Ruin Probability in a Semi-Markov Risk Model with Constant Interest Force and Heavy-Tailed Claims

In the present paper, we consider a kind of semi-Markov risk model (SMRM) with constant interest force and heavy-tailed claims, in which the claim rates and sizes are conditionally independent, both fluctuating according to the state of the risk business. First, we derive a matrix integro-differential equation satisfied by the survival probabilities. Second, we analyze the asymptotic behaviors of ruin probabilities in a two-state SMRM with special claim amounts. It is shown that the asymptotic behaviors of ruin probabilities depend only on the state 2 with heavy-tailed claim amounts, not on the state 1 with exponential claim sizes.     

理赔额与理赔间隔相依的风险模型的若干结论

本文研究了一类具有相依结构的风险模型.利用无穷小方法,得到了Gerber-Shiu罚金折现期望函数所满足的积分-微分方程,给出了破产时刻,破产赤字及破产前瞬时盈余的拉普拉斯变换的积分-微分方程的应用.最后,在具有常数红利边界下的同-风险模型中,分析了红利支付的期望现值.     

ESTIMATIONS OF THE CONSTANTS IN INVERSE INEQUALITIES FOR FINITE ELEMENT FUNCTIONS

In this paper, we estimate the constants in the inverse inequalities for the finite ele- ment functions. Furthermore, we obtain the least upper bounds of the constants in inverse inequalities for the low-order finite element functions. Such explicit estimates of the con- stants can be used as computable error bounds for the finite element method.     

应用数学方法 深化化学认知——以高中阶段速率平衡的常见结论的证明为例

选取了在高中课堂教学中出现的关于速率平衡的几个常见的结论,以阿伦尼乌斯公式为模型讨论了温度对反应速率的影响;推导并梳理了反应物转化率随投料量的变化关系;基于浓度商的单调性证明了平衡状态的"殊途同归"结论在数学上的合理性.在加深对常见结论认识的同时,通过对证明过程中应用的数学方法的总结,实现对几个相似化学问题证明方法的统...     

Optical and mechanical properties of a new second order nonlinear optical crystal urea l‐threonine

A new second order non‐linear optical organic crystal Urea L‐threonine has been grown by aqueous solution slow cooling technique. The grown crystal is non hygroscopic and transparent in the visible region. The solubility of the grown crystal was found. The crystal structure and perfection were determined using powder XRD and High resolution XRD. The molecular structure was confirmed by ¹H‐NMR spectrum. Thermal properties of the crystal have been studied using thermogravimetric (TG) and differential thermal analysis (DTA). The dielectric response of the crystal with varying frequencies at different temperatures was studied. UV‐Visible spectrum was recorded to study the optical transparency of the grown crystals. The second order non linear optical property was examined by Kurtz powder technique and found that the second order susceptibilities is 1.2 KDP at wavelength 1064 nm. The mechanical behaviour was studied by Vickers Microhardness test. The results are discussed in detail. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Molecular design for a write-by-light/erase-by-heat recording system using photochromic diarylethenes with thermal cycloreversion

We designed and synthesized photochromic diarylethenes for a write-by-light/erase-by-heat recording system. The introduction of polar substituents at both sides of the diarylethene maintained the photocyclization and photocycloreversion reactivities, but significantly affected the thermal cycloreversion reactivity. The introduction of electron-withdrawing substituents accelerated the thermal reaction and the introduction of electron-donating substituents suppressed the thermal reaction. The rate constants of the thermal reaction were well correlated with Brown-Okamoto's substituent constant σ⁺ that is a modified value of Hammett's substituent constant σ. The large rate constants are ascribed to the lower activation energy for the thermal reaction. These results provide new knowledge for the molecular design of diarylethenes for a write-by-light/erase-by-heat recording system.     

