Abstract:
We consider positive solutions of the problem \begin{equation} \left\{\begin{array}{l}-\mbox{div}(x_{n}^{a}\nabla u)=0\qquad \mbox{in}\;\;\mathbb{R}_+^n,\\ \frac{\partial u}{\partial \nu^a}=u^{q} \qquad \mbox{on}\;\;\partial \mathbb{R}_+^n,\\ \end{array} \right. \end{equation} where $a\in (-1,0)\cup(0,1)$, $q>1$ and $\frac{\partial u}{\partial \nu^a}:=-\lim_{x_{n}\rightarrow 0^+}x_{n}^{a}\frac{\partial u}{\partial x_{n}}$. We obtain some qualitative properties of positive axially symmetric solutions in $n\geq3$ for the case $a\in (-1,0)$ under the condition $q\geq\frac{n-a}{n+a-2}$. In particular, we establish the asymptotic expansion of positive axially symmetric solutions.

A scheme for chaotic signal generation in a
semiconductor ring laser (SRL) with optical feedback is presented. Part of the
output is returned to the SRL, resulting in chaotic oscillation.

Abstract:
In order to improve the anticoagulant function of Auricularia auricula, Auricularia auricula polysaccharide(AAP)was converted into its derivatives by the microbial fermentation method and then polysaccharide derivatives with stronger anticoagulant activity were prepared. The optimal conditions for fermenting the polysaccharide from A. auricula were examined and the in vitro anticoagulant activities of transformed and untransformed polysaccharides were compared. Response surface tests and an orthogonal experiment indicated that the best conditions for microbial conversion of AAP3 were an AAP3 concentration of 4.0 mg/mL, a ratio of substrate(AAP3)to donor(p-hydroxybenzoic acid)of 40∶1, and a pH of 6.0. Bacillus subtilis Bs-07 was inoculated and then placed on a rotary shaker(120 r/min), followed by fermentation for 48 h at 35 ℃.The conversion rate was found to be greater than 40%. The result of in vitro anticoagulant activity showed that the transformed polysaccharide improved activated partial thromboplastin time, prothrombin time, and thrombin time values and greatly enhanced anticoagulant activity compared to the untransformed polysaccharide.

Abstract:
Let $\lambda^{*}>0$ denote the largest possible value of $\lambda$ such that $$ \{{array}{lllllll} \Delta^{2}u=\frac{\lambda}{(1-u)^{p}} & \{in}\ \ B, 01$ and $n$ is the exterior unit normal vector. We show that for $\lambda=\lambda^{*}$ this problem possesses a unique weak solution $u^{*}$, called the extremal solution. We prove that $u^{*}$ is singular when $n\geq 13$ for $p$ large enough and $1-C_{0}r^{\frac{4}{p+1}}\leq u^{*}(x)\leq 1-r^{\frac{4}{p+1}}$ on the unit ball, where $ C_{0}:=(\lambda^{*}/\bar{\lambda})^{\frac{1}{p+1}}$ and $\bar{\lambda}:=\frac{8(p-1)}{(p+1)^{2}}[n-\frac{2(p-1)}{p+1}][n-\frac{4p}{p+1}]$. Our results actually complete part of the open problem which \cite{D} lef

Abstract:
We use density functional plus $U$ methods to study the effects of a tensile or compressive substrate strain on the charge-ordered insulating phase of LuNiO$_3$. The numerical results are analyzed in terms of a Landau energy function, with octahedral rotational distortions of the perovskite structure included as a perturbation. Approximately 4% tensile or compressive strain leads to a first-order transition from an insulating structure with large amplitude breathing mode distortions of the NiO$_6$ octahedra to a metallic state in which breathing mode distortions are absent but Jahn-Teller distortions in which two Ni-O bonds become long and the other four become short are present. Compressive strain produces uniform Jahn-Teller order with the long axis aligned perpendicular to the substrate plane while tensile strain produces a staggered Jahn-Teller order in which the long bond lies in the plane and alternates between two nearly orthogonal in-plane directions forming a checkerboard pattern. In the absence of the breathing mode distortions and octahedral rotations, the tensile strain-induced transition to the staggered Jahn-Teller state would be of second order.

Abstract:
We study the nonequilibrium dynamics of photoexcited electrons in the narrow-gap Mott insulator VO$_2$. The initial stages of relaxation are treated using a quantum Boltzmann equation methodology, which reveals a rapid ($\sim$ femtosecond time scale) relaxation to a pseudothermal state characterized by a few parameters that vary slowly in time. The long-time limit is then studied by a Hartree-Fock methodology, which reveals the possibility of nonequilibrium excitation to a new metastable $M_1$ metal phase that is qualitatively consistent with a recent experiment. The general physical picture of photoexcitation driving a correlated electron system to a new state that is not accessible in equilibrium may be applicable in similar materials.

Abstract:
Cognitive Radio (CR) is an efficient way to solve the problem of the lack of the spectrum resource. In a Cognitive Radio Network the unlicensed users (secondary users) must incessantly monitor the spectrum for the presence of the licensed users (primary users) to avoid the interference to primary users. In this study, a spectrum sensing scheme based on adaptive optimal SVM (support vector machine) is proposed. A prototype system and the simulation experiments show that in low SNR the algorithm can also get a reasonable probability of detection and a low probability of false alarm.

Abstract:
As an important area of reserve land resources, the Yellow River Delta is faced with the problem of soil salinization. Grasping the characteristics of soil salinity as well as its spatial variation patterns is an important foundation of prevention, control and utilization of saline soil. This study selected Kenli County of the Yellow River Delta, obtained soil salinity data through field survey and lab experiment, and used statistical, GIS interpolation and buffer analysis methods to analyze the characteristics of soil salinity and its spatial variation patterns. Our results showed that the general soil salinity in the study area was mainly moderate and there was a significant positive correlation between different soil layers of 0 - 15 cm, 15 - 30 cm and 30 - 45 cm and soil salinity increased with the increase of soil depth. The areas with high soil salinity in each soil layer mainly distributed in the east near the Bo Sea in the county, while the areas with lower soil salinity mainly distributed in the southwest, centre and the two sides of the Yellow River in the northeast. Soil salinity showed a trend of decrease with the increase in distance to the Bo Sea, while stretching from the Yellow River, it showed increase tendency with the increase in distance to the Yellow River. The order from high soil salinity to low of different vegetation types was naked land → suaeda glauca → tamarix → vervain → reed → couch grass → paddy → cotton → winter wheat → maize; the order for different geomorphic types was depression → slightly sloping ground → slow hillock → high flood land. This study preliminary delineated the characteristics of soil salinity as well as its spatial variation patterns in the study area, and provided scientific basis for soil resource sustainable utilization in the Yellow River Delta.