Nonmonotone travelling waves in a single species reaction-diffusion equation with delay

We prove the existence of a continuous family of positive and generally nonmonotone travelling fronts for delayed reaction-diffusion equations , when g∈C²(R₊,R₊) has exactly two fixed points: x₁=0 and x₂=K>0. Recently, nonmonotonic waves were observed in numerical simulations by various authors. Here, for a wide range of parameters, we explain why such waves appear naturally as the delay h increases. For the case of g with negative Schwarzian, our conditions are rather optimal; we observe that the well known Mackey-Glass-type equations with diffusion fall within this subclass of (∗). As an example, we consider the diffusive Nicholson's blowflies equation.     

Growup of solutions for a semilinear heat equation with supercritical nonlinearity

We consider a Cauchy problem for a semilinear heat equation

(P)     

Carleson embeddings for Sobolev spaces via heat equation

Let u(t,x) be the solution of the heat equation (∂_t-Δ_x)u(t,x)=0 on subject to u(0,x)=f(x) on Rⁿ. The main goal of this paper is to characterize such a nonnegative measure μ on that f(x)?u(t²,x) induces a bounded embedding from the Sobolev space , p∈[1,n) into the Lebesgue space , q∈(0,∞).     

Optical properties and g factors of GaAs quantum rods

The Hamiltonian of the zinc-blende quantum rods in the framework of eight-band effective-mass approximation in the presence of external homogeneous magnetic field is given. The electronic structure, optical properties and electron g factors of GaAs quantum rods are investigated. We found that the electron g factors are very sensitively dependent on the dimensions of the quantum rods. As some of the three dimensions increase, the electron g factors decrease. The more the dimensions increase, the more the electron g factors decrease. The dimensions perpendicular to the direction of the magnetic field affect the electron g factors more than the other dimension.     

Magneto optics of single photons emitted from single InAs/GaAs self-assembled quantum dots in a planar microcavity

We fully characterize the fine spectral structure of neutral and negatively charged single microcavity quantum dot excitons, using polarization-sensitive magneto-photoluminescence spectroscopy. We show that the microcavity allows the simultaneous detection of both the bright and dark excitons using Faraday configuration. Thus, we were able to fully determine the fine structure and the g-factors of the neutral and negatively charged single exciton states within the same single quantum dot. Our measurements are in excellent agreement with novel, many carrier model calculations, which take into account Coulomb and exchange interactions among all the confined e–h pair states.     

Estimates of Europa’s ice shell thickness and strain rate from flanking cracks and bulge along Ridge R

Europa, the second Galilean satellite outward from Jupiter, has an outer layer of water of about 100 km thick and an outmost ice shell. The thickness of the ice shell is very important in understanding Europa’s habitability and thermal history, but estimates from different studies are very inconsistent, ranging from 0.2 to 30 km. Here we obtain an estimate of the ice shell thickness from locations of flanking crack and forebulge along Ridge R. Considering the water’s heating process to nearby ice shell in the crack, a flexure model is applied and it suggests the thickness of an ice shell to be 500–1500 m without a convective layer. Compared with previous studies using the same method but ignoring the water’s heating process, the rationality and accuracy have been improved dramatically in our results. We also get some constraints on the strain rate and the characteristic temperature T _c, which defines the base of the elastic layer.     

极大多线性Bochner—Riesz算子Herz型估计

设Bδ^A,是由Bochner—Riesz算子生成的极大多线性Bochner—Riesz算子,其中D^γA∈Aβ（｜γ｜=m）．获得这个算子及其变形在中心Campanato空间的连续性．     

Lipschitz spaces and Q_K type spaces

If f(z) =Σ∞ n=0 anzn and g(z) =Σ∞n=0bnzn for functions f, g are analytic in the unit disc, the Hadamard products of f and g is defined by f * g = ∞ n=0 a n b n z n . In this paper, the Lipschitz spaces Λ(s, α) and QK type spaces are studied in terms of the Hadamard products.     

Group invariant solution for a free jet on a hemi-spherical shell

When two circular jets impinge upon each other along the axis of a hemi-spherical shell then a free jet on a hemi-spherical shell is formed. The governing equations are Prandtl’s momentum boundary layer equation and the continuity equation. The conserved quantity is required for the free jet on a hemi-spherical shell. The conserved quantity for the free jet on a hemi-spherical shell is established with the help of a conserved vector. The group invariant solution for the third-order partial differential equation for the stream function is constructed.     

Sequences generating permutations

Linear recurring sequences generating permutations of the elements of a finite ring are introduced and examined. A complete answer to the discussed problems is given for the second-order sequences over Z_M. The possibilities for applications are also discussed.