Smash Products of H-Simple Module Algebras

Let H be a finite-dimensional Hopf algebra and A a finite-dimensional H-simple left H-module algebra. We show that the smash product A#H is isomorphic to End _A′(V ? H*), where V ≠ 0 is a finite-dimensional left A-module and (A′, V′) the stabilizer of (A, V). As an application it is proved that A#H is isomorphic to a full matrix algebra over A′ when H is semisimple and dim V|dim A.     

AsH(X~3∑~-)及AsH_2(X~2B_1)自由基的分子结构与解析势能函数

运用Gaussian 03程序包中的单双迭代三重激发耦合簇理论和相关一致五重基优化了AsH_2的基态结构,并在优化结构的基础上计算了它的离解能和振动频率.结果表明:AsH_2基态的平衡构型具有C_(2v)对称性,键长R_(As-H)=0,1508 nm,键角∠HAsH=91.2231°,离解能D_e(Has-H)=2.8795 eV,振动频率ν_1(α_1)=1013.3361 cm~(-1),ν_2(α_1)=2225.1347 cm~(-1),ν_3(α_1)=2233.7565 cm~(-1).这些结果与实验值较为相符.对H_2的基态使用优选出的cc-pV6Z基组、对AsH的基态使用优选出的cc-pV5Z基组进行平衡几何与谐振频率的计算并进行单点能扫描,且将扫描结果拟合成了Murrell-Sorbie函数.与实验数据及其他理论结果的比较表明,本文关于AsH(X~3∑~-)自由基光谱常数(D_0,D_e,R_e,ω_e,B_e,α_e和ω_eX_e)的计算结果达到了很高的精度并最为完整.采用多体项展式理论导出了AsH_2(C_(2v),X~2B_1)自由基的解析势能函数,其等值势能图准确再现了它的离解能和平衡结构特征.首次报导了AsH_2(C_(2v),X~2B_1)自由基对称伸缩振动等值势能图中存在的两个对称鞍点,对应于反应AsH+H→ABH_2,势垒高度约0.1512×4.184 kJ/mol.

Abstract：

The CCSD(T) theory in combination with the cc-pV5Z basis set is used to determine the equilibrium geometry, dissociation energy and vibrational frequencies of AsH_2 (C_(2v), X~2B_1) radical. By comparison, excellent agreement can be found between the present results and the experiments. The values obtained at present are of 0.1508 ran for the equilibrium bond length R_(As-H), 91.2231° for the bond angle ∠ HASH, 2. 8795 eV for the dissociation energy D_e (HAs-H) and 1013.3361 cm~(-1), 2225.1347 cm~(-1) and 2233.7565 cm~(-1) for the vibrational frequencies ν_1(α_1), ν_2(α_1) and ν_3(α_1), respectively. The equilibrium geometry,harmonic frequency and potential energy curve of the AsH(X~3∑~-) radical are calculated at the CCSD(T)/cc-pV5Z level of theory. The ab initio results are fitted to the Murrell-Sorbie function with the least-square method. The spectroscopic parameters are in excellent agreement with the experiments. The analytic potential energy function of the AsH_2 (C_(2v), X~2 B_1) radical is derived by using the many-body expansion theory. This function correctly describes the configuration and dissociation energy of the AsH_2 (C_(2v), X~2B_1) radical. Two symmetrical saddle points have been found at (0.160 nm,0.296 nm) and (0.296 nm,0.160 nm) ,respectively. And the barrier height is equal to 0.1512×4.184 kJ/mol.     

Growth of high-quality ZnO thin films on (11\bar{2}0) a-plane sapphire substrates by plasma-assisted molecular beam epitaxy

High-quality ZnO thin films were grown on a-plane sapphire substrates by plasma-assisted molecular beam epitaxy. X-ray diffraction and transmission electron microscopy reveal that the ZnO films have high structural quality and an atomically sharp ZnO/Al₂O₃ interface. The full width at half maximum values of the 0002 and $30\bar{3}2$ ZnO ω-rocking curves are 467.8 and 813.5 arc sec for a 600 nm thick ZnO film. A screw dislocation density of 4.35×10⁸ cm^?2 and an edge dislocation density of 3.38×10⁹ cm^?2 are estimated by X-ray diffraction. The surface of the ZnO epilayers contains hexagonal pits, which can be observed in the Zn-polar ZnO. The films have a resistivity of 0.119 Ω?cm, an electron concentration of 6.85×10¹⁷ cm^?3, and a mobility of 76.5 cm²?V^?1?s^?1 at room temperature. Low temperature photoluminescence measurements show good optical properties comparable to ZnO single crystals.     

基于MCPT解法器库的专用辐射探测模拟软件研发与应用北大核心CSCD

甲状腺内^(131)I放射性活度与辐射探测结果的比例关系与甲状腺几何尺寸、探测距离等因素相关,是估算甲状腺内^(131)I含量与其可能造成的辐照损伤的关键参数。基于MCPT辐射输运数值模拟算法器库开发了用于开展NaI探测器伽马辐射测量模拟的应用程序,进而建立了多组具有不同容积的甲状腺型容器和不同探测距离的物理模型,最终通过蒙特卡罗数值计算得到了不同测量状态下探测器的探测效率。在甲状腺型容器与探测器距离较远时,数值模拟给出的结果与理论计算结果一致,证明此应用程序可用于定量分析NaI的探测效率。数值模拟结果表明,小距离模型的结果受甲状腺样容器的大小和距离的显著影响,模拟给出的探测效率表为开展深入细致的实验研究奠定了基础。     

An algorithm for outerplanar graphs with parameter

For n-vertex outerplanar graphs, it is proven that O(n^2.87) is an upper bound on the number of breakpoints of the function which gives the maximum weight of an independent set, where the vertex weights vary as linear functions of a parameter. An O(n^2.87) algorithm for finding the solution is proposed.     

Hardy–Littlewood–Sobolev and Stein–Weiss inequalities and integral systems on the Heisenberg group

In this paper, we study two types of weighted Hardy–Littlewood–Sobolev (HLS) inequalities, also known as Stein–Weiss inequalities, on the Heisenberg group. More precisely, we prove the |u|$\left|u\right|$ weighted HLS inequality in Theorem 1.1 and the |z|$\left|z\right|$ weighted HLS inequality in Theorem 1.5 (where we have denoted u=(z,t)$u=(z,t)$ as points on the Heisenberg group). Then we provide regularity estimates of positive solutions to integral systems which are Euler–Lagrange equations of the possible extremals to the Stein–Weiss inequalities. Asymptotic behavior is also established for integral systems associated to the |u|$\left|u\right|$ weighted HLS inequalities around the origin. By these a priori estimates, we describe asymptotically the possible optimizers for sharp versions of these inequalities.     

Convex analysis in financial mathematics

Using the language of convex analysis, we describe key results in several important areas of finance: portfolio theory, financial derivative trading and pricing and consumption based asset pricing theory. We hope to emphasize the importance of convex analysis in financial mathematics and also draw the attention of researchers in convex analysis to interesting issues in financial applications.