Derivation techniques on the Hermitian surface

We discuss derivation‐like techniques for transforming one locally Hermitian partial ovoid of the Hermitian surface H(3,q²) into another one. These techniques correspond to replacing a regulus by its opposite in some naturally associated projective 3‐space PG(3,q) over a square root subfield. © 2006 Wiley Periodicals, Inc. J Combin Designs 15: 478–486, 2007     

Anion substitution effects on structure and magnetism in the chromium chalcogenide Cr5Te8—Part I: Cluster glass behavior in trigonal Cr(1+x)Q2 with basic cell (Q=Te, Se; Te:Se=7:1)

The effect of substitution of the anion Te by Se in non-stoichiometric Cr₅Te₈ has been investigated with respect to its crystal structure, magnetic properties, and electronic structure. The compounds Cr_(1+x)Q₂ (Q=Te, Se; Te:Se=7:1; (1+x)=1.234(6), 1.264(6), 1.300(7)) were synthesized at elevated temperatures followed by quenching the samples to room temperature. The crystal structures have been refined with X-ray powder diffraction data with the Rietveld method in the trigonal space group with lattice parameters a=3.8651(1)-3.8831(1) Å and c=5.9917(2)-6.0528(2) Å. The structure is related to the NiAs structure with full and deficient metal layers stacking alternatively along the c-axis. The irreversibility in the field-cooled/zero-field-cooled magnetization suggests that the substitution effects of one Te by one Se is strong enough to cause cluster-glass behavior, from ferromagnetic Cr₅Te₈ to cluster-glass Cr_(1+x)Q₂. Non-saturation magnetizations at 5.5 T and the magnetic relaxation results further support the existence of cluster-glass behavior. Accompanying SPR-KKR (spin-polarized relativistic Korringa-Kohn-Rostoker) band structure calculations strongly support the observation that the Cr(1) sites are preferentially occupied by Cr atoms and predict that these compounds are metallic. Results for the spin-resolved DOS and magnetic moments on each crystallographic sites are presented.     

Über einige Eigenschaften von Zinkphosphiten mit Berücksichtigung ihrer Wasserstoffbrückenbindung

Zinc phosphites ZnPHO₃·2.5 H₂O, Zn₂H₂P₃H₃O₉·H₂O, Zn₃H₄P₅H₅O₁₅·1.5 H₂O, ZnH₂H₂P₂H₂O₆ have been studied at higher temperatures and by X-rays and molecular spectroscopy. Hydrates ZnPHO₃·2.5 H₂O and Zn₂H₂P₃H₃O₉·H₂O, when heated, yield an anhydrous salt. Thermal decomposition of dihydrogen triorthophosphite and tetrahydrogen pentaorthophosphite leads, before oxidation of the anion, to a mixture of zinc phosphite ZnPHO₃ and dihydrogen diorthophosphite ZnH₂P₂H₂O₆ and then after loss of water of constitution dihydrogen diorthophosphite converts to zinc diphosphite ZnP₂H₂O₅. The results of the thermal decomposition study were confirmed by X-ray investigation. Anhydrous zinc dihydrogen triorthophosphite Zn₂H₂P₃H₃O₉ and zinc diphosphite ZnP₂H₂O₅ were hitherto unknown. Infrared spectra confirmed the existence of hydrogen bonding in all the phosphites studied and in the case of zinc phosphite ZnPHO₃·2.5 H₂O exhibited a symmetry decrease of the anion PHO₃ ^2– from the point group C_3v to C_s. In the crystal lattice of ZnPHO₃·2.5 H₂O hydrogen bonding by water molecules participates, with polyorthophosphites hydrogen bonding shares in the production of anions and in the case of their hydrates there is in addition hydrogen bonding by water molecules.

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Mit 3 Abbildungen     

On some contact problems for composite half-spaces PMM vol. 31, no. 6, 1967, pp. 1001–1008

Solutions are presented herein of some contact problems connected with the torsion of a composite half-space. In the general case the problem of the torsion of a composite elastic half-space is examined by means of the rotation of a stiff finite cylinder welded into a vertical recess of this half-space. Moreover, the following particular problems on the torsion of such a half-space are considered.

1. 1) A composite half-space with a vertical elastic infinite core, twisted by means of the rotation of a stiff stamp affixed to the upper endplate of the elastic core.

2. 2) A half-space with a vertical cylindrical infinite hole, twisted by means of the rotation of a stiff finite cylinder welded into the upper part of this hole.

In the general case the solution of the problem reduces to the solution of an integral equation of the second kind on a half-line. The question of the solvability of this fundamental integral equation is investigated, and it is shown that its solution may be constructed by successive approximations.

Let us note that the problem of the torsion of a homogeneous half space and of an elastic layer by means of rotation of a stiff stamp has been considered by Rostovtsev [1], Reissner and Sagoci [2], Ufliand [3], Florence [4], Grilitskii [5] and others.

The problem of the torsion of a circular cylindrical rod and the half-space welded to it which are subject to a torque applied to the free endface of the rod has been considered by Grilitskii and Kizyma[6].

