Best Approximation and Perturbation Property in Hilbert Spaces

We study the perturbation property of best approximation to a set defined by an abstract nonlinear constraint system. We show that, at a normal point, the perturbation property of best approximation is equivalent to an equality expressed in terms of normal cones. This equality is related to the strong conical hull intersection property. Our results generalize many known results in the literature on perturbation property of best approximation established for a set defined by a finite system of linear/nonlinear inequalities. The connection to minimization problem is considered.The authors thank the referees for valuable suggestions.K.F. Ng - This author was partially supported by Grant A0324638 from the National Natural Science Foundation of China and Grants (2001) 01GY051-66 and SZD0406 from Sichuan Province. Y.R. He -This author was supported by a Direct Grant (CUHK) and an Earmarked Grant from the Research Grant Council of Hong Kong.     

Inclusive fragment production in84Kr +197Au atE/A=35 MeV

Inclusive cross sections of intermediate mass fragments from the reaction⁸⁴Kr+¹⁹⁷Au atE/A=35 MeV were measured over the range 8°≦Θ _lab≦70° with a low detection threshold. A moving-source parameterization was used to fit the double-differential cross sections. The integrated cross section for fragment production exceeds the total reaction cross section thus indicating a large probability for multi-fragment processes. The deduced large temperature parameters can be explained by assuming emission from a rotating source. From the comparison to reactions with¹²C and⁴⁰Ar projectiles at E/A=30 MeV a systematics of inclusive fragment production as a function of the projectile mass is obtained.     

Flexible capacity strategy with multiple market periods under demand uncertainty and investment constraint

We establish a flexible capacity strategy model with multiple market periods under demand uncertainty and investment constraints. In the model, a firm makes its capacity decision under a financial budget constraint at the beginning of the planning horizon which embraces n market periods. In each market period, the firm goes through three decision-making stages: the safety production stage, the additional production stage and the optimal sales stage. We formulate the problem and obtain the optimal capacity, the optimal safety production, the optimal additional production and the optimal sales of each market period under different situations. We find that there are two thresholds for the unit capacity cost. When the capacity cost is very low, the optimal capacity is determined by its financial budget; when the capacity cost is very high, the firm keeps its optimal capacity at its safety production level; and when the cost is in between of the two thresholds, the optimal capacity is determined by the capacity cost, the number of market periods and the unit cost of additional production. Further, we explore the endogenous safety production level. We verify the conditions under which the firm has different optimal safety production levels. Finally, we prove that the firm can benefit from the investment only when the designed planning horizon is longer than a threshold. Moreover, we also derive the formulae for the above three thresholds.     

Distribution-free vessel deployment for liner shipping

One important problem faced by the liner shipping industry is the fleet deployment problem. In this problem, the number and type of vessels to be assigned to the various shipping routes need to be determined, in such a way that profit is maximized, while at the same time ensuring that (most of the time) sufficient vessel capacity exists to meet shipping demand. Thus far, the standard assumption has been that complete probability distributions can be readily specified to model the uncertainty in shipping demand. In this paper, it is argued that such distributions are hard, if not impossible, to obtain in practice. To relax this oftentimes restrictive assumption, a new distribution-free optimization model is proposed that only requires the specification of the mean, standard deviation and an upper bound on the shipping demand. The proposed model possesses a number of attractive properties: (1) It can be seen as a generalization of an existing variation of the liner fleet deployment model. (2) It remains a mixed integer linear program and (3) The model has a very intuitive interpretation. A numerical case study is provided to illustrate the model.     

Spacer effect on triazole-linked sugar-based surfactants

A series of alkyl triazole glycoside surfactants, ATGs, differing in the length of the alkyl linker between the sugar and the triazole, was synthesized and investigated on their surfactant properties and phase behavior in water. The results indicate no significant impact of the linker on surface and interphase properties, whereas the phase behavior is affected. Higher affinity for the bicontinuous cubic phase potentially favors methylene-linked ATGs over higher homologs for drug-delivery applications. A comparison of glucose and xylose reveals a tendency for high Krafft points for propargyl xyloside based ATGs. This disfavors these surfactants with respect to both glucose analogs and higher homologs.     

Validation of a HPLC/MS method for simultaneous quantification of clonidine,morphine and its metabolites in human plasma

A high‐performance liquid chromatography–tandem mass spectrometry method was developed and validated for the simultaneous quantification of morphine, morphine's major metabolites morphine‐3‐glucuronide and morphine‐6‐glucuronide, and clonidine, to support the pharmacokinetic analysis of an ongoing double‐blinded randomized clinical trial that compares the use of morphine and clonidine in infants diagnosed with neonatal abstinence syndrome. Plasma samples were processed by solid‐phase extraction and separated on an Inertsil ODS‐3 (4 μm) column using an 0.1% formic acid in water–0.1% formic acid in methanol gradient. Detection of the analytes was conducted in the positive multiple reaction monitoring mode. The range of quantitation was 1–1000 ng/mL for morphine, morphine‐3‐glucuronide and morphine‐6‐glucuronide, and 0.25–100 ng/mL for clonidine. Intra‐day and inter‐day accuracy and precision were ≤15% for all analytes across the quantitation range. Extraction recovery rates were ≥94% for morphine, ≥90% for M3G, ≥87% for M6G and ≥ 79% for clonidine. Matrix effect ranged from 85–94% for clonidine to 101–106% for M3G. The method fulfilled all predetermined acceptance criteria and required only 100 μL of starting plasma volume. Furthermore, it was successfully applied to 30 clinical trial plasma samples.     

转动分辨的H2+ (X2Σ+g , v+=0-18)真空紫外脉冲场电离光电子谱

测量了氢气离子转动分辨的真空紫外脉冲场电离光电子谱．涵盖了15.30?18.09 eV能量范围内的H2+(X2§+g , v+=0?18,N+=0?5)?H2(X1§+g , v00=0, J00=0?4)的电离跃迁． 通过基于Buckingham-Orr-Sichel(BOS)模型的光谱拟合和对氢气离子振动带H2+(X2§+g ,v+=0?18)的转动光谱的分析, 发现实验上只观察到对应于￠N=N+-J00=0,§2的转动跃迁． 振动量子数v+ 越高，￠N=0的转动跃迁越占主导地位， 而转动谱线强度受邻