The rhombidodecahedral tessellation of 3-space and a particular 15-vertex triangulation of the 3-dimensional torus

It is well known that the unique 7-vertex triangulation of the 2-dimensional torus S¹×S¹ is a consequence of the relationship between two hexagonal lattices in the euclidean plane: it is just the quotient of the triangular tessellation of the plane by a translation group. Each vertex star is a regular hexagon and the symmetry group of this triangulation is the affine group A(1,₇) in one dimension over ₇. In this paper we describe a particular 15-vertex triangulation of the 3-dimensional torus S¹×S¹×S¹ whose symmetry group is the affine group A(1,₁₅) and which is similarly related to two lattices in euclidean 3-space: it is just the quotient of a particular tessellation of 3-space by a translation group. Each vertex star happens to be a rhombidodecahedron, the dual of a (semiregular) cuboctahedron.     

Eine globalanalytische Behandlung des Douglas'schen Problems

In this paper we consider the Douglas problem of genus O. Starting point is the global analysis for minimal surfaces of the type of the disc which was developed by A.J. Tromba. The set of all k-connected minimal surfaces of genus O has a product structure, which is a consequence of the variation of the conformal type. The base space is the space of domain parameters and the fibres are the manifolds of k-connected minimal surfaces of constant conformal type (cf.[7]). It is possible to develop a global analysis also for the more general situation considered here with the following results:

-The map which assigns to every minimal surface its boundary curve (in the sense of the Douglas problem) is a Fredholm operator. The index depends on the number and the total order of the branch points.

-The analysis allows to prove isolatedness and stability results in a relatively simple way.

     

Registrierende Messung des mechanischen Verlustes von Kunststoffproben

Zusammenfassung Ein neues Verfahren, das eine unmittelbare und kontinuierliche Registrierung des mechanischen Verlustwinkels über einen weiten Temperaturbereich erm?glicht, wird beschrieben. Die Probe wird einer periodischen Biegung (f=2,5 Hz) unterworfen; die Zeit des Kraftnulldurchgangs relativ zur Bewegung ist dem Verlustwinkel proportional und wird elektronisch ermittelt. Das Me\ergebnis ist weitgehend von der Probenform und deren ?nderung w?hrend der Messung (Krümmung der Probe, thermische Ausdehnung usw). unabh?ngig. Der Deutschen Forschungsgemeinschaft sei für die Unterstützung dieser Arbeit verbindlichst gedankt.     

Band structure of even and ions of odd polyenes

The analysis of experimental data for singlet transitions (E _n) of even polyenes (I), cations (II) and anions (III) of odd polyenes show that for infinite chains E (I)/E (II)=E (I)/E (III) = 2:1. It is shown that the energy gap is equal for the three systems. In cases (II) and (III) there is a level (NBMO) in the gap which is vacant in (II) and occupied in (III). That is why the first optical transition in (II) and (III) depends on the semiwidth of the gap.     

Wedderburnzerlegung für Jordan-Paare

In the first section we summarize some properties of Jordan pairs. Then we state some results about some groups defined by Jordan pairs.In the next section we construct a Lie algebra to a Jordan pair. This construction is a generalization of the wellknown Koecher-Tits-construction. We calculate the radical of this Lie algebra in terms of the given Jordan pair.In the last section we prove a Wedderburn decomposition theorem for Jordan pairs in the characteristic zero case. Some special cases in arbitrary characteristic have been shown by R. Carlson (see [5]). Also we show that any two such decompositions are conjugate under a certain group of automorphism. Analogous theorems will be shown for Jordan Triples.     

Lotketten in Speziellen Hjelmslev-Gruppen

Let be given a geometric structure with a set of lines and a symmetric orthogonality relation. F. Bachmann defined in [3] chains of perpendiculars in such a structure, and studied those chains in Hjelmslev-groups. All AGS-groups (= groups treated in [1]) are Hjelmslev-groups, and the theory of Hjelmslev-groups includes also Hjelmslev's concept of Allgemeine Kongruenzlehre. In Hjelmslev-groups, chains of perpendiculars are closely related to the group generated by the points. We establish some results about chains of perpendiculars in special classes of Hjelmslev-groups.     

Über geschlossene Regelflächen im elliptischen Raum

On a ruled closed surface in the elliptic 3-space two integral invariants are considered: the aperture distance of a curve orthogonal to the generating lines of , and the aperture angle of an orthogonally circumscribed tangent surfaces. By means of these integral invariants and by considering certain ruled surfaces associated to one finds the geometric meaning of further integral invariants. If is generated by the binormals of a curve one obtains some properties of closed curves in the elliptic 3-space.     

SIMS and flash desorption studies of nickel oxygen interaction

O₂ exposure of polycrystalline nickel at 300 K results in characteristics changes of secondary ion emission. These can be described by a model which is in good agreement with corresponding LEED, AES, XPS, and ΔΦ results of other authors. According to this model, oxygen can be bonded on Ni in at least five different phases:

1. chemisorption, indicated by a rapid increase of Ni⁺, Ni ₂ ⁺ , and Ni₂O⁺ (≦5 L);
2. a rearranged chemisorption layer, characterized by a drastic decrease of Ni⁺, Ni ₂ ⁺ , and Ni₂O⁺ (5–15 L);
3. nickel oxide (NiO) responsible for a strong NiO^?- and NiO ₂ ^? -emission (≦40 L);
4. oxygen on top of this NiO layer, producing a final increase of Ni⁺ and NiO⁺ and a O₂-flash signal at 400 K (>40 L);
5. bulk dissolved oxygen in thermal equilibrium with a chemisorption layer (after several exposure/heating cycles).

During ion bombardment of a 100 L O₂ exposed Ni surface these different binding states occur in a reversed order of succession. O₂-flash signals at 400 and 1100 K, related to drastic changes in secondary ion emission at 400, 700, and 1100 K, reflect the disappearance of various oxygen binding states. The exchange between different oxygen phases was studied by¹⁶O₂/¹⁸O₂ isotope experiments.     

Density fluctuations from elastic dipoles in glasses at low temperatures

The contribution of the population fluctuations of two-level systems in glasses to the dynamic structure factor is calculated using the concept of elastic dipoles. Describing the two-level systems by the tunneling model, with reasonable assumptions about the distribution of tunneling frequencies an essentially logarithmic decay in time of is obtained.