Turánnical hypergraphs

This paper is motivated by the question of how global and dense restriction sets in results from extremal combinatorics can be replaced by less global and sparser ones. The result we consider here as an example is Turán's theorem, which deals with graphs G = ([n],E) such that no member of the restriction set \begin{align*}\mathcal {R}\end{align*} = \begin{align*}\left( {\begin{array}{*{20}c} {[n]} \\ r \\ \end{array} } \right)\end{align*} induces a copy of K_r. Firstly, we examine what happens when this restriction set is replaced by \begin{align*}\mathcal {R}\end{align*} = {X∈ \begin{align*}\left( {\begin{array}{*{20}c} {[n]} \\ r \\ \end{array} } \right)\end{align*}: X ∩ [m]≠??}. That is, we determine the maximal number of edges in an n ‐vertex such that no K_r hits a given vertex set. Secondly, we consider sparse random restriction sets. An r ‐uniform hypergraph \begin{align*}\mathcal R\end{align*} on vertex set [n] is called Turánnical (respectively ε ‐Turánnical), if for any graph G on [n] with more edges than the Turán number t_r(n) (respectively (1 + ε)t_r(n) ), no hyperedge of \begin{align*}\mathcal {R}\end{align*} induces a copy of K_r in G. We determine the thresholds for random r ‐uniform hypergraphs to be Turánnical and to be ε ‐Turánnical. Thirdly, we transfer this result to sparse random graphs, using techniques recently developed by Schacht [Extremal results for random discrete structures] to prove the Kohayakawa‐?uczak‐Rödl Conjecture on Turán's theorem in random graphs.© 2012 Wiley Periodicals, Inc. Random Struct. Alg., 2012     

Orthogonal and Skew-Symmetric Operators in Real Hilbert Space

In the theory of traces on operator ideals, it is desirable to treat not only the complex case. Several proofs become much easier when the underlying operators are represented by real matrices. Motivated by this observation, we prove two theorems which, to the best of our knowledge, are not available in the real setting: (1) every operator is a finite linear combination of orthogonal operators, and (2) every skew-symmetric compact operator S is a commutator [A, T], where certain properties of S are inherited to T. In our opinion, theses results are interesting for their own sake. They will also be used in future studies of trace theory by the second-named author.     

Sulphur isotope fractionation during the reduction of elemental sulphur and thiosulphate by Dethiosulfovibrio spp

Stable sulphur isotope fractionation was investigated during reduction of thiosulphate and elemental sulphur at 28°C by growing batch cultures of the sulphur- and thiosulphate-reducing bacteria Dethiosulfovibrio marinus (type strain DSM 12537) and Dethiosulfovibrio russensis (type strain DSM 12538), using citrate as carbon and energy source. The cell-specific thiosulphate reduction rate in the growth phase was 7.4±3.9?fmol?cell(-1)?d(-1). The hydrogen sulphide produced was enriched in (32)S by 10.3±1?‰ compared with total thiosulphate sulphur, close to previous experimental results observed for other sulphate- and non-sulphate-reducing bacteria. Elemental sulphur reduction yields sulphur isotope enrichment factors between-1.3 and-5.2?‰ for D. russensis and-1.7 and-5.1?‰ for D. marinus. The smaller fractionation effects are observed in the exponential growth phase (cellular rates between 5 and 70?fmol?S°?cell(-1)?d(-1)) and enhanced discrimination under conditions of citrate depletion and cell lysis (cellular rates between 0.3 and 3?fmol?S°?cell(-1)?d(-1)).     

On the best constants in inequalities of the Markov and Wirtinger types for polynomials on the half-line

The main topic of the paper is best constants in Markov-type inequalities between the norms of higher derivatives of polynomials and the norms of the polynomials themselves. The norm is the L² norm with Laguerre weight. The leading term of the asymptotics of the constants is determined and tight bounds for the principal coefficient in this term, which is the operator norm of a Volterra operator, are given. For best constants in inequalities of the Wirtinger type, the limit is computed and an asymptotic formula for the error term is presented.     

