Markov Property and Cokernels of Local Operators

We discuss Gaussian generalized random fields indexed by smoothsections of vector bundles with respect to Markov properties.We propose a new set-up which is suitable for the present questionand within which new phenomena are detected naturally. In particular,we give a counterexample to the belief that locality in theRKHS implies the germ Markov property. We also prove the closeconnection between the Markov property and cokernels of localoperators. Furthermore, we prove the Markov property for a verydegenerate Gaussian random field.     

Spectroscopical Investigation of Ski Base Materials

Summary: Raman spectroscopy was applied to perform a comprehensive morphological analysis of polyethylene (PE) ski base materials at different processing levels. The morphological characterization included determination and evaluation of Raman spectra and examination of the crystallinity values by differential scanning calorimetry (DSC). A good agreement between Raman and DSC crystallinity fractions was obtained, thus corroborating the Raman spectroscopy approach. While for the PE grade with the lowest average molar mass no significant morphological changes due to processing from the raw material via the extruded film to the post-treated film was found, higher molar mass PE grades exhibited a decrease of crystallinity, but an increase of the amorphous fraction along the process chain.     

A unique approach to accurately measure thickness in thick multilayers

X‐ray optics called multilayer Laue lenses (MLLs) provide a promising path to focusing hard X‐rays with high focusing efficiency at a resolution between 5 nm and 20 nm. MLLs consist of thousands of depth‐graded thin layers. The thickness of each layer obeys the linear zone plate law. X‐ray beamline tests have been performed on magnetron sputter‐deposited WSi₂/Si MLLs at the Advanced Photon Source/Center for Nanoscale Materials 26‐ID nanoprobe beamline. However, it is still very challenging to accurately grow each layer at the designed thickness during deposition; errors introduced during thickness measurements of thousands of layers lead to inaccurate MLL structures. Here, a new metrology approach that can accurately measure thickness by introducing regular marks on the cross section of thousands of layers using a focused ion beam is reported. This new measurement method is compared with a previous method. More accurate results are obtained using the new measurement approach.     

Singly and doubly lithium doped silicon clusters: geometrical and electronic structures and ionization energies

The geometric structures of neutral and cationic Si(n)Li(m)(0/+) clusters with n = 2-11 and m = 1, 2 are investigated using combined experimental and computational methods. The adiabatic ionization energy and vertical ionization energy (VIE) of Si(n)Li(m) clusters are determined using quantum chemical methods (B3LYP/6-311+G(d), G3B3, and CCSD(T)/aug-cc-pVxZ with x = D,T), whereas experimental values are derived from threshold photoionization experiments in the 4.68-6.24 eV range. Among the investigated cluster sizes, only Si(6)Li(2), Si(7)Li, Si(10)Li, and Si(11)Li have ionization thresholds below 6.24 eV and could be measured accurately. The ionization threshold and VIE obtained from the experimental photoionization efficiency curves agree well with the computed values. The growth mechanism of the lithium doped silicon clusters follows some simple rules: (1) neutral singly doped Si(n)Li clusters favor the Li atom addition on an edge or a face of the structure of the corresponding Si(n)(-) anion, while the cationic Si(n)Li(+) binds with one Si atom of the bare Si(n) cluster or adds on one of its edges, and (2) for doubly doped Si(n)Li(2)(0/+) clusters, the neutrals have the shape of the Si(n+1) counterparts with an additional Li atom added on an edge or a face of it, while the cations have both Li atoms added on edges or faces of the Si(n)(-) clusters.     

Notes on the Roots of Ehrhart Polynomials

We determine lattice polytopes of smallest volume with a given number of interior lattice points. We show that the Ehrhart polynomials of those with one interior lattice point have largest roots with norm of order n², where n is the dimension. This improves on the previously best known bound n and complements a recent result of Braun where it is shown that the norm of a root of a Ehrhart polynomial is at most of order n². For the class of 0-symmetric lattice polytopes we present a conjecture on the smallest volume for a given number of interior lattice points and prove the conjecture for crosspolytopes. We further give a characterisation of the roots of Ehrhart polyomials in the three-dimensional case and we classify for n ≤ 4 all lattice polytopes whose roots of their Ehrhart polynomials have all real part -1/2. These polytopes belong to the class of reflexive polytopes.     

Molecular associations of [2.2]paracyclophanearylhydrazones with organic acceptors,VIII

Summary Molecular complexes of mono and disubstituted [2.2]paracyclophanehydrazones with organic acceptors have been studied by means of thermodynamic and spectroscopic properties. Furthermore, the enhancement of the donor strength, induced by the hydrazono group, is viewed in the light of substituent as well as transannular effects.

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Molekulare Assoziation von [2.2]Paracyclophanarylhydrazonen mit organischen Akzeptoren, 8. Mitt.

Zusammenfassung Es wurden Molekülkomplexe von mono- und disubstituierten [2.2]Paracyclophanarylhydrazonen mit organischen Akzeptoren mittels thermodynamischer und spektroskopischer Methoden untersucht. Zusätzlich wird der Anstieg in der Donorstärke, der von der Hydrazonogruppe induziert wird, im Hinblick auf Substituenten- und auch transannulare Effekte diskutiert.

     

Molecular zinc phosphonates: synthesis and X-ray crystal structures of [[(ZnMe)4(THF)2][tBuPO3]2] and [[(ZnEt)3(Zn(THF))3][tBuPO3]4[mu3-OEt]

The reactions of zinc alkyls with tert-butylphosphonic acid in 2 : 1 and 1 : 1 molar ratios afforded [[(ZnMe)(4-)(THF)2][tBuPO3]2] (2) and [[(ZnEt)3(Zn(THF))3][tBuPO3]4[mu3-OEt]] (3), respectively. Compounds 2 and 3 have been fully characterised by means of spectroscopic and analytical methods. Single-crystal X-ray diffraction studies revealed that zinc phosphonates 2 and 3 are tetra- and hexa-nuclear, respectively. This is in contrast to the dodecanuclear zinc phosphonate [[Zn2(THF)2(ZnEt)6Zn4(mu4-O)][(tBuPO3)8]] (1) obtained in a 1.5 : 1 reaction between zinc alkyls and tBuP(O)(OH)2.     

Mechanistic insights into the reductive dehydroxylation pathway for the biosynthesis of isoprenoids promoted by the IspH enzyme

Here, we report an integrated quantum mechanics/molecular mechanics (QM/MM) study of the bio-organometallic reaction pathway of the 2H⁺/2e^– reduction of (E)-4-hydroxy-3-methylbut-2-enyl pyrophosphate (HMBPP) into the so called universal terpenoid precursors isopentenyl pyrophosphate (IPP) and dimethylallyl pyrophosphate (DMAPP), promoted by the IspH enzyme. Our results support the viability of the bio-organometallic pathway through rotation of the OH group of HMBPP away from the [Fe₄S₄] cluster at the core of the catalytic site, to become engaged in a H-bond with Glu126. This rotation is synchronous with π-coordination of the C2C3 double bond of HMBPP to the apical Fe atom of the [Fe₄S₄] cluster. Dehydroxylation of HMBPP is triggered by a proton transfer from Glu126 to the OH group of HMBPP. The reaction pathway is completed by competitive proton transfer from the terminal phosphate group to the C2 or C4 atom of HMBPP.