Oscillation and non‐oscillation results for solutions of perturbed half‐linear equations

The purpose of this paper is to describe the oscillatory properties of second‐order Euler‐type half‐linear differential equations with perturbations in both terms. All but one perturbations in each term are considered to be given by finite sums of periodic continuous functions, while coefficients in the last perturbations are considered to be general continuous functions. Since the periodic behavior of the coefficients enables us to solve the oscillation and non‐oscillation of the considered equations, including the so‐called critical case, we determine the oscillatory properties of the equations with the last general perturbations. As the main result, we prove that the studied equations are conditionally oscillatory in the considered very general setting. The novelty of our results is illustrated by many examples, and we give concrete new corollaries as well. Note that the obtained results are new even in the case of linear equations.     

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.     

Novel low-dielectric constant and soluble polyimides from diamines containing fluorene and pyridine unit

Polyimides (PI's) with low-dielectric constant and excellent organic solubility have broad application prospects in the electronic field. Herein, this study designed a series of novel, low dielectric, organic soluble PI films by creatively introducing fluorene and pyridine ring into diamine monomers. Because of the noncoplanar structure of fluorenyl and the polarization of pyridine ring, PI films achieved a low-dielectric constant (2.22–3.09 at 10 MHz) and excellent organic solubility. Even in some organic solvents with low-boiling points, these PI films still exhibited outstanding solubility. In addition, all the films possessed high-tensile strength (≈120 MPa) and excellent optical transparency (>70%, 450 nm). It was worth noting that the glass transition temperature of films was all above 280°C and 5% weight loss temperature (T_5%) was at 486–553°C. In general, the novel high-performance low-dielectric PI films are expected to be used in the field of microelectronics.     

光栅衍射实验中测量光栅常数的两种辅助方法

衍射光栅可以将不同波长的光在空间上分离开,在光谱分析领域中有广泛应用.利用光栅的衍射来测量光栅常数是大学物理实验中的一个典型实验,而本文介绍的正是光栅衍射实验中的两个有趣现象:一是旋转光栅时,谱线的偏转角存在一个最小值;二是光栅旋转到一定角度时,衍射光斑会逐渐消失在视野中.论文从理论上分析解释这两种现象,并设计出两种测量光栅常数的方法,在实验上进行验证.与传统的用最小偏转角测光栅常数的方法相比,本文重点分析了由判定最小偏转角位置偏差所带来的影响,并提出了对称旋转测量的方法来进一步减小误差.     

Fast Cysteine Bioconjugation Chemistry

Cysteine bioconjugation serves as a powerful tool in biological research and has been widely used for chemical modification of proteins, constructing antibody-drug conjugates, and enabling cell imaging studies. Cysteine conjugation reactions with fast kinetics and exquisite selectivity have been under heavy pursuit as they would allow clean protein modification with just stoichiometric amounts of reagents, which minimizes side reactions, simplifies purification and broadens functional group tolerance. In this concept, we summarize the recent advances in fast cysteine bioconjugation, and discuss the mechanism and chemical principles that underlie the high efficiencies of the newly developed cysteine reactive reagents.     

Can (H2O) n (n = 1–2) as effective catalysts in the CH2OO + H2S reaction under tropospheric conditions?

The addition reaction of CH₂OO?+?H₂S → HSCH₂OOH without and with catalyst X (X?=?H₂O and (H₂O)₂) has been investigated by CCSD(T)-F12a/VTZ-F12//B3LYP/aug-cc-pVTZ method and canonical variational transition state theory with small curvature tunneling correction. When H₂O was introduced in the CH₂OO?+?H₂S reaction, it not only acts as a catalyst for producing HSCH₂OOH, but also plays as a reactant to forming HOCH₂OOH. The formation channel of HSCH₂OOH is more important than the formation channel of HOCH₂OOH with its calculated rate constant larger by 11.0–43.2 times within the temperature 280–320?K. Then, (H₂O)₂ catalysed CH₂OO?+?H₂S → HSCH₂OOH reaction has been taken into account with its rate lower 1.9–4.2 times than the reaction of CH₂OO?+?H₂S → HSCH₂OOH with water. Also, CH₂OO?+?H₂S with H₂O cannot compete with the CH₂OO?+?H₂S reaction without water. This is different from CH₂OO?+?(H₂O)₂ reaction, which is about 4 orders of magnitude larger than the rate constant for CH₂OO?+?H₂O reaction. Such discrepancy is possible because C(CH₂OO)···O(H₂O) interaction has been enhanced more obviously by H₂O as compared to that of C(CH₂OO)···O(H₂S) interaction.     

On a multiple credit rating migration model with stochastic interest rate

In this paper, we explore a pricing model for corporate bond accompanied with multiple credit rating migration risk and stochastic interest rate. The bond price volatility strongly depends on potentially multiple credit rating migration and stochastic change of interest rate. A free boundary problem of partial differential equation is presented, which is the equivalent transformation of the pricing model. The existence, uniqueness, and regularity for the free boundary problem are established to guarantee the rationality of the pricing model. Due to the stochastic change of interest rate, the discontinuous coefficient in the free boundary problem depends explicitly on the time variable but is convergent as time tends to infinity. Accordingly, an auxiliary free boundary problem is constructed, whose coefficient is the convergent limit of the coefficient in the original free boundary problem. With some constraint on the risk discount rate satisfied, we prove that a unique traveling wave exists in the auxiliary free boundary problem. The inductive method is adopted to fit the multiplicity of credit rating. Then we show that the solution of the original free boundary problem converges to the traveling wave in the auxiliary free boundary problem. Returning to the pricing model with multiple credit rating migration and stochastic interest rate, we conclude that the bond price profile can be captured by a traveling wave pattern coupling with a guaranteed bond price with face value equal to one at the maturity.     

Optimal portfolio for a defined-contribution pension plan under a constant elasticity of variance model with exponential utility

Based on the Lie symmetry method, we derive the explicit optimal invest strategy for an investor who seeks to maximize the expected exponential (CARA) utility of the terminal wealth in a defined-contribution pension plan under a constant elasticity of variance model. We examine the point symmetries of the Hamilton-Jacobi-Bellman (HJB) equation associated with the portfolio optimization problem. The symmetries compatible with the terminal condition enable us to transform the (2+ 1)-dimensional HJB equation into a (1+ 1)-dimensional nonlinear equation which is linearized by its infinite-parameter Lie group of point transformations. Finally, the ansatz technique based on variables separation is applied to solve the linear equation and the optimal strategy is obtained. The algorithmic procedure of the Lie symmetry analysis method adopted here is quite general compared with conjectures used in the literature.     

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.