Solutions of Dirac Equation for Makarov Potential with Pseudospin Symmetry

The pseudospin symmetry in the Makarov potential is investigated systematically by solving the Dirac equation. The analytical solution for the Makarov potential with pseudospin symmetry is obtained by Nikiforov-Uvarov （N-U） method. The eigenfunctions and eigenenergies are presented with equal mixture of vector and scalar potentials in opposite signs, for which is exact.     

影子价格及其在资源配置中的应用研究

为了应用影子价格实现资源在全社会的最优配置,本文通过线性规划的对偶理论和非线性优化问题的Kuhn-Tucker条件揭示了影子价格的本质,在资源配置优化问题中线性规划模型中的影子价格就是其对偶问题的最优解,非线性规划模型中的影子价格就是与最优解相对应的拉格朗日乘数。根据松紧定理解释了资源影子价格与资源限量之间的关系,还对线性规划模型与非线性规划模型中影子价格的不同表现进行了分析。最后阐明了影子价格在资源配置中的应用。     

Spatiotemporal complexity of a diffusive planktonic system with prey-taxis and toxic effects

In this paper, we propose a three-species reaction-diffusion planktonic system with prey-taxis and toxic effects, in which the zooplankton can recognize the nontoxic and toxin-producing phytoplankton and can make proper response. We first establish the existence and stability of the unique positive constant equilibrium solution by utilizing the linear stability theory for partial differential equations. Then we obtain the existence and properties of nonconstant positive solutions by detailed steady state bifurcation analysis. In addition, we obtain that change of taxis rate will result in the appearance of time-periodic solutions. Finally, we conduct some numerical simulations and give the conclusions.     

基于双因子已实现GARCH模型的波动率预测研究

准确地预测金融市场的波动率对市场管理者和参与者而言都是至关重要的。本文在标准已实现GARCH模型基础上,将条件方差乘性分解为长期方差和短期方差两部分,分别构造包含杠杆函数的长期方差方程和短期方差方程,用以捕捉波动率的长记忆性和短期微观波动。运用上证综指和日经指数的日收盘价、已实现方差和已实现核波动此类高频数据进行实证分析,结果表明:与标准已实现GARCH模型相比,两指数的双因子已实现GARCH模型在样本内表现出更大的似然估计值;通过样本外误差函数分析和DM检验,双因子已实现GARCH模型也取得更好表现。     

一类时滞捕食系统的Hopf分支

研究了一类具有修正的Leslie-Gower和Holling-IV类功能性反应函数的时滞捕食系统,讨论了该系统的局部稳定性和Hopf分支存在性, 并利用中心流形定理和规范型理论确定了Hopf分支的方向和分支周期解的稳定性.仿真实例证明了理论分析结果的正确性.     

En 中n维单形二面角的角平分面的性质

利用距离几何的理论与方法研究了En中n维单形内二面角与外二面角的角平分面的性质,获得了n维单形内二面角与外二面角平分面的2个定理.     

以5-(3-吡啶基)-1H-吡唑-3-羧酸为配体的钴共晶配合物的合成、晶体结构及电化学性质

采用溶剂热法合成了一种新型的钴（Ⅱ）基配合物,即{[Co（Hppc）₂][Co₂（4,4''-bipy）（H₂O）₄]（SO₄）₂·2H₂O}_n （1）,其中H₂ppc=5-（3-吡啶基）-1H-吡唑-3-羧酸,4,4''-bipy=4, 4''-联吡啶。配体H₂ppc是由吡啶环、吡唑环和羧基共同组成,同时兼具了刚性和柔性。通过单晶X射线衍射对配合物1进行了结构测定。结果显示所合成的配合物1结晶在单斜晶系C2/c空间群,包括2个晶体学独立部分：二维层状[Co（Hppc）₂]和一维链状[Co₂（4,4''-bipy）（H₂O）₄]^2-,并形成具有{4⁴·6²}{4}₂拓扑网络结构的共晶化合物。此外,配合物1呈现出良好的电化学发光（ECL）性能以及良好的超级电容器性能。     

Singularly perturbed reaction diffusion equations with time delay

Abstract A class of initial boundary value problems of differential-difference equations for reaction diffusion with a small time delay is considered. Under suitable conditions and by using the stretched variable method, a formal asymptotic solution is constructed. Then, by use of the theory of differential inequalities, the uniform validity of the solution is proved.     

Crystal structure and dielectric properties of the mixed Aurivillius phase Bi7Ti4NbO21

The crystal structure of the ferroelectric mixed Aurivillius phase Bi₇Ti₄NbO₂₁ was determined for the first time by X-ray diffractometry using a single crystal obtained by a flux method in Bi₂O₃ excess. It can be described as a regular stacking of double and triple perovskite-type slabs interleaved by Bi₃O₂ layers along the a axis. Nb is located in the double perovskite-type layers only with a random Nb/Ti distribution whereas the octahedral sites within the triple perovskite-type layers are occupied by Ti only. The thermal evolution of the dielectric constant between room temperature and 900 °C show two phase transitions at 650 and 830 °C. Combined analyses of experimental data support that the highest transition temperature corresponds to the Curie temperature, whereas the lowest one could be assigned to a phase transition within the orthorhombic symmetry by a change of the space group.     

A meglumine catalyst–based synthesis,molecular docking,and antioxidant studies of dihydropyrano[3, 2-b]chromenedione derivatives

A simple method was employed for the synthesis of dihydropyrano[3, 2-b]chromenedione derivatives ( 4a-o) in high yields by condensation of 5, 5-dimethylcyclohexane-1, 3-dione( 1 ), different aromatic aldehydes ( 2a-o ), and 5-hydroxy-2-(hydroxymethyl)-4H-pyran-4-one( 3 ), using meglumine as a stable and reusable catalyst. Meglumine, an amino sugar, was employed as an environmentally benign catalyst, due to its splendid properties such as being inexpensive, recyclable, and biodegradable. The accomplished protocol employs low catalyst loading and easy work-up for the synthesis of 5-hydroxy-2-(hydroxymethyl)-4H-pyran-4-one derivatives. A great asset is that without any significant loss, the catalyst could be recovered and reused for extended synthetic steps. This offer huge advantage to overcome recyclability issues. Our synthesized compounds were analyzed by IR, ¹H, ¹³C NMR, mass spectra and evaluated for their antioxidant properties by 1, 1-diphenyl-2-picryl hydrazyl radical (DPPH), hydrogen peroxide(H₂O₂), and nitric oxide (NO) scavenging methods. The correlation in exhibition of antioxidant activity was effective at all doses. The binding interactions and molecular docking studies for entitled compounds were studied against 3MNG protein; 4k exhibited marked binding affinity with excellent docking score of −7.6 Kcal/mol and emerged as a lead compound.