Spectrum and analyticity of semigroups arising in elasticity theory and hydromechanics

Cauchy problems for a second order linear differential operator equation

On the residue classes of integer sequences satisfying a linear three term recurrence formula

In this paper we investigate linear three-term recurrence formulae with sequences of integers (T(n))_n?0 and (U(n))_n?0, which are ultimately periodic modulo m, e.g.

     

New adaptive mixed finite element method (AMFEM)

The need to develop reliable and efficient adaptive algorithms using mixed finite element methods arises from various applications in fluid dynamics and computational continuum mechanics. In order to save degrees of freedom, not all but just some selected set of finite element domains are refined and hence the fundamental question of convergence requires a new mathematical argument as well as the question of optimality. We will present a new adaptive algorithm for mixed finite element methods to solve the model Poisson problem, for which optimal convergence can be proved. The a posteriori error control of mixed finite element methods dates back to Alonso (1996) Error estimators for a mixed method. and Carstensen (1997) A posteriori error estimate for the mixed finite element method. The error reduction and convergence for adaptive mixed finite element methods has already been proven by Carstensen and Hoppe (2006) Error Reduction and Convergence for an Adaptive Mixed Finite Element Method, Convergence analysis of an adaptive nonconforming finite element methods. Recently, Chen, Holst and Xu (2008) Convergence and Optimality of Adaptive Mixed Finite Element Methods. presented convergence and optimality for adaptive mixed finite element methods following arguments of Rob Stevenson for the conforming finite element method. Their algorithm reduces oscillations, before applying and a standard adaptive algorithm based on usual error estimation. The proposed algorithm does this in a natural way, by switching between the reduction of either the estimated error or oscillations. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A network approach to the modelling of active magnetic bearings

The modelling of active magnetic bearings based on a network approach is considered. Unlike in the standard modelling approach, where a linearization of the current-force relation for the centred shaft position is used, network models permit to include the position dependence of the bearing force in the force model. This becomes necessary when model based controllers are used to stabilize a magnetically supported shaft in tracking applications.

The approach is based on the well known application of network models to magnetic circuits. Further simplifying assumptions are discussed which allow one to obtain a network with a limited number of lumped parameters describing the magnetic behaviour of a magnetic bearing. The modelling of a combined radial and axial bearing serves as an example for the application of the proposed approach. Furthermore, the fitting of the network based model to measured characteristic force curves is discussed. In this context, a method for including saturation effects in the model is sketched.     

A short proof of w1n (Hom(C2r+1, Kn+2)) = 0 for all n and A graph colouring theorem by Babson and Kozlov

We show that the n-th power of the first Stiefel-Whitney class of the ℤ₂-action on the graph complex Hom(C _2r+1, K _n+2) is zero, confirming a conjecture by Babson and Kozlov. This yields a considerably simplified proof of their graph colouring theorem, which is also known as the Lovsz conjecture. This research was supported by the Deutsche Forschungsgemeinschaft within the European graduate program “ Combinatorics, Geometry, and Computation” (No. GRK 588/2)     

Radical S‐Adenosyl Methionine Epimerases: Regioselective Introduction of Diverse D‐Amino Acid Patterns into Peptide Natural Products

PoyD is a radical S‐adenosyl methionine epimerase that introduces multiple D ‐configured amino acids at alternating positions into the highly complex marine peptides polytheonamide A and B. This novel post‐translational modification contributes to the ability of the polytheonamides to form unimolecular minimalistic ion channels and its cytotoxic activity at picomolar levels. Using a genome mining approach we have identified additional PoyD homologues in various bacteria. Three enzymes were expressed in E. coli with their cognate as well as engineered peptide precursors and shown to introduce diverse D ‐amino acid patterns into all‐L peptides. The data reveal a family of architecturally and functionally distinct enzymes that exhibit high regioselectivity, substrate promiscuity, and irreversible action and thus provide attractive opportunities for peptide engineering.     

Development of Polar Order in the Liquid Crystal Phases of a 4‐Cyanoresorcinol‐Based Bent‐Core Mesogen with Fluorinated Azobenzene Wings

A bent‐core mesogen consisting of a 4‐cyanoresorcinol unit as the central core and laterally fluorinated azobenzene wings forms four different smectic LC phase structures in the sequence SmA–SmC_s–SmC_sP_AR–M, all involving polar SmC_sP_S domains with growing coherence length of tilt and polar order on decreasing temperature. The SmA phase is a cluster‐type de Vries phase with randomized tilt and polar direction; in the paraelectric SmC_s phase the tilt becomes uniform, although polar order is still short‐range. Increasing polar correlation leads to a new tilted and randomized polar smectic phase with antipolar correlation between the domains (SmC_sP_AR) which then transforms into a viscous polar mesophase M. As another interesting feature, spontaneous symmetry breaking by formation of a conglomerate of chiral domains is observed in the non‐polar paraelectric SmC_s phase.     

