The Method of Virtual Experts in Mathematical Diagnostics

Mathematical Diagnostics (MD) deals with identification problems arising in different practical areas. Some of these problems can be described by mathematical models where it is required to identify points belonging to two or more sets of points. Most of the existing tools provide some identification rule (a classifier) by means of which a given point is assigned (attributed) to one of the given sets. Each classifier can be viewed as a virtual expert. If there exist several classifiers (experts), the problem of evaluation of experts’ conclusions arises. In the paper for the case of supervised classification the method of virtual experts (the VE-method) is described. Based on this method, a generalized VE method is proposed where each of the classifiers can be chosen from a given family of classifiers. As a result, a new optimization problem with a discontinuous functional is stated. Examples illustrating the proposed approach are provided. The work of the second author was supported by the Russian Foundation for Fundamental Studies (RFFI) under Grant No 03-01-00668.     

Equality and inequality constrained optimization algorithms with convergent stepsizes

In this paper, we consider two algorithms for nonlinear equality and inequality constrained optimization. Both algorithms utilize stepsize strategies based on differentiable penalty functions and quadratic programming subproblems. The essential difference between the algorithms is in the stepsize strategies used. The objective function in the quadratic subproblem includes a linear term that is dependent on the penalty functions. The quadratic objective function utilizes an approximate Hessian of the Lagrangian augmented by the penalty functions. In this approximation, it is possible to ignore the second-derivative terms arising from the constraints in the penalty functions.The penalty parameter is determined using a strategy, slightly different for each algorithm, that ensures boundedness as well as a descent property. In particular, the boundedness follows as the strategy is always satisfied for finite values of the parameter.These properties are utilized to establish global convergence and the condition under which unit stepsizes are achieved. There is also a compatibility between the quadratic objective function and the stepsize strategy to ensure the consistency of the properties for unit steps and subsequent convergence rates.This research was funded by SERC and ESRC research contracts. The author is grateful to Professors Laurence Dixon and David Mayne for their comments. The numerical results in the paper were obtained using a program written by Mr. Robin Becker.     

Mannich bases as model compounds for intramolecular hydrogen bonding I. Solid state structures and molecular calculations

Summary A survey of the structures and the properties of the hydrogen bonds inortho-aminomethylphenols and -naphthols in the solid state is presented. The results are compared with molecular structure calculations. The solid state complexes can exist in the molecular or in zwitterionic form. In the last case, only intermolecular hydrogen bonds forming cyclic dimers or linear chains were detected.

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Mannich-Basen als Modelle für Intramolekulare Wasserstoffbrücken, 1. Mitt. Festkörperstrukturen und Molekülrechnungen

Zusammenfassung Eine Übersicht über Strukturen und Eigenschaften von Wasserstoffbrücken inortho-Aminomethylphenolen und -naphtholen wird präsentiert. Die Ergebnisse werden mit Molekülrechnungen verglichen. Im Festkörper existieren diese Verbindungen in neutraler oder in zwitterionischer Form. Für den zweiten Fall können nur intermolekulare Wasserstoffbrücken nachgewiesen werden, und zwar in Dimeren oder in linearen Ketten.

     

Representing workloads in GI/G/1 queues through the preemptive-resume LIFO queue discipline

We give in this paper a detailed sample-average analysis of GI/G/1 queues with the preemptive-resume LIFO (last-in-first-out) queue discipline: we study the long-run state behavior of the system by averaging over arrival epochs, departure epochs, as well as time, and obtain relations that express the resulting averages in terms of basic characteristics within busy cycles. These relations, together with the fact that the preemptive-resume LIFO queue discipline is work-conserving, imply new representations for both actual and virtual delays in standard GI/G/1 queues with the FIFO (first-in-first-out) queue discipline. The arguments by which our results are obtained unveil the underlying structural explanations for many classical and somewhat mysterious results relating to queue lengths and/or delays in standard GI/G/1 queues, including the well-known Bene's formula for the delay distribution in M/G/l. We also discuss how to extend our results to settings more general than GI/G/1.     

