Quartic double solids with ordinary singularities

We study the mixed Hodge structure on the third homology group of a threefold which is the double cover of projective three-space ramified over a quartic surface with a double conic. We deal with the Torelli problem for such threefolds.Comment: 14 pages, presented at the Conference Arnol'd 7

A Tverberg type theorem for matroids

Let b(M) denote the maximal number of disjoint bases in a matroid M. It is shown that if M is a matroid of rank d+1, then for any continuous map f from the matroidal complex M into the d-dimensional Euclidean space there exist t \geq \sqrt{b(M)}/4 disjoint independent sets \sigma_1,\ldots,\sigma_t \in M such that \bigcap_{i=1}^t f(\sigma_i) \neq \emptyset.Comment: This article is due to be published in the collection of papers "A Journey through Discrete Mathematics. A Tribute to Jiri Matousek" edited by Martin Loebl, Jaroslav Nesetril and Robin Thomas, due to be published by Springe

Kappia lobulata (Apocynaceae, Periplocoideae), a new genus from South Africa

Kappia, a new genus from the Fish River Valley in the Eastern Cape Province, South Africa is presented. At first described as Raphionacme lobulata Venter and R.L.Verh. [Venter, H.J.T., Verhoeven, R.L. 1988. Raphionacme lobulata (Periplocaceae), a new species from the eastern Cape Province, South Africa. South African Journal of Botany 54, 603–606.] based on a single specimen collected in 1936, recently discovered plants of this species proved it to be a new genus. In habit Kappia resembles Baseonema Schltr. and Rendle, Batesanthus N.E.Br., Mondia Skeels and Stomatostemma N.E.Br. However, as far as floral structure is concerned, Kappia reveals more affinity with Raphionacme Harv. DNA sequence data show Kappia to be distinct from Batesanthus, Mondia and Raphionacme Harv. and weakly supported as a sister to Stomatostemma

Combustion waves in a model with chain branching reaction and their stability

In this paper the travelling wave solutions in the adiabatic model with two-step chain branching reaction mechanism are investigated both numerically and analytically in the limit of equal diffusivity of reactant, radicals and heat. The properties of these solutions and their stability are investigated in detail. The behaviour of combustion waves are demonstrated to have similarities with the properties of nonadiabatic one-step combustion waves in that there is a residual amount of fuel left behind the travelling waves and the solutions can exhibit extinction. The difference between the nonadiabatic one-step and adiabatic two-step models is found in the behaviour of the combustion waves near the extinction condition. It is shown that the flame velocity drops down to zero and a standing combustion wave is formed as the extinction condition is reached. Prospects of further work are also discussed.Comment: pages 32, figures 2

Cohomogeneity one manifolds and selfmaps of nontrivial degree

We construct natural selfmaps of compact cohomgeneity one manifolds with finite Weyl group and compute their degrees and Lefschetz numbers. On manifolds with simple cohomology rings this yields in certain cases relations between the order of the Weyl group and the Euler characteristic of a principal orbit. We apply our construction to the compact Lie group SU(3) where we extend identity and transposition to an infinite family of selfmaps of every odd degree. The compositions of these selfmaps with the power maps realize all possible degrees of selfmaps of SU(3).Comment: v2, v3: minor improvement

From double Lie groupoids to local Lie 2-groupoids

We apply the bar construction to the nerve of a double Lie groupoid to obtain a local Lie 2-groupoid. As an application, we recover Haefliger's fundamental groupoid from the fundamental double groupoid of a Lie groupoid. In the case of a symplectic double groupoid, we study the induced closed 2-form on the associated local Lie 2-groupoid, which leads us to propose a definition of a symplectic 2-groupoid.Comment: 23 pages, a few minor changes, including a correction to Lemma 6.

