Sequential properties of function spaces with the compact-open topology

The main results of the paper are:

(1)

If X is metrizable but not locally compact topological space, then Ck(X) contains a closed copy of S₂, and hence does not have the property AP;

(2)

For any zero-dimensional Polish X, the space Ck(X,2) is sequential if and only if X is either locally compact or the derived set X^′ is compact; and

(3)

All spaces of the form Ck(X,2), where X is a non-locally compact Polish space whose derived set is compact, are homeomorphic, and have the topology determined by an increasing sequence of Cantor subspaces, the nth one nowhere dense in the (n+1)st.

     

Combining the regularization strategy and the SQP to solve MPCC — A MATLAB implementation

Mathematical Program with Complementarity Constraints (MPCC) plays a very important role in many fields such as engineering design, economic equilibrium, multilevel games, and mathematical programming theory itself. In theory its constraints fail to satisfy a standard constraint qualification such as the linear independence constraint qualification (LICQ) or the Mangasarian-Fromovitz constraint qualification (MFCQ) at any feasible point. As a result, the developed nonlinear programming theory may not be applied to MPCC class directly. Nowadays, a natural and popular approach is trying to find some suitable approximations of an MPCC so that it can be solved by solving a sequence of nonlinear programs.This work aims to solve the MPCC using nonlinear programming techniques, namely the SQP and the regularization scheme. Some algorithms with two iterative processes, the inner and the external, were developed. A set of AMPL problems from MacMPEC database (Leyffer, 2000) [8] were tested. The comparative analysis regarding performance of algorithms was carried out.     

“一锅法”制备C18-硅胶杂化毛细管整体柱及其应用

本文发展了一种“一锅法”制备C18-硅胶杂化毛细管整体柱的方法。发展了一种“一锅法”制备有机-无机杂化毛细管整体柱的方法。首先将四甲氧基硅烷、乙烯基三甲氧基硅烷在弱酸条件下水解,然后加入有机单体(甲基丙烯酸-N,N-二甲基十八烷基溴化铵乙酯)及自由基聚合引发剂,同步原位完成硅羟基间的缩聚反应及双键间的自由基聚合反应,从而制成C18-硅胶杂化整体柱;同时用毛细管电色谱(CEC)和毛细管液相色谱(CLC)对其柱效和分离能力进行了初步评价,并将其应用到微柱液相色谱-串联质谱对牛血清白蛋白酶解液的分离分析。结果表明,该C18-硅胶杂化整体柱具有较高的柱效和较好的重现性,在分离分析复杂生物样品方面具有较大的应用前景。此外,本文所发展的方法在制备杂化整体柱的过程中不借助相应的硅烷试剂,为杂化整体柱的制备提供了一种新的思路。     

3-乙基-2-丙基喹啉衍生物的合成工艺研究

以芳胺和正丁醛为原料,对甲基苯磺酸(TsOH)为促进剂,采用"一锅法"合成了3-乙基-2-丙基喹啉衍生物,系统地考察了原料比例、溶剂以及芳胺上取代基对反应的影响,比较了不同的质子酸促进剂对喹啉衍生物产率以及选择性的影响,并对产物进行了核磁共振表征.实验结果表明当用对甲基苯磺酸(TsOH)为促进剂时,3乙基-2-丙基喹啉收率可达到59%,同时生成40%N-丁基苯胺;磷钼酸、浓硫酸也可以选择性地得到喹啉衍生物,但收率较低,分别只有28%和24%.同时,考察了苯胺环上取代基对喹啉收率的影响,当苯环上有供电子基时,有利于喹啉的生成,而吸电子基则不利于喹啉的生成.并推测了反应机理.     

Direct experimental evidence for the high chemical reactivity of α- and β-xylopyranosides adopting a (2,5)B conformation in glycosyl transfer

The effect of a (2,5)B boat conformation on xyloside reactivity has been investigated by studying the hydrolysis and glycosylation of a series of synthetic xyloside analogues based on a 2-oxabicyclo[2.2.2]octane framework, which forces the xylose analogue to adopt a (2,5)B conformation. The locked β-xylosides were found to hydrolyze 100-1200 times faster than methyl β-D-xylopyranoside, whereas the locked α-xylosides hydrolyzed up to 2×10(4) times faster than methyl α-D-xylopyranoside. A significant rate enhancement was also observed for the glycosylation reaction. The high reactivity of these conformers can be related to the imposition of a (2,5)B conformation, which approximates a transition state (TS) boat conformation. In this way, the energy penalty required to go from the chair to the TS conformation is already paid. These results parallel and support the observation that the GH-11 xylanase family force their substrate to adopt a (2,5)B conformation to achieve highly efficient enzymatic glycosidic bond hydrolysis.     

The detection and estimation of the change point in a disccrete-time stochastic system

A piecewise-constant process containing a single jump is observed under noise in the context of discrete time. The conditional density and maximum a posteriori (MAP) estimator of the jump time as well as the Bayes detector of the jump itself are determined using the powerful measure transformation approach. The Bayes detector provides a convenient sequential detection rule for practical on-line implementation. An asymptotic result for the distribution of the MAP estimator's estimation error and the corresponding convergence rate are derived. This result provides a reference measure of optimal performance for jump-time estimators in discrete-time stochastic systems that does not depend on the jump time's prior distribution     

An optimal sequential procedure for a multiple selling problem with independent observations

We consider a sequential problem of selling K identical assets over the finite time horizon with a fixed number of offers per time period and no recall of past offers. The objective is to find an optimal sequential procedure which maximizes the total expected revenue. In this paper, we derive an effective number of stoppings for an optimal sequential procedure for the selling problem with independent observations.     

Limit Behavior of Sequential Empirical Measure Processes

In this article, we obtain some uniform laws of large numbers and functional central limit theorems for sequential empirical measure processes indexed by classes of product functions satisfying appropriate Vapnik-?ervonenkis properties.     

Sequential Monte Carlo Samplers: Error Bounds and Insensitivity to Initial Conditions

This article addresses finite sample stability properties of sequential Monte Carlo methods for approximating sequences of probability distributions. The results presented herein are applicable in the scenario where the start and end distributions in the sequence are fixed and the number of intermediate steps is a parameter of the algorithm. Under assumptions which hold on noncompact spaces, it is shown that the effect of the initial distribution decays exponentially fast in the number of intermediate steps and the corresponding stochastic error is stable in 𝕃 _p norm.