A Representation of a Point Symmetric 2-Structure by a Quasi-Domain

In a symmetric 2-structure ${\Sigma =(P,\mathfrak{G}_1,\mathfrak{G}_2,\mathfrak{K})}$ we fix a chain ${E \in \mathfrak{K}}$ and define on E two binary operations “+” and “·”. Then (E,+) is a K-loop and for ${E^* := E {\setminus}\{o\}}$ , (E ^*,·) is a Bol loop. If ${\Sigma}$ is even point symmetric then (E,+ ,·) is a quasidomain and one has the set ${Aff(E,+,\cdot) := \{a^+\circ b^\bullet | a \in E, b \in E^*\}}$ of affine permutations. From Aff(E, +, ·) one can reproduce via a “chain derivation” the point symmetric 2-structure ${\Sigma}$ .     

Symmetric 2-Structures,a Classification

We classify symmetric 2-structures ${(P, \mathfrak{G}_1, \mathfrak{G}_2, \mathfrak{K})}$ , i.e. chain structures which correspond to sharply 2-transitive permutation sets (E, Σ) satisfying the condition: “ ${(*) \, \, \forall \sigma, \tau \in \Sigma : \sigma \circ \tau^{-1} \circ \sigma \in \Sigma}$ ”. To every chain ${K \in \mathfrak{K}}$ one can associate a reflection ${\widetilde{K}}$ in K. Then (*) is equivalent to “ ${(**) \, \, \forall K \in \mathfrak{K} : \widetilde{K}(\mathfrak{K}) = \mathfrak{K}}$ ” and one can define an orthogonality “ ${\perp}$ ” for chains ${K, L \in \mathfrak{K}}$ by “ ${K \perp L \Leftrightarrow K \neq L \wedge \widetilde{K}(L) = L}$ ”. The classification is based on the cardinality of the set of chains which are orthogonal to a chain K and passing through a point p of K. For one of these classes (called point symmetric 2-structures) we proof that in each point there is a reflection and that the set of point reflections forms a regular involutory permutation set.     

Singular Yamabe Metrics and Initial Data with Exactly Kottler–Schwarzschild–de Sitter Ends

We construct large families of initial data sets for the vacuum Einstein equations with positive cosmological constant which contain exactly Delaunay ends; these are non-trivial initial data sets which coincide with those for the Kottler–Schwarzschild–de Sitter metrics in regions of infinite extent. From the purely Riemannian geometric point of view, this produces complete, constant positive scalar curvature metrics with exact Delaunay ends which are not globally Delaunay. The ends can be used to construct new compact initial data sets via gluing constructions. The construction provided applies to more general situations where the asymptotic geometry may have non-spherical cross-sections consisting of Einstein metrics with positive scalar curvature. Submitted: October 19, 2007. Accepted: February 11, 2008.     

Correlation Effects in the Moshinsky Model

We investigate quantum correlations in the ground state of the Moshinsky model formed by N harmonically interacting particles confined in a harmonic potential. The model is solvable which allows an exact determination of entanglement between the subset of p particles and the remaining N ? p particles. We study linear entropies and von Neumann entropies of the bipartitions and compare their behavior with that of the relative correlation energy and of the statistical Kutzelnigg coefficient.     

A new approach to the study of the α–σ phase transformation

It is demonstrated that the kinetics of the α-σ phase transformation in the Fe-Cr based alloys can be studied from the average isomer shift. Using this new approach it is shown that the size of grains significantly affects the formation of the σ-phase, while that of the α-phase does not depend on the microstructure. This revised version was published online in August 2006 with corrections to the Cover Date.     

Studies of the out-of-plane emission of pions in symmetric heavy-ion collisions

Triple differential cross-sections of midrapidity pions from ²⁰⁹Bi+²⁰⁹Bi collisions were measured with the Kaon Spectrometer at SIS at incident energies of 400, 700 and 1000 AMeV. The azimuthal emission pattern of the pions has been investigated in dependence of beam energy and impact parameter. An enhanced emission of pions perpendicular to the reaction plane is observed. The strength of the anisotropy increases with beam energy and pion transverse momentum. In contrast to the nucleons the anisotropy varies only little with the impact parameter. No difference in the behaviour of positive and negative pions is observed.     

