Das nichtkooperative Nichtnullsummen-Zwei-Personen-Spiel

Zusammenfassung Als Grundlage für die Theorie des Nichtnullsummen-Zwei-Personen-Spiels werden die Begriffe Gleichgewichtspunkt, Sattelpunkt, präventive und defensive Strategie, Felddominanz, Strategiendominanz und mehrere Unterbegriffe davon definiert. Mit ihrer Hilfe wird eine Anzahl von Sätzen bewiesen, die unmittelbar zu einer Lösung dieses Spieltyps führen: Es zeigt sich, daß es zwei Klassen von Nichtnullsummenspielen gibt: solche mit spielbedingten und solche mit persönlichkeitsbestimmten Lösungen. Erstere umfassen alle Spiele, die einen einzigen, nichtdominierten Gleichgewichtspunkt besitzen. Dieser ist die Lösung. Bei allen übrigen Spielen ist die Persönlichkeit der Spieler sozusagen selbst Teil des Spiels. Auch hierfür werden Lösungen angegeben.

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Summary The following terms being the basis of the two-person non-zero-sum games will be defined: equilibrium point, saddle point, preventive and defensive strategy, field dominance, strategy dominance, and several other sub-terms. Using these terms a number of theorems leading directly to a solution of this type of games will be proved. It is shown that there are two types of non-zero-sum games: one type with game-determined solutions and another one with personality-determined solutions. The first one includes all games having a single non-dominated equilibrium point, which is the solution. In all other games the player's intention must be considered as part of the game. Here as well solutions are given.

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Der Grundgedanke wurde von Professor Dr.W. Krelle auf der Jahrestagung der DGU vom 9. bis 11. September 1963 in Braunschweig vorgetragen und anschließend in Zusammenarbeit mit Diplom-MathematikerDieter Coenen in eine druckreife Form gebracht.     

Numerical description of axisymmetric blue whirls over liquid-fuel pools

This numerical investigation is focused on determining the structures of blue whirls, recently found to occur in laboratory investigations of fire whirls when the circulation becomes sufficiently large to produce a vortex breakdown that drastically shortens the fire whirl and correspondingly reduces residence times, so that the yellow flames turn blue. The computations address axisymmetric configurations for round pools of liquid fuels flush with and at the center of a larger solid horizontal disc, at the outer edge of which vanes of adjustable angles cause the entrained air to enter with a controllable azimuthal component of velocity. The nondimensionlized conservation equations employed include realistic Lewis numbers with temperature-dependent transport coefficients and a one-step chemical-kinetic approximation that correctly reproduces laminar burning velocities. Buoyancy and radiant energy transport from the flames to the liquid surface are both taken into account, the latter being found to be essential for the blue whirl. Along with the vaporization-equilibrium and energy-conservation boundary conditions at the fuel surface, inflow boundary conditions are provided by a recently developed solution for the boundary-layer flow over the solid disc, while zero-gradient outflow conditions are applied above the whirl. Controlling nondimensional parameters, besides Reynolds, Damköhler, and Froude numbers, are a ratio of radiant to convective energy flux and a ratio of azimuthal to inward radial flow velocity in the boundary layer at the edge of the disc. The computed conditions for the onset of the blue whirl, as well as the computed structure of the whirl itself, bear close resemblance to what was found experimentally.     

Separation of radioarsenic from irradiated germanium oxide targets for the production of <Superscript>71</Superscript>As and <Superscript>72</Superscript>As

A method for the separation of no-carrier-added arsenic radionuclides from the bulk amount of proton-irradiated GeO₂ targets as well as from coproduced radiogallium was developed. The radionuclides ⁶⁹Ge and ⁶⁷Ga produced during irradiation of GeO₂ were used as tracers for Ge and Ga in the experiments. After dissolution of the target the ratio of As(III) to As(V) was determined via thin layer chromatography (TLC). The extraction of radioarsenic by different organic solvents from acid solutions containing alkali iodide was studied and optimized. The influence of the concentration of various acids (HCl, HClO₄, HNO₃, HBr, H₂SO₄) as well as of KI was studied using cyclohexane. The optimum separation of radioarsenic was achieved using cyclohexane with 4.75 M HCl and 0.5 M KI and its back-extraction with a 0.1% H₂O₂ solution. The separation leads to high purity radioarsenic containing no radiogallium and <0.001% [⁶⁹Ge]Ge. The overall radiochemical yield is 93 ± 3%. The practical application of the optimized procedure in the production of ⁷¹As and ⁷²As is demonstrated and batch yields achieved were in the range of 75–84% of the theoretical values.     

Low temperature lattice conductivity of some two-dimensional magnetic crystals

The low temperature lattice conductivity of the two-dimensional Heisenberg ferromagnets (C_nH_2n+1NH₃)₂CuCl₄, n = 1, 2 have been measured in high magnetic fields up to 6.5T. From these measurements information is obtained about the dimensionality of the acoustical phonon spectrum. An estimate of the phonons mean free path and of the dislocation density of the crystals is made.     