Mechanism and rate constants of the CH2 + CH2CO reactions in triplet and singlet states: A theoretical study

Ab initio and density functional CCSD(T)-F12/cc-pVQZ-f12//B2PLYPD3/6-311G** calculations have been performed to unravel the reaction mechanism of triplet and singlet methylene CH₂ with ketene CH₂CO. The computed potential energy diagrams and molecular properties have been then utilized in Rice–Ramsperger–Kassel–Marcus-Master Equation (RRKM-ME) calculations of the reaction rate constants and product branching ratios combined with the use of nonadiabatic transition state theory for spin-forbidden triplet-singlet isomerization. The results indicate that the most important channels of the reaction of ketene with triplet methylene lead to the formation of the HCCO + CH₃ and C₂H₄ + CO products, where the former channel is preferable at higher temperatures from 1000 K and above. In the C₂H₄ + CO product pair, the ethylene molecule can be formed either adiabatically in the triplet electronic state or via triplet-singlet intersystem crossing in the singlet electronic state occurring in the vicinity of the CH₂COCH₂ intermediate or along the pathway of CO elimination from the initial CH₂CH₂CO complex. The predominant products of the reaction of ketene with singlet methylene have been shown to be C₂H₄ + CO. The formation of these products mostly proceeds via a well-skipping mechanism but at high pressures may to some extent involve collisional stabilization of the CH₃CHCO and cyclic CH₂COCH₂ intermediates followed by their thermal unimolecular decomposition. The calculated rate constants at different pressures from 0.01 to 100 atm have been fitted by the modified Arrhenius expressions in the temperature range of 300–3000 K, which are proposed for kinetic modeling of ketene reactions in combustion. © 2018 Wiley Periodicals, Inc.     

Dielectric and elastic properties of fluorine-containing tricyclic isothiocyanate liquid crystal

The dielectric and elastic properties of liquid crystals (LCs) generally depend on the molecule structure, such as polar group and carbon chain length. For further investigation of the influence of molecular structure on the dielectric and elastic properties of fluorine-containing tricyclic isothiocyanate LC, the experimental temperature was controlled at 25°C by precision hot stage, and a precision LCR meter was used to measure the capacitance of six LC cells under the voltage from 0.1 to 20 V at 1 kHz. An LC cell capacitance model and a dual-cell model were adopted to obtain the dielectric anisotropy, and the capacitance–voltage curves of six LC materials were plotted. The threshold voltage of Fréedericksz transition was analysed, and a finite difference iterative method was used to attain specific values of three elastic constants. The influence of molecular structure on the dielectric and elastic constants was finally analysed. Experimental results showed that the introduction of meta-difluoro group would increase the dielectric anisotropy and reduce the threshold voltage of LC. As the length of the alkyl carbon chain increased, the dielectric anisotropy would have an odd–even alternation effect, which would lead to changes in the elastic constants of LC.     

简谈普适气体常量R——贯穿普化教育的重要常量

The universal gas constant R is an important constant in physics, and one of the vital fundamental constant throughout the teaching of general chemistry. This article aims to present a general review about the universal gas constant to the science and engineering majored students, including its history, determination, physical meaning and applications in chemical education. The choice of R values under various conditions is also provided to help students better understand and master basic concepts.     

一个对2,4,6-三硝基苯酚和Fe3+离子具有双重荧光传感行为的层状镉(Ⅱ)-有机配位聚合物

通过水热法合成了一个由三连接的2,3-喹啉二甲酸桥联扭曲的Cd²⁺八面体形成的二维层状配位聚合物[Cd（QDA）]_n（1）。该配合物发射出较强的蓝色荧光并具有很高的热稳定性和化学稳定性。更为重要的是,该配合物在乙醇分散体系中可快速识别痕量的2,4,6-三硝基苯酚和Fe³⁺离子,其对2,4,6-三硝基苯酚的淬灭常数（K_sv）和检测限（LOD）分别为6.61×10⁴ L·mol^-1和0.83 μmol·L^-1,对Fe³⁺离子的淬灭常数和检测限分别为1.74×10⁴ L·mol^-1和2.70 μmol·L^-1。