Syntheses, structures, and photophysical properties of mono- and dinuclear sulfur-rich gold(I) complexes

The dinuclear gold complexes [{Au(PPh 3)} 2(mu- dmid)] ( 1) ( dmid = 1,3-dithiole-2-one-4,5-dithiolate) and [{Au(PPh 3)} 2(mu- dddt)] ( 2) ( dddt = 5,6-dihydro-1,4-dithiine-2,3-dithiolate) were synthesized and characterized by X-ray crystallography. Both complexes exhibit intramolecular aurophilic interactions with Au...Au distances of 3.1984(10) A for 1 and 3.1295(11) A for 2. A self-assembly reaction between 4,5-bis(2-hydroxyethylthio)-1,3-dithiole-2-thione ( (HOCH 2 CH 2 ) 2 dmit) and [AuCl(tht)] affords the complex [AuCl{ (HOCH 2 CH 2 ) 2 dmit}] 2 ( 4), which possesses an antiparallel dimeric arrangement resulting from a short aurophilic contact of 3.078(6) A. This motif is extended into two dimensions due to intra- and intermolecular hydrogen bonds via the hydroxyethyl groups, giving rise to a supramolecular network. Three compounds were investigated for their rich photophysical properties at 298 and 77 K in 2-MeTHF and in the solid state; [Au 2(mu- dmid)(PPh 3) 2] ( 1), [Au 2(mu- dddt)(PPh 3) 2] ( 2), and [AuCl{( HOCH 2 CH 2 ) 2 dmit}] ( 4). 1 exhibits relatively long-lived LMCT (ligand-to-metal charge transfer) emissions at 298 K in solution (370 nm; tau e approximately 17 ns, where M is a single gold not interacting with the other gold atom; i.e., the fluxional C-SAuPPh 3 units are away from each other) and in the solid state (410 nm; tau e approximately 70 mus). At 77 K, a new emission band is observed at 685 nm (tau e = 132 mus) and assigned to a LMCT emission where M is representative for two gold atoms interacting together consistent with the presence of Au...Au contacts as found in the crystal structure. In solution at 77 K, the LMCT emission is also red-shifted to 550 nm (tau e approximately 139 mus). It is believed to be associated to a given rotamer. 2 also exhibits LMCT emissions at 380 nm at 298 K in solution and at 470 nm in the solid state. 4 exhibits X/MLCT emission (halide/metal to ligand charge transfer) where M is a dimer in the solid state with obvious Au...Au interactions, resulting in red-shifted emission band, and is a monomer in solution in the 10 (-5) M concentration (i.e., no Au...Au interactions) resulting in blue-shifted luminescence. Both fluorescence and phosphorescence are observed for 4.     

Synthese und Metallierung des Diaminosiloxans O(SiiPr2NH2)2

Synthesis and Metalation of the Diaminosiloxane O(SiiPr₂NH₂)₂ The 1,3‐diaminoldisiloxane O(SiiPr₂NH₂)₂ ( 1 ) was obtained from the reaction of O(SiiPr₂Cl)₂ with NH₃. The reactions of 1 with AlEt₃ or GaEt₃ produced the compounds [O{SiiPr₂N(H)MEt₂}{SiiPr₂NMEt}]₂ ( 2 : M = Al; 3 : M = Ga). The crystal structures of 2 and 3 were determined by single crystal X‐ray diffraction, showing a polycyclic M₄N₄Si₄O₂ core structure of these molecules.     

Phytotherapy in Integrative Oncology—An Update of Promising Treatment Options

Modern phytotherapy is part of today’s conventional evidence-based medicine and the use of phytopharmaceuticals in integrative oncology is becoming increasingly popular. Approximately 40% of users of such phytopharmaceuticals are tumour patients. The present review provides an overview of the most important plants and nature-based compounds used in integrative oncology and illustrates their pharmacological potential in preclinical and clinical settings. A selection of promising anti-tumour plants and ingredients was made on the basis of scientific evidence and therapeutic practical relevance and included Boswellia, gingko, ginseng, ginger, and curcumin. In addition to these nominees, there is a large number of other interesting plants and plant ingredients that can be considered for the treatment of cancer diseases or for the treatment of tumour or tumour therapy-associated symptoms. Side effects and interactions are included in the discussion. However, with the regular and intended use of phytopharmaceuticals, the occurrence of adverse side effects is rather rare. Overall, the use of defined phytopharmaceuticals is recommended in the context of a rational integrative oncology approach.