Nonspecific protein adsorption at the single molecule level studied by atomic force microscopy

Liquid tapping atomic force microscopy was used to study the nonspecific adsorption of horse spleen ferritin at a bare gold surface at single molecule resolution. The majority of ferritin molecules adsorbed irreversible on gold surfaces in accordance with the random sequential adsorption (RSA) mechanism frequently used to describe irreversible adsorption processes. However, the time-resolved data also reveal events that go beyond the RSA model, i.e., lateral mobility and fragility of some molecules, resulting in desorption, chain formation, and subunit dissociation. Scanning effects of the AFM tip were observed, resulting in diminished protein coverage in the scanned area.     

Influences of stoichiometry on steadily propagating triple flames in counterflows

Most studies of triple flames in counterflowing streams of fuel and oxidizer have been focused on the symmetric problem in which the stoichiometric mixture fraction is 1/2. There then exist lean and rich premixed flames of roughly equal strengths, with a diffusion flame trailing behind from the stoichiometric point at which they meet. In the majority of realistic situations, however, the stoichiometric mixture fraction departs appreciably from unity, typically being quite small. With the objective of clarifying the influences of stoichiometry, attention is focused on one of the simplest possible models, addressed here mainly by numerical integration. When the stoichiometric mixture fraction departs appreciably from 1/2, one of the premixed wings is found to be dominant to such an extent that the diffusion flame and the other premixed flame are very weak by comparison. These curved, partially premixed flames are expected to be relevant in realistic configurations. In addition, a simple kinematic balance is shown to predict the shape of the front and the propagation velocity reasonably well in the limit of low stretch and low curvature.     

Kristallisationskinetik von Natrinmdisilikat

Zusammenfassung An Natriumdisilikat wurde die integrale isotherme Kristallisation bei verschiedenen Temperaturen zwischen 650 und 900 °C als Funktion der Zeit durch die ?nderung des spezifischen Volumens verfolgt. Das Volumen wurde durch Auftrieb der Schmelze in Luft gemessen. Auf die Me?werte wurden die Ans?tze nach Volmer und Frenkel angewandt. Die Kinetik konnte durch die Avrami-Gleichungen beschrieben werden. Aus den Messungen ging die eindeutige Unterscheidung zwischen Temperaturgebieten mit „thermischer” und solchen mit „athermischer” Keimbildung hervor. (Unter „athermischer” Keimbildung ist zu verstehen, da? das Kristallwachstum geschwindigkeitsbestimmend ist. Die eigentliche Keimbildung ist stets „thermisch”.) „Thermische” Keimbildung lag vor in dem Temperaturgebiet von T _S = 884 °C bis etwa 840 °C. In diesem Gebiet ging der Kristallisation eine Volumenkontraktion mit nachfolgender Aufweitung vorauf, die mit einer Mikroentmischung erkl?rt wird. Nach Dietzel besteht diese Mikroentmischung darin, da? neben disilikatischen auch metasilikatische und allseitig vernetzte SiO₄-Gruppen vorliegen. In der Volumentemperaturkurve der kristallinen Substanz ist das Temperaturgebiet der „thermischen” Keimbildung gekennzeichnet durch ausgepr?gte statistische Schwankungen, darin sichtbar, da? der Schmelzpunkt sich schon etwa 50 °C unterhalb anmeldet. In dem Gebiet der „athermischen” Keimbildung, das sich von 840 °C bis etwa 680 °C erstreckt, galt der Zusammenhang zwischen Keimbildungsgeschwindigkeit und Unterkühlungsgrad nach Volmer und Frenkel. In diesem Gebiet war keine Volumenkontraktion vor der Kristallisation zu beobachten. Es wird gefolgert, da? die Schmelze hier homogen ist, soweit mit der beschriebenen Me?methode erfa?bar. Inhomogenit?ten, die anfangs existieren, werden in so kurzen Zeiten aufgel?st, da? sie nicht mehr zu messen sind. Bei dem untersuchten System kann man für das Kristallwachstum die gleichen thermischen und kinetischen Konstanten annehmen wie für die Keimbildung. Mit 7 Abbildungen und 2 Tabellen Auszugsweise vorgetragen auf der Sitzung des FA I der DGG am 30. 10. 1962 in Frankfurt.     

Measurements on the fermi surface of PdSb

Measurements of the de Haas-van Alphen effect in the metallic compound PdSb (NiAs structure) have been performed. By means of a Fourier expansion analysis we have been able to ascribe most of the frequency branches to three sheets of the Fermi surface. These show a partial resemblance to results on the isomorphic and isoelectronic compound AuSn of Edwardset al.     

Kinetics and mechanism of the hydrogenation of cyclohexene

The rate of hydrogenation of cyclohexene, catalyzed by CoH₃(PPh₃)₃, has been measured under various conditions and, based on these data, a mechanism has been postulated. For the individual steps of the mechanism enthalpy and entropy differences have been determined. The interpretation of these parameters gives evidence for a more detailed mechanism, in which solvent molecules play an important part as “stand-in” for ligands, dissociated from the catalyst species.