Erd?s-Szekeres theorem with forbidden order types

According to the classical Erd?s-Szekeres theorem, every sufficiently large set of points in general position in the plane contains a large subset in convex position. Parallel to the Erd?s-Hajnal problem in graph-Ramsey theory, we investigate how large such subsets must a configuration contain if it does not have any sub-configuration belonging to a fixed order type.     

Sensitivity- and Gradient-Enhanced Hetero (ω1) Half-Filtered TOCSY Experiment for Measuring Long-Range Heteronuclear Coupling Constants

An enhanced version of the X(ω₁) half-filtered TOCSY experiment for measurement of long-range heteronuclear coupling constants is proposed which yields high-quality spectra with substantially increased sensitivity and resolution. The modified method features gradient-enhanced X filtering sequences, broadband homonuclear decoupling duringt₁, optional¹J_XHscaling in theF₁domain, and gradient coherence selection in combination with the sensitivity-enhanced protocol for the TOCSY transfer. These modifications extend the applicability of the method—coupling constants can be measured accurately for natural abundance samples at low concentrations and for compounds yielding complex spectra. Computer-aided analysis of E.COSY-type multiplets is applied for the determination of heteronuclear long-range coupling constants.     

Direct elemental analysis of cancer cell lines by total reflection X-ray fluorescence

The elemental content of Cu, Fe and Zn in two human adenocarcinoma cell lines was investigated by total reflection X-ray fluorescence (TXRF) spectrometry. Cancer cells were sedimented directly to the quartz plates using a modified cytospin slide holder setup. Special glass stands and caps were also constructed to hold the quartz plates with the cells during the vapour-phase microwave assisted digestion. The method was validated by analysis of certified reference materials. The signal-to-noise ratio was optimized by washing the cells with different solutions. The technique was applied to the determination of Cu, Fe and Zn content of HT-29 and HCA-7 colorectal adenocarcinoma cell lines. Dry mass of the centrifuged cells were determined and the elemental analysis data reported for the two cell lines were referred either to cell numbers, to the total protein content or to the dry mass.     

Stereochemical studies—75 : Saturated heterocycles—62. connection between the diastereoselectivity and the dominant conformation in the formation of condensed- skeleton 1,3-oxazines,first X-ray diffraction evidence of N-outside conformation

The rapid, spontaneous epimerization occurring at the C(2) chirality centre of a new diastereomeric (r-4,c-2,c-5)-2-(p-nitrophenyl)-3-methyl-4,5-tetramethylenetetrahydro-1,3-oxazine led to the conclusion that the configuration at C(2) of the bicyclic 1,3-oxazines formed by the cyclization of alicyclic 1,3-aminoalcohols with aldehydes is determined by the dominant conformation of the product. The first X-ray diffraction evidence is given for the N-outside conformation of compounds of this type.     

Syntheses and NMR,MS and X‐ray investigations of homoadamantane‐fused pyridopyrimidinones

The reactions of ethyl 5‐oxotricyclo[4.3.1.1^3,8]undecane‐4‐carboxylate (2) with methyl‐substituted 2‐aminopyridines in polyphosphoric acid (PPA) gave two products, linearly‐condensed pyridopyrimidinones 4a‐c and 2‐pyridylcarboxamides 5a‐c , whereas the reactions with amino, hydroxy and nitro derivatives of 2‐aminopyridine furnished only linearly‐condensed pyridopyrimidinones (4g‐j). Use of a mixture of PPA and phosphorus oxychloride as solvent afforded both linearly‐ (4a‐c,e,f) and angularly‐condensed (6a–c,e,f) pyridopyrimidinones. In toluene, with p‐toluenesulfonic acid as catalyst, 2‐pyridylcarboxamides 5a‐f were obtained. In a mixture of PPA and phosphorus oxychloride at 80–120 °C, 5a‐f yielded angularly‐condensed pyridopyrimidinones 6a‐f. All the products exhibited characteristic features, as determined by NMR and electron ionization mass spectrometry and X‐ray crystallography.     

