Homogeneous algebraic varieties defined by Jordan pairs

Every Jordan pair defines an algebraic varietyX containing as a dense open subset.X is projective (affine) if and only if is separable (radical). The Picard group ofX is generated by the irreducible factors of the generic norm of . If is separable then the automorphism group ofX is the projective group of .     

The relation between the molecular weight and intrinsic viscosity of polymethyl acrylate

Summary A series of unfractionated and fractionated samples of polymethyl acrylate of different low molecular weights have been prepared by homogeneous solution. polymerization in dimethyl formamide in presence of , '-azo-(-cyano-n-valeric acid) as initiator under a variety of conditions. The number-average molecular weights have been determined by end-group titrations and vapour pressure osmometry. The following []-M relationships for polymethyl acrylate have been obtained.[] = 33.5 x 10^–5M^0.63 for unfractionated samples in benzene at 25 °C. [] = 3.89 x 10^–5M^0.843 for fractionated samples in benzene at 35 °C.With 2 tables     

Strukturviskosität von verdünnten Lösungen von Biopolymeren

The importance of the rheological behaviour of solutions of macromolecules is briefly evaluated. The viscosity of the solutions depends on concentration, shear rate and time of shear, this relation being determined by the structure of the dissolved molecules. In dilute solutions shear dependence of viscosity is very frequently caused by the preferential orientation of anisotropic molecules. In such a case the particle dimensions can be calculated from the true limiting viscosity number, an anisotropy factor, the rotational diffusion constant and the effective particle density. These numbers can be derived from the flow curve, which has been extrapolated to zero concentration. It is necessary to measure the flow curve at shear gradients, which are sufficiently low to allow for an extrapolation to vanishing shear rate. By comparing the experimental flow curve with a choice of theoretical ones, the rotational diffusion constant and the anisotropy factor (axial ratio) can be found. From the limiting viscosity number and the axial ratio, the particle density can be calculated.     

Komplexe von 2,6-Dimethylpyridin-1-oxid mit Lanthanidjodiden

Complexes of 2,6-dimethylpyridine 1-oxide with lanthanide iodides of the formulaeLn(2,6-LTNO)₅I₃ whereLn=La, Tb and Yb,Ln(2,6-LTNO)₄I₃ whereLn=Pr and Nd and Er(2,6-LTNO)_4.5I₃ have been prepared and characterised by chemical analysis, infrared and conductance studies. Infrared and conductance data have been interpreted in terms of dimeric (or polymeric) structures involving bridging amine oxide groups.

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Mit 2 Abbildungen     

Über die Synthese von 5-(o-Trifluormethylphenyl)-1H-thieno[3,4—e]-1,4-diazepin-2(3H)-onen

The synthesis of 5-(o-trifluoromethylphenyl)-1H-thieno-[3,4-e]1,4-diazepin-2(3H)-one (7) and its nitration and chlorination in pos. 8 are described.     

Berechnung von mittleren Schwingungsamplituden einiger tetraedrischer Moleküle und Ionen nach der Methode der charakteristischen Schwingungen

Mean amplitudes of vibration of a series of tetrahedralXY ₄ molecules and ions (hydrides, halides, oxides and oxoanions) have been calculated using the “Method of the Characteristic Vibrations” ofA. Müller. The results indicate that this method leads to very good values for most of the investigated species, and especially in the cases of highM _X/M_Y mass ratio.     

Untersuchung der Temperaturabhängigkeit der kernmagnetischen Spin-Gitter-Relaxation an Dimethylsiloxanen

Zusammenfassung Es wurden die longitudinalen Protonen-RelaxationszeitenT ₁ der beiden Systeme Hexamethyldisiloxan und Dekamethylcyclopentasiloxan im Temperaturbereich von 20 bis 300 K untersucht. Das Relaxationsverhalten des Hexamethyldisiloxans wird in diesem Temperaturbereich durch drei Bewegungsmechanismen bestimmt: die Methylgruppenrotation um die C₃-Achse, die Segmentrotation um die Si-O-Bindung und einen noch nicht näher identifizierten Bewegungsprozeß, der zu einer sprunghaften Änderung der Spin-Gitter-Relaxationszeit führt. Diese Bewegungsmechanismen werden mit Ausnahme der Segmentrotation auch beim Dekamethylcyclopentasiloxan gefunden. Es wird eine Gegenüberstellung der experimentellen Daten der beiden hier untersuchten Systeme und eines polymeren Dimethylsiloxans gegeben. Dabei ist als interessantes Ergebnis hervorzuheben, daß die Methylgruppenrotation im Hexamethyldisiloxan die stärkste Behinderung erfährt.

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Summary In this experiment the longitudinal proton relaxation timesT ₁ of hexamethyldisiloxane and decamethylcyclopen-tasiloxane were measured in the temperature range from about 20 K up to 300 K. Three motional mechanisms, the methyl group rotation about the C₃-axis, the segmental rotation about the Si-O-bond and a motional process, not yet identified, which leads to a discontinuity ofT ₁ have been found to be responsible for the spin-lattice relaxation of hexamethyldisiloxane in this temperature range. With the exception of segmental rotation these motional processes also determine the spin-lattice relaxation of decamethylcyclopentasiloxane. A comparison of experimental data of the two systems actually investigated and a polymeric dimethylsiloxane is presented, showing the methyl group rotation being most strongly hindered in the case of hexamethyldisiloxane.

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Mit 4 Abbildungen und 1 Tabelle     

Photo-induced cellulose radicals capable of initiating graft copolymerization

The decay behavior of cellulose radicals produced by photo-irradiation at room temperature and the characteristics of photo-irradiated cellulose samples to initiate graft copolymerization of methyl methacrylate (MMA) were investigated. ESR spectra of such untreated, swollen, oximated, and ferric ion-sensitized samples irradiated at room temperature were constructed mainly of a single absorption line with a line width of 20 to 22 gauss and a g value of 2.003, and it is surely conceivable that the radicals showing a singlet spectrum should agree with those of alkoxy end produced at either the C₁ or C₄ position of the glucose unit by the scission of glucosidic bonds. The decay of radicals was accelerated by contact of various solvents with the samples, the activity decreasing in the order, water ≈ methanol ? acetone > dioxane. On the other hand, the decay of radicals by vinyl monomers became smaller in the order, methacrylic acid > MMA ≈ styrene. Graft copolymerization of MMA by a photo-irradiated sample was effectively initiated with the use of a certain amount of water or methanol, but not with acetone and dioxane. As no initiation can occur with the unirradiated sample, it is concluded that the initiation of graft copolymerization on the photo-irradiated sample is attributable to cellulose radicals showing a singlet spectrum which are formed in photo-irradiation at room temperature.     

Gleichverteilung und Quadratwurzelschnecke

A new proof of a theorem of W. Neiss is given that the rays of the Quadratwurzelschnecke are uniformly distributed mod 2 . The exact order of the discrepancy of the sequence is determined. Multidimensional generalizations of this sequence are also considered. It is shown that the Quadratwurzelschnecke is something like a roulette.

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Herrn Prof. R. M. Redheffer in Freundschaft zum 60. Geburtstag gewidmet     

Der quadratfreie Kern der Eulerschen φ-Funktion

It is shown by a simple induction that any square-free natural number is the square-free kernel of Euler's -function of infinitely many natural numbers. Furthermore every square-free natural number >1 is the square-free kernel of Euler's -function of infinitely many square-numbers.