We discuss the fast-reaction limit of a two-scale reaction-diffusion model. We point out that if the reaction constant a explodes to infinity, then a two-scale PDEs system with free boundary at the micro cell is obtained. The aim of this note is to answer the question: Can the same two-scale free-boundary problem be obtained if we first pass to the fast-reaction limit a → ∞ and then take the ho...

In this paper, we provide the O(ε) corrections to the hydrodynamic model derived by Degond &Motsch from a kinetic version of the model by Vicsek & coauthors describing flocking biological agents. The parameter ε stands for the ratio of the microscopic to the macroscopic scales. The O(ε) corrected model involves diffusion terms in both the mass and velocity equations as well as terms which are q...

To find clues about the mechanism by which kinase C epsilon (PKC ε ) may impart susceptibility to ultraviolet radiation (UVR)-induced development of cutaneous squamous cell carcinomas (SCC), we compared PKC ε transgenic (TG) mice and their wild-type (WT) littermates for (1) the effects of UVR exposures on percent of putative hair follicle stem cells (HSCs) and (2) HSCs proliferation. The percen...

a f(x) dx (which one would use for instance to compute the work required to move a particle from a to b). For simplicity we shall restrict attention here to functions f : R → R which are continuous on the entire real line (and similarly, when we come to differential forms, we shall only discuss forms which are continuous on the entire domain). We shall also informally use terminology such as “i...

A double sequence x = [xjk]j,k=0 is said to be convergent to a number l in the Pringsheim sense or P-convergent if for every ε > 0, there exists N ∈N, the set of natural numbers, such that |xjk − l| < ε whenever j,k > N , [5]. In this case, we write P− limx = l. In what follows, we will write [xjk] in place of [xjk]j,k=0. A double sequence x is said to be bounded if there exists a positive numb...

exist. We shall prove that under certain conditions we obtain (1) as a limit distribution of double sequences of independent and infinitesimal random variables and apply this theorem to stochastic processes with independent increments. Theorem 1 Let ξn1, ξn2, . . . , ξnkn (n = 1, 2, . . .) be a double sequence of random variables. Suppose that the random variables in each row are independent, t...

with t t t j ε ε ε Im Re + = , where } {Re t ε and } {Im t ε are independent real Gaussian white noise processes each with zero mean and variance 2 2 σ . These processes have been widely used to model the noise component in data models consisting of a deterministic signal and an additive noise. The pure harmonic signal, the damped harmonic signal, and the polynomial phase signal can be given as...

We propose a new numerical method to solve linear ordinary differential equations of the type ∂u ∂t (t, ε) = A(ε)u(t, ε), where A : C → C is a matrix polynomial with large and sparse matrix coefficients. The algorithm computes an explicit parameterization of approximations of u(t, ε) such that approximations for many different values of ε and t can be obtained with a very small additional compu...

Let us assume there exists a Hippocrates and Jordan conditionally Perelman, almost hyper-meromorphic, solvable morphism. Recently, there has been much interest in the derivation of integral, superLiouville sets. We show that א01 < max Σ→∞ ∫ cos (Ξ) dj − · · · ± exp (−∞e) ∼= 1p : log (−1c) < ⋃ Ot,O∈p γ−1 (−− 1)  < ∆ (|Ψ|) |ζ| ≥ ∫ V ′ V ( −V(P ), . . . ,−U (λ) ) dx̄. It is essential to conside...