Strict error bounds in Romberg quadrature

Two procedures are given for obtaining strict error bounds in Romberg quadrature. Sufficient conditions for their validity are derived. The simpler procedure only uses quantities already calculated in the Romberg scheme. The general procedure is based on a majorant concept.     

Metabolites of bird's nest fungi. Part 18. new oxygenated cadinane derivatives from cyathus striatus

The bird's nest fungusCyathus striatus Willd. ex Pers. when grown in aerated liquid culture produces three sesquiterpenes which are identified as schizandronol 1, 7α - hydroxy - schizandronol3 and schizandronol - 8,13β - oxide 5. The identification is based on spectral investigation of the compounds and their derivatives. This is the first reported isolation of 1 from a fungal source. Compounds 3 and 5 have not been reported previously.     

Further exploration of antimicrobial ketodihydronicotinic acid derivatives by multiple parallel syntheses

A synthetic reexamination of a series of ketodihydronicotinic acid class antibacterial agents was undertaken in an attempt to improve their therapeutic potential. A convenient new synthesis was developed involving hetero Diels-Alder chemistry producing 74 new analogs in a multiple parallel synthetic manner and these were examined in vitro for their antimicrobial potential. Several compounds demonstrated significant broad-spectrum activity against clinically derived bacterial strains but previously known 1-(2,4-difluorophenyl)-6-(4-dimethylaminophenyl)-4-pyridone-3-carboxylic acid (7) remained the most potent compound in this class. Cross-resistance with ciprofloxacin supported a commonality of mode of action. Permiabilization of Escherichia coli cells by polymyxin B significantly enhanced potency with these agents suggesting that poor cellular uptake was primarily responsible for the disappointing activity against bacteria that some of the analogs exhibited.     

A sol-gel based surface treatment for preparation of water repellent antistatic textiles

In this paper a surface treatment is described for preparation of hydrophobic sol-gel coatings that simultaneously offer antistatic properties for an appropriate finishing of textiles and refinement of polymer foils. Sol-gel based formulations are modified with both hydrophilic and hydrophobic components simultaneously. Hydrophobic components are, e.g., alkoxysilanes modified with alkyl chains while the hydrophilic ones are amino-functionalized alkoxysilanes. The basic idea is that due to an enrichment of hydrophobic groups at the solid/air interface the surface of the as prepared coatings will be hydrophobic while the deeper region will be more hydrophilic. Textiles finished with these coatings exhibit sufficient water repellence and simultaneously absorb sufficient amounts of humidity in the deeper areas of the coating guaranteeing antistatic properties. This concept offers interesting approaches for the preparation of multifunctional surface coatings not only focussing on combining water repellence with antistatic properties for textile materials.     

Formation of Sim and SimCn clusters by C60 sputtering of Si

The secondary ion mass spectrum of silicon sputtered by high energy C₆₀⁺ ions in sputter equilibrium is found to be dominated by Si clusters and we report the relative yields of Si_m⁺ (1 ≤ m ≤ 15) and various Si_mC_n⁺ clusters (1 ≤ m ≤ 11 for n = 1; 1 ≤ m ≤ 6 for n = 2; 1 ≤ m ≤ 4 for n = 3). The yields of Si_m⁺ clusters up to Si₇⁺ are significant (between 0.1 and 0.6 of the Si⁺ yield) with even numbered clusters Si₄⁺ and Si₆⁺ having the highest probability of formation. The abundances of cluster ions between Si₈⁺ and Si₁₁⁺ are still significant (>1% relative to Si⁺) but drop by a factor of ∼100 between Si₁₁⁺ and Si₁₃⁺. The probability of formation of clusters Si₁₃⁺-Si₁₅⁺ is approximately constant at ∼5 × 10⁻⁴ relative to Si⁺ and rising a little for Si₁₅⁺, but clusters beyond Si₁₅ are not detected (Si_m≥16⁺/Si⁺ < 1 × 10⁻⁴). The probability of formation of Si_m⁺ and Si_mC_n⁺ clusters depends only very weakly on the C₆₀⁺ primary ion energy between 13.5 keV and 37.5 keV. The behaviour of Si_m⁺ and Si_mC_n⁺ cluster ions was also investigated for impacts onto a fresh Si surface to study the effects that saturation of the surface with C₆₀⁺ in reaching sputter equilibrium may have had on the measured abundances. By comparison, there are very minor amounts of pure Si_m⁺ clusters produced during C₆₀⁺ sputtering of silica (SiO₂) and various silicate minerals. The abundances for clusters heavier than Si₂⁺ are very small compared to the case where Si is the target.The data reported here suggest that Si_m⁺ and Si_mC_n⁺ cluster abundances may be consistent in a qualitative way with theoretical modelling by others which predicts each carbon atom to bind with 3-4 Si atoms in the sample. This experimental data may now be used to improve theoretical modelling.     

Local and union boxicity

The boxicity $box\left(H\right)$ of a graph $H$ is the smallest integer $d$ such that $H$ is the intersection of $d$ interval graphs, or equivalently, that $H$ is the intersection graph of axis-aligned boxes in ${\mathbb{R}}^d$. These intersection representations can be interpreted as covering representations of the complement $H^c$ of $H$ with co-interval graphs, that is, complements of interval graphs. We follow the recent framework of global, local and folded covering numbers (Knauer and Ueckerdt, 2016) to define two new parameters: the local boxicity ${box}_{?}\left(H\right)$ and the union boxicity $\overline{box}\left(H\right)$ of $H$. The union boxicity of $H$ is the smallest $d$ such that $H^c$ can be covered with $d$ vertex–disjoint unions of co-interval graphs, while the local boxicity of $H$ is the smallest $d$ such that $H^c$ can be covered with co-interval graphs, at most $d$ at every vertex.We show that for every graph $H$ we have ${box}_{?}\left(H\right)\le \overline{box}\left(H\right)\le box\left(H\right)$ and that each of these inequalities can be arbitrarily far apart. Moreover, we show that local and union boxicity are also characterized by intersection representations of appropriate axis-aligned boxes in ${\mathbb{R}}^d$. We demonstrate with a few striking examples, that in a sense, the local boxicity is a better indication for the complexity of a graph, than the classical boxicity.