Showing papers by "Bielefeld University published in 1976"

First order phase transition in the plane rotator ferromagnetic model in two dimensions

Abstract: We show that the two-dimensional isotropic ferromagnetic rotator model exhibits a first order phase transition if the interaction decays asr −α with 2<α<4

Die Kristall- und Molekülstruktur von 2r, 4c-Bis[bis(trimethylsilyl)-amino]-2,4-bis-(tert-butylimino)-1,3,2λ5,4λ5-dithiadiphosphetan

Abstract: Die Struktur der Titelverbindung 1 wurde aus bei −130°C gemessenen Diffraktometer-Einkristalldaten bestimmt und fur 3368 Reflexe zu einem R-Wert von 4.2% verfeinert. Die Verbindung Kristallisiert monoklin, Raumgruppe C2/c. 1 wurde bisher. als Monomeres beschrieben, liegt im Festkorper jedoch dimer vor, wobei aus sterischen Grunden die Bildung des Dithiadiphosphetans gegenuber dem Diazadiphosphetidin bevorzugt ist. Das Molekul besitzt im Festkorper C2-Symmetrie mit cis-Stellung der exocyclischen Liganden. Im nahezu ebenen P2S2-Vierring betragt der mittlere P-S-Abstand 2.144A, ∢ S-P-S: 90.4, °, ∢P–S–P–P: 89.2°. P–NAmin-und P–NImin-Abstand wurden zu 1.662 bzw. 1.529 A beobachtet. The Crystal and Molecular Structure of 2r, 4c-Bis[bis(trimethylsilyl)amino]-2,4-bis(tert-butylimino)-1,3,2λ54λ5-dithiadiphosphetane The crystal structure of the title compound 1 has been determined from single crystal X-ray data (measured at −130°C) and has been refined to R = 0.042 for 3368 reflections. The compound crystallizes in the monoclinic space group C2/c. The dimeric molecules of 1 have previously been reported to be monomeric. For steric reasons the dimerisation results in the formation of a dithiadiphosphetane rather than a diazadiphosphetidine ring system. In the solid state the molecule of 1, has C2 symmetry, the exocyclic ligands adapting a cis-configuration. The fourmembered P2S2 ring is almost planar. The mean P–S bond length is 2.144 A, ∢ S–P–S: 90.4°, ∢P–S–P: 89.2°. The P-Namine and P-Nimine bond lenghts were found to be 1.662 and 1.529 A, respectively.

Every bad code has a good subcode: a local converse to the coding theorem

Abstract: The Local Converse The transmission probabilities P of a discrete memoryless channel (DMC) with alphabets 5F and Y/are given by P(y\"]x\")= ~ w(ytlx,) (1) t=l n n where x\" = (x 1 .... , x,) ~ 2F\" = 1~ 5F, y\" = (y~ ..... y,) ~ ~d\" = I~ @', and where w is a IX[ x l~l-stochastic matrix, z 1 An (n, N, 2)-code for the DMC is a system of pairs {(u~, D~)[i= 1, ..., N} with ui~Y' and pairwise disjoint subsets D i of ~\" (i= 1 .... , N), and with This result was stated (without proof) in [1] as Theorem 12. The inequality liminf n-1 log N(n, ' > /~)=C, 0<2<1 (4) noD oD (the coding theorem) was proved in [3] and in [5]. It was shown in [2] that (weak converse) inf limsup n-1 log N(n, 2)< C (5) 2>0 n-,oo and finally in [4] that the strong converse holds, i.e. limsup n-1 log N(n, 2) < C, 0 < 2 < 1.

S3N2-Ringe mit fluorhaltigen Substituenten

Abstract: Aus der Zinnverbindung 1 wurde mit SOF2 ein funfgliedriges Schwefel-Stickstoff-Oxid 2 hergestellt. 2 reagiert mit FSO2NSO, CF3SO2NSO bzw. CF3SO2NCO und n-C4F9SO2NSO zu den 1-Sulfonylimino 1λ42,4λ4,3,5-trithiadiazolen 3,4 und 5 unter SO2-Abspaltung. Die Rontgenstrukturanalyse von 3 wird mitgeteilt. CH3SO2NSO, CF3S(O)NSO und (CH3)3SiNSO ergeben mit 2 lediglich Schwefel und S4N4. In 1 lassen sich die Methylgruppen mit SnCl4 gegen Chloratome unter Bildung von 7 austauschen. S3N2-Rings with Fluorine Containing Substituents From the tin compound 1 and SOF2 the five-membered sulfur-nitrogen oxide 2 was prepared. 2 reacts with FSO2NSO, CF3SO2NSO, as well as with CF3SO2NCO and n-C4F9SO2NSO to yield the 1-sulfonylimino-1λ4,2,4λ4,3,5-trithiadiazoles 3,4 and 5 under evolution of SO2 as well as CO2. The X-ray structure analysis of 3 is reported. CH3SO2NSO, CF3S(O)NSO, and (CH3)3SiNSO react with 2 to form only sulfur and S4N4. In 1 the methyl-groups can be exchanged for chlorine atoms to give 7.

