Striktionseigenschaften von Regelscharen imE n

Let ={e(u)|uI} be a one-parameter family of straight lines forming a ruledC ^r-2-surface E ⁿ (n2,r1) without singular generatorse(u) (uI). As a synopsis, a generalization and an improvement of various results already known about the strictional properties of ruled surfaces E ⁿ (especially in the casen=3) the author demonstrates a uniform geometrical way of defining and uniquely obtaining thestriction point S(u) and theparameter of distribution d(u) of a generatore(u) under the minimal assumptions thate(u)E ⁿ (n2) be noncylindrical andr1. Other methods of obtainingS(u) andd(u) are discussed in comparison, and special strictional properties ofskew ruled surfaces E ⁿ are proved.

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Herrn Prof. Dr. H. R. Müller zum 65. Geburtstag     

A variational proof of the Gauss-Bonnet formula

The classical Gauss-Bonnet formula has the form I(g_ij)=2, where I(g_ij) represents a sum of three terms each of which depends on the metric tensor g_ij. It is shown that the first variation I of I(g_ij) with respect to the metric g_ij vanishes and that for the Euclidean metric _ij we have I(_ij)=2. From this the formula I(g_ij)=2 follows. In the process, explicit expressions are obtained for the first variation of each of the three terms which comprise I(g_ij). Furthermore, a general expression for the first variation of a multiple integral whose integrand is a scalar density depending on the metric tensor g_ij and its derivatives up to the second order is obtained with the aid of results of Rund [1].     

Mean value estimates in lattice point theory

LetQ(u) be a positive definite quadratic form inr2 variables with a real symmetric coefficient matrix of determinantD. Given a real vectorb with 0b _j <1, forx>0 letA(x) be the number of lattice points in the ellipsoidQ(u+b)x, letV(x) be the volume of this ellipsoid andP(x)=A(x)–V(x). Let . By introduction of a parameter we shall show how the treatment of estimates onP(x) and onM(x) can be unified.     

Lexicographic quasiconcave multiobjective programming

Summary Letf _i :A R ben real-valued objective functions on a convex setA -K ^m ,K:=R orC, n, mN. Letg: A R ⁿ be defined by , where for eachxA, (i ₁ (x), ..., i _n (x)) is a permutation of (1, ...,n) such that . In this paper we treat the problem of findingx ^*A such that , wherel-max denotes the lexicographic maximum. If the f_i's are strongly quasiconcave we can reduce the problem stepwise until finally it is in the form of a scalar programming problem. Further, we consider conditions for the existence and uniqueness of a solution and discuss the relationship of the problem to the vector maximum (i.e. Pareto) and maxmin (i.e. Chebychev) problems.

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Zusammenfassung f _i :AR seienn reellwertige Zielfunktionen über einer konvexen MengeA-K ^m ,K:=R oderC, n, mN. g:AR ⁿ sei definiert durch , wobei für jedesxA (i ₁ (x), ... i _n (x)) eine Permutation von (1, ...,n) derart ist, daß Wir betrachten das Problem, einx ^*A so zu finden, daß , wobeil-max das lexikographische Maximum bedeute. Falls dief _i stark quasikonkav sind, läßt sich das Problem stufenweise reduzieren, bis es schließlich die Gestalt eines skalaren Optimierungsproblems annimmt. Wir geben Existenz- und Eindeutigkeitsbedingungen an und besprechen Zusammenhänge mit dem Vektormaximumproblem (d.h. Pareto-Optimierung) und dem Maxmin-Problem (d.h. Tschebyscheff-Optimierung).

     

TiO2-CdS-MCM-41复合纳米材料的合成和表征

利用γ-巯丙基三甲氧基硅烷及表面预吸附水解技术在MCM-41介孔分子筛孔道内部以化学键合的形式依次引入了CdS和TiO2纳米粒子.紫外-可见吸收光谱结果表明,借助于巯基的络合能力,MCM-41能有效地从反胶束中萃取CdS纳米粒子.利用小角XRD谱图成功地跟踪观察到了MCM-41介孔分子筛随纳米粒子的引入而产生的孔径变化.     