The torsion of an elastic half-space with a vertical cylindrical inclusion of some other material by the rotation of a stiff stamp on the surface of this half-space has been considered in [7], wherein it has been assumed that the stamp is symmetrically disposed relative to the axis of the inclusion and lies simultaneously on both materials.     

A Bruen chain forq=19

The one-to-one correspondence between the class of two-dimensional translation planes of orderq ² and the collection of spreads ofPG(3,q) has long provided a natural context for describing new planes. The method often used for constructing interesting spreads is to start with a regular spread, corresponding to a desarguesian plane, and then replace some nice subset of lines by another partial spread covering the same set of points. Indeed the first approach was replacing the lines of a regulus by the lines of its opposite regulus, or doing this process for a set of disjoint reguli. Nontrivial generalizations of this idea include thechains of Bruen and thenests of Baker and Ebert. In this paper we construct a replaceable subset of a regular spread ofPG (3, 19) which is the union of 11 reguli double covering the lines in their union, hence is a chain in the terminology of Bruen or a 11-nest in the Baker-Ebert terminology.     

Polymer diffusion in quenched disorder: A renormalization group approach

We study the diffusion of polymers through quenched short-range correlated random media by renormalization group (RG) methods, which allow us to derive universal predictions in the limit of long chains and weak disorder. We take local quenched random potentials with second momentv and the excluded-volume interactionu of the chain segments into account. We show that our model contains the relevant features of polymer diffusion in random media in the RG sense if we focus on the local entropic effects rather than on the topological constraints of a quenched random medium. The dynamic generating functional and the general structure of its perturbation expansion inu andv are derived. The distribution functions for the center-of-mass motion and the internal modes of one chain and for the correlation of the center of mass motions of two chains are calculated to one-loop order. The results allow for sufficient cross-checks to have trust in the one-loop renormalizability of the model. The general structure as well as the one-loop results of the integrated RG flow of the parameters are discussed. Universal results can be found for the effective static interactionwu–v0 and for small effective disorder coupling on the intermediate length scalel. As a first physical prediction from our analysis, we determine the general nonlinear scaling form of the chain diffusion constant and evaluate it explicitly as for .     

Crystal Structures of Hydrochlorides of 2,3-Pentamethylene-3, 4-dihydroquinazolin-4-one

The crystal structures of hydrate (1) and anhydrate (2) forms of 2,3-pentamethylene-3,4-dihydroquinazolin-4-one hydrochloride have been determined by X-ray structure analysis. Crystal data of 1 are 2(C₁₃H₁₄N₂O)*3(HCl)*4.5 (H₂O), triclinic P?1, Z=2, a=8.004(5), b=13.129(7), c=15.725(7) Å, α=106.45(4), β=92.61(4), γ=97.98(5), R=0.0652 and 2 are C₁₃H₁₄N₂O*HCl, monoclinic C2/c, Z=8, a=21.360(4), b=5.954(1), c=21.263(4), β=117.89(3), R=0.0556. The crystal of the hydrate form 1is unstable. This form collapses easily with evaporation of H₂O and part of HCl molecules from crystals. By recrystallizing destroyed form has been obtained stable crystal form 2.     

Conformational Studies on Polytripeptides as a Model of Collagen

To study the role of glycine residues in stabilizing the collagen triple helix, the glycine residues in the polytripeptide (Pro-Ala-Gly)_n were partially replaced by alanine. The proline content was kept constant. The stability of the helical conformation of these polypeptides was studied by IR- and X-ray measurements in the solid state and by ORD, CD and viscometry in solution. The renaturation was followed as a function of time. All the polytripeptides studied, with the exception of (-Pro-Ala-Ala-)_n attained the polyproline II conformation. However the stability decreased with increasing alanine content. Obviously the molecules of (-Pro-Ala-Gly-) are highly associated by intermolecular hydrogen bonds and one may therefore suppose that a triple-stranded helix aggregation occurs. The results of the refolding process show that the stability of the helices seems to also affect the refolding rate in terms of the optical rotation, Two transitions appeared: the first one is responsible for a rapid reversible change in conformation and the second one for a further slow and irreversible change in the hydrodynamic shape. The latter seems to be due to the partial helical nature, leading to higher chain mobility.     

Über den Einfluß von Temperatur und Fremdionen auf Eigenschaften und Bau der Natriumwasserglaslösungen

The Influence of Temperature and Impurities Addition on the Properties and the Constitution of Sodium Water Glass Solutions Sodium water glass (NaWG-)solutions of constant composition (SiO₂/Na₂O = 3,3; C_SiO2 = 6,2 M) and different concentration of impurities (Fe, Al, Ti, Cu, chloride, sulfate) were investigated in dependence on temperature by means of the dye absorption method, ¹H- and ²³Na-NMR spectroscopy. It is shown, that the differences in the dye absorption spectra of normalized technical NaWG-solutions, mainly depend on the Fe-concentration in the solutions and their thermal history. From the results follow a crosslinking of polymeric silicate species by Fe? O? Si bonds and/or hydrogen bridges and a fully or partially degradation of these bonds at higher temperatures (150°C).