Ringstrukturen auf dem Burnsidering der Permutationsdarstellungen einer endlichen Gruppe

Abstract: Viele der aus universellen Konstruktionen hervorgehenden Grothendieckringe, wie der Ring K(X) der Vektorraumbiindel fiber einem kompakten Raum und der komplexe Darstellungsring R(G) einer kompakten topologischen Gruppe, tragen in natiirlicher Weise die Struktur eines 2-Ringes. Dies bedeutet, dab man eine Folge von Abbildungen {~"},~N des jeweiligen Grothendieckringes in sich hat, und daB fiir diese Operationen 2" folgende Identit~iten gelten:

Greens Functions, Hamiltonians and Modular Automorphisms

Abstract: We demonstrate, under circumstances that allow the construction of a “thermodynamic” hamiltonian, that Gibbs equilibrium states ω are modular states in the Tomita-Takesaki sense. The thermodynamic Greens functionsG are connected to these modular states, and the associated group of modular automorphisms σ, by the identification $$G(A, B; t) = \omega (A\sigma _t (B))$$ (A andB are observables) whenever the thermodynamic Hamiltonian is self-adjoint and defines a derivation of the algebra of observables in a certain sense. Our results apply to a class of interacting quantum gases at small fugacity and Bose gases with repulsive interactions at all fugacitiesz<1.

Non-Equilibrium Quantum Statistical Mechanics

Abstract: Through the study of a particular model, the aim of these lectures is to indicate how the so-called “algebraic approach” can help understanding the statistical mechanics of quantum stochastic transport processes.

Crowding: Effects of Group Size, Room Size, or Density?

Abstract: The separate effects of group size, room size, and density (space per person) were investigated for subjects responding interactively or coactively to perceptual and cognitive tasks. The major findings are that crowding has greater effects on “feelings” and “interpersonal perceptions” than on task performance. Where crowding did have effects, they appeared to be mediated more by group size and, to some degree, room size than by density, especially for males. Female subjects appeared somewhat more density oriented than male subjects.

Exact perturbation-theory of multiphoton processes at high intensities

Abstract: In this work we investigate the perturbation theory for multiphoton processes at high intensities and describe an analytical method of summing the perturbation series to extract the contribution from all terms that give rise to the absorption ofN photons by an atomic system. The method is first applied to the solution of a simple model problem and the result is confirmed by direct integration of the model Schrodinger equation. The usual lowest (nonvanishing)-order perturbation-theoretical calculation is also carried out for this model to demonstrate explicitly that the full result correctly reproduces that of the lowest-order theory in the limit of low intensity. The method is then extended to the case of an atomic system with well-developed spectrum (e.g. H atom) and theN-photonT-matrix is derived in terms of a «photon matrix»\(\bar a_N \), for which a three-term recurrence relation is established. Next, from the vantage point of the general result obtained here, we have probed into the nature of several approximate nonperturbative solutions that have appeared in the literature in the past. It is shown here that their applicability is severely restricted by the requirement of the essential spectral degeneracy of the atomic system. Finally, in appendix A we have outlined a prescription of computing the photon matrix\(\bar a_N \), which (as in the usual lowest-order perturbation-theoretical calculation) requires a knowledge of the eigenfunctions and eigenvalues of the atomic Hamiltonian only.

Zwei Klassen lokalkompakter maximal fastperiodischer Gruppen

Abstract: In this paper we study the class\(\mathfrak{A}\) of all locally compact groupsG with the property that for each closed subgroupH ofG there exists a pair of homomorphisms into a compact group withH as coincidence set, and the class\(\mathfrak{D}\) of all locally compact groupG with the property that finite dimensional unitary representations of subgroups ofG can be extended to finite dimensional representations ofG. It is shown that [MOORE]-groups (every irreducible unitary representation is finite dimensional) have these two properties. A solvable group in\(\mathfrak{D}\) is a [MOORE]-group. Moreover, we prove a structure theorem for Lie groups in the class [MOORE], and show that compactly generated Lie groups in [MOORE] have faithful finite dimensional unitary representations.