Global optimization of univariate Lipschitz functions: II. New algorithms and computational comparison

We consider the following global optimization problems for a Lipschitz functionf implicitly defined on an interval [a, b]. Problem P: find a globally-optimal value off and a corresponding point; Problem Q: find a set of disjoint subintervals of [a, b] containing only points with a globally-optimal value and the union of which contains all globally optimal points. A two-phase algorithm is proposed for Problem P. In phase I, this algorithm obtains rapidly a solution which is often globally-optimal. Moreover, a sufficient condition onf for this to be the case is given. In phase II, the algorithm proves the-optimality of the solution obtained in phase I or finds a sequence of points of increasing value containing one with a globally-optimal value. The new algorithm is empirically compared (on twenty problems from the literature) with a best possible algorithm (for which the optimal value is assumed to be known), with a passive algorithm and with the algorithms of Evtushenko, Galperin, Shen and Zhu, Piyavskii, Timonov and Schoen. For small, the new algorithm requires only a few percent more function evaluations than the best possible one. An extended version of Piyavskii's algorithm is proposed for problem Q. A sufficient condition onf is given for the globally optimal points to be in one-to-one correspondance with the obtained intervals. This result is achieved for all twenty test problems.The research of the authors has been supported by AFOSR grants 0271 and 0066 to Rutgers University. Research of the second author has been also supported by NSERC grant GP0036426, FCAR grant 89EQ4144 and partially by AFOSR grant 0066. We thank Nicole Paradis for her help in drawing the figures.     

高空核电磁脉冲模拟波形的双指数函数拟合法

 许多标准和公开出版物中都用双指数函数描述高空核电磁脉冲典型波形。通过数值方法，研究了双指数函数一项重要的性质。根据该性质，详细讨论了高空核电磁脉冲模拟波形数值拟合中，双指数函数特征参数与脉冲峰值、前沿、后沿以及半宽等物理参数的关系，从而提出一种简单有效的脉冲参数计算方法。通过IEC标准中规定的高空核电磁脉冲参数的估计与一个实测高空核电磁脉冲模拟波形的数值拟合，验证了该方法的有效性和可靠性。该方法能够适应多种峰值、前沿和半宽的高宽核电磁脉冲模拟波形的数值拟合。     

温跃层边界提取的组合算法*

本文提出一种用于海洋温跃层边界提取的组合算法,该算法基于调整判定阈值后的垂直梯度法和一种改进函数模型几何形态后的拟阶梯函数逼近法。为验证该算法对于温跃层边界提取的适应性、客观性,利用中国Argo实时资料中心发布的全球海洋Argo网格资料集（BOA_Argo）,选取2018年夏季0°~30°N,135°E~165°E所在的太平洋区域的温度剖面数据进行处理,结果表明,该算法对低纬度海区温度剖面拟合质量较好,拟合均方根误差普遍低于1.3℃,而且提取到的温跃层上下边界在纬向更加平缓,然而对于中高纬度海区的温度剖面,组合算法的处理效果不佳,更适合直接通过垂直梯度法进行温跃层的提取。     

Approximations to Isentropic Planar Magneto-Hydrodynamics Equations by Relaxed Euler-Type Systems

In this paper, the authors consider an approximation to the isentropic planar Magneto-hydrodynamics (MHD for short) equations by a kind of relaxed Euler-type system. The approximation is based on the generalization of the Maxwell law for nonNewtonian fluids together with the Maxwell correction for the Amp`ere law, hence the approximate system becomes a first-order quasilinear symmetrizable hyperbolic systems with partial dissipation. They establish the global-in-time smooth solutions to the approximate Euler-type equations in a small neighbourhood of constant equilibrium states and obtain the global-in-time convergence towards the isentropic planar MHD equations. In addition, they also establish the global-in-time error estimates of the limit based on stream function techniques and energy estimates for error variables.     

Structural Characteristics,Antioxidant and Hypoglycemic Activities of Polysaccharide from Siraitia grosvenorii

The structural characterization, the in vitro antioxidant activity, and the hypoglycemic activity of a polysaccharide (SGP-1-1) isolated from Siraitia grosvenorii (SG) were studied in this paper. SGP-1-1, whose molecular weight is 19.037 kDa, consisted of Gal:Man:Glc in the molar ratio of 1:2.56:4.90. According to the results of methylation analysis, GC–MS, and NMR, HSQC was interpreted as a glucomannan with a backbone composed of 4)-β-D-Glcp-(1→4)-, α-D-Glcp-(1→4)-, and 4)-Manp-(1 residues. α-1,6 linked an α-D-Galp branch, and α-1,6 linked an α-D-Glcp branch. The study indirectly showed that SGP-1-1 has good in vitro hypoglycemic and antioxidant activities and that these activities may be related to the fact that the SGP-1-1’s monosaccharide composition (a higher proportion of Gal and Man) is the glycosidic-bond type (α- and β-glycosidic bonds). SGP-1-1 could be used as a potential antioxidant and hypoglycemic candidate for functional and nutritional food applications.     

