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.

---

---

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.     

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.

---

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.

     

Density fluctuations in amorphous and semicrystalline polymers

Summary The small-angle scattering of amorphous and semicrystalline polymers contains an intensity component due to density fluctuations within the crystalline and amorphous domains.For amorphous polymers, the density fluctuations aboveT _g correspond to the theoretical value for a fluid system in thermodynamic equilibrium. BelowT _g , a temperature dependence proportional to T is observed over a range of about 50°. At lower temperatures, a linear relationship with a smaller slope has been found which extrapolates to a non-zero value at 0 °K. This value corresponds to the frozen-in disorder, the slope at low temperatures is related to thermal vibrations and can be evaluated in terms of photon-phonon scattering.Semicrystalline polymers show a temperature dependence of the density fluctuation similar to that of the amorphous polymers. At constant temperature the density fluctuations vary linearly with crystallinity.Natural rubber shows an increase of the density fluctuations with increasing cross-linking densities from which information on the density changes in the vicinity of a cross-link and on the statistics of the distribution of cross-linking can be obtained.

---

Zusammenfassung Die Kleinwinkelstreuung amorpher und teilkristalliner Polymere besitzt eine Intensitätskomponente, die von Dichtefluktuationen innerhalb der kristallinen und amorphen Bezirke herrührt. Für amorphe Polymere entspricht die Dichtefluktuation oberhalb vonT _g dem theoretischen Wert für ein fluides System im thermodynamischen Gleichgewicht. UnterhalbT _g wird eine Temperaturabhängigkeit proportional zuT über einen Bereich von etwa 50° beobachtet. Bei tieferen Temperaturen wird eine lineare Beziehung mit einer geringeren Steigung gefunden, welche zu einem endlichen Wert bei 0 °K extrapoliert werden kann. Dieser Wert bezieht sich auf die eingefrorene Fehlordnung, die Steigung bei tiefen Temperaturen ist auf thermische Schwingungen zurückzuführen und kann als Photon-Phonon-Streuung ausgewertet werden.Teilkristalline Polymere zeigen eine Temperaturabhängigkeit der Dichtefluktuation, die der von amorphen Polymeren ähnlich ist. Bei konstanter Temperatur ändert sich die Dichtefluktuation linear mit der Kristallinität.Naturkautschuk zeigt eine mit der Vernetzungsdichte ansteigende Dichtefluktuation, aus der man Information über die Dichteänderung in der Umgebung eines Netzpunktes und die Statistik der Netzpunktverteilung erhalten kann.

     

Photochemistry of artificial photosynthetic reaction centers in liquid crystals probed by multifrequency EPR (9.5 and 95 GHz)

Photoinduced charge separation and recombination in a carotenoid-porphyrin-fullerene triad C-P-C(60)(1) have been followed by multifrequency time-resolved electron paramagnetic resonance (TREPR) at intermediate magnetic field and microwave frequency (X-band) and high field and frequency (W-band). The electron-transfer process has been characterized in the different phases of two uniaxial liquid crystals (E-7 and ZLI-1167). The triad undergoes photoinduced electron transfer, with the generation of a long-lived charge-separated state, and charge recombination to the triplet state, localized in the carotene moiety, mimicking different aspects of the photosynthetic electron-transfer process. Both the photoinduced spin-correlated radical pair and the spin-polarized recombination triplet are observed starting from the crystalline up to the isotropic phase of the liquid crystals. The W-band TREPR radical pair spectrum has allowed unambiguous assignment of the spin-correlated radical pair spectrum to the charge-separated state C(.+)-P-C(60)(.-). The magnetic interaction parameters have been evaluated by simulation of the spin-polarized radical pair spectrum and the spin-selective recombination rates have been derived from the time dependence of the spectrum. The weak exchange interaction parameter (J = +0.5 +/- 0.2 G) provides a direct measure of the dominant electronic coupling matrix element V between the C(.+)-P-C(60)(.-) radical pair state and the recombination triplet state (3)C-P-C(60). The kinetic parameters have been analyzed in terms of the effect of the liquid crystal medium on the electron-transfer process. Effects of orientation of the molecular triad in the liquid crystal are evidenced by simulations of the carotenoid triplet state EPR spectra at different orientations of the external magnetic field with respect to the director of the mesophase. The order parameter (S = 0.5 +/- 0.05) has been evaluated.     

Untersuchungen an Kristallhydraten anorganischer Salze, 8. Mitt. Interpretation der Schwingungsspektren vonM(BF4)2·6H2O fürM=Fe2+, Co2+, Ni2+

The infrared and Raman spectra were recorded in the range 4000–160 cm^–1 forM(BF₄)₂·6 H₂O whereM=Fe²⁺, Co²⁺, Ni²⁺. The spectroscopic data support the X-ray structural data in showing that in the crystal hydrates studied two kinds of hydrogen bonds are present: H₂O...H₂O and OH₂... F₄B^–. The energies and molecular force constants (f _OH and fH₂O) andr _OH for OH₂...F₄B^– were calculated for the three crystal hydrates. It was found that the bond OH₂... F₄B^– is comparatively weak, with mean energy 3.7–3.3 kcal/mol. Two types of water molecule with different structures are existing as the first are participating in H₂O...H–O–H...F₄B^– and the second in BF₄ ^–...H–O–H...F₄B^–.