Peak recognition technique by a computer program copying the human judgement

Summary It is still difficult to determine peaks and peak boundaries properly, though peak recognition is very important for the precision of quantitative data. A new computer program overcomes these problems using a method which is adapted from human judgements. The algorithm was developed for HPLC but can also be used in other fields of analytical chemistry.     

Interval estimation of the critical value in a general linear model

Summary This paper concerns interval estimation of the critical value θ which satisfies under the general linear model,Y _i =μ(x _i )+ε _i (i=1,2,···), where for and the functional forms off _j ^′ s are known. From an asymptotic expansion it is shown that, under reasonable conditions, the limiting distribution of is normal. Thus in the large-sample case a confidence interval for θ can be obtained. Such a result is useful when one is interested in carrying out a retrospective analysis rather than designing the experiment (as in the Kiefer-Wolfowitz procedure). In Section 3 a sequential procedure is considered for confidence intervals with fixed width 2d. It is shown that, for a given stopping variableN, is also asymptotically normal asd→0. Thus the coverage probability converges to 1−α (preassigned) asd→0. An example of application in estimating the phase parameter in circadian rhythms is given for the purpose of illustration. Research partially supported by the NSF Grant DMS-8502346.     

Existence of finitely optimal solutions for infinite-horizon optimal control problems

In this paper, we investigate the existence of finitely optimal solutions for the Lagrange problem of optimal control defined on [0, ) under weaker convexity and seminormality hypotheses than those of previous authors. The notion of finite optimality has been introduced into the literature as the weakest of a hierarchy of types of optimality that have been defined to permit the study of Lagrange problems, arising in mathematical economics, whose cost functions either diverge or are not bounded below. Our method of proof requires us to analyze the continuous dependence of finite-interval Lagrange problems with respect to a prescribed terminal condition. Once this is done, we show that a finitely optimal solution can be obtained as the limit of a sequence of solutions to a sequence of corresponding finite-horizon optimal control problems. Our results utilize the convexity and seminormality hypotheses which are now classical in the existence theory of optimal control.This research forms part of the author's doctoral dissertation written at the University of Delaware, Newark, Delaware under the supervision of Professor Thomas S. Angell.     

Partial molar volumes of cryptand-222 in organic solvents at 25°C

The partial molar volumes at infinite dilution of cryptand-222 (C-222) in water, methanol, acetonitrile, ethanol, dimethylsulfoxide, propanol, 2-propanol, chloroform, benzene, 1-butanol, cyclohexane, butyl-methylketone, hexane, tetrahydronaphthalene, heptane, octane, cyclohexylbenzene and decane were measured at concentrations ranging from 0.01 to 0.1 mol-L^–1 at 25°C. The partial molar volumes at infinite dilution showed remarkable dependency on the molar volume of the solvent. The partial molar volumes at infinite dilution for C-222 increase as the solvent molar volume increases.     

Dawson结构杂多化合物(C_5H_6N)_(4.5)H_(1.5)(P_2W_(18)O_(62))·1.5H_2O的水热合成及晶体结构

用水热合成方法制备了Dawson结构杂多化合物(C5H6N)4.5H1.5(P2W18O62).1.5H2O,通过红外光谱和X射线单晶衍射对其进行了表征.结果表明,该化合物属于单斜晶系,C2/m空间群.a=2.6970(3)nm,b=1.39730(16)nm,c=2.0777(2)nm,β=102.33(0)°,V=7.64927(364)nm3,Z=4,R=0.0412,wR2=0.1016.标题化合物阴离子通过质子化的吡啶分子在氢键作用下形成了一维无限链状结构.     

Thermody namic functions of 1,2-alkanediols in dilute aqueous solutions

The heat capacities of binary aqueous solutions of 1,2-ethanediol, 1,2-propanediol and 1,2-butanediol were measured at temperatures ranging from 283.15 to 338.15 K by differential scanning calorimetry. The partial molar heat capacities at the infinite dilution were then calculated for the respective alkanediols. For 1,2-ethanediol or 1,2-propanediol, the partial molar heat capacities at the infinite dilution of increased with increasing temperature. In contrast, the partial molar heat capacities of 1,2-butanediol at the infinite dilution decreased with increasing temperature. Heat capacity changes by dissolution of the alkanediols were also determined. Heat capacity changes caused by the dissolution of 1,2-ethanediol or 1,2-propanediol were increase with increasing temperature. On the other hand, heat capacity changes caused by the dissolution of 1,2-butanediol are decrease with increasing temperature. Thus our results indicated that the structural changes of water caused by the dissolution of 1,2-butanediol differed from that of the two other alkanediols. This revised version was published online in July 2006 with corrections to the Cover Date.     

Aqueous Solubilities, Infinite Dilution Activity Coefficients and Octanol–Water Partition Coefficients of Tricyclic Analogs of Acyclovir

Solubilities of tricyclic analogs of acyclovir have been determined in water at 25, 35, and 45°C and in octanol, water-saturated octanol, and octanol-saturated water at 25°C. Octanol-water partition coefficients were determined at 25°C. Melting temperatures and molar enthalpies of fusion were measured. Activity coefficients in water, octanol, and in aqueous octanol solutions were determined and are discussed. The effect of hydrophilic and hydrophobic substituents in the tricyclic analogs on their thermodynamic properties are discussed. The standard Gibbs energy of transfer between the saturated phases were found to correlate with known values of the melting point of the solvents and the solubilities of the solute. For a number of the compounds examined, correlations between the minimum inhibitory concentration against the herpes simplex virus type 1 (HSV-1) and type 2 (HSV-2), varicella-zoster virus (VZV), thymidine kinase-deficient (TK^–) strains of VZV and were established. Detailed conclusions have been derived concerning the relationships between the structure and the thermodynamic parameters of the compounds examined.     

考虑偏差值的中立型区间交叉效率研究

在不确定性环境下,当决策单元(DMU)的投入产出数据为区间数形式时,为解决决策单元之间既不是合作也不是竞争关系时的交叉评价问题,本文提出一种中立型区间交叉效率模型。从所有被评价者的角度出发解决评价权重的选取问题,以决策单元投入得分的平均偏差与产出得分的平均偏差之和最小化为目标,建立决策单元在最佳和最差两种生产状态下的中立型区间交叉效率模型。在本文提出的中立型模型视角下,DMU的投入得分平均偏差和产出得分平均偏差之和达到最小。算例结果表明该中立型区间交叉效率模型的有效性,解决了不确定性环境下的交叉评价问题,保证评价的客观公正,更加符合现实。     

Equivalent conditions involving common fixed points for maps on the unit interval

Let be a continuous self-map of the unit interval . Equivalent conditions are given to ensure that has a common fixed point with every continuous map that commutes with on a suitable subset of . This extends a recent result of Gerald Jungck.

     

A game locating a needle in a circular haystack

A complete solution of the following Hider-Seeker zero-sum game is obtained. The hider hides a needle of lengtha, 0<a2, in the closed unit dise, and the seeker tries to locate it by shooting in a straight line across the disc. The payoff to the seeker is 1 if he hits the needle and 0 otherwise.