一类利用回归关系的计量指标抽样方案

在产品质量判定的抽样检验问题中,当目标指标需用破坏性试验才能得其值时,更为常用的是用非破坏性试验可得量值的协变指标量来预报它。但在产品抽样验收问题上,未能形成理论较为严密的方法,这是由于预报误差这个关键问题的处理尚未解决得好,即给不出抽样方案的功效计算的正确或是近似性较好的公式。本文通过建立合理的数学模型,把对目标指标的质量要求化为对协变指标量的统计要求,从而利用两者的回归关系,结合两种复杂的抽样方案,给出功效函数的计算公式和计算方法,并进行了分析。     

Study Hankel Transforms and Properties of Bessel Function via Entangled State Representation Transformation in Quantum Mechanics

In Phys. Lett. A 313 (2003) 343 we have found that the self-reciprocal Hankel transformation (HT) is embodied in quantum mechanics by a transform between two entangled state representations of continuum variables. In this work we study Hankel transforms and properties of Bessel function via entangled state representations' transformation in quantum mechanics.     

Multiple Jacobi Elliptic Function Solutions to Integrable Higher Order Broer-Kaup Equation in (2+1)-Dimensional Spaces

In this paper, we improve the method for deriving Jacobi elliptic function solutions of nonlinear evolution equations given in Ref. [12] and apply it to the integrable higher-order Broer-Kaup system in (2 1)-dimensional spaces.Some new elliptic function solutions are obtained.     

Anticonvulsant Effect of Turmeric and Resveratrol in Lithium/Pilocarpine-Induced Status Epilepticus in Wistar Rats

Epilepsy is a chronic neurological disorder that lacks a cure. The use of plant-derived antioxidant molecules such as those contained in turmeric powder and resveratrol may produce short-term anticonvulsant effects. A total of 42 three-month-old male Wistar rats were divided into six groups (n = 7 in each group): Vehicle (purified water), turmeric (150 and 300 mg/kg, respectively), and resveratrol (30 and 60 mg/kg, respectively), administered per os (p.o.) every 24 h for 35 days. Carbamazepine (300 mg/kg/5 days) was used as a pharmacological control for anticonvulsant activity. At the end of the treatment, status epilepticus was induced using the lithium–pilocarpine model [3 mEq/kg, intraperitoneally (i.p.) and 30 mg/kg subcutaneously (s.c.), respectively]. Seizures were evaluated using the Racine scale. The 300 mg/kg of turmeric and 60 mg/kg of resveratrol groups had an increased latency to the first generalized seizure. The groups treated with 150 and 300 mg/kg of turmeric and 60 mg/kg of resveratrol also had an increased latency to status epilepticus and a decreased number of generalized seizures compared to the vehicle group. The chronic administration of turmeric and resveratrol exerts anticonvulsant effects without producing kidney or liver damage. This suggests that both of these natural products of plant origin could work as adjuvants in the treatment of epilepsy.     

Age Analysis of Status Updating System with Probabilistic Packet Preemption

The age of information (AoI) metric was proposed to measure the freshness of messages obtained at the terminal node of a status updating system. In this paper, the AoI of a discrete time status updating system with probabilistic packet preemption is investigated by analyzing the steady state of a three-dimensional discrete stochastic process. We assume that the queue used in the system is Ber/Geo/1/2*/η, which represents that the system size is 2 and the packet in the buffer can be preempted by a fresher packet with probability η. Instead of considering the system’s AoI separately, we use a three-dimensional state vector (n,m,l) to simultaneously track the real-time changes of the AoI, the age of a packet in the server, and the age of a packet waiting in the buffer. We give the explicit expression of the system’s average AoI and show that the average AoI of the system without packet preemption is obtained by letting η=0. When η is set to 1, the mean of the AoI of the system with a Ber/Geo/1/2* queue is obtained as well. Combining the results we have obtained and comparing them with corresponding average continuous AoIs, we propose a possible relationship between the average discrete AoI with the Ber/Geo/1/c queue and the average continuous AoI with the M/M/1/c queue. For each of two extreme cases where η=0 and η=1, we also determine the stationary distribution of AoI using the probability generation function (PGF) method. The relations between the average AoI and the packet preemption probability η, as well as the AoI’s distribution curves in two extreme cases, are illustrated by numerical simulations. Notice that the probabilistic packet preemption may occur, for example, in an energy harvest (EH) node of a wireless sensor network, where the packet in the buffer can be replaced only when the node collects enough energy. In particular, to exhibit the usefulness of our idea and methods and highlight the merits of considering discrete time systems, in this paper, we provide detailed discussions showing how the results about continuous AoI are derived by analyzing the corresponding discrete time system and how the discrete age analysis is generalized to the system with multiple sources. In terms of packet service process, we also propose an idea to analyze the AoI of a system when the service time distribution is arbitrary.