On a conjecture of R. E. Miles about the convex hull of random points

Denoty byp _d+i (B _d ,d+m) the probability that the convex hull ofd+m points chosen independently and uniformly from ad-dimensional ballB _d possessesd+i(i=1,...,m) vertices. We prove Mile's conjecture that, given any integerm, p _d+m (B _d ,d+m)»1 asd». This is obvious form=1 and was shown by Kingman form=2 and by Miles form=3. Further, a related result by Miles is generalized, and several consequences are deduced.Dedicated to Professor E. Halwaka on the occasion of his seventieth     

Structure and in vitro antifungal activity of [2,6‐bis(dimethylaminomethyl)phenyl]diphenyltin(IV) compounds

A set of seven [2,6‐bis(dimethylaminomethyl)phenyl]diphenyltin(IV) ({[(CH₃)₂NCH₂]₂(C₆H₃)}­(C₆H₅)₂Sn⁺X^?) ionic organotin(IV) compounds (X = Br, NO₃, CN, SCN, SeCN, BF₄ and PF₆) has been prepared and characterized by electrospray ionization mass spectrometry, ¹H NMR spectroscopy in CDCl₃,¹¹⁹Sn NMR in CDCl₃ and DMSO‐d₆ solution, as well as by ¹³C and ¹¹⁹Sn CP/MAS NMR spectroscopy and X‐ray diffraction techniques in the solid state. The in vitro antifungal activity of these water‐soluble ionic organotin(IV) compounds was compared with starting compounds and the antifungal drugs currently in clinical use. Copyright © 2002 John Wiley & Sons, Ltd.     

Supercritical fluid extraction of amino acids from birch (Betula pendula Roth) leaves and their liquid chromatographic determination with fluorimetric detection

A method for supercritical fluid extraction (SFE) of amino acids was adapted and optimal experimental conditions were selected for a matrix consisting of dry leaves. The matrix-dependent SFE method uses a mixture of MeOH-H(2)O-acetonitrile (10:10:1 v/v/v) as a modifier (0.5 mL in situ, 300 muL on-line) at 70 degrees C and 40 MPa and no HCl is needed as an entrainer. The amino acids were quantified using high-performance liquid chromatography with fluorimetric detection (HPLC/FLD) after gradient elution on Zorbax Eclipse AAA columns (4.6x150 mm, 3.5 mum) with aqueous Na(2)HPO(4 )buffer of pH 7.8 and ACN-MeOH-water as a mobile phase. In comparison with Soxhlet extraction, SFE gave higher recovery and selectivity, but it required longer extraction time (90 min) and it was more labor-intensive (clean-up step after the pre-concentration). Both methods should be used separately or in combination according to the matrix, number of samples, and levels of ballast compounds.     

Synthesis and antifungal activity of alkyland arylsulfanylpyridinylguanidines

A series of alkyl- and arylsulfanylpyridylguanidines was synthesized and their antimicrobial activity was evaluated in vitro against eight potentially pathogenic strains of fungi. Compounds with an alkylsulfanyl substitution have antifungal activity, which improves with increasing length of the aliphatic chain.     

Distribution-independent properties of the convex hull of random points

Denote byV _n ^(d) the expected volume of the convex hull ofn points chosen independently according to a given probability measure in Euclideand-spaceE ^d. Ifd=2 ord=3 and is the measure corresponding to the uniform distribution on a convex body inE ^d, Affentranger and Badertscher derived that

Zur Kenntnis der unterhalogenigen Säuren und der Hypohalogenite

Ohne ZusammenfassungVgl. A. Skrabal, Monatshefte für Chemie,28 (1907), 319;30 (1909), 51;32 (1911), 167, 185 und 815;33 (1912), 99.Der experimentelle Teil vorliegender Untersuchungen wurde im Wintersemester 1911/12 im Laboratorium für analytische Chemie der Wiener Technischen Hochschule durchgeführt, die Niederschrift der Arbeit hat sich aber zufolge Übersiedlung des einen von uns nach Graz um zwei Jahre verzögert. Es drängt uns, dem Vorstand des genannten Laboratoriums, Herrn Hofrat Prof. Dr. G. Vortmann, für die Unterstützung und Förderung unserer Arbeit auch an dieser Stelle Dank zu sagen.     

Open-source machine learning: R meets Weka

Two of the prime open-source environments available for machine/statistical learning in data mining and knowledge discovery are the software packages Weka and R which have emerged from the machine learning and statistics communities, respectively. To make the different sets of tools from both environments available in a single unified system, an R package RWeka is suggested which interfaces Weka’s functionality to R. With only a thin layer of (mostly R) code, a set of general interface generators is provided which can set up interface functions with the usual “R look and feel”, re-using Weka’s standardized interface of learner classes (including classifiers, clusterers, associators, filters, loaders, savers, and stemmers) with associated methods.     

Substituted pyrazinecarboxamides: synthesis and biological evaluation

Condensation of the corresponding chlorides of some substituted pyrazine-2-carboxylic acids (pyrazine-2-carboxylic acid, 6-chloropyrazine-2-carboxylic acid, 5-tert-butylpyrazine-2-carboxylic acid or 5-tert-butyl-6-chloropyrazine-2-carboxylic acid) with various ring-substituted aminothiazoles or anilines yielded a series of amides. The syntheses, analytical and spectroscopic data of thirty newly prepared compounds are presented. Structure-activity relationships between the chemical structures and the anti-mycobacterial, antifungal and photosynthesis-inhibiting activity of the evaluated compounds are discussed. 3,5-Bromo-4-hydroxyphenyl derivatives of substituted pyrazinecarboxylic acid, 16-18, have shown the highest activity against Mycobacterium tuberculosis H(37)Rv (54-72% inhibition). The highest antifungal effect against Trichophyton mentagrophytes, the most susceptible fungal strain tested, was found for 5-tert-butyl-6-chloro-N-(4-methyl-1,3-thiazol-2-yl)pyrazine-2-carboxamide (8, MIC =31.25 micromol x mL(-1)). The most active inhibitors of oxygen evolution rate in spinach Molecules 2006, 11,243 chloroplasts were the compounds 5-tert-butyl-6-chloro-N-(5-bromo-2-hydroxyphenyl)- pyrazine-2-carboxamide (27, IC(50) = 41.9 micromol x L(-1)) and 5-tert-butyl-6-chloro-N-(1,3- thiazol-2-yl)-pyrazine-2-carboxamide (4, IC50 = 49.5 micromol x L(-1)).