Darstellung und Kristallstruktur von CsTe4

Preparation and Crystal Structure of CsTe₄ CsTe₄ results from a melting reaction at 570°C in sealed quartztubes. The starting materials Cs and Te in the molar ratio 1:4 are produced in a first step by controlled decomposition of the CsN₃ from mixtures of CsN₃ and Te (1:4) at 350°C. CsTe₄ is monoclinic, space group P2₁/c, with a = 7.857(1) Å, b = 7.286(1) Å, c = 14.155(2) Å, β = 93.83(1)°, and Z = 4. The tellurium atoms form a two-dimensional puckered layer built of from pseudo-trigonal-bipyramidal, T-shaped units Te₄^?. The central tellurium atom of this unit may be considered as a pseudo iodine. The compound is compared with other tellurides MTe_n having some like that unexpected principles of connection.     

Hexafluoroacetone as Protecting and Activating Reagent. Glycosylated Malic, Citramalic, and Thiomalic Acid Derivatives, New Glycosylated Building Blocks for Drug Design [1]

Summary. Glycosylated -hydroxy and -mercapto acids have been synthesized starting from malic/citramalic/thiomalic acid and Ac₄--D-Glc-NH₂/Bzl₄--D-Glc-NH₂ using hexafluoroacetone as protecting and activating reagent.Dedicated to Prof. Dr. Horst Wilde on the occasion of his 65^th birthday     

Hydrophobic Silica Sol Coatings on Textiles—the Influence of Solvent and Sol Concentration

Hydrophobic silica sol coatings on textiles were investigated with respect to the influence of the solvents and the concentration of the sol. For this purpose, two silica sols, prepared with the hydrophobic additives octyltriethoxysilane and perfluoroctyltriethoxysilane were diluted by different solvents: water, ethanol and aceton.In case of using pure water for dilution, the hydrophobicity of coated textiles decreases drastically with increasing dilution of the applied sol. For coatings on polyester fabrics or mixed fabrics made from polyester and cotton, the use of the organic solvents ethanol or aceton leads to significant hydrophobicity even in case of strong dilution down to a sol concentration < 1%. The hydrophobic effect of coated polyamide textile is less. The reason for different hydrophobicity of coated textiles resulting from the use of water instead of organic solvents is explained by different surface morphologies of the coatings deposited on the textile fibres, as observed by REM. In case of using organic solvents the coatings contain a more flat morphology which covers the fibres completely. In contrast, sols with higher water content lead to less adhesive coatings with crack formation.The use of a combination of water with less inflammable organic solvents such as di(propylene glycol) n-propyl ether (Dowanol^TM DPnP) in hydrophobic silica sols yields textile coatings with good hydrophobicity, even in case of low sol concentration. For practical application of textile coatings, especially silica sols with high water content are of interest, due to less risk of inflammation and lower ecological impact. Therefore, the use of water diluted hydrophobic silica sols with small amounts of DPnP offers a chance for textile refinement by the sol–gel technique.     

Nickel(II)‐Komplexe von Oxalamidinen und Oxalamidinaten mit zusätzlichen R2P‐Donorgruppen

Complexes of Nickel(II) with Oxalic Amidines and Oxalic Amidinates with Additonal R₂P‐Donor Groups Oxalamidines R¹N=C(NHR²)‐C(=NHR²)=NR¹, which bear additional donor atoms at two of the four N substituents ( H₂A : R¹ = mesityl, R² = ‐(CH₂)₃‐PPh_2; H₂B : R¹ = tolyl, R² = ‐(CH₂)₃‐PMe₂) form binuclear complexes with Nickel(II) in which very different coordination modes are realized. In the complex [ (A) Ni₂Br₂] (1) the two nickel atoms at each side of the bridge are in a square‐planar environment, coordinated by the two N donor atoms of the oxalic amidinate framework, a bromide and a Ph₂P group. An analogous coordination has the organometallic compound [ (A) Ni₂Me₂] (2) . In contrast, the two nickel atoms in the compound {[( B )][Ni(acac)]₂} (5) differ in their coordinative environment. At one side of the oxalic amidinate bridging ligand a (acac)Ni fragment is coordinated by the two N donor atoms resulting in a square‐planar environment. At the opposite side the (acac)Ni fragment is coordinated at the both N donor ligands of the bridging ligand as well as at the two PMe₂ groups of the side chains resulting in an octahedral coordination for this nickel atom.