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.     

Spectral regions selection to improve prediction ability of PLS models by changeable size moving window partial least squares and searching combination moving window partial least squares

Changeable size moving window partial least squares (CSMWPLS) and searching combination moving window partial least squares (SCMWPLS) are proposed to search for an optimized spectral interval and an optimized combination of spectral regions from informative regions obtained by a previously proposed spectral interval selection method, moving window partial least squares (MWPLSR) [Anal. Chem. 74 (2002) 3555]. The utilization of informative regions aims to construct better PLS models than those based on the whole spectral points. The purpose of CSMWPLS and SCMWPLS is to optimize the informative regions and their combination to further improve the prediction ability of the PLS models. The results of their application to an open-path (OP)/FT-IR spectra data set show that the proposed methods, especially SCMWPLS can find out an optimized combination, with which one can improve, often significantly, the performance of the corresponding PLS model, in terms of low prediction error, root mean square error of prediction (RMSEP) with the reasonable latent variable (LVs) number, comparing with the results obtained using whole spectra or direct combination of informative regions for a compound. Regions consisting of the combinations obtained can easily be explained by the existence of IR absorption bands in those spectral regions.     

Measurement of attachment force of microbial cells

A parallel-plate flow chamber consisting of two transparent electro-conductive glass plates was constructed. The two glass plates were set parallel to each other and connected to a potentiostat apparatus to regulate the strength of the electric field between the plates. A microbial cell suspension was flowed through the chamber. This system enabled the application of an electrostatic force to suspend charged particles, e.g. microbial cells, existing between the two plates. The time course of the cell attachment of Pseudomonas syringae pv. atropurpurea NIAES 1309 suspended in 10 mM phosphate buffer solution (pH 7.0) to the glass plate was investigated at various electric field strengths ranging from −4.2 to +4.1 V cm⁻¹. The attachment rate and the maximum number of attached cells increased linearly with the increase in the strength of the positive electric field. In contrast, the rate and the number of cells decreased linearly with the decrease in the strength of the negative electric field. These linear relations gave a specific value for the strength of the electric field (−5.9 ± 0.7 V cm⁻¹) where the electrostatic repulsion and the microbial attachment force were thought to be equal, resulting in no cell attachment. From this value, the electrostatic repulsion, i.e. the microbial attachment force, was calculated to be 5.0 × 10⁻¹¹ N cell⁻¹ for cells of average size.     

Rapid quantification of HIV protease inhibitors in human plasma by high-performance liquid chromatography coupled with electrospray ionization tandem mass spectrometry

HIV protease inhibitors are important antiretroviral drugs which have substantially reduced the morbidity and mortality associated with HIV-1 infection. Recent data have shown relationships between plasma concentrations of the protease inhibitors and clinical response, which makes therapeutic drug monitoring valuable. We have developed and validated an assay, using liquid chromatography coupled with electrospray tandem mass spectrometry (LC/MS/MS), for the routine quantification of the six licensed protease inhibitors (amprenavir, indinavir, lopinavir, nelfinavir, ritonavir and saquinavir) and the pharmacologically active nelfinavir metabolite M8 in plasma. The sample pretreatment consisted of protein precipitation with a mixture of methanol and acetronitrile using only 100 microl of plasma. Chromatographic separation was performed on an Inertsil ODS3 column (50 x 2.0 mm i.d., particle size 5 microm), with a quick stepwise gradient using an acetate buffer (pH 5) and methanol, at a flow rate of 0.5 ml min(-1). The analytical run time was 5.5 min. The use of a 96-well plate autosampler allowed batch sizes up to 150 patient samples. The triple-quadrupole mass spectrometer was operated in the positive ion mode and multiple reaction monitoring was used for drug quantification. The method was validated over the concentration ranges 0.01-10 microg ml(-1) for indinavir and saquinavir, 0.1-10 microg ml(-1) for amprenavir, 0.05-10 microg ml(-1) for nelfinavir and ritonavir, 0.1-20 microg ml(-1) for lopinavir and 0.01-5 microg ml(-1) for M8. Saquinavir-d(5) and indinavir-d(6) were used as internal standards. The coefficients of variation were always <10% for both intra-day and inter-day precisions for each compound. Mean accuracies were also between the designated limits (+/-15%). The validated concentration ranges proved to be adequate in daily practice. This robust and fast LC/MS/MS assay is now successfully applied for routine therapeutic drug monitoring and pharmacokinetic studies in our hospital.     

