A special anisotropic model of the universe (II)

By means of exponential laws we show a Bianchi Type I model of the universe where we define overall deceleration and Hubble's parameters that have constant values. We employ a convenient relation for defining the radius of the universe. Pressure and density have constant values, too.     

Gasdynamische Untersuchung des Jouleschen Überströmversuches

Zusammenfassung Es wird die zeitabhängige Strömung beim Ausgleichsvorgang zwischen zwei endlichen Behältern untersucht. Den Überlegungen wird eine eindimensionale, reibungsfreie und quasistationäre Strömung zugrunde gelegt. Während bei überkritischer Strömung eine analytische Lösung möglich ist, wird das Problem bei unterkritischer Strömung numerisch gelöst.Dem Druckausgleich zwischen den beiden Behältern folgt ein isobarer Wärme- und Massenaustausch, bis sich das thermodynamische Gleichgewicht eingestellt hat.

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Gasdynamical investigation of Joule's overflow experiment

The time-dependent flow of an exchange process between two big insulated tanks is considered. The problem is treated on the basis of a one-dimensional, inviscid and quasi-steady flow. An analytical solution is obtained for supercritical flow, while for subcritical flow the problem is solved numerically.After the pressure-equilibrium between the two-tanks an isobar heat and mass exchange follows, until the thermodynamic equilibrium is reached.

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Formelzeichen a Schallgechwindigkeit - A engster Querschnitt - c Geschwindigkeit - c _p spezifische Wärme bei konstantem Druck - c _v spezifische Wärme bei konstantem Volumen - e innere Energie - i Enthalpie - m Masse - M Machzahl - p Druck - spezielle Gaskonstante - s Stromlinie, spezifische Entropie - t dimensionsbehaftete Zeit - T Temperatur - V Volumen - Konstante - Abkürzung - Volumenverhältnis - Verhältnis der spezifischen Wärmen - Dichte - dimensionslose Zeit Indizes 0 Zustand zur Zeitt=0 - 1 Zustand im Überdruckbehälter - 2 Zustand im Überströmbehälter - * Zustand im engsten Querschnitt - K kritisch - M Zustand bei Druckausgleich - E Endzustand bei Temperaturausgleich Herrn Prof. Dr. B. Schmidt in Dankbarkeit zum 60. Geburtstag gewidmet     

Eine direkt formulierte lineare Theorie für viskoelastische Platten und Schalen

Übersicht Eine Möglichkeit der Entwicklung einer allgemeinen Theorie für Platten und Schalen besteht in der Modellierung des Flächentragwerks durch ein zweidimensionales deformierbares Kontimmm und der direkten Ableitung der kinematischen Beziehungen, der Bewegungsgleichungen und der konstitutiveu Gleichungen. Eine so erhaltene Theorie ist mathematisch und physikalisch widerspruchsfrei, jedoch ist es für ihre Anwendung notwendig, die sogenannten Ersatzeigenschaften zu ermitteln. Im Beitrag wird eine geometrisch und physikalisch lineare Theorie behandelt. Jeder Punkt des Kontinuums ist ein infinitesimal kleiner Starrkörper mit nur 5 Freiheitsgraden (3 Translationen, 2 Rotationen). Bei Annahme dieser Einschränkungen gelingt es, eine Theorie direkt abzuleiten, wobei alle Ersatzeigenschaften des Flächentragwerks bestimmt werden können. Im Beitrag werden die Möglichkeiten der allgemeinen Theorie am Beispiel isotropen viskoelastischen Materials mit über die Dicke veränderlichen Eigenschaften gezeigt. Die Theorie schließt die Betrachtung mehrschichtiger Flächentragwerke ein.

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A directly formulated linear theory of viscoelastic plates and shells

Summary One kind to develop a general theory for plates and shells is the modelling of the structure as a two-dimensional deformable continuum and the direct approach to the kinematical relations, equations of motion and constitutive equations. Such a theory is physically and mathematically correct. For the application of such directly formulated theories it is nessecery to identify the so-called effective properties. In the paper the theory is formulated for geometrical and physical linearity. Each point of the continuum is an infinitesimal small rigid body with only 5 degrees of freedom (3 translations, 2 rotations). For such a kinematical assumption it is possible to develop a direct theory and to determinate all effective properties of the structure. The paper demonstrates the possibilities of the general theory for an isotropic viscoelastic plate with material properties varying over the thickness. The theory includes also the analysis of multilayered plates and shells.

     

Plane contact problems for a periodic two-layered elastic composite

Summary This paper deals with the two-dimensional static punch problems in the presence of friction for a periodically layered half-space. Within the framework of the homogenized model of linear elasticity with microlocal parameters [8–11] the exact solutions of the considered problems are obtained. The case of the indentation of the composite body by a rigid rectangular punch has been discussed in detail.

