Moderate deviation for the single point catalytic super-Brownian motion

We establish the moderate deviation for the density process of the single point catalytic super-Brownian motion. The main tools are the abstract Grtner-Ellis theorem, Dawson-Grtner theorem and the contraction principle. The rate function is expressed by the Fenchel-Legendre transform of log-exponential moment generation function.     

Persistence of centrality in random growing trees

We investigate properties of node centrality in random growing tree models. We focus on a measure of centrality that computes the maximum subtree size of the tree rooted at each node, with the most central node being the tree centroid. For random trees grown according to a preferential attachment model, a uniform attachment model, or a diffusion processes over a regular tree, we prove that a single node persists as the tree centroid after a finite number of steps, with probability 1. Furthermore, this persistence property generalizes to the top K ≥ 1 nodes with respect to the same centrality measure. We also establish necessary and sufficient conditions for the size of an initial seed graph required to ensure persistence of a particular node with probability , as a function of ϵ: In the case of preferential and uniform attachment models, we derive bounds for the size of an initial hub constructed around the special node. In the case of a diffusion process over a regular tree, we derive bounds for the radius of an initial ball centered around the special node. Our necessary and sufficient conditions match up to constant factors for preferential attachment and diffusion tree models.     

On the invariant translation approximation property for discrete groups

Recently J.Roe considered the question of whether for a discrete group the reduced group -algebra is the fixed point algebra of Ad acting on the uniform Roe algebra . is said to have the invariant translation approximation property in this case. We consider a slight generalization of this property which, for exact , is equivalent to the operator space approximation property of . We also give a new characterization of exactness and a short proof of the equivalence of exactness of and exactness of for discrete groups.

     

Copositive approximation of periodic functions

Let f be a real continuous 2π-periodic function changing its sign in the fixed distinct points y _i ∈ Y:= {y _i } _i∈ℤ such that for x ∈ [y _i , y _i−1], f(x) ≧ 0 if i is odd and f(x) ≦ 0 if i is even. Then for each n ≧ N(Y) we construct a trigonometric polynomial P _n of order ≦ n, changing its sign at the same points y _i ∈ Y as f, and

UNIFORM BOUNDEDNESS AND STABILITY OF SOLUTIONS TO A CUBIC PREDATOR-PREY SYSTEM WITH CROSS-DIFFUSION

Using the energy estimate and Gagliardo-Nirenberg-type inequalities,the existence and uniform boundedness of the global solutions to a strongly coupled reaction-diffusion system are proved. This system is a generalization of the two-species Lotka-Volterra predator-prey model with self and cross-diffusion. Suffcient condition for the global asymptotic stability of the positive equilibrium point of the model is given by constructing Lyapunov function.     

Donor-Acceptor Typed AIE Luminogens with Near-infrared Emission for Super-resolution Imaging

Aggregation-induced emission(AIE)luminogens(AIEgens)with high brightness in aggregates exhibit great potentials in biological imaging,but these AIEgens are seldom applied in super-resolution biological imaging,especially in the imaging by using the structural illumination microscope(SIM).Based on this consideration,we synthesized the donor-acceptor typed AIEgen of DTPA-BTN,which not only owns high brightness in the near-infrared(NIR)emission region from 600 nm to 1000 nm(photoluminescence quantum yield,PLQYs=11.35%),but also displays excellent photo-stability.In addition,AIE nanoparticles based on 4,7-ditriphenylamine-[1,2,5]-thiadiazolo[3,4-c]pyridine(DTPA-BTN)were also prepared with highly emissive features and excellent biocompatibility.Finally,the developed DTPA-BTN-based AIE nanoparticles were applied in the super-resolution cellular imaging via SIM,where much smaller full width at half-maximum values and high signal to noise ratios were obtained,indicating the superior imaging resolution.The results here imply that highly emissive AIEgens or AIE nanoparticles can be promising imaging agents for super-resolution imaging via SIM.     

不依赖于统计模型的手性毛细管电泳分离多指标同时优化

考虑到手性毛细管电泳分离机理的复杂性，提出了不依赖于统计模型的二进制编码遗传算法多目标优化策略。根据实验参数的多少及其重要性，采用均匀设计安排完成初步实验。并用Derringer功效函数作为多指标同时优化的评价指标，以取得较高的分离度和较快分离速度；通过对实验参数给予编码，转化为二进制字符串，根据得到的总功效函数值大小进行遗传算法操作，产生新的一组实验条件。重复上述过程直到得到最佳分离条件为止。此方法成功地应用于华法令对映体的毛细管电泳分离条件优化。     

Heterogeneous/homogeneous and inclined magnetic aspect of infinite shear rate viscosity model of Carreau fluid with nanoscale heat transport

The study of the inclined flow along with the heterogeneous/homogeneous reactions in the fluid has been widely used in many industrial and engineering applications, such as petrochemical, pharmaceutical, materials science, heat exchanger design, fluid flow through porous media, etc. The purpose of this study is to present an infinite shear rate viscosity model using the inclined Carreau fluid with nanoscale heat transport. The model considers the effect of inclined angle on the fluid’s viscosity and the transfer of heat at the nanoscale. The result shows that the viscosity of the fluid decreases by increasing the inclination angle and the coefficient of heat transfer also increases with the inclination. The model can be used to predict the viscosity and heat transfer fluid’s behavior in the inclined systems that is widely used in the industrial and engineering applications. The results provide a better understanding of the inclined flow behavior of fluids and the heat transfer at the nanoscale, which can be useful in heat exchanger design, fluid flow through porous media, etc. Greater Infinite shear rate viscosity parameter gives the higher magnitude of Carreau fluid velocity. Moreover, inclined magnetic field reduces the velocity due to Lorentz force. Two numerical schemes are used to solve the model, BVP4C and Shooting.     

Template Based Synthesis of Porous Graphdiyne Nanosheet for Reversible and Fast NO2 Detection by UV Irradiation

Two-dimensional graphdiyne (GDY) formed by sp and sp² hybridized carbon has been found to be an efficient toxic gas sensing material by density functional theory (DFT). However, little experimental research concerning its gas sensing capability has been reported owing to the complex preparation process and harsh experimental conditions. Herein, porous GDY nanosheets are successfully synthesized through a facile solvothermal synthesis technique by using CuO microspheres (MSs) as both template and source of catalyst. The porous GDY nanosheets exhibit a broadband optical absorption, rendering it suitable for the light-driven optoelectronic gas sensing applications. The GDY-based gas sensor was demonstrated to have excellent reversible to NO₂ behaviors at 25 °C for the first time. More importantly, higher response value and faster response-recovery time once exposed to NO₂ gas molecules are achieved by the illumination of UV light. In this way, our work paves the way for the exploration of GDY-based gas detection experimentally.