激光脉冲放大器增益通量耦合系统解

研究了一个激光脉冲放大器增益通量系统解的问题.首先讨论了较一般的系统, 然后引入一个同伦映射.再利用映射的性质, 引进一个人工参数, 将求解非线性问题转化为求解一系列线性问题.再逐次地求出对应的线性问题的解, 最后得到了原模型解的近似展开式.可以看出, 同伦映射方法是一个解析的方法.它是通过函数的解析运算并用初等函数来表达近似解,其不同于用离散数值运算的数值计算方法.因此通过同伦映射解, 还可以对它继续进行解析运算, 从而可以进行微分和积分等运算来得到与激光脉冲放大器增益通量相关的其他物理量的性态.     

双参数非线性非局部奇摄动抛物型初始-边值问题的广义解

研究了一类广义抛物型方程奇摄动问题.首先在一定的条件下, 提出了一类具有两参数的非线性非局部广义抛物型方程初始 边值问题.其次证明了相应问题解的存在性.然后, 通过Fredholm积分方程得到了初始 边值问题的外部解.再利用泛函分析理论和伸长变量及多重尺度法, 分别构造了初始 边值问题广义解的边界层、初始层项,从而得到了问题的形式渐近展开式.最后利用不动点理论证明了对应的非线性非局部广义抛物型方程的奇异摄动初始 边值问题的广义解的渐近展开式的一致有效性.     

Locating a minisum annulus: a new partial coverage distance model

The problem is to find the best location in the plane of a minisum annulus with fixed width using a partial coverage distance model. Using the concept of partial coverage distance, those demand points within the area of the annulus are served at no cost, while for ‘uncovered’ demand points there will be additional costs proportional to their distances to the annulus. The objective of the problem is to locate the annulus such that the sum of distances from the uncovered demand points to the annulus (covering area) is minimized. The distance is measured by the Euclidean norm. We discuss the case where the radius of the inner circle of the annulus is variable, and prove that at least two demand points must be on the boundary of any optimal annulus. An algorithm to solve the problem is derived based on this result.     

Rigidity Theorems for Complete Sasakian Manifolds with Constant Pseudo-Hermitian Scalar Curvature

The orthogonal decomposition of the Webster curvature provides us a way to characterize some canonical metrics on a pseudo-Hermitian manifold. We derive some subelliptic differential inequalities from the Weitzenböck formulas for the traceless pseudo-Hermitian Ricci tensor of Sasakian manifolds with constant pseudo-Hermitian scalar curvature and the Chern–Moser tensor of the Sasakian pseudo-Einstein manifolds, respectively. By means of either subelliptic estimates or maximum principle, some rigidity theorems are established to characterize Sasakian pseudo-Einstein manifolds among Sasakian manifolds with constant pseudo-Hermitian scalar curvature and Sasakian space forms among Sasakian pseudo-Einstein manifolds, respectively.     

Optimal mean–variance asset-liability management with stochastic interest rates and inflation risks

This paper considers an optimal asset-liability management problem with stochastic interest rates and inflation risks under the mean–variance framework. It is assumed that there are \(n+1\) assets available in the financial market, including a risk-free asset, a default-free zero-coupon bond, an inflation-indexed bond and \(n-2\) risky assets (stocks). Moreover, the liability of the investor is assumed to follow a geometric Brownian motion process. By using the stochastic dynamic programming principle and Hamilton–Jacobi–Bellman equation approach, we derive the efficient investment strategy and efficient frontier explicitly. Finally, we provide numerical examples to illustrate the effects of model parameters on the efficient investment strategy and efficient frontier.     