Kinetics and mechanism of the iodine oxidation of hydroxylamine

Studies of the stoichiometry and kinetics of the reaction between hydroxylamine and iodine, previously studied in media below pH 3, have been extended to pH 5.5. The stoichiometry over the pH range 3.4–5.5 is 2NH₂OH + 2I₂ = N₂O + 4I^? + H₂O + 4H⁺. Since the reaction is first-order in [I₂] + [I₃^?], the specific rate law, k₀, is k₀ = (k₁ + k₂/[H⁺]) {[NH₃OH⁺]₀/(1 + K_p[H⁺])} {1/(1 + K_I[I^?])}, where [NH₃OH⁺]₀ is total initial hydroxylamine concentration, and k₁, k₂, K_p, and K_I are (6.5 ± 0.6) × 10⁵ M^?1 s^?1, (5.0 ± 0.5) s^?1, 1 × 10⁶ M^?1, and 725 M^?1, respectively. A mechanism taking into account unprotonated hydroxylamine (NH₂OH) and molecular iodine (I₂) as reactive species, with intermediates NH₂OI₂^?, HNO, NH₂O, and I₂^?, is proposed.     

Estimation of the Mean of a Wiener Sheet

A shifted Wiener sheet is observed above a decreasing curve Γ. By the help of a direct discrete approach and under weaker assumptions than in the paper of Arató [Comput. Math. Appl. 33 (1997), 13–25], an explicit formula is derived for the maximum likelihood estimator of the shift parameter. This estimator is a weighted linear combination of the values at the endpoints of the curve Γ and weighted integrals of the observed process and its normal derivative along the curve Γ. This revised version was published online in June 2006 with corrections to the Cover Date.     

Representation of molecules by atomic charges: A new population analysis

For the calculation of atomic charges in molecules, a new fast procedure based on extended Mulliken population analysis is presented. The reliability of the new population analysis is tested within the AM1 approximation and the results are compared in detail with those obtained by different methods reported in the literature.     

Crystal structure of rosmanol-9-ethylether

The title compound: 2H-10,4a-(epoxy-methano)-phenantren-12-one-1,3,4,9,10,10a-hexahydro-5,6-dihydroxy-9-etoxy-1,1-dirnethyl-7-(1-methylethyl), was isolated fromSalvia officinalis L. andHyssopus officinalis L. C₂₂H₃₀O₅, orthorhombic, P2₁2₁2₁, (No. 19)a=8.309(1),b=11.320(2),c=22.060(3) Å,V=2075.0(9) ų,Z=4,D _x=1.199 g·cm^–3, (CuK)=1.54184 Å,=6.43 cm^–1, F(000)=808,T=296(1) K. The structure was solved by direct methods and refined toR=0.047 for 1824 observed reflections collected on a CAD-4 diffractometer. In the course of structure refinement conformational disorder of the isopropyl moiety and the terminal methyl group pertaining to the ethoxy ligand was established. They result altogether in four different conformers.Alternatively it can be termed 9-ethoxyrosmanol.     

Ion‐Selective Electrodes Based on Hydrophilic Ionophore‐Modified Nanopores

We report the synthesis and analytical application of the first Cu²⁺‐selective synthetic ion channel based on peptide‐modified gold nanopores. A Cu²⁺‐binding peptide motif (Gly‐Gly‐His) along with two additional functional thiol derivatives inferring cation‐permselectivity and hydrophobicity was self‐assembled on the surface of gold nanoporous membranes comprising of about 5 nm diameter pores. These membranes were used to construct ion‐selective electrodes (ISEs) with extraordinary Cu²⁺ selectivities, approaching six orders of magnitude over certain ions. Since all constituents are immobilized to a supporting nanoporous membrane, their leaching, that is a ubiquitous problem of conventional ionophore‐based ISEs was effectively suppressed.