Volume 242, Nº 1 (2019)
- Ano: 2019
- Artigos: 10
- URL: https://journals.rcsi.science/1072-3374/issue/view/15027
Article
Nina Nikolaevna Uraltseva (Portrait)
Density–Dependent Feedback in Age–Structured Populations
Resumo
The population size has far-reaching effects on the fitness of a population that in turn influences the population extinction or persistence. Understanding the density- and age-dependent factors will facilitate more accurate predictions about the population dynamics and its asymptotic behavior. In this paper, we develop a rigorous mathematical analysis of the study of positive and negative effects of the increased population density in the classical nonlinear age-structured population model. One of the main results expresses the global stability of the system in terms of the newborn function only. We establish the existence of a threshold population size implying the population extinction, which is well known in the population dynamics as the Allee effect.
Two-Phase Problem for Quasilinear Parabolic Systems with Nondiagonal Principal Matrix. Regularity of Weak Solutions
Resumo
We study the regularity of weak solutions to the two-phase the problem for quasilinear parabolic systems with nondiagonal principal matrices. We prove the Hölder continuity of solutions on a set of full measure with an estimate for the admissible singular set. For solutions to the corresponding linear problem we establish the Hölder continuity in a neighborhood of the medium interface.
Local Limit Theorems for Densities in Orlicz Spaces
Resumo
Necessary and sufficient conditions for the validity of the central limit theorem for densities are considered with respect to the norms in Orlicz spaces. The obtained characterization unites several results due to Gnedenko and Kolmogorov (uniform local limit theorem), Prokhorov (convergence in total variation) and Barron (entropic central limit theorem).
Equations of Symmetric Boundary Layer for the Ladyzhenskaya Model of a Viscous Medium in the Crocco Variables
Resumo
We consider the system of boundary layer equations governing a viscous medium subject to the nonlinear rheological law in the sense of Ladyzhenskaya. Owing to the use of the Crocco transformation for reducing the system to a single quasilinear equation, it becomes possible to study both stationary and nonstationary boundary layers. We obtain asymptotic estimates for the solution.
Strengthening of Kolmogorov Type Inequalities for Derivatives and Differences
Resumo
We propose a new method for constructing extremal operators in the problem for obtaining the best approximation of the differentiation operator by bounded operators. Using the new form of extremal operators and their deviations, we strengthen the Kolmogorov inequality by expanding the right-hand side with respect to differences of a function and its higher order derivative with preservation of sharpness.
Algorithms for Wavelet Decomposition of of the Space of Hermite Type Splines
Resumo
For the space of (not necessarily polynomial) Hermite type splines we develop algorithms for constructing the spline-wavelet decomposition provided that an arbitrary coarsening of a nonuniform spline-grid is a priori given. The construction is based on approximate relations guaranteeing the asymptotically optimal (with respect to the N-diameter of standard compact sets) approximate properties of this decomposition. We study the structure of restriction and extension matrices and prove that each of these matrices is the one-sided inverse of the transposed other. We propose the decomposition and reconstruction algorithms consisting of a small number of arithmetical actions.
Homogenization of a Singular Perturbation Problem
Resumo
We discuss homogenization of the singular perturbation problem
with a constant boundary value on the ball. Here, Δp is the usual p-Laplacian operator. It is generally understood that the two parameters δ and ε are in competition and two different behaviors may be exhibited, depending on which parameter tends to zero faster. We consider one scenario where we assume that ε, the homogenization parameter, tends to zero faster than δ, the singular perturbation parameter. We show that there is a universal speed for which the limit solves a standard Bernoulli free boundary problem.