Temporal logic control for stochastic linear systems using abstraction refinement of probabilistic games

We consider the problem of computing the set of initial states of a dynamical system such that there exists a control strategy to ensure that the trajectories satisfy a temporal logic specification with probability 1 (almost-surely). We focus on discrete-time, stochastic linear dynamics and specifications given as formulas of the Generalized Reactivity(1) fragment of Linear Temporal Logic over linear predicates in the states of the system. We propose a solution based on iterative abstraction-refinement, and turn-based 2-player probabilistic games. While the theoretical guarantee of our algorithm after any finite number of iterations is only a partial solution, we show that if our algorithm terminates, then the result is the set of all satisfying initial states. Moreover, for any (partial) solution our algorithm synthesizes witness control strategies to ensure almost-sure satisfaction of the temporal logic specification. While the proposed algorithm guarantees progress and soundness in every iteration, it is computationally demanding. We offer an alternative, more efficient solution for the reachability properties that decomposes the problem into a series of smaller problems of the same type. All algorithms are demonstrated on an illustrative case study.     

Comparative study of degree-based molecular descriptors of cyclodextrins through M-polynomial and NM-polynomial

Cyclodextrins are natural oligosaccharides used to increase the solubility of drugs. It has numerous applications in drug discovery, food storage and other fields. Loftsson et al. explained about applications of Cyclodextrins(CDs) in administrating the drugs through various ways. Jansook et al. has given insights into the structure, physicochemical properties and pharmaceutical applications of CDs. In the present work, cyclodextrin and its derivatives such as α, β, γ CDs are studied for which various degree and neighborhood degree-based topological indices are computed through M-polynomial and NM-polynomial respectively and the comparison of the indices for all three types of cyclodextrins are presented which are of great importance in QSPR/QSAR studies.     

A potential pentaerythritol-based bio-lubricants from 10-undecylenic acid: Its physico-chemical assessment

In this study, renewable, non-toxic, sulphur free bio-lubricants are synthesized as alternative for fossil fuels. We utilized a bio-derived 10-undecylenic acid (UDA) and pentaerythritol (PE) as raw materials to synthesize bio-lubricants by two-step chemical processes like esterification and followed by epoxidation reactions. And achieved a UDA-PE epoxide yielded 73.4%. The formation of UDA-PE ester and UDA-PE epoxide was confirmed by spectral analysis such as NMR (¹H and ¹³C), FTIR and mass spectra, Physico-chemical and basic lubricant properties by standard American Society for Testing and Materials methods (ASTM). The results showed that the products of UDA-PE ester and UDA-PE epoxide had high viscosity index (262 and 200), good pour points (−29 °C to −15 °C), high flash points (296 °C and 301 °C) respectively and these met the ISO VG (International Organization for Standardization-Viscosity grade) 22 and 220 standard values. In general, both synthesized products are plausible to be employed as bio-lubricant in industrial application.     

Production of high-purity carbon dioxide and sodium bicarbonate by lime cellar gas cleaning and chemical recycling: Process simulation and techno-economic analysis

The cement industry is responsible for 8% of total global CO₂ emissions, which mainly originate from limestone calcination and fuel combustion. In view of the application potential of using CO₂ to produce chemicals, this paper developed a novel process based on the Aspen Plus process simulation for the co-production of 99.99% CO₂ by means of Methyldiethanolamine (MDEA) absorption/desorption and NaHCO₃ by carbonization of CO₂, NH₃ and Na₂SO₄. The effects of absorption temperature, NH₃ and Na₂SO₄ feeding amount, crystallizer temperature and pressure on CO₂ capture rate and utilization rate were explored. The results showed that the best CO₂ capture rate was achieved when the cellar gas inlet temperature of the absorber tower was 37 °C; Saturated Na₂SO₄ solution was favorable for CO₂ absorption, and the CO₂ utilization rate increased with the increase of Na₂SO₄ dosage; NaHCO₃ yield decreased with the increase of crystallizing temperature, and the best NaHCO₃ yield was achieved when the crystallizer temperature was 35.5 °C; Crystallizing pressure had little impact on the reaction. Economic analysis showed that the project will start to be profitable in 6.48 years with a Net Return Rate (NRR) value of 13.51%. It indicates that the project has economic benefits and provides a new way to reduce CO₂ emissions from lime cellar gas.