延迟微分方程单支θ方法的非线性稳定性

本文讨论了一类延迟量满足Lipschitz条件且最小Lipschitz常数小于 1的非线性变延迟微分方程初值问题 ,得到了带线性插值的单支θ方法的非线性稳定性结果     

Synthesis and Crystal Structures of the Molybdenum(II) Complexes with the N,N‐dimethylthiocarbamoyl Containing Ligand: Crystal Structures of [Mo(CO)2(η2‐S2COEt)(η2‐SCNMe2)(PPh3)] and [Mo(CO)2(η2‐S2CNC4H8)(η2‐SCNMe2)(PPh3)]

The reaction of the thiocarbamoyl‐molybdenum complex [Mo(CO)₂(η²‐SCNMe₂)(PPh₃)₂Cl] 1 , with EtOCS2K and C4H8NCS2NH4 in dichloromethane at room temperature yielded the seven coordinated ethyldithiocarbonate thiocarbamoyl‐molybdenum complex [Mo(CO)₂(η²‐S₂COEt)(η²‐SCNMe₂)(PPh₃)] 2 , and the dithiocarbamate thiocarbamoyl‐molybdenum complex [Mo(CO)₂(η²‐S₂CNC₄H₈)(η²‐SCNMe₂)(PPh₃)] 3 . The geometry around the metal atom of compounds 2 and 3 are capped octahedrons as revealed by X‐ray diffraction analyses. The thiocarbamoyl and ethyldithiocarbonate or pyrrolidinyldithiocarbamate ligands coordinate to the molybdenum metal center through the carbon and sulfur and two sulfur atoms, respectively. Structure parameters, NMR, IR and Mass spectra are in agreement with the crystal chemistry of the two compounds.     

A topological degree counting for some Liouville systems of mean field type

Let A = (a_ij)_{n × n} be an invertible matrix and A⁻¹ = (a^ij)_{n × n} be the inverse of A. In this paper, we consider the generalized Liouville system (0.1) where 0 < h_j ∈ C¹(M) and \input amssym $\rho_j \in \Bbb R^+$ , and prove that, under the assumptions of (H₁) and (H₂) (see Introduction), the Leray‐Schauder degree of (0.1) is equal to if ρ = (ρ₁, …, ρ_n) satisfies Equation (0.1) is a natural generalization of the classic Liouville equation and is the Euler‐Lagrangian equation of the nonlinear function Φ_ρ: The Liouville system (0.1) has arisen in many different research areas in mathematics and physics. Our counting formulas are the first result in degree theory for Liouville systems. © 2010 Wiley Periodicals, Inc.     

Uniqueness and symmetry results for solutions of a mean field equation on 𝕊2 via a new bubbling phenomenon

Motivated by the study of gauge field vortices, we consider a mean field equation on the standard sphere 𝕊² involving a Dirac distribution supported at a point P ∈ 𝕊². Consistently with the physical applications, we show that solutions “concentrate” precisely around the point P for some limiting value of a given parameter. We use this fact to obtain symmetry (about the axis ) and uniqueness property for the solution. The presence of the Dirac measure makes such a task particularly delicate to handle from the analytical point of view. In fact, the bubbling phenomenon about the singularity allows the existence of solution sequences with a double‐peak profile near P. The new and more delicate part of this paper is to exclude this possibility by using the method of moving planes together with the Alexandrov‐Bol inequality. © 2011 Wiley Periodicals, Inc.     

On generalized inverse transversals

Let S be a regular semigroup, S° an inverse subsemigroup of S.S° is called a generalized inverse transversal of S, if V（x）∩S°≠Ф. In this paper, some properties of this kind of semigroups are discussed. In particular, a construction theorem is obtained which contains some recent results in the literature as its special cases.     

相对论重离子碰撞实验中混合事件方法的研究

把RQMD(Relativistic Quantum Molecular Dynamics)产生器产生的数据输入作为原始事例取样,讨论了在比较复杂的背景情况下,一种新的混合事件方法,用以证实在相对论重离子碰撞实验中高能量激发共振态的存在.并以共振态重子Δ⁺⁺为例演示了这一方法的应用.     

Facile One‐Pot Synthesis of Oxazolidin‐2‐ones from Phenyl 2‐Hydroxyalkyl Selenides

A novel, convenient, efficient, three‐step, one‐pot synthesis of 2‐oxazolidinones from phenyl 2‐hydroxyalkyl selenides was developed. Using this methodology, 2‐oxazolidinones are obtained in good yields (76–85%) by reaction of phenyl 2‐hydroxyalkyl selenides with benzoyl isocyanate and subsequent oxidation/cyclization, followed by hydrolysis with hydrochloric acid solution.     

AFM-tip-induced crystallization of poly(ethylene oxide) melt droplets

The AFM-tip-induced crystallization of poly(ethylene oxide) (PEO) melt droplets was studied. The melt droplets with a height of 50–100 nm and a lateral size of 2–3 μm were obtained by melting the PEO ultra-thin films on a mica surface. For the PEO samples with average molecular weights (M _n) ranging from 1.0 × 10³ g/mol to 1.0 × 10⁴ g/mol, the lateral perturbation from the AFM tip in the hard-tapping or nanoscratch modes could not induce the growth of the flat-on lamellae. In contrast, under AFM nanoindentation mode, the tip-induced crystallization occurred when a sufficiently high vertical tip force was applied to the melt droplets of PEO with M _n ⩾ 1.0 × 10⁴ g/mol. Moreover, the experimental results indicated that the AFM-tip-induced crystallization of PEO in the nanoindentation process had molecular weight dependence. Translated from Acta Polymerica Sinica, 2006, (4): 553–556 (in Chinese)     

VALUE-AT-RISK的核估计理论

如何根据历史数据估计Value-at-Risk（VaR）;是风险分析与管理中一个重要的基本问题.木文基于非参数核估计方法,通过拟合实际数据过程的分布,构造了VaR的估计.在合适的相依数据条件下,证明了该估计量的渐近正态性,并给出了渐近方差的估计.由此表明:本文所构造的估计量不仅比参数模型具有更广泛的适应性,而且如同参数模型具有n~（-1/2）的收敛速度.本文假设的数据过程避免使用混合性,可很好地适用于金融管理中广泛应用的ARMA与GARCH模型族及非线性模型.     

半导体中相干控制光电流对光场的偏振依赖性

采用黄金定则方法和Kane六能带模型，分析了半导体中的量子干涉控制光生电流效应.计算了不同偏振光场下载流子在动量空间的初始布居分布，从微观上阐明了相干电流对光场的偏振依赖特性.在平行线偏振情况下，相干电流方向沿光场的偏振方向；而在正交线偏振情况下，电流方向与倍频光的偏振方向相同.还证明了只有当单光子跃迁和双光子跃迁相平衡时才能获得最大的电流注入效率. 关键词： 量子干涉 光电流 线偏振光