On the relative strength of split,triangle and quadrilateral cuts

Integer programs defined by two equations with two free integer variables and nonnegative continuous variables have three types of nontrivial facets: split, triangle or quadrilateral inequalities. In this paper, we compare the strength of these three families of inequalities. In particular we study how well each family approximates the integer hull. We show that, in a well defined sense, triangle inequalities provide a good approximation of the integer hull. The same statement holds for quadrilateral inequalities. On the other hand, the approximation produced by split inequalities may be arbitrarily bad.     

The History of the Discovery of the Molybdenum Cofactor and Novel Aspects of its Biosynthesis in Bacteria

Biosynthesis of the molybdenum cofactor in bacteria is described with a detailed analysis of each individual reaction leading to the formation of stable intermediates during the synthesis of molybdopterin from GTP. As a starting point, the discovery of molybdopterin and the elucidation of its structure through the study of stable degradation products are described. Subsequent to molybdopterin synthesis, the molybdenum atom is added to the molybdopterin dithiolene group to form the molybdenum cofactor. This cofactor is either inserted directly into specific molybdoenzymes or is further modified by the addition of nucleotides to the molybdopterin phosphate group or the replacement of ligands at the molybdenum center.     

Multinuclear cytotoxic metallodrugs: physicochemical characterization and biological properties of novel heteronuclear gold-titanium complexes

An unprecedented series of titanocene-gold bi- and trimetallic complexes of the general formula [[(η(5)-C(5)H(5))(μ-η(5):κ(1)-C(5)H(4)(CH(2))(n)PPh(2))TiCl(2)](m)AuCl(x)](q+) (n = 0, 2, or 4; m = 1, x = 1, q = 0 or m = 2, x = 0, q = 1) have been prepared and characterized spectroscopically. The luminescence spectroscopy and photophysics of one of the compounds, [[(η(5)-C(5)H(5))(μ-η(5):κ(1)-C(5)H(4)PPh(2))TiCl(2)](2)Au]PF(6), have been investigated in 2MeTHF solution and in the solid state at 77 and 298 K. Evidence for interfragment interactions based on the comparison of electronic band positions and emission lifetimes, namely, triplet energy transfer (ET) from the Au- to the Ti-containing chromophores, is provided. The cytotoxicity of the complexes was evaluated on A2780 ovarian cancer cells and on their cisplatin-resistant cell line A2780cisR; the compounds showed activity in the low micromolar range that was markedly more active than the corresponding titanocene-phosphine precursors [(η(5)-C(5)H(5))(η(5)-C(5)H(4)(CH(2))(n)PPh(2))TiCl(2)], cisplatin, and, for some of them, the gold analogue [(PPh(3))AuCl]. In an attempt to draw preliminary structure-activity relationships, cell uptake measurements and interaction studies with plasmid DNA and the model protein ubiquitin (Ub) have been undertaken on some of the compounds.     

Minimum number of below average triangles in a weighted complete graph

Let G be an edge weighted graph with n nodes, and let A(3,G) be the average weight of a triangle in G. We show that the number of triangles with weight at most equal to A(3,G) is at least (n−2) and that this bound is sharp for all n≥7. Extensions of this result to cliques of cardinality k>3 are also discussed.     

Cleavable hydrophilic linker for one-bead-one-compound sequencing of oligomer libraries by tandem mass spectrometry

We have developed a method for the rapid and unambiguous identification of sequences of hit compounds from one-bead-one-compound combinatorial libraries of peptide and peptoid ligands. The approach uses a cleavable linker that is hydrophilic to help reduce nonspecific binding to biological samples and allows for the attachment of a halogen tag, which greatly facilitates post-screening sequencing by tandem mass spectrometry (MS/MS). The linker is based on a tartaric acid unit, which, upon cleavage from resin, generates a C-terminal aldehyde. This aldehyde can then be derivatized with a bromine-containing amino-oxy compound that serves as an isotope tag for subsequent MS/MS analysis of y-ion fragments. We have applied this linker and method to the syntheses of a number of peptoids that vary in sequence and length and have also demonstrated single-bead sequencing of a peptoid pentamer. The linker is also shown to have very low levels of nonspecific binding to proteins.     

Identification of pharmaceutical tablets by Raman spectroscopy and chemometrics

Raman spectroscopy has become an attractive tool for the analysis of pharmaceutical solid dosage forms. In the present study it is used to ensure the identity of tablets. The two main applications of this method are release of final products in quality control and detection of counterfeits. Twenty-five product families of tablets have been included in the spectral library and a non-linear classification method, the Support Vector Machines (SVMs), has been employed. Two calibrations have been developed in cascade: the first one identifies the product family while the second one specifies the formulation. A product family comprises different formulations that have the same active pharmaceutical ingredient (API) but in a different amount. Once the tablets have been classified by the SVM model, API peaks detection and correlation are applied in order to have a specific method for the identification and allow in the future to discriminate counterfeits from genuine products. This calibration strategy enables the identification of 25 product families without error and in the absence of prior information about the sample. Raman spectroscopy coupled with chemometrics is therefore a fast and accurate tool for the identification of pharmaceutical tablets.     

Dehydrierungsversuche am Sitosterin

Ohne Zusammenfassung