The exact bound in the Erdös-Ko-Rado theorem

This paper contains a proof of the following result: ifn≧(t+1)(k?t?1), then any family ofk-subsets of ann-set with the property that any two of the subsets meet in at leastt points contains at most \(\left( {\begin{array}{*{20}c} {n - t} \\ {k - t} \\ \end{array} } \right)\) subsets. (By a theorem of P. Frankl, this was known whent≧15.) The bound (t+1)(k-t-1) represents the best possible strengthening of the original 1961 theorem of Erdös, Ko, and Rado which reaches the same conclusion under the hypothesisn≧t+(k?t) \(\left( {\begin{array}{*{20}c} k \\ t \\ \end{array} } \right)^3 \) . Our proof is linear algebraic in nature; it may be considered as an application of Delsarte’s linear programming bound, but somewhat lengthy calculations are required to reach the stated result. (A. Schrijver has previously noticed the relevance of these methods.) Our exposition is self-contained.     

A metabonomic investigation of the biochemical effects of mercuric chloride in the rat using 1H NMR and HPLC-TOF/MS: time dependent changes in the urinary profile of endogenous metabolites as a result of nephrotoxicity

The effects of the administration of a single dose of the model nephrotoxin mercuric chloride (2.0 mg kg(-1), subcutaneous) to male Wistar-derived rats on the urinary metabolite profiles of a range of endogenous metabolites has been investigated using (1)H NMR and HPLC-MS. Urine samples were collected daily for 9 days from both dosed and control animals. Analysis of these samples revealed marked changes in the pattern of endogenous metabolites as a result of HgCl(2) toxicity. Peak disturbances in the urinary metabolite profiles were observed (using both NMR and HPLC-MS) at 3 days post dose. Thereafter the urinary metabolite profile gradually returned to a more normal composition. Markers of toxicity identified by (1)H NMR spectroscopy were raised concentrations of lactate, alanine, acetate, succinate, trimethylamine (TMA), and glucose. Reductions in the urinary excretion of citrate and alpha-ketoglutarate were also seen. Markers identified by HPLC-MS, in positive ion mode, were kynurenic acid, xanthurenic acid, pantothenic acid and 7-methylguanine which decreased after dosing. In addition an ion at m/z 188, probably 3-amino-2-naphthoic acid, was observed to increase after dosing. As well as these identified compounds other ions at m/z 297 and 267 decreased after dosing. In negative ion mode a range of sulfated compounds were observed, including phenol sulfate and benzene diol sulfate, which decreased after dosing. As well as the sulfated components an unidentified glucuronide at m/z 326 was also observed to decrease after dosing. The results of this study demonstrate the complementary nature of the NMR and MS-based techniques for metabonomic analysis.     

Molecular fluorescence excitation-emission matrices relevant to tissue spectroscopy

In vivo and ex vivo studies of fluorescence from endogenous and exogenous molecules in tissues and cells are common for applications such as detection or characterization of early disease. A systematic determination of the excitation-emission matrices (EEM) of known and putative endogenous fluorophores and a number of exogenous fluorescent photodynamic therapy drugs has been performed in solution. The excitation wavelength range was 250-520 nm, with fluorescence emission spectra collected in the range 260-750 nm. In addition, EEM of intact normal and adenomatous human colon tissues are presented as an example of the relationship to the EEM of constituent fluorophores and illustrating the effects of tissue chromophore absorption. As a means to make this large quantity of spectral data generally available, an interactive database has been developed. This currently includes EEM and also absorption spectra of 35 different endogenous and exogenous fluorophores and chromophores and six photosensitizing agents. It is intended to maintain and extend this database in the public domain, accessible through the Photochemistry and Photobiology website (http://www.aspjournal. com/).     

Matrix-isolation-FTIR spectroscopy with an integrating sphere

The use of an integrating sphere for the measurement of absorption spectra of thin films is described. The thin film (for example a rare gas matrix) is grown directly on the inside surface of the sphere. Multiple reflections inside the integrating sphere lead to significant enhancement of weak absorptions of the film, increasing the sensitivity of such measurements.     

The Dinitramide Anion, N(NO(2))(2)(-)

The infrared and Raman spectra of the NH(4)(+), K(+), and Cs(+) salts of N(NO(2))(2)(-) in the solid state and in solution have been measured and are assigned with the help of ab initio calculations at the HF/6-31G and MP2/6-31+G levels of theory. In agreement with the variations observed in the crystal structures, the vibrational spectra of the N(NO(2))(2)(-) anion are also strongly influenced by the counterions and the physical state. Whereas the ab initio calculations for the free N(NO(2))(2)(-) ion indicate a minimum energy structure of C(2) symmetry, Raman polarization measurements on solutions of the N(NO(2))(2)(-) anion suggest point group C(1) (i.e., no symmetry). This is attributed to the very small (<3 kcal/mol) N-NO(2) rotational barrier in N(NO(2))(2)(-) which allows for easy deformation.     

Determination of aflatoxins in food products by chromatography.

Several chromatographic methods for the determination of aflatoxins in agricultural and food products are reviewed. During the past two decades, identification and determination of aflatoxins were done by thin-layer chromatography (TLC) because it was easy, fast and inexpensive. However, high-performance liquid chromatography (HPLC) using fluorescence detection is now the method of choice for determining aflatoxins and is also growing in popularity for their identification. The reasons for selecting HPLC over TLC can be summarized as the ability to analyze for a wide variety of compounds, including compounds that are easily degraded by heat, light or air, the ease of adaptation to confirmatory procedures, the potential for automation and the dramatic improvement in instrumentation, including the development of increasingly sensitive fluorescence and electrochemical detectors and short, high-resolution, reversed-phase columns.     

Artificial metalloenzymes: The powerful alliance between protein scaffolds and organometallic catalysts

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Synthesis and small molecule reactivity of uranium(IV) alkoxide complexes with both bound and pendant N-heterocyclic carbene ligands

The syntheses of two tetravalent uranium alkoxide-carbene complexes are reported, [UIL3], and [UL4] where L = OCMe2CH2[1-C(NCHCHNiPr)]. The latter shows dynamic behaviour of the alkoxycarbene ligands in solution at room temperature, and the crystal structure of [UL4] shows that one carbene group remains uncoordinated. The unbound N-heterocyclic carbene group is trapped by a range of reagents such as 16-valence-electron metal carbonyl fragments and BH3 moieties, forming, for example, [UL3(mu-L)W(CO)5], [UL2(mu-L)2Mo(CO)4], and [UL(n)(L-BH3)(4-n)] (n = 1-4), demonstrating the potential for these hemilabile electropositive metal-carbene complexes to participate in the bifunctional activation of small molecules.     

Aggregation of PMe3-stabilized molybdenum sulfides and the catalytic dehydrogenation of H2S

The reactivity of [MoS(4)](2-) (1) toward PMe(3) was explored in the presence and absence of proton donors. Whereas MeCN solutions of (Et(4)N)(2)[MoS(4)] and PMe(3) are stable, in the presence of H(2)S such solutions catalyze formation of H(2) and SPMe(3). Addition of NH(4+) to such solutions afforded MoS(2)(PMe(3))(4) (2), which can be prepared directly from (NH(4))(2)[1]. Compound 2 is reactive toward thiols via a process proposed to involve the initial dissociation of one PMe(3) ligand, a hypothesis supported by the relative inertness of trans-MoS(2)(dmpe)(2). Benzene solutions of 2 react with EtSH to give Mo(2)(mu-S)(mu-SH)(PMe(3))(4)(SEt)(3) (3Et). Analogous reactions with thiocresol