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.     

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.

     

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.

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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.

     

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^–.     

Low spin ferric hemoglobin complexes

A caloulation has been made of the energy eigenfunotions and eigenvalues of low spin ferric ion in complexes with a strong cubic crystal field including the effects of tetragonal and rhombic distortions and of spin-orbit coupling among the ground state components and with excited states. Using the resultant, spin-orbit coupled eigenfunotions as a basis set, the magnetic susceptibility, the components of magnetic field energy, and the lattice and valence contributions to an electric field gradient at the iron nucleus were all calculated as a function of rhombic, tetragonal, and spin-orbit coupling strength used as parameters: R, u and . All of the calculated results agree reasonable well with experiment for the values of parameters R=1000 cm^–1, u=2000 cm^–1 and the free ion value (=420 cm^–1. These values of parameters were selected for the excellent fit they gave of the calculated values of g _x, g_y and g _z compared with the experimental ones obtained from single crystal electron spin resonance of ferrihemoglobin azide. With them, a value of 2.29 Bohr magnetons was calculated for the effective magnetic moment compared to the experimental value of 2.35. The total field gradient calculated under the same conditions, predicts a nuclear quadrupole moment Q in the range of. 107 –127. Barns, which is smaller than the range predicted from the high spin ferric ion results. Reasons for this discrepancy are discussed.

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Zusammenfassung Ausgehend von einem starken kubischen Ligandenfeld und unter Berücksichtigung tetragonaler (R) und rhombischer (u) Verzerrung sowie der Spin-Bahn-Kopplung () werden Eigenfunktionen und Energien fur Low-Spin-Ferrihämoglobinkomplexe berechnet. Mit den Parametern R=1000 cm^–1, u=2000 cm^–1, =420 cm^–1 erhält man für Suszeptibilität, elektrischen Feldgradienten am Fe und g-Werte gute Übereinstimmung mit experimentellen Daten. Aus dem berechneten Feldgradienten folgt ein Quadrupolmoment des Fe⁵⁷ von 0.107–0.127 Barn, im Gegensatz zu den viel höheren Resultaten bei High-Spin-Fe(III)-Verbindungen; diese Diskrepanz wird diskutiert.

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Résumé Les fonctions propres et les énergies du complexe Ferrihémoglobine «low spin» sont calculées pour un fort champ de ligandes à symétrie cubique, en tenant compte des distortions tétragonale (R) et rhomboédrique (u), ainsi que du couplage spin-orbite (). Avec les parametres R=1000 cm^–1, u=2000 cm^–1, =420 cm^–1, on trouve pour la susceptibilité, le gradient du champ électrique à l'emplacement de Fe et le facteur g des valeurs en bon accord avec les données expérimentales. On déduit du gradient de champ calculé un moment quadrupolaire de Fe⁵⁷ de 0,107 à 0,127 Barn, en désaccord avec les résultats beaucoup plus élevés obtenus à partir des associations Fe (III) «high spin». Ce désaccord fait l'objet d'une discussion.

     

Morphologie und Wachstumskinetik von Crazes in amorphen Polymeren

Zusammenfassung Im vorfibrillaren Stadium besitzt die Crazematerie eine in Verformungsrichtung deformierte Netzwerkstruktur, die sich bei Polystyrol und Styrol-Acrylnitril-Copolymerisat elektronenoptisch an Oberflächenabdrücken sauerstoffionengeätzter Proben nachweisen läßt. Während die durchschnittlichen Globulitverformungen zumeist deutlich unterhalb von 50% liegen, werden partiell Spitzenwerte von bis zu 300% erreicht. Am Beispiel des Polystyrols verdeutlichen quantitative Strukturvergleiche mit warmgerecktem Material, daß die molekulare Beweglichkeit während des Crazewachstums und der Schulter-Hals-Verstreckung derjenigen entspricht, die für thermisch aktiviertes Material oberhalb der Glastemperatur charakteristisch ist.Mit 7 Abbildungen und 2 Tabellen     

Abbau von Palustrin zu (−)-Dihydropalustraminsäure ((2R, 6S, 1′S)-[6-(1′-Hydroxypropyl)-2-piperidyl]essigsäure) und Struktur von Palustrin und Palustridin. Mitteilung über Schachtelhalmalkaloide

Degradation of palustrin to (?)-dihydropalustramic acid ((2R,6S,1′S)-[6-(1′-hydroxypropyl)-2-piperidyl]acetic acid), and the structure of palustrin and palustridin The structure of the macrocyclic alkaloid palustrin is shown to be 1a . Its piperidine unit can be obtained as (?)-dihydropalustramic acid ( 6a ) by the following sequence of degradation reactions (Scheme 1): catalytic hydrogenation of 1a followed by methylation and Hofmann degradation provides the allyl base 4 . the regioselectivity of the Hofmann elimination is explained by intramolecular proton abstraction at C(3) by C(18)-O^?. Catalytic reduction of 4 and subsequent acidic hydrolysis yielded 6a and N, N-dimethylputrescine (?N,N-dimethyl-1,4-butanediamine; 7 ). Loss of the N-alkyl group in the formation of 6a occurs during the catalytic hydrogenation step. This interpretation is supported by the results of model experiments. The position of the double bond in 1a is deduced from the IR. spectrum of the bromo-δ-lactone 19 prepared by treatment of 1a with N-bromosuccinimide at pH 4 (Scheme 3). Some of our previously published results on the degradation of dihydropalustrin ( 2a ) are obviously at variance with the newly proposed structure for palustrin ( 1a ). They can easily be explained by assuming a partial hydrogenolysis of the C(17)-N(1) bond during the preparation of dihydropalustrin from palustrin. Periodate cleavage of dihydropalustramic acid methyl ester ( 6b ) liberates propionaldehyde, which can be trapped by working at pH 7.5 (Scheme 2); at lower pH values it condenses rapidly with the simultaneously generated 3,4,5,6-tetrahydropyridine derivative 15 . The structure of the condensation product is proposed to be 16 on the basis of the isolation of its hydrogenation product, an isomeric dihydropalustramic acid ( 17 ).     

Electrostatic representations of molecular groups

The treatment of electrostatic interactions between molecular groups is based on quantum mechanical electron density distributions. A general method is suggested using tesseral harmonic multipole expansions and representing each set of point multipoles by a cluster of discrete charges small with respect to atomic dimensions. The procedure is carried out for the amino group with an electron density derived from the wave function of ammonia. We evaluate the optical rotation of two aminopyrrolidones as a test case. Expansions are compared for several approximate wave functions for ammonia.