一维螺旋状3，6-哒嗪二甲酸镉(Ⅱ)配位聚合物的合成与结构

Using the ligand pyridazine-3，6-dicarboxylate (H₂pzdc)， a coordination polymer [Cd₂(pzdc)₂(H₂O)₄] was synthesized and characterized by elemental analysis， thermal analysis， IR and single-crystal X-ray diffraction. The complex crystallizes in the tetragonal system with space group I4₁/a. The crystallographic data are: a=1.470 6(4) nm， c=1.489 8(6) nm， V=3.222 0(19) nm³， Z=16， μ=2.725 mm^-1， D_c=2.594 g·cm^-3， R₁=0.017 8， wR₂=0.044 6. In the complex， the cadmium(Ⅱ) ions with the eight-coordinated dodecahedral geometry are linked by the pzdc ligands to generate one-dimensional chains， which are associated into the three-dimensional architecture via O-H…O hydrogen bonding. CCDC: 658853.     

Re_2(edt)_4的电子结构和电子吸收光谱的从头算研究

用密度泛函理论中的B3LYP/CEP-4G方法对Re2（edt）4进行了结构优化和自然键轨道计算,并用单电子激发组态相互作用方法（CIS）计算了Re2（edt）4的分子轨道和激发态。结果表明Re-Re之间不存在明显的三重键,进而很好地解释了Re2（edt）4分子的电子吸收光谱。     

硅酸盐中桥联键的机制及其性质的CNDO/2法研究

法计算模型,分析了桥联键的成键机制,解释了硅酸盐的通常性质。以体系总能量随桥角变化关系,解释了硅酸盐矿物及沸石分子筛中桥角Si-O-T出现的范围和几率。 由计算结果还发现,桥氧上具有较高的非键p-电子电荷Q_o~n,并随桥氧的第三配原子性质和距离R(M-O~(br))而变化,使桥氧具有授受电子的双重性质。在此基础上,探讨了沸石分子筛的碳离子催化活性机理,提出了锁与匙匹配原子对的催化活性中心的新观点。     

二(邻香草醛缩丙醇胺)异硫氰酸根合锰(Ⅲ)的合成与晶体结构

本文报道了一个新配合物—二(邻香草醛缩丙醇胺根)异硫氰酸根合锰(Ⅲ)的合成及其晶体结构。配合物属于单斜晶系，空间群为P2₁/c，晶胞参数为：a=8.565(1), b=21.814(2), c=12.787(2)?, β=92.80(1)°。锰为六配位，在两个邻香草醛缩丙醇胺Schiff碱配体中，一个为三齿配体，另一个为双齿配体。NCS^-离子以N在轴向上与锰发生配位，由于Jahn-Teller效应，其键长为2.193?。另外晶胞中存在着罕见的H……S-C≡N氢键。     

Microwave-assisted direct addition of cycloethers to alkynes

Under microwave conditions, tetrahydrofuran (THF), tetrahydropyran and 1,4-dioxane are added directly onto alkynes and generated various vinyl cycloethers.     

二(三苯基膦)水杨酸铜(Ⅰ)乙醇溶剂配合物的晶体结构

0IntroductionThestudyofcopper?complexesisinvestigatedinmanylaboratories.Amongthereasonsforcarryingouttheinvestigationofsuchspeciesaretheirstructuralfeatures犤1犦,theusefulnessofcopper?compoundsinorganicsyntheses犤2犦andthewell-documentedimpor-tanceofcopper?centersattheactivesitesofanumberofprotein犤3犦.Concerningcopper?carboxy-latesafurtherinterestexists,stemmingfromtheiruseinhomogeheouscatalysedhydrogenation犤4犦.Thecopper?bis(triphenylphosphine)cationisasoft,butflexi-bleacceptorionthatcanacc…