Modifications and extensions of the conjugate gradient-restoration algorithm for mathematical programming problems

In this paper, the problem of minimizing a functionf(x) subject to a constraint (x)=0 is considered, wheref is a scalar,x ann-vector, and aq-vector, withq <n. Several conjugate gradient-restoration algorithms are analyzed: these algorithms are composed of the alternate succession of conjugate gradient phases and restoration phases. In the conjugate gradient phase, one tries to improve the value of the function while avoiding excessive constraint violation. In the restoration phase, one tries to reduce the constraint error, while avoiding excessive change in the value of the function.Concerning the conjugate gradient phase, two classes of algorithms are considered: for algorithms of Class I, the multiplier is determined so that the error in the optimum condition is minimized for givenx; for algorithms of Class II, the multiplier is determined so that the constraint is satisfied to first order. Concerning the restoration phase, two topics are investigated: (a) restoration type, that is, complete restoration vs incomplete restoration and (b) restoration frequency, that is, frequent restoration vs infrequent restoration.Depending on the combination of type and frequency of restoration, four algorithms are generated within Class I and within Class II, respectively: Algorithm () is characterized by complete and frequent restoration; Algorithm () is characterized by incomplete and frequent restoration; Algorithm () is characterized by complete and infrequent restoration; and Algorithm () is characterized by incomplete and infrequent restoration.If the functionf(x) is quadratic and the constraint (x) is linear, all of the previous algorithms are identical, that is, they produce the same sequence of points and converge to the solution in the same number of iterations. This number of iterations is at mostN* =n –q if the starting pointx _s is such that (x _s)=0, and at mostN*=1+n –q if the starting pointx _s is such that (x _s) 0.In order to illustrate the theory, five numerical examples are developed. The first example refers to a quadratic function and a linear constraint. The remaining examples refer to a nonquadratic function and a nonlinear constraint. For the linear-quadratic example, all the algorithms behave identically, as predicted by the theory. For the nonlinear-nonquadratic examples, Algorithm (II-), which is characterized by incomplete and infrequent restoration, exhibits superior convergence characteristics.It is of interest to compare Algorithm (II-) with Algorithm (I-), which is the sequential conjugate gradient-restoration algorithm of Ref. 1 and is characterized by complete and frequent restoration. For the nonlinear-nonquadratic examples, Algorithm (II-) converges to the solution in a number of iterations which is about one-half to two-thirds that of Algorithm (I-).This research was supported by the Office of Scientific Research, Office of Aerospace Research, United States Air Force, Grant No. AF-AFOSR-828-67.     

2,2-亚戊基-1,3-二氧六环-4,6-二酮与原甲酸三乙酯和芳香胺的反应

剂,在有机合成中已有一定应用。开展Meldrum's 酸系列化合物的研究,旨在:1.寻找有结构特点的新试剂,2.合成一系列新化合物,3.研究新化合物的应用。本文通过控制反应温度(28～29℃)催化剂用量(比文献用量多近一倍),提高了2,2-亚戊基-1,3-二氧六环-4,6-二酮(PDDO,3)的制备得率(由15%     

甘氨酸衍生化β-环糊精键合硅胶液相色谱固定相的合成与评价

 β-环糊精键合硅胶经对甲苯磺酰化后,与甘氨酸反应得到甘氨酸衍生化β-环糊精键合硅胶固定相(GCDS)。考察了GCDS对位置异构体、丹磺酰化氨基酸异构体、苯丙酸类药物等的分离性能,研究了流动相中甲醇浓度、pH以及柱温对色谱保留行为的影响。     

Ion-selective electrodes based on p-tert-butyl-homooxacalixarene di(ethyl)amides

The diethyl amides of p-tert-butyldihomooxacalix[4]arene (1), p-tert-butylhexahomotrioxacalix[3]arene (2) and p-tert-butylcalix[4]arene (3) were used as active materials in ion-selective membrane electrodes to check the detection of different kinds of cations (Na⁺, K⁺, Cs⁺, Mg^2 + , Ca^2 + , Mn^2 + , Cu^2 + , Zn^2 + , Cd^2 + , Pb^2 +  and tetramethylammonium cation). The electrode characteristics and selectivity coefficients were determined and compared. Optimisation of the PVC membrane composition was achieved using three different plasticisers (bis(2-ethylhexyl) adipate, o-nitrophenyl octyl ether and bis(2-butylpentyl) adipate). Amide 3 shows selectivity for Na⁺, whereas compounds 1 and 2 exhibit the highest selectivity for Pb^2 +  among all the studied cations. The X-ray crystal structure of dihomooxacalix[4]arene tetra(diethyl)amide (1) was determined, revealing it to be in the cone conformation.     

