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.     

氢部分选择性催化还原NO反应研究

在低钯含量活性非均布Pd/Al2O3催化剂上，实现了富氧条件下，氢部分选择性催化还原NO过程，低温、富氧条件下NO的转化率高达80％－100％。NO直接分解实验表明，600℃，NO分解转化率在无氧时为17．3％，有0．5％氧存在时接近于0。氢非选择性还原NO条件下，100℃以下，NO转化率为100％。根据实验结果及文献，推测了氢部分选择性还原NO过程中可能存在的反应，不同的反应温度下，NO脱除反应有所不同。在115℃以下，NO还原产物为NH3；115℃－155℃，NO还原产物为NH3、N2O和N2；155℃以上，NO还原产物中无NH3存在。NO还原反应与氢氧反应是平行的竞争反应。     

聚乙烯塑料在连续超临界水反应器中的油化研究

在连续超临界水（SCW）反应器中考察了反应温度、停留时间和反应压力对聚乙烯（PE）降解油化的影响。实验结果表明，在120s、25MPa下，从500℃提高到550℃，液体收率呈现先升后降的趋势，在530℃达到最大值（79%）；在520℃、25MPa下，随停留时间的延长，PE裂解程度加深，产物轻质化程度提高，导致液体收率降低，停留240s时，气体收率达到43%；反应压力对产物收率的影响较小，气、液产物中烯/烷比随反应压力的增加而增大。     

不依赖于统计模型的手性毛细管电泳分离多指标同时优化

考虑到手性毛细管电泳分离机理的复杂性，提出了不依赖于统计模型的二进制编码遗传算法多目标优化策略。根据实验参数的多少及其重要性，采用均匀设计安排完成初步实验。并用Derringer功效函数作为多指标同时优化的评价指标，以取得较高的分离度和较快分离速度；通过对实验参数给予编码，转化为二进制字符串，根据得到的总功效函数值大小进行遗传算法操作，产生新的一组实验条件。重复上述过程直到得到最佳分离条件为止。此方法成功地应用于华法令对映体的毛细管电泳分离条件优化。     

Determination of total phosphorus and nitrogen in turbid waters by oxidation with alkaline potassium peroxodisulfate and low pressure microwave digestion, autoclave heating or the use of closed vessels in a hot water bath: comparison with Kjeldahl digestion

The evaluation of the use of alkaline peroxodisulfate digestion with low pressure microwave, autoclave or hot water bath heating for the determination of total phosphorus and nitrogen in turbid lake and river waters is described. The efficiency of these digestion procedures were compared to a Kjeldahl digestion procedure with sulphuric acid-potassium sulfate and copper sulfate. The final solution before digestion was 0.045 M in potassium peroxodisulfate and 0.04 M in sodium hydroxide. Procedures were evaluated by the analysis of suspensions of two reference materials, National Institute of Environmental Science, Japan, no. 3 Chlorella and no. 2 pond sediment and natural turbid waters. Best recoveries of phosphorus and nitrogen by microwave heating were obtained when solutions were digested at 95 °C for 40 min. Quantitative recoveries of phosphorus from Chlorella suspensions up to 1000 mg/l were obtained by all three heating procedures, but incomplete recoveries of nitrogen occurred above 20 mg N/l in the digested sample. Good recoveries of phosphorus and nitrogen from suspended sediment suspensions were obtained only from solutions containing <150 mg/l of suspended sediments. Recoveries of phosphorus from phosphorus compounds containing COP and CP bonds added to distilled water were quantitative (94-113%) except for polyphosphates (microwave, 34±8; autoclave, 114±6; water bath, 96±4) and aluminium phosphate (8-23%). Recoveries of nitrogen compounds containing CN bonds added to distilled water were quantitative (94-96%). The analysis of a range of natural turbid water samples by alkaline peroxodisulfate and microwave, autoclave and water bath heating gave similar total phosphorus and nitrogen results. All procedures using alkaline peroxodisulfate underestimate phosphorus concentrations at high suspended sediment concentrations (>150 mg/l) and are only suitable for the analysis of very turbid samples when the turbidity is due to organic matter (algal cells, plant detritus). Underestimation of nitrogen occurs when samples contain more than 20 mg N/l.     

Erosion of efficiency in non-uniform linear chromatography

In linear chromatography (i.e. chromatography performed in the absence of sample overloading), when the plate height of a column is roughly uniform along its length, variations in the velocities of solutes are the only possible causes of erosion of efficiency. The sources of these variations (variations in capacity ratio and in the density of the mobile phase, etc.) play no direct role in the erosion of efficiency except through their effect on solute velocities. In other words, what eventually causes the erosion of efficiency is merely variation in the time required for solutes to traverse equally small segments of a column. Significant erosion can only arise from abrupt and deep deceleration of solutes in one or several relatively small segments of a column. If erosion of efficiency caused by pressure gradients in linear SFC is to be large, the depth and the sharpness of the deceleration of a solute must go beyond that hitherto confirmed experimentally. Many relevant examples are analyzed graphically.     

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)     

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.     

Sequential estimation of a parameter of an exponential distribution

We consider the problem of minimum risk point estimation for the parameter =a+b of the exponential distribution with unknown location parameter and scale parameter when the loss function is squared error plus linear cost. In this paper, we propose a sequential estimator of and show that the associated risk is asymptotically one cost less than that given by Ghosh and Mukhopadhyay (1989,South African Statist. J.,23, 251–268).