悬链曲面上的点粒子动力学及扩展空间约束系统量子化

扩张型正则量子化方案的核心内容是位置、动量以及哈密顿量同时量子化. 通过分析悬链面上粒子的扩张型正则量子化方案, 并且与薛定谔理论进行比较, 发现内禀几何中二维悬链面给不出与薛定谔理论相一致的结果, 而考虑将二维悬链面嵌入在三维欧氏空间之后, 还需要将正则量子化方案进行扩张, 可以得到体系的几何势能和几何动量, 并与薛定谔理论相一致.     

Hamiltonian index is NP-complete

In this paper we show that the problem to decide whether the hamiltonian index of a given graph is less than or equal to a given constant is NP-complete (although this was conjectured to be polynomial). Consequently, the corresponding problem to determine the hamiltonian index of a given graph is NP-hard. Finally, we show that some known upper and lower bounds on the hamiltonian index can be computed in polynomial time.     

On the expected discounted penalty function for risk process with tax

In this paper we consider the generalized Cramér-Lundberg risk model including tax payments. We investigate how tax payments affect the behavior of a Cramér-Lundberg surplus process by defining an expected discounted penalty function at ruin. We derive an explicit expression for this function by solving a differential equation. Consequently, the explicit formulas for the discounted probability density function of the surplus immediately before ruin and the discounted joint probability density function of the surplus immediately before ruin and the deficit at ruin are obtained. We also give explicit expressions for the function for exponential claims.     

有关拓扑学与覆盖粗糙集的一些结论

引入了拓扑覆盖的概念,并结合最小描述元对有限论域上的拓扑覆盖加于研究,得出了拓扑覆盖的最简覆盖和基与最小描述元之间的关系.介绍了在基于有限论域U上的覆盖,构造U上的一个拓扑的方法.并且在最小描述元的基础上将划分下的粗糙隶属函数推广至一般覆盖下的粗糙隶属函数,而后介绍了其相关运用.     

Direct Electrochemistry and Electrocatalysis of Myoglobin with Ionic Liquid through Multilayers Film on Carbon Ionic Liquid Electrode

Multilayers of myoglobin (Mb) with ionic liquid 1‐ethyl‐3‐methylimidazolium tetrafluoroborate ([EMIM]BF₄) was assembled on carbon ionic liquid electrode (CILE) based on the electrostatic attraction between the negatively charged Mb and the positively charged imidazolium ion of IL. The CILE was fabricated with 1‐ethyl‐3‐methylimidazolium ethylsulfate ([EMIM]EtOSO₃) as the modifier, which exhibited imidazolium ion on the electrode surface. Then Mb molecules were assembled on the surface of CILE step‐by‐step to get a {IL/Mb}_n multilayer film modified electrode. UV‐Vis adsorption and FT‐IR spectra indicated that Mb remained its native structure in the IL matrix. In deaerated phosphate buffer solution (pH 7.0) a pair of well‐defined quasi‐reversible redox peaks appeared with the apparent formal potential (E^0′) as ‐0.212 V (vs. SCE), which was the characteristic of Mb heme Fe(III)/Fe(II) redox couples. The results indicated that the direct electron transfer of Mb was realized on the modified electrode. The {IL/Mb}_n/CILE displayed excellent electrocatalytic ability to the trichloroacetic acid reduction in the concentration range from 2.0 to 22.0 mmol/L with the detection limit of 0.6 mmol/L (3σ). The proposed method provides a new platform to fabricate the third generation biosensor based on the self‐assembly of redox protein with ILs.     

Facile electrosynthesis and thermoelectric performance of electroactive free-standing polythieno[3,2-b]thiophene films

Polythieno[3,2-b]thiophene (PTT) was electrosynthesized by facile anodic oxidation of thieno[3,2-b]thiophene (TT) in three systems: boron trifluoride diethyl etherate (BFEE), acetonitrile (ACN), and dichloromethane solutions. The onset oxidation potential of TT in BFEE was determined to be 0.62?V vs. Ag/AgCl, which was much lower than those in ACN and dichloromethane solutions. PTT films exhibited excellent electrochemical property, high thermal stability, good redox activity, and stability. Free-standing PTT films with good mechanical property can be obtained from BFEE solution, whose structure and morphology were characterized by FT-IR, UV?Cvisible spectra, and scanning electron microscopy. With an electrical conductivity of 1.5?S?cm^?1 and a Seebeck coefficient of 85???V?K^?1 at 306?K, the as-prepared free-standing PTT films showed a certain thermoelectric property. The dimensionless figure-of-merit of PTT films was estimated to be 2.3?×?10^?3 at 306?K, which was much higher than those of some organic thermoelectric materials reported previously. All these results indicated that PTT films may have potential applications in the thermoelectric field.     

Global existence and blow-up of solutions of nonlocal diffusion problems with free boundaries

In this paper, we investigate some nonlocal diffusion problems with free boundaries. We first give the existence and uniqueness of local solution by the ODE basic theory and the contraction mapping principle. Then we provide a complete classification for the global existence and finite time blow-up of solutions. Moreover, estimates of blow-up rate and blow-up time are also obtained for the blow-up solution.     

激光驻波中运动电子的谐波自发辐射

 采用单电子模型分析了电子在线极化激光驻波中的动力学及谐波自发辐射谱,数值计算了电子在驻波中的运动情况及辐射谱。结果表明:电子在波节和波腹处入射后,其辐射谱出现不同的特征;电子在波节处垂直磁场入射后,在洛伦兹力作用下快速振动并向前运动,其向后辐射的光谱发生红移,向前辐射的光谱发生蓝移,谱线出现展宽;当激光强度或者电子初始能量增大时,这些效应更加突出,以至于产生更高阶谐波,形成连续谱;而电子在波腹处以平行电场的方向入射后,仅在电场作用下作直线运动,其自发辐射谱线没有发生移动和展宽。     

1H NMR spectral studies on the polymerization mechanism of indole and its derivatives

The existence of NH bond according to the hydrogen nuclear magnetic resonance ((1)H NMR) spectra of polyindole and its derivatives, such as poly(5-bromoindole), poly(5-cyanoindole), poly(5-nitroindole), poly(5-methylindole), proved polymerization of high-quality polyindoles, which were electrosynthesized from middle strong Lewis acid boron trifluoride diethyl etherate (BFEE) and its mixed electrolytes with additional diethyl ether, occurred at 2,3-position. The elongation of the conjugation length made the chemical shift of all the protons of polyindoles to lower field in comparison with those of monomers.