Hydrogen activation by an intramolecular boron lewis acid/zirconocene pair

Let's split: Reaction of the zirconium complex A with Piers' borane [HB(C(6) F(5) )(2) ] yields the unusual borylalkyne zirconocene complex B which reacts with dihydrogen, activating it to give the doubly hydrido bridged alkyne zirconium complex C.     

Symbiotic cooperation in the biosynthesis of a phytotoxin

Division of labor: A combination of genetic, microbial, and chemical analyses solved the riddle of the dual epoxidation in the biosynthesis of rhizoxin, the causative agent of rice seedling blight. Bacterial endosymbionts of Rhizopus microsporus mediate the first epoxidation by a dedicated cytochrome P450 monooxygenase. The second oxirane ring is introduced by the fungal host and results in a substantially increased potency of the phytotoxin.     

Carboboration Reactions of 1,2‐Bis[(diarylphosphino)ethynyl]benzenes with Tris(pentafluorophenyl)borane

The 1,2‐bis[(diarylphosphino)ethynyl]benzene derivatives 1a (R=Ph) and 1b (R=o‐tolyl) undergo 1,1‐carboboration at one of their acetylene units upon treatment with (C₆F₅)₃B at elevated temperature to give the products 5a and 5b , respectively. At room temperature, we observed the formation of the corresponding phosphireniumborate zwitterions, 7a and 7b , respectively, which may be intermediates of the 1,1‐carboboration reactions. The reaction of the more bulky 1,2‐bis[(dimesitylphosphino)ethynyl]benzene 1c with (C₆F₅)₃B takes a different course. At 110°, we observed the complete conversion to the benzopentafulvene derivative 8 which is probably formed in a typical carbocation rearrangement sequence after the initial (C₆F₅)₃B Lewis acid‐addition step. The compounds 5a, 5b, 7b , and 8 were characterized by X‐ray crystal‐structure analyses.     

Communication: a minimal model for the diffusion-relaxation backbone dynamics of proteins

We present a model for the local diffusion-relaxation dynamics of the C(α)-atoms in proteins describing both the diffusive short-time dynamics and the asymptotic long-time relaxation of the position autocorrelation functions. The relaxation rate spectra of the latter are represented by shifted gamma distributions, where the standard gamma distribution describes anomalous slow relaxation in macromolecular systems of infinite size and the shift accounts for a smallest local relaxation rate in macromolecules of finite size. The resulting autocorrelation functions are analytic for any time t ≥ 0. Using results from a molecular dynamics simulation of lysozyme, we demonstrate that the model fits the position autocorrelation functions of the C(α)-atoms exceptionally well and reveals moreover a strong correlation between the residue's solvent-accessible surface and the fitted model parameters.     

New organometallic single-source precursors for CuGaS(2)-polytypism in gallite nanocrystals obtained by thermolysis

The complex [((i)Pr(3)PCu)(2)(Me(2)Ga)(2)(SCH(2)CH(2)S)(2)] (4) was synthesized from trimethylgallium, [((i)Pr(3)PCu)(4)(SCH(2)CH(2)S)(2)] (1) and ethanedithiol by elimination of methane. The related monomethyl compound [((i)Pr(3)PCu)(2)(MeGaSPh)(2)(SCH(2)CH(2)S)(2)] (5) has been prepared from [((i)Pr(3)PCuSPh)(3)] (2) and [(MeGaSCH(2)CH(2)S)(2)] (3) by a ligand exchange reaction in tetrahydrofuran solution. The molecular structures of 1 and 3-5 were determined by single crystal X-ray diffraction. Thermolysis of 4 and 5 results in the formation of the ternary semiconductor CuGaS(2), gallite. The residue of 5 was characterized using X-ray powder diffraction, energy dispersive X-ray spectroscopy and transmission electron microscopy. The CuGaS(2) crystals obtained are mainly hexagonal plates of around 200 to 300 nm diameter and 10 to 30 nm thickness, exhibiting an unusual metastable hexagonal crystal structure, related to wurtzite. Partially, the usual tetragonal chalcopyrite structure or its disordered cubic zinc-blende analogue is realized by stacking faults, resulting in an overall similarity to the zinc-blende-wurtzite polytypism in ZnS and related compounds.     

On the streamer discharges emitted from the head of a person located in the vicinity of lightning strikes and their possible consequences

In this paper the currents associated with the streamer discharges generated from the head of a person located in the vicinity of a lightning strike are investigated. In the analysis the location of the person with respect to the lightning strike is selected in such a way that only a streamer burst, without the formation of a connecting leader, is emitted from the head. The current associated with these streamer bursts could exceed several hundreds of mA and may last for several hundreds of microseconds. The results of the calculation show that the passage of the streamer currents through the body of the person could create electric fields in the brain large enough to excite neurons. Depending on the strength of lightning flash and the distance to the strike point these streamer bursts can give rise to phosphenes which are a form of visual experience that occurs when the visual cortex is stimulated by electric currents.     

Remarks on the thermodynamics and the vacuum energy of a quantum Maxwell gas on compact and closed manifolds

The quantum Maxwell theory at finite temperature at equilibrium is studied on compact and closed manifolds in both the functional integral and Hamiltonian formalism. The aim is to shed some light onto the interrelation between the topology of the spatial background and the thermodynamic properties of the system. The quantization is not unique and gives rise to inequivalent quantum theories which are classified by θ-vacua. Based on explicit parametrizations of the gauge orbit space in the functional integral approach and of the physical phase space in the canonical quantization scheme, the Gribov problem is resolved and the equivalence of both quantization schemes is elucidated. Using zeta-function regularization the free energy is determined and the effect of the topology of the spatial manifold on the vacuum energy and on the thermal gauge field excitations is clarified. The general results are then applied to a quantum Maxwell gas on an n-dimensional torus providing explicit formulae for the main thermodynamic functions in the low- and high-temperature regimes, respectively.     

A Basis of Bideterminants for the Coordinate Ring of the Orthogonal Group

We give a basis of bideterminants for the coordinate ring K[O(n)] of the orthogonal group O(n,K), where K is an infinite field of characteristic not 2. The bideterminants are indexed by pairs of Young tableaux which are O(n)-standard in the sense of King–Welsh. We also give an explicit filtration of K[O(n)] as an O(n,K)-bimodule, whose factors are isomorphic to the tensor product of orthogonal analogs of left and right Schur modules.     

The Tits Alternative for Groups Defined by Periodic Paired Relations

The class of groups defined by periodic paired relations, as introduced by Vinberg, includes the generalized triangle groups, the generalized tetrahedron groups, and the generalized Coxeter groups. We observe that any group defined by periodic paired relations Γ can be realized as a so-called “Pride group”. Using results of Howie and Kopteva we give necessary and sufficient conditions for this Pride group to be non-spherical. Under such conditions, we show that Γ satisfies the Tits alternative.

Communicated by A. Olshanskiy     

Graphical convergence of continuous functions

Let X and Y be metrizable spaces. We show that convergence of a net of continuous functions 〈f _λ 〉 to a continuous function f in the graph topology for C(X,Y) is equivalent to the uniform convergence of the net of associated distance functionals for the graphs with respect to each compatible metric on X×Y. Remarkably, no weaker convergence results if uniform convergence is replaced by pointwise convergence in the last statement.