有机杂化硫代碲酸盐化合物(H_2en)TeS_3和[Ni(en)_3]TeS_3的溶剂热合成与表征

用低温溶剂热法合成了2种分立结构的有机杂化硫代碲(Ⅳ)酸盐化合物(H2en)TeS3(1)和[Ni(en)3]TeS3(2)(en=乙二胺),通过X-射线单晶衍射,红外光谱,元素分析等手段对它们的结构进行了表征。晶体结构解析结果表明:2个化合物均属单斜晶系,空间群分别为P21和P21/c。化合物1和2具有孤立三角锥[TeS3]2-阴离子,化合物1的平衡阳离子为双质子化乙二胺[H2en]2+,阴离子基团[TeS3]2-和阳离子基团[H2en]2+之间通过N-H…S氢键连接。化合物2的阳离子基团为过渡金属Ni与乙二胺的配合物[Ni(en)3]2+。另外,对该2种晶体进行了紫外-可见漫反射光谱测试和热重分析。     

羧基膦酸改性氧化锆固定相的制备及其色谱性能

用十二胺-N乙酸-N亚甲基膦酸（DAPA）改性氧化锆制备了一种新的锆基质色谱固定相（DAPAZ），研究发现，DAPA在氧化锆表面有两种结合方式：红外光谱中1611cm^-1处的特征吸收表明羧基主要与胺基形成偶极离子，以羧酸根离子形式存在，大部分的DAPA分子通过膦酸基团与氧化锆结合；而与钼酸的显色反应则表明有少量DAPA以羧居与氧化锆结合，另外，对固定相的屏蔽效应、碱性条件（pH9．5）下的稳定性等色谱性能的研究也证实这两种吸附方式同时存在，但以膦酸基结合为主。     

INDUCED OSCILLATIONS GENERATED BY PROTECTIVE THRESHOLD POLICIES IN THE MANAGEMENT OF EXPLOITED POPULATIONS

Abstract Management and conservation of exploited populations have been a central issue in theoretical and empirical studies. In this work, it is shown that threshold policies can induce cyclic behavior in an otherwise exploited stable population as a consequence of the combination of harvest pressure and excessively protective threshold densities. Moreover, the dynamical outcomes generated by these extremely protective policies may vary according to the initial densities. These results may be of significant concern in conservation as well as in management of exploited population.     

Luminescence-Based Optical Fiber Chemical Sensors

Abstract

A scheme for the simultaneous determination of temperature and analyte concentration for application in luminescence-based chemical sensors is proposed. This scheme is applied to an optical oxygen sensor, which is based on the quenching of the fluorescence of a ruthenium complex. Temperature measurement is performed using the excitation radiation and an absorption long-pass filter. Preliminary results are presented that show the viability of an oxygen measurement that is independent of temperature and optical power level. The possibility of self-referenced temperature measurements with semiconductor nanoparticles is also investigated. In order to optimize the sensor design, several different optical fiber probe geometries for oxygen sensing are tested and compared, including different methods of coupling radiation into the optical fiber system. Polyvinyl alcohol (PVA) and polyacrylamide membranes are tested as supports for sensor immobilization in fiber-optical pH sensing devices in aqueous solution. Some results are presented that show the feasibility of using fiber-optical pH indicators for remote monitoring.     

Modelling the metabolic action of human and rat CYP1A2 and its relationship with the carcinogenicity of heterocyclic amines

Cytochrome P450 (CYP) is a family of enzymes responsible for organism detoxification. However, some of the members of the CYP1A subfamily also catalyse the activation of heterocyclic amines (HAs), present in cooked meat, to carcinogenic compounds which have been shown to increase the risk of breast, colorectal and lung cancer. In humans, CYP1A2 is the enzyme with the most significant action in HA metabolism but in rodents CYP1A1 is also important in this biotransformation. Understanding the metabolic action of these enzymes is essential to predict the factors that enable the formation of the carcinogenic products. We have built two models of CYP1A2, one for the human enzyme and one for the rat homologue. The templates chosen include the only X-ray structure published to date for a mammal CYP, a quimeric C2A5 from rabbit, as well as CYPs belonging to Bacillus megaterium (CYPBm-3), Pseudomonas putida (CYPcam), Pseudomonas sp. (CYPterp), and Saccharopolyspora erythraea (CYPeryf). Two HAs, MeIQ (2-amino-3,4-dimethylimidazo[4,5-?]quinoline) and MeIQx (2-amino-3,8-dimethylimidazo[4,5-?]quinoxaline), known substrates of human and rat CYPIA2, were docked in the active site of the models, providing information regarding the different catalytic rates associated with the metabolisms in both enzymes. This is important for analysing the behaviour of animal models concerning the testing of anticancer drugs.