Abel differential equations admitting a certain first integral

In this work algebro-geometric conditions to have a certain first integral for an Abel differential equation are given. These conditions establish a bridge with classical Galois theory because we transform the differential problem of finding a first integral for an Abel equation into an algebraic problem.     

改进的积分第一中值定理的应用

提供若干实例用以说明积分第一中值定理中的中值点ε∈[a，b]加强为ε∈（a，b）后所带来的好处．     

Lithium Salt of NH_2-substituted Graphene Nanoribbon with Twofold Donor-acceptor Framework: Large Nonlinear Optical Property

Based on graphene, a new class of second-order nonlinear optical(NLO) material, the lithium salt of NH2-substituted graphene nanoribbon with the twofold donor(D)/acceptor(A) mode, was reported. Eight stable 2Li-2NH2-GNR lithium salts, especially cis lithium salts, display considerably large β0 values. The combination of NH2-substituting and cis Li-doping makes β0 greatly increased from 0(GNR) to 1.2×105―2.9×105 a.u.(cis-2Li- 2NH2-GNRs). Our largest β0 value(2.9×105 a.u.) for cis-2Li-1,3-2NH2-AGNR is compara...     

On the Wang–Uhlenbeck Problem in Discrete Velocity Space

The arguably simplest model for dynamics in phase space is the one where the velocity can jump between only two discrete values, ±v with rate constant k. For this model, which is the continuous-space version of a persistent random walk, analytic expressions are found for the first passage time distributions to the origin. Since the evolution equation of this model can be regarded as the two-state finite-difference approximation in velocity space of the Kramers–Klein equation, this work constitutes a solution of the simplest version of the Wang–Uhlenbeck problem. Formal solution (in Laplace space) of generalizations where the velocity can assume an arbitrary number of discrete states that mimic the Maxwell distribution is also provided.     

微通道板增益模型的首次碰撞问题

研究了入射电子首次碰撞微通道板(MCP)所产生的二次电子的初能量对基于“能量正比假设”的MCP增益模型的影响,给出的增益公式与实验结果在很大的电压范围内符合较好。     

Calculus of variations on time scales: weak local piecewise Crd solutions with variable endpoints

A nonlinear calculus of variations problem on time scales with variable endpoints is considered. The space of functions employed is that of piecewise rd-continuously Δ-differentiable functions (C¹_prd). For this problem, the Euler-Lagrange equation, the transversality condition, and the accessory problem are derived as necessary conditions for weak local optimality. Assuming the coercivity of the second variation, a corresponding second order sufficiency criterion is established.     

A new structural model for the SiC(0 0 0 1)(3 × 3) surface derived from first principles studies

A new structural model with fluctuant Si-trimers and missing Si-adatom is proposed for Si-terminated 6H-SiC(0 0 0 1)(3 × 3) reconstruction. The atomic and electronic structures of the model are studied using first principles pseudopotential density-functional approach. The calculated surface electronic density of states coincides quantitatively with the experimental results of photoemission and electron energy loss spectroscopy. Based on the calculations, the Patterson map and scanning tunneling microscopic (STM) images simulated for the new model agree more satisfactorily with the experimental X-ray diffraction and STM observations than that for previously proposed models. The calculations of formation energies suggest that the new structure would be formed under the environment of dilute Si vapor around the surface in the preparation process.     

单层分散阈值和负载型催化剂的阈值效应

自发单层分散原理认为,许多负载型催化剂的活性组分可在载体表面自发分散。活性组分在载体表面的单层分散阈值可通过XRD相定量外推法等实验方法进行测定。通过单层分散阈值的测定可获取负载型催化剂表面结构、分散状态的有益信息,并为选择最佳的催化剂制备工艺条件提供依据。许多负载型催化剂活性组分的配比都可通过考察其单层分散阈值得以优化。负载型催化剂的许多物理化学性质突变值都与其单层分散阈值相联系,催化剂的阈值效应是明显的,阈值效应的提出为催化剂的研究提供了指导。     

Biomimetic synthesis of the dinaphthofuranquinone violet-quinone, utilizing oxidative dimerization with the ZrO2/O2 system

The first total and biomimetic synthesis of violet-quinone (1), which has a dinaphthofuranquinone (DNFQ) framework, is described. This synthesis features the oxidative dimerization of 1-naphthol 4 and the construction of the DNFQ framework by photochemical ring closure of 2,2′-binaphthoquinone 7 as a key intermediate. Compound 7 was prepared by the novel oxidative dimerization of 4 with a semiconductor (such as ZrO₂) in the presence of dioxygen, followed by oxidation of the resulting 2,2′-binaphthyl-1,1′-quinone 6 with HNO₃.     

烟草中Fe,Co一阶导数分光光度法同时测定的研究

本文研究了在ｐＨ４．０时，ｍｅｓｏ－四（４－磺酸基苯基）卟啉与铁、钴同时络合显色的反应条件以及一阶导数光谱行为。此体系一阶导数的灵敏度比零阶导数灵敏度高。Ｆｅ￣（３＋）～０．１８μｇ／ｍＬ、Ｃｏ￣（２＋）０～０．２４μｇ／ｍｌ，范围内符合比耳定律；检测限为：Ｆｅ￣（３＋）＝０．４８ｎｇ／ｍＬ，Ｃｏ￣（２＋）＝０．２ｎｇ／ｍＬ。回收率为：Ｆｅ９８．５％～１００．８％，Ｃｏ９９．２％～１０１．３％。此方法用于烟草中痕量Ｆｅ、Ｃｏ测定，与ＡＡＳ值相比较，结果令人满意。