Beiträge zur Chemie der Alkylverbindungen von Übergangsmetallen. XLIV. Tetrakis(alkoxycarbonylmethyl)titan-Verbindungen

Contributions to the Chemistry of Transition Metal Alkyl Compounds. XLIII. Tetrakis(alkoxycarbonylmethyl)titanium Compounds Organotitanium(IV) compounds of the type (ROCOCH₂)₄Ti (R ? C₂H₅, i-C₃H₇, t-C₄H₉, C₆H₅, C₆H₅CH₂) were obtained by reactions of ROCOCH₂Li derivatives with TiCl₄ at low temperature. The compounds which decompose only above 90°C were characterized by the hydrolysis products, anaerobic reactions with iodine, and the i.r. spectra. The bond conditions are discussed.     

On the determination of polarity parameters of silica by means of solvatochromic probe dyes

Empirical solvent parameters of silica surfaces are determined by means of solvatochromic dyes, e.g., Cu(tmen) (acac)⁺ ClO ₄ ^– /B(C₆H₅) ₄ ^– , Fe(phen)₂(CN)₂, and Michlers Ketone dissolved in 1,2-dichloroethane or cyclohexane. The values obtained by UV/VIS-measurements are compared with both the polarity scales of Kamlet and Taft and with Gutmann's donor and acceptor numbers. Kamlet and Taft's -parameter (the hydrogen-bond donation capacity of a solvent) is determined independently by means of salicylideneaniline. The ^* of silica is determined using 5-N,N-dimethylamino-5-nitro-2,2-bithiophene and the complex of tetracyanoethylene with Michlers Ketone, respectively. Further on the reliabilities of the obtained Kamlet-Taft parameters , , and ^* are checked by comparism with experimental and calculated values of theE _T(30)-parameter of silica by means of multi-parameter regression analysis. The surface properties of silica are influenced mainly by HBD-properties (75%) and dipolarity/polarizability ^* (20%), but hardly by the HBA-properties (<5%). UV/VIS-measurements were carried out in a special equipment with glass fiber optics, A drawing of the apparatus is given.     

Formation of the surface charge on silica in mixed solvents

At sufficiently high concentrations of methanol and of alkali salts in aqueous silica dispersions, the negative -potentials of the particles are decreased. This effect is more pronounced with lithium than with other alkali cations, and it is independent on the anion. The NMR spectra indicate lithium adsorption on silica from mixed solvents, but not in the absence of alcohol.Supported by a contract with the XMX Corporation, Burlington, Massachusetts, USA     

Die Strommer-Zykliden des Flaggenraumes

According to H. BRAUNER a flag space is a three-dimensional affine space with an absolute {,f,F}, wheref is a line in the plane of infinity andF a point onf. A cyclide is a surface of order 4 that intersects only atf. A STROMMER-cyclide is a cyclide generated by translation of a circle in an isotropic plane. In this paper we proof that all STROMMER-cyclides can be generated by translation of an isotropic circle along a divergent Newton-parabola or a conic in a full isotropic plane. We give normal-forms and CAD-pictures of these surfaces. Finaly some geometrical results about STROMMER-cyclides are developed.

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Herrn o.Prof. Dr. Gy. Strommer zum 70. Geburtstag gewidmet.     

On locally optimal nonparametric tests

Summary There is an abundancy of problems in which no parametric model realistically describes the situation and in which, accordingly, we have to resort to nonparametric methods. As the numerical problems connected with nonparametric tests are becoming less and less important, rank tests, permutation tests and the like are becoming more and more part of the standard armatory of applied statisticians. The lack of tabulated critical values, for instance, should no longer be a serious objection against the use of permutation tests in practice; cf. Edgington (1987).The rationale underlying permutation and rank tests has been outlined in quite a number of text books and papers; cf. Fraser (1957), Lehmann (1959), Hájek-Sidák (1967) or Witting (1970). Roughly speaking, permutation tests are constructibel if the data can be condensed by means of a sufficient and complete statistic allowing for the proper kind of conditioning. Rank tests arise if the underlying problem is invariant with respect to (w.r.t.) a large group of transformations which leads to a maximal invariant statistic consisting of (signed) ranks.Most practical nonparametric problems, however, are too complex to be tractable by just one of those approaches. Many of them, however, can be handled by a combination of both techniques. In this paper we outline the logic underlying that combined reduction method and apply it to construct locally most powerful tests. Moreover, we discuss what we label Hoeffding's transfer problem, i.e. the uniformity aspect of locally most powerful tests with respect to the starting point at the boundary. We are concentrating on the discussion of the nonparametric two-sample location and scale problem. Further important problems are mentioned in Section III.This is a written account of an invited lecture delivered by the third author on occasion of the 14th Symposium über Operations Research, Ulm, September 6–8, 1989.     

Distribution of values of σ2 (n) in residue classes

IntegersN for which ₂ (n has weak uniform distribution (modN) are determined.     

Dirichletsche Reihen auf arithmetischen Progressionen

A characterisation of all real Δ≠0 is given, such that $$\overline {f(\sigma + i\Delta \mathbb{N})} = \overline {f(\sigma + i\mathbb{R})} $$ holds for all Dirichlet seriesf(s)=Σa _n n ^?s and all σ greater than the abscissa of absolute convergence off. For only countably many Δ relation (*) is not valid. By using transcendental results it is shown, that (*) holds in the special case, Δ=1.     

On a classical Nicoletti boundary value problem

We shall derive existence, uniqueness and comparison results for the functional differential equationx(t)=f(t, x), a. e.tI, with classical Nicoletti boundary conditionsx _i(t_i)=y _iX, iA, whereI is a real interval,A is a nonempty set andX is a Banach space.     

Sur les séries de Taylor et les transformations de Möbius

Given a non-empty closed subsetF of the unit circle |z|=1, and a Möbius transformationM(z) of the unit disc |z|1, such thatM(0)0, there exists a functionf(z) holomorphic in the unit disc,F being the singular set at the boundary, whose Taylor coefficients tend to zero while the Taylor coefficients off(M(z)), do not tend to zero.     

Ein Algorithmus zur Lösung eines Verteilungsproblems

Zusammenfassung Bei der Lastverteilung eines Elektrizitätsversorgungsunternehmens besteht die Möglichkeit, durch eine Tonfrequenzrundsteueranlage die Last optimal aufzuteilen. Eine Zielsetzung besteht darin, durch Zu- und Wegschalten von Verbrauchergruppen die Lastspitze möglichst klein zu halten. Dabei muß allerdings jedem Verbraucher in einem gewissen Zeitraum eine gewisse Einschaltdauer garantiert sein. Der zur Lösung herangezogene Algorithmus basiert im wesentlichen auf dem Prinzip der dynamischen Optimierung und der Idee von Branch- and-Bound-Verfahren.

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Summary One aim of electric load management is to keep load peaks low by switching on and off water heaters of different groups of customers. There is a restriction that those heaters have to be switched on within a certain period of time for some fixed time. The optimal switching strategy for this distribution problem is computed using dynamic programming and the idea of branch and bound methods.