This paper is concerned with the existence, uniqueness and asymptotic stability of traveling wave solutions in a delayed competitive system spatial diffusion. When interspecific competition strong, corresponding functional differential has two stable unstable steady states. Firstly, we establish existence bistable by theory monotone semiflows. With help squeezing technique based on comparison p...

In this paper, we investigate infinite product representation of the solution of a Sturm- Liouville equation with an indefinite weight function which has two zeros and/or singularities in a finite interval. First, by using of the asymptotic estimates provided in [W. Eberhard, G. Freiling, K. Wilcken-Stoeber, Indefinite eigenvalue problems with several singular points and turning points, Math. N...

For a class of linear autonomous delay differential equations with parameter α we give upper bounds for the integral ∞ 0 |X (t, α)| dt of the fundamental solution X (·, α). The asymptotic estimations are sharp at a critical value α0 where x = 0 loses stability. We use these results to study the stability properties of perturbed equations.

In this paper, we show that there is no negative upper bound for the sectional curvature of Teichmüller space of Riemann surfaces with the Weil–Petersson metric. Mathematics Subject Classifications (2000). 32G15, 53C21, 30F60.

The classical theory of firmly attached time-mean turbulent boundary layers, exhibiting fully developed broadband turbulence, in the limit of large Reynolds numbers, Re, is extended in two ways, where the focus lies on their stability and receptivity. At first, the description of non-unique equilibrium flows having a so-called moderately large velocity deficit is generalised as weak spanwise va...

For analysis of time-to-event data with incomplete information beyond right-censoring, many generalizations of the inference of the distribution and regression model have been proposed. However, the development of martingale approaches in this area has not progressed greatly, while for right-censored data such an approach has spread widely to study the asymptotic properties of estimators and to...

We study the onset of sustained oscillations in a classical state-dependent delay (SDD) differential equation inspired by control theory. Owing to the large delays considered, the Hopf bifurcation is singular and the oscillations rapidly acquire a sawtooth profile past the instability threshold. Using asymptotic techniques, we explicitly capture the gradual change from nearly sinusoidal to sawt...

This paper concerns steady, high-Reynolds-number flow around a semi-infinite, rotating cylinder placed in an axial stream and uses boundary-layer type of equations which apply even when the boundary-layer thickness is comparable to the cylinder radius, as indeed it is at large enough downstream distances. At large rotation rates, it is found that a wall jet appears over a certain range of downs...

In this paper, we study the asymptotic behavior of the volume of spheres in metric measure spaces. We first introduce a general setting adapted to the study of asymptotic isoperimetry in a general class of metric measure spaces. Let A be a family of subsets of a metric measure space (X, d, μ), with finite, unbounded volume. For t > 0, we define: I ↓ A(t) = inf A∈A,μ(A)≥t μ(∂A). We say that A is...

Outcome-dependent, two-phase sampling designs can dramatically reduce the costs of observational studies by judicious selection of the most informative subjects for purposes of detailed covariate measurement. Here we derive asymptotic information bounds and the form of the efficient score and influence functions for the semiparametric regression models studied by Lawless, Kalbfleisch and Wild (...