重氮树脂与十二烷基硫酸钠相互作用研究

重氮树脂与十二烷基硫酸钠相互作用研究罗杨磊曹维孝（北京大学化学与分子工程学院北京１００８７１）关键词重氮树脂，十二烷基硫酸钠，负性ＰＳ版随着化学与生命科学领域的发展，大分子与小分子在溶液的相互作用越来越受到关注．表面活性剂因其具有自组装能力，...     

Lamination Design Optimization for Continuous Fiber Reinforced Composites of Variable Thicknesses北大核心CSCD

由于具备高的比强度、比刚度,利用连续纤维增强复合材料代替传统金属材料以实现结构轻量化正受到设计者们的广泛关注。然而,结构的复杂性给复合材料的铺层设计与优化带来了很大的挑战。针对航空用复合材料铺层设计约束多的问题,通过逐步构建设计变量准确表达结构的铺层信息。基于经典遗传算法框架,结合各设计变量特点,定义了铺层优化算法中的遗传算子,通过引入“修复”策略保证了每一代解都能满足设计约束,分布在可行域区间内。最后利用精英保留策略提高了算法的局部寻优能力,可以降低复杂复合材料结构铺层设计的计算成本。通过解决经典benchmark问题并与已有优化结果的比较,验证了前述铺层优化算法的全局、局部寻优能力,为工程实际中的复合材料铺层设计优化提供了理论支撑。     

A stream tube model for miscible flow

A simple theoretical model is described for deriving a 1-dimensional equation for the spreading of a tracer in a steady flow at the field scale. The originality of the model is to use a stochastic appoach not in the 3-dimensional space but in the 1-D space of the stream tubes. The simplicity of calculation comes from the local relationship between permeability and velocity in a 1-D flow. The spreading of a tracer front is due to local variations in the cross-sectional area of the stream tubes, which induces randomness in travel time. The derived transport equation is averaged in the main flow direction. It differs from the standard dispersion equation. The roles of time and space variables are exchanged. This result can be explained by using the statistical theory of Continuous Time Random Walk instead of a standard Random Walk. However, the two equations are very close, since their solutions have the same first and second moments. Dispersivity is found to be equal to the product of the correlation length by the variance of the logarithm of permeability, a result similar to Gelhar's macrodispersion.Nomenclature A total cross-section area of the sample - C (resident) concentration of tracer - D,D ^* dispersion coefficient - F flux of tracer - G probability distribution function for permeability in the stream-tube segments - I tracer intensity (mass crossing a surface per unit time) - K permeability - L length of the medium - M number of stream tubes in the medium - N number of segments along a stream tube - P pressure - Q total flow rate in the sample - a length of an elementary stream-tube segment - g probability distribution function for permeability in the space - i, j indices, tube numbers - q flow rate in each stream tube - s variable cross-section area of a stream tube - t, t time - u front velocity - x space variable in the flow direction - small local variation in time - , _t longitudinal, transverse dispersivity - porosity of the porous medium - correlation length in the permeability field - viscosity of the fluid - time for filling an elementary stream tube segment - standard deviation of a stochastic variable - probability distribution of arrival times (Gaussian)     

LOWLAD: a locally weightedL 1 smoothing spline algorithm with cross validated choice of smoothing parameters

The computation ofL ₁ smoothing splines on large data sets is often desirable, but computationally infeasible. A locally weighted, LAD smoothing spline based smoother is suggested, and preliminary results will be discussed. Specifically, one can seek smoothing splines in the spacesW _m (D), with [0, 1] ⁿ D. We assume data of the formy _i =f(t _i )+ _i ,i=1,..., N with {t _i } _i=1 ^N D, the _i are errors withE( _i )=0, andf is assumed to be inW _m . An LAD smoothing spline is the solution,s , of the following optimization problem

ContinuousK-theory

We study arithmetical properties of homotopy groups of thel-adic completion of Quillen'sK-theory space of number field, with a view on the Dwyer-Friedlander comparison map into étaleK-theory. The relation of these groups toK-theory is a complete analogy to the relation of continuous étale cohomology to étale cohomology. We identify the torsion subgroup of the resulting term with the subgroup of divisible elements inK _2n (F). We prove that this term is sent isomorphically into étaleK-theory, giving some further evidence for the Lichtenbaum-Quillen conjectures.     

Chains of strongly non-reflexive dual groups of integer-valued continuous functions

Answering a question of Eklof-Mekler (Almost free modules, set-theoretic methods, North-Holland, Amsterdam, 1990), we prove: (1) If there exists a non-reflecting stationary set of consisting of ordinals of cofinality for each , then there exist abelian groups such that and for each . (2) There exist abelian groups such that for each and for each . The groups are the groups of -valued continuous functions on a topological space and their dual groups.