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Ebene Kontaktprobleme für ein periodisches elastisches Zweischichten-Komposit

Übersicht In dieser Arbeit wird das zweidimensionale statische Stempelproblem mit Reibung für einen periodisch geschichteten Halbraum betrachtet. Im Rahmen eines Homogenisierungsmodells der linearen Elastizitätstheorie mit mikropolaren Parametern werden die exakten Lösungen der betrachteten Probleme gewonnen. Im Detail wird das Eindringen eines rechteckigen starren Stempels behandelt.

     

4-Amino-imidazole durchThorpe-Cyclisierung

The alkylation of arylaminomethylenecyanamides1 or cyano-imidothiocarbamates2 with -halogen carbonyl compounds followed by base catalysed cyclization yields substituted 4-amino-imidazoles4. Imidazo[4,5-d]pyrimidones5, 6 and imidazo[4,5-b]pyridines7 can be obtained from4.     

The electrocapillarity of polyacrylates

Summary The electrocapillary properties of polyacrylic acid have been studied by two methods. Exploratory measurements have been made of the effect of the polymer on the differential capacity of a mercury drop in 0.1 m sodium perchlorate. They showed that the polymer was strongly adsorbed over a wide range of potentials but that it did not appear to form a monolayer. The surface excess of polymer obtained from drop weight data showed a maximum at very low concentrations and then a decline at higher concentrations. The bulk of the work was carried out by making surface tension measurements, using a sessile mercury drop, in solutions of a fraction of polyacrylic acid (mol. wt. 7.02×10⁴) in potassium chloride at 0.01, 0.1, 0.2, and 0.5 m at 25°C.The data have been used to evaluate the surface excesses of the polymer and of the inorganic ions. The distribution of K⁺ and Cl^– in the electrical double layer and the contact adsorption of Cl^– on the mercury were very little affected by the presence of the polymer. The surface excess of polymer was always found to be greatest at low concentrations, to decrease steeply at first as the concentration was increased and then to decrease more slowly at higher concentrations.Possible explanations of this behaviour are discussed and it is concluded that the rapid decrease is a consequence of molecular weight dispersion and the stronger adsorption of high molecular weight polymer. The slow decrease in surface excess at higher concentrations may be a result of configurational changes of the polymer molecules.Surface pressure data show that, despite this decrease in the surface excess, the surface coverage reaches a high level at very low polymer concentrations and then continues to increase slowly as the concentration of polymer is increased. This apparent contradiction is due to changes in configuration of the adsorbed polymer molecules. At higher bulk concentrations the chain configurations are more compact and each adsorbed molecule makes more contacts with and so occupies a greater area of the mercury surface than at low concentrations.The conclusion is reached that the surface excess of polymer is mostly contained in a layer probably more than 1000 Å thick. It consists of a concentrated and entangled mass of polymer chains. Relatively few of these chains are in contact with the mercury at any istant. The concentration in this surface layer decreases steadily with increasing distance from the mercury surface and it merges without discontinuity into the bulk solution.With 10 figures in 22 details     

Stereochemie von Metallocenen, 40. Mitt.

Starting from optically active methylferrocene-- and--carboxylic acids (1 a and1 b) of known absolute configuration and enantiomeric purity about 15 chiral ferrocenes (of each isomeric series— and ) were obtained by suitable ligand transformations. Thereby (almost) all possible chiral combinations of the ligands CH₃, COOH (COO^–), COOCH₃, CN and NH₂ (NH₃ ⁺) were accessible which are necessary for a potential test of approximations of chirality functions for compounds with basic symmetry C_5v. The chiroptical properties of these disubstituted ferrocenes are recorded.Preliminary tests using a shortened Ansatz revealed large discrepancies between calculated () and found [M]_D-values. Possible reasons for this failure are discussed.

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61. Mitt. über Ferrocenderivate

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39. Mitt.:A. Meyer, H. Neudeck undK. Schlögl, Chem. Ber.110, 1403 (1977).

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60. Mitt.:V. Rapi, K. Schlögl undB. Steinitz, J. Organometal. Chem.94, 87 (1975).     

Neue Wege der Analytik durch Kombination der direkten quantitativen Dünnschicht-Chromatographie mit elektronischer Datenverarbeitung

A computer program for direct evaluation of thin-layer chromatograms, which already was described earlier [3] has been tested with a laboratory and some technical formulations of a pesticide. Results have been compared with those obtained by two conventional methods. Mean relative standard deviation calculated from results compiled by electronic data processing (method A) is about 6%, compared to 10% received by graphic method (method C) which is employed by most investigators. In addition, overall time of analysis is 34% higher if graphic method is used. Method A saves time and expense especially in routine analysis because working of the process is easier and may be performed even by assistent personal. The proposed method is suitable for the determination of different active ingredients and impurities even in difficult technical products.