Two photon-induced fluorescence intensity and anisotropy decays of diphenylhexatriene in solvents and lipid bilayers

We measured the fluorescence intensity and anisotropy decays of 1,6-diphenyl-1,3,5-hexatriene (DPH)-labeled membranes resulting from simultaneous two-photon excitation of fluorescence. Comparison of these two-photon data with the more usual one-photon measurements revealed that DPH displayed identical intensity decays, anisotropy decays, and order parameters for one- and two-photon excitation. While the anisotropy data are numerically distinct, they can be compared by use of the factor 10/7, which accounts for the two-photon versus one-photon photoselection. The increased time 0 anisotropy of DPH can result in increased resolution of complex anisotropy decays. Global analysis of the one- and two-photon data reveals consistency with a single apparent angle between the absorption and the emission oscillators. The global anisotropy analysis also suggests that, except for the photoselection factor, the anisotropy decays are the same for one-and two-photon excitation. This ideal behavior of DPH as a two-photon absorber, and its high two-photon cross section, makes DPH a potential probe for confocal two-photon microscopy and other systems where it is advantageous to use long-wavelength (680- to 760-nm) excitation.     

Free convection from horizontal screened plates

Experimental investigations of laminar free convection from horizontal isothermal surfaces screened by cylindrical vertical walls are presented. Screen diameters (D) were equal to the diameter of a heating plate while their heights (H) were varied. Results obtained for several heating fluxes and two different liquids indicate that depending on the (H/D) ratio of cylindrical screens, the heat flux transferred from the heating plate to the liquid varies. Three subranges of screening effect have been distinguished: primary inhibition, intensification and secondary inhibition. For primary inhibition, a theoretical model has been proposed and critical ratio of (H/D) has been predicted. The results of flow visualization are also discussed.

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Freie Konvektion von horizontalen, seitlich abgeschirmten Platten

Zusammenfassung Es werden experimentelle Untersuchungen der laminaren freien Konvektion an horizontalen, isothermen Flächen mit vertikalen zylindrischen Abschirmflächen beschrieben. Die Schirmdurchmesser (D) waren gleich dem einer Heizplatte, während die Schirmhöhen (H) variiert wurden. Die Resultate, welche für mehrere Wärmeflüsse und mit zwei verschiedenen Flüssigkeiten gewonnen wurden, zeigen, daß — abhängig von VerhältnisH/D der zylindrischen Schirme — der von der Heizplatte an das Fluid übergehende Wärmestrom stark variiert. Drei Bereiche konnten bezüglich des Abschirmeffektes unterschieden werden: erste Hemmung, Verstärkung und zweite Hemmung. Für den Fall der ersten Hemmung wird ein theoretisches Modell vorgeschlagen und das kritischeH/D-Verhältnis vorausberechnet. Abschließend erfolgt die Diskussion von Ergebnissen, welche aus der sichtbaren Darstellung des Strömungsfeldes gewonnen wurde.

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Nomenclature a thermal diffusivity [m²/s] - D external diameter of the plate, internal diameter of screens [m] - g gravitational acceleration [m/s²] - H height of screen [m] - Nu= D/ Nusselt number - Nu _(H/D)=0 Nusselt number for plate without screens - Nu _H/D Nusselt number for plate with screen of heightH - Ra=g (T _w1–T _F)D ³/( a) Rayleigh number - Ra _H=g (T _w–T _w1)H ³/( a) Rayleigh number inside screen - q heat flux density [W/m²] - T _w surface temperature of the heating plate [°C] - T _w1 boundary temperature of the motionless liquid [°C] - T _F bulk temperature of the liquid [°C] - heat transfer coefficient [W/(m²·K)] - coefficient of volumetric expansion [1/K] - kinematic viscosity - thermal conductivity [W/(m·K)]     

Influence of the soft segment length on the properties of water‐cured poly(carbonate‐urethane‐urea)s

Poly(carbonate‐urethane‐urea)s (PCUU) based on oligocarbonate diols (M_n ≈ 2000) with different length of the hydrocarbon chain as soft segments were synthesized and investigated. Carbonate oligomerols were obtained in a two‐step method from dimethyl carbonate (DMC) and linear α,ω‐diols (1,4‐butanediol, 1,5‐pentanediol, 1,6‐hexanediol, 1,9‐nonanediol, 1,10‐dekanediol and 1,12‐dodecanediol). Oligo(trimethylene carbonate) diol was synthesized using ring‐opening polymerization of trimethylence carbonate. PCUUs were obtained by prepolymer method using isophorone diisocyanate (IPDI) and water as a chain extender. Changes in polymers properties with increase of methylene group number between carbonate linkages were investigated by differential scanning calorimetry (DSC), dynamic mechanical thermal analysis (DMTA), tensile strength and hardness measurements. The thermal stability was also analyzed by means of thermogravimetric analysis (TGA). Based on FTIR analysis influence of methylene groups number between carbonate linkages on phase separation and concentration of allophanate and biuret groups in the samples were investigated. The obtained poly(carbonate‐urethane‐urea)s exhibited very good mechanical properties. Tensile strength and elongation at break were 40 MPa and 400–600%, respectively, depending on the oligocarbonate used. Copyright © 2014 John Wiley & Sons, Ltd.