A Free Boundary Problem for Some Modified Predator-Prey Model in a Higher Dimensional Environment

Applications of Mathematics - We focus on the free boundary problems for a Leslie-Gower predator-prey model with radial symmetry in a higher dimensional environment that is initially well populated...     

金属衬底在石墨烯化学气相沉积生长中的作用

以过渡金属为催化衬底的化学气相沉积法(Chemical Vapor Deposition，CVD)已经可以制备与机械剥离样品相媲美的石墨烯，是实现石墨烯工业应用的关键技术之一。原子尺度理论研究能够帮助我们深刻理解石墨烯生长机理，为实验现象提供合理的解释，并有可能成为将来实验设计的理论指导。本文从理论计算的角度，总结了各种金属衬底在石墨烯CVD生长过程中的各种作用与相应的机理，包括在催化碳源裂解、降低石墨烯成核密度等，催化加快石墨烯快速生长，修复石墨烯生长过程中产生的缺陷，控制外延生长石墨烯的晶格取向，以及在降温过程中石墨烯褶皱与金属表面台阶束的形成过程等。在本文最后，我们对当前石墨烯生长领域中亟需解决的理论问题进行了深入探讨与展望。     

Examples of compactλ-hypersurfaces in Euclidean spaces

In this paper,we first construct compact embeddedλ-hypersurfaces with the topology of torus which are calledλ-torus in Euclidean spaces?n^+1.Then,we give many compact immersedλ-hypersurfaces in Euclidean spaces?n^+1.     

On the $$\bar\partial$$ -problem and dressing method for the complex vector modified KdV equation

Theoretical and Mathematical Physics - Starting from a $$5\times 5$$ local matrix $$\bar\partial$$ -problem, we successfully use the $$\bar\partial$$ -dressing method to derive a hierarchy of...     

On Minimal Asymptotic Bases

Mathematical Notes - Let $$\mathbb N$$ denote the set of all nonnegative integers, and let $$A\subseteq\mathbb N$$ . Let $$h,n\in\mathbb N$$ , $$h\ge 2$$ and $$r_h(A,n)=\#\{(a_1,\dots,a_h)\in...     

LWE from non-commutative group rings

Designs, Codes and Cryptography - The Learning-With-Errors (LWE) problem (and its variants including Ring-LWE and Module-LWE), whose security are based on hard ideal lattice problems, has proven to...     

基于摩擦磨损的KDP晶体固结磨料抛光垫优化

本文通过固结磨料球与KDP晶体对磨的单因素试验探究固结磨料球中反应物种类、磨粒浓度、反应物浓度、基体硬度对摩擦系数、磨痕截面积和磨痕处粗糙度的影响,试验结果表明:KHCO₃固结磨料球对磨后磨痕对称性好,磨痕处的粗糙度值低;磨痕截面积随磨粒和反应物浓度的增加而增大,随基体硬度的增大而降低;磨痕处粗糙度随磨粒和反应物浓度的增加先降低后上升,随基体硬度的增大先上升后降低;摩擦系数受磨粒和反应物浓度影响不明显,随基体硬度的增大而降低。选择KHCO₃作为反应物,Ⅰ基体,磨粒浓度为基体质量的100%,反应物浓度为15%制备固结磨料球与KDP晶体对磨后的磨痕轮廓对称度好且磨痕处粗糙度值低,以该组分制备固结磨料垫干式抛光KDP晶体,可实现晶体表面粗糙度Sa值为18.50 nm,材料去除率为130 nm/min的高效精密加工。     

o-Trityl phenoxy-imino vanadium (III) complexes: synthesis,characterization, and catalysis on ethylene (co)polymerization

Several phenoxy-imine ligands bearing o-trityl group in phenoxy moiety RN=CHArOH (Ar = C₆H₂(CPh₃)^tBu, R = 2,6-Me₂C₆H₃ ( L ₁ H ); 2,6-ⁱPr₂C₆H₃ ( L ₂ H ); 3,5-(CF₃)₂C₆H₃ ( L ₃ H ); 3,5-(OMe)₂C₆H₃ ( L ₄ H ); CHPh₂ ( L ₅ H ); CPh₃ ( L ₆ H )) were synthesized and characterized by¹H NMR and ¹³C NMR spectroscopy. The vanadium complexes based on these ligands LVCl₂(THF)₂ ( 1–6 ) were synthesized via conventional transmetalation reaction in moderate to high yields. Complexes 1–6 were fully characterized by FT-IR, elemental analyses and the molecular structures of 1 , 2 ·H₂O, (2 ·H₂O ) ₂ (μ-Cl) ₂ , 4 , and 5 were confirmed by X-ray crystallographic analysis in which the six-coordinated vanadium centers are in a typical octahedral geometry. Upon activation with Et₂AlCl in toluene, complexes 1–6 showed high activities in ethylene polymerization affording polymers with moderate molecular weight (5.9–11.8 × 10⁴ Da). Moreover, in hexane or CH₂Cl₂, 1–6 /Et₂AlCl exhibited enhanced activities. When activated with MAO or MMAO in toluene, these complexes showed relatively low activities but afforded polymers with ultra-high molecular weight (up to 3.30 × 10⁶ Da). 1–6 /Et₂AlCl also showed high activities in ethylene/1-hexene copolymerization at room temperature giving moderate molecular-weight polymers (6.5–11.4 × 10⁴ Da) with co-monomer incorporation being of 6.0 ~ 7.8%.     

Alkaloids from Juglans Mandshurica maxim induce distinctive cell death in hepatocellular carcinoma cells

The aim of this work was to further investigate the anticancer potential of Juglans mandshurica Maxim, including the separation of active constituents and their anti-proliferative effects with underlying mechanism of action. Five alkaloids (1–5) were isolated from the bark of J. mandshurica. Among them, 1 showed the highest cytotoxic activities against Hep3B and HepG2 cells with an IC50 values of 61.80 and 56.24 μM, respectively. Therefore, the cellular mechanism involved 1 was subsequently studied. Our results showed that 1 markedly caused apoptosis and autophagy, but without cell cycle arrest in HepG2 cells. Interestingly, only autophagic cell death was induced in 1-treated Hep3B cells. It is concluded that the isolated alkaloids exerted a certain anti-hepatoma potential, and our results may provide a basis for the further investigation of the alkaloids extracted from J. mandshurica.