The Crystal Structure of Trimethyl Borate by Neutron and X‐ray Powder Diffraction

The crystal structure of one of the simplest organoboron compounds, trimethyl borate does not appear to have been determined hitherto. The compound is of interest for the study of π‐donor ligands and their interaction with the π‐acceptor behavior of trigonal boron and the consequences of such interactions on molecular structure. We used powder neutron (with isotopically labeled material) and X‐ray diffraction to determine the crystal structure of trimethyl borate at 15 K and 200 K (neutron) and 200 K (X‐ray). The material is hexagonal (Z = 2) with a = b = 6.950(8) Å and c = 6.501(3) Å at 15 K. The unit cell volume is 272.00(1) ų. The space group is P6₃/m (SG 176) at 15 K and 200 K. This is the first crystal structure solved on the Neutron Powder Diffractometer (NPDF) at the Lujan Center.     

A sequential reaction process to assemble polysubstituted indolizidines, quinolizidines and quinolizidine analogues

The ω-iodo-α,β-alkynoates and their ketone, sulfone or phosphonate analogues react with δ-chloropropylamines in MeCN assisted with K₂CO₃ to undergo a sequential S_N2/Michael addition/S_N2/S_N2 reaction process, giving polysubstituted indolizidines or quinolizidines in good to excellent yields. This sequential reaction process is also compatible with three other substituted α,β-alkynoates, affording quinolizidine analogues in moderate to good yields.     

Isobutane chemical ionization mass spectra of unsaturated alcohols

Analysis of the isobutane chemical ionization mass spectra of hexenols, cyclohexenols and various syn/anti pairs of bicyclic and tricyclic homoallylic alcohols shows that: (i) the spectra of the allylic alcohols are dominated by [M + H – H₂O]⁺ and [M + C₄H₉–H₂O]⁺ ions and contain traces of [M + H]⁺ ions; (ii) [M + H]⁺ ions are prominent in the spectra of acyclic and certain cyclic homoallylic alcohols; and (iii) [M + H]⁺ ions dominate the spectra of other acyclic unsaturated alcohols. The [M + H]⁺ ions may result from either: (a) protonation of the hydroxyl group, followed by a very rapid intramolecular proton transfer from the protonated hydroxyl group to the carbon–carbon double bond or internal solvation of the protonated hydroxyl group by the carbon–carbon double bond; and/or (b) direct protonation of the carbon–carbon double bond with significant internal solvation of the resulting carbocation by the hydroxyl group, which may lead to carbon–oxygen bond formation to give a protonated cyclic ether. The consequences of placing various geometric constraints on the possible intramolecular interactions between the hydroxyl group and the carbon–carbon double bond in unsaturated alcohols are explored.     

Microdetermination of sulfite with a piezoelectric crystal detector

A piezoelectric method is proposed for the determination of sulfite in concentration range 1 × 10^–7–1 × 10^–5 mol/1. The method is based on the redox reaction of sulfite with iodine followed by measuring frequency change of the piezoelectric crystal caused by the unreacted iodine. The method is applied to the determination of sulfite in liquor.     

Study on interaction between drug and membrane by using liposome coated zirconia-magnesia chromatography

The interactions between drug molecules and membrane were studied using the new chromatography stationary phase of liposome coated zirconia–magnesia. log K_s(ZrO₂–MgO) on this new chromatography for some drugs, compared with that on liposome coated silica chromatography and other reported data, fair correlations were observed between them when excluding effect of special adsorption. log K_s(ZrO₂–MgO) values for barbitalum, diazepam, benzene, benzocaine and toluene correlated well with corresponding values on liposome coated silica chromatography (R = 0.99778, P < 0.001; R = 0.98229, P < 0.003; R = 0.9985, P < 0.0001; R = 0.99925, P < 0.0001, pH value of mobile phase at pH 7.4, 7.0, 6.4 and 5.4, respectively). They also correlated well with the literature data on immobilized artificial membrane chromatography (R = 0.99999, P < 0.004 at pH 7.4) and liposome chromatography (R = 0.99994, P < 0.008) for procaine, lidocaine and bupivacaine. Liposome coated zirconia–magnesia chromatography can thus be used for studying drug–membrane interaction and prediction of drug absorption as another liposome chromatography method.