which consist of two or more overlapping subdomains. The solution is approximated by an infinite sequence of functions which results from solving a sequence of elliptic boundary value problems in each of the subdomains. In this paper, proofs of convergence of some Schwarz alternating methods for nonlinear elliptic problems which are known to have solutions by the monotone method (also known as the method...
On neural networks
On Nonlinear Dynamics of Predator-Prey Models with Discrete Delay
In this survey, we briefly review some of our recent studies on predator-prey models with discrete delay. We first study the distribution of zeros of a second degree transcendental polynomial. Then we apply the general results on the distribution of zeros of the second degree transcendental polynomial to various predator-prey models with discrete delay, including Kolmogorov-type predator-prey models, generalized Gause-type predator-prey models with harvesting, etc. Bogdanov-Takens bifurcations...
On one problem of Smale.
On oscillation of a food-limited population model with time delay.
On Oscillatory Instability in Convective Burning of Gas-Permeable Explosives
The experimentally known phenomenon of oscillatory instability in convective burning of porous explosives is discussed. A simple phenomenological model accounting for the ejection of unburned particles from the consolidated charge is formulated and analyzed. It is shown that the post-front hydraulic resistance induced by the ejected particles provides a mechanism for the oscillatory burning.
On oscillatory pattern of malaria dynamics in a population with temporary immunity.
On parameter estimation in an in vitro compartmental model for drug-induced enzyme production in pharmacotherapy
A pharmacodynamic model introduced earlier in the literature for in silico prediction of rifampicin-induced CYP3A4 enzyme production is described and some aspects of the involved curve-fitting based parameter estimation are discussed. Validation with our own laboratory data shows that the quality of the fit is particularly sensitive with respect to an unknown parameter representing the concentration of the nuclear receptor PXR (pregnane X receptor). A detailed analysis of the influence of that parameter...
On permutation symmetries of Hopfield model neural network.
On Popov-type stability criteria for neural networks.
On radially symmetric solutions of some chemotaxis system
This paper contains some results concerning self-similar radial solutions for some system of chemotaxis. This kind of solutions describe asymptotic profiles of arbitrary solutions with small mass. Our approach is based on a fixed point analysis for an appropriate integral operator acting on a suitably defined convex subset of some cone in the space of bounded and continuous functions.
On regularly varying and history-dependent convergence rates of solutions of a Volterra equation with infinite memory.
On Representations of Algebraic Polynomials by Superpositions of Plane Waves
* The author was supported by NSF Grant No. DMS 9706883.Let P be a bi-variate algebraic polynomial of degree n with the real senior part, and Y = {yj }1,n an n-element collection of pairwise noncolinear unit vectors on the real plane. It is proved that there exists a rigid rotation Y^φ of Y by an angle φ = φ(P, Y ) ∈ [0, π/n] such that P equals the sum of n plane wave polynomials, that propagate in the directions ∈ Y^φ .