An SIRS Epidemic Model Incorporating Media Coverage with Time Delay

An SIRS epidemic model incorporating media coverage with time delay is proposed. The positivity and boundedness are studied firstly. The locally asymptotical stability of the disease-free equilibrium and endemic equilibrium is studied in succession. And then, the conditions on which periodic orbits bifurcate are given. Furthermore, we show that the local Hopf bifurcation implies the global Hopf bifurcation after the second critical value of the delay. The obtained results show that the time delay in media coverage can not affect the stability of the disease-free equilibrium when the basic reproduction number R0<1. However, when R0>1, the stability of the endemic equilibrium will be affected by the time delay; there will be a family of periodic orbits bifurcating from the endemic equilibrium when the time delay increases through a critical value. Finally, some examples for numerical simulations are also included

Effect of an InP/In0.53_{0.53}Ga0.47_{0.47}As Interface on Spin-orbit Interaction in In0.52_{0.52}Al0.48_{0.48}As/In0.53_{0.53}Ga0.47_{0.47}As Heterostructures

We report the effect of the insertion of an InP/In$_{0.53}$Ga$_{47}$As Interface on Rashba spin-orbit interaction in In$_{0.52}$Al$_{0.48}$As/In$_{0.53}$Ga$_{0.47}$As quantum wells. A small spin split-off energy in InP produces a very intriguing band lineup in the valence bands in this system. With or without this InP layer above the In$_{0.53}$Ga$_{47}$As well, the overall values of the spin-orbit coupling constant $\alpha$ turned out to be enhanced or diminished for samples with the front- or back-doping position, respectively. These experimental results, using weak antilocalization analysis, are compared with the results of the $\mathbf{k\cdot p}$ theory. The actual conditions of the interfaces and materials should account for the quantitative difference in magnitude between the measurements and calculations.Comment: Submitted for publication; v2 to adjust Eq.6; v3 to correct the figure file name; v4, a revised version accepted for publication in Phys. Rev.

Conservation Laws and Exact Solutions for a Reaction-Diffusion Equation with a Variable Coefficient

In this paper a variable-coefficient reaction-diffusion equation is studied. We classify the equation into three kinds by different restraints imposed on the variable coefficient b(x) in the process of solving the determining equations of Lie groups. Then, for each kind, the conservation laws corresponding to the symmetries obtained are considered. Finally, some exact solutions are constructed

Probing onset of strong localization and electron-electron interactions with the presence of direct insulator-quantum Hall transition

We have performed low-temperature transport measurements on a disordered two-dimensional electron system (2DES). Features of the strong localization leading to the quantum Hall effect are observed after the 2DES undergoes a direct insulator-quantum Hall transition with increasing the perpendicular magnetic field. However, such a transition does not correspond to the onset of strong localization. The temperature dependences of the Hall resistivity and Hall conductivity reveal the importance of the electron-electron interaction effects to the observed transition in our study.Comment: 9 pages, 4 figure

Community structure of tenebrionid beetles in the Ulan Buh Desert (Inner Mongolia, China) (Coleoptera: Tenebrionidae)

Tenebrionids are a conspicuous faunal component of Central Asian deserts, but little is known about their community ecology. We investigated how tenebrionid community structure varied along a vegetational gradient in the Ulan Buh Desert (Gobi Desert). Sampling was done with pitfall traps in three sites with different vegetation cover. Species abundance distributions were fitted by the geometric series model, which expresses the "niche pre-emption" hypothesis. Community structure was investigated using different measures of diversity (number of species, Margaleff richness and Shannon-Weaner index), dominance (Simpson and Berger-Parker indexes) and evenness (Pielou's index). The observed tenebrionid species richness was similar to that known from other Gobi Desert sites. The three investigated sites have similar species-abundance patterns, but the most dominant species varied among them. This suggests that the local environment operates a filtering action on the same basic fauna, allowing different species to dominate under different conditions. Overall, the highest total abundance was observed in the true desert site, however this site had a community structure similar to that observed in the site with more vegetation. By contrast, the investigated site with intermediate conditions showed a higher diversity and evenness, and a lower dominance. Thus, intermediate conditions of plant cover favour tenebrionid diversity, whereas a dense cover or a very sparse cover increases the dominance