局部分数阶拉普拉斯算子的狄利克雷问题弱解的细正则性

In this paper, we study the Holder regularity of weak solutions to the Dirichlet problem associated with the regional fractional Laplacian (-△)^αΩ on a bounded open set Ω ■R(N ≥ 2) with C^(1,1) boundary ■Ω. We prove that when f ∈ L^p(Ω), and g ∈ C(Ω), the following problem (-△)^αΩu = f in Ω, u = g on ■Ω, admits a unique weak solution u ∈ W^(α,2)(Ω) ∩ C(Ω),where p >N/2-2α and 1/2< α < 1. To solve this problem, we consider it into two special cases, i.e.,g ≡ 0 on ■Ω and f ≡ 0 in Ω. Finally, taking into account the preceding two cases, the general conclusion is drawn.     

Distribution dependent stochastic differential equations

Due to their intrinsic link with nonlinear Fokker-Planck equations and many other applications, distribution dependent stochastic differential equations (DDSDEs) have been intensively investigated. In this paper, we summarize some recent progresses in the study of DDSDEs, which include the correspondence of weak solutions and nonlinear Fokker-Planck equations, the well-posedness, regularity estimates, exponential ergodicity, long time large deviations, and comparison theorems.     

移动加热器法生长碲锌镉晶体的组分输运与界面形貌研究

移动加热器法(THM)生长碲锌镉晶体时,界面稳定性对晶体生长的质量有很大影响。本文基于多物理场有限元仿真软件Comsol建立了THM生长碲锌镉晶体的数值模拟模型,讨论了Te边界层与组分过冷区之间的关系,对不同生长阶段的物理场、Te边界层与组分过冷区进行仿真研究,最后讨论了微重力对物理场分布的影响,并对比了微重力与正常重力下的生长界面形貌。模拟结果表明,Te边界层与组分过冷区的分布趋势是一致的,在不同生长阶段,流场中次生涡旋的位置会发生移动,从而导致生长界面的形貌随着生长的进行发生变化,同时微重力条件下形成的生长界面形貌最有利于单晶生长。因此,在晶体生长的中前期,对次生涡旋位置的控制和对组分过冷的削弱,是THM生长高质量晶体的有效方案。     

Normal approximation and fourth moment theorems for monochromatic triangles

Given a graph sequence denote by T₃(G_n) the number of monochromatic triangles in a uniformly random coloring of the vertices of G_n with colors. In this paper we prove a central limit theorem (CLT) for T₃(G_n) with explicit error rates, using a quantitative version of the martingale CLT. We then relate this error term to the well-known fourth-moment phenomenon, which, interestingly, holds only when the number of colors satisfies . We also show that the convergence of the fourth moment is necessary to obtain a Gaussian limit for any , which, together with the above result, implies that the fourth-moment condition characterizes the limiting normal distribution of T₃(G_n), whenever . Finally, to illustrate the promise of our approach, we include an alternative proof of the CLT for the number of monochromatic edges, which provides quantitative rates for the results obtained in [7].     

Synthesis of 29H,31H-phthalocyanine and chloro (29H,31H-phthalocyaninato) aluminum derivatives showed anti-cancer and anti-bacterial actions

Continuous administration of most chemotherapeutic drugs can induce different types of side effects. There has been growing interest in exploring an alternative approach to synthesizing compounds that are most effective and have fewer side effects. We synthesized 29H,31H-Phthalocyanine, and Chloro (29H,31H- phthalocyaninato) aluminum at low temperatures using lithium in the present study with diisopropylamide as the nucleophile. The physical characteristics of 29H,31H-Phthalocyanine, and Chloro (29H,31H- phthalocyaninato) aluminum were confirmed by FT-IR method, XRD, SEM, and the impact of these compounds on human colorectal carcinoma (HCT-116) and human cervical cells (HeLa) was examined. Treatment with 29H,31H-Phthalocyanine significantly decreased cancer cell growth and proliferation, as determined by MTT and DAPI staining analysis. In contrast, Chloro (29H,31H- phthalocyaninato) aluminum treatment did not show any inhibitory action on colon or cervical cancer cells. We also calculated the inhibitory concentration (IC50) of 29H,31H-Phthalocyanine, which was 30 µg/ml (HCT-116) and 33 µg/ml (HeLa cells). The antibacterial effectiveness of 29H,31H-Phthalocyanine, and chloro (29H,31H- phthalocyaninato) aluminum was studied using Enterococcus faecalis (E. faecalis). The CFU (colony frequency unit) assay confirmed significant activity against the test bacterium after treatment with 29H,31H-Phthalocyanine. However, no activity was seen upon treatment with chloro (29H,31H- phthalocyaninato) aluminum against E. faecalis.     

One-pot,one-step,and selective terpolymerization of ethylene oxide,propylene oxide,and COS to copoly(thioether)s with tunable thermal properties

Facile construction of sulfur-rich polymers using readily available raw chemicals is an area aggressively pursued but challenging. Herein we use common feedstocks of ethylene oxide (EO), propylene oxide (PO), and carbonyl sulfide (COS) to synthesize copoly(thioether)s which are traditionally produced from unpleasant and difficult to store episulfides. In this protocol, the EO/COS coupling selectively generates a pure poly(ethylene sulfide) (PES) with melting temperature (T_m) values up to 172°C and high yields up to 98%. The EO/PO/COS terpolymerization leads to the incorporation of soft poly(propylene sulfide) (PPS) and hard PES segments together, affording a random PES-co-PPS copoly(thioether) with the complete consumption of EO and PO. Additionally, by simply varying the EO/PO feeding ratio, the obtained copoly(thioether)s possess tunable thermal properties, T_m values in the range of 76–144°C, and excellent solubility. These copolymerizations are conducted in one-pot/one-step at industrially favored reaction temperatures of 100–120°C using catalysts of common organic bases, suggesting a facile and practical manner. Especially, the copoly(thioether) exhibits high refractive indices up to 1.68 owing to its high sulfur content, suggesting a broad application prospect in optical materials.     

Four-Step Spin Crossover in a New Cyano-Bridged Iron-Silver Coordination Polymer

Spin-crossover complexes with multistep transitions attract much attention due to their potential applications as multi-switches and for data storage. A four-step spin crossover is observed in the new iron(II)-based cyanometallic guest-free framework compound Fe(2-ethoxypyrazine)₂{Ag(CN)₂}₂ during the transition from the low-spin to the high-spin state. A reverse process occurs in three steps. Crystallographic studies reveal an associated stepwise evolution of the crystal structures. Multiple transitions in the reported complex originate from distinct Fe^II sites which exist due to the packing of the ligand with a bulky substituent.