Influence of slim rod material properties to the Siemens feed rod and the float zone process

The identification and understanding of material properties influencing the float zone process is important to crystallize high purity silicon for high efficiency solar cells. Also the knowledge of minimal requirements to crystallize monocrystalline silicon with the float zone process is of interest from an economic point of view. In the present study, feed rods for the float zone process composed of a central slim rod and the deposited silicon from the Siemens process are investigated. Previous studies have shown that the slim rod has a significant impact on the purity and suitability for further crystallization processes. In particular, contaminations like substitutional carbon and the presence of precipitates as well as the formation of oxide layers play an important role and are investigated in detail. For this purpose different slim rod materials were used in deposition and float zone crystallization experiments. Samples were prepared by cross sectioning and core drilling of Siemens rods, which were recrystallized with the float zone process. Recrystallized drilled cores are analyzed with FT-IR spectrometry concerning the carbon and oxygen content. To estimate the grain growth behavior on the slim rod surface in dependence of the used slim rod material, EBSD mappings inside a SEM are performed on squared and circular slim rods. TEM analysis was used to investigate the presence of an oxide layer at the interface between slim rod and deposited polycrystalline silicon. Additionally the influence of a nitrogen-containing gas atmosphere during the slim rod pulling is investigated by IR microscopy and ToF-SIMS regarding Si3N4 precipitation

Structural and chemical investigations of adapted Siemens feed rods for an optimized float zone process

The optimization of the float zone process for industrial application is a promising way to crystallize high purity silicon for high efficiency solar cells with reduced process costs. We investigated two differently produced Siemens rods which should be used as feed material for the float zone process. The aim is to identify and to improve material properties of the feed rods which have a high impact to the float zone process. We show here microstructural and chemical analysis comparing feed rods manufactured under standard conditions and under float zone adapted conditions. To resolve the growth behavior of the grains SEM/EBSD mappings are performed at different positions. TEM analyses are used to investigate the interface region between the mono- and the multicrystalline silicon within the Siemens feed rod. Additionally, drilled cores are cut out from the feed rods containing the region of the slim rod. Afterwards, the drilled cores are crystallized with the float zone process. Finally, carbon and oxygen measurements with FT-IR spectrometry on different positions of the crystallized drilled cores of the Siemens feed rods show the influence of the slim rod material to the float zone process

Makorin 1 controls embryonic patterning by alleviating Bruno1-mediated repression of oskar translation.

Makorins are evolutionary conserved proteins that contain C3H-type zinc finger modules and a RING E3 ubiquitin ligase domain. In Drosophila, maternal Makorin 1 (Mkrn1) has been linked to embryonic patterning but the mechanism remained unsolved. Here, we show that Mkrn1 is essential for axis specification and pole plasm assembly by translational activation of oskar (osk). We demonstrate that Mkrn1 interacts with poly(A) binding protein (pAbp) and binds specifically to osk 3' UTR in a region adjacent to A-rich sequences. Using Drosophila S2R+ cultured cells we show that this binding site overlaps with a Bruno1 (Bru1) responsive element (BREs) that regulates osk translation. We observe increased association of the translational repressor Bru1 with osk mRNA upon depletion of Mkrn1, indicating that both proteins compete for osk binding. Consistently, reducing Bru1 dosage partially rescues viability and Osk protein level in ovaries from Mkrn1 females. We conclude that Mkrn1 controls embryonic patterning and germ cell formation by specifically activating osk translation, most likely by competing with Bru1 to bind to osk 3' UTR

Three-dimensionality of space and the quantum bit: an information-theoretic approach

It is sometimes pointed out as a curiosity that the state space of quantum two-level systems, i.e. the qubit, and actual physical space are both three-dimensional and Euclidean. In this paper, we suggest an information-theoretic analysis of this relationship, by proving a particular mathematical result: suppose that physics takes place in d spatial dimensions, and that some events happen probabilistically (not assuming quantum theory in any way). Furthermore, suppose there are systems that carry "minimal amounts of direction information", interacting via some continuous reversible time evolution. We prove that this uniquely determines spatial dimension d=3 and quantum theory on two qubits (including entanglement and unitary time evolution), and that it allows observers to infer local spatial geometry from probability measurements.Comment: 13 + 22 pages, 9 figures. v4: some clarifications, in particular in Section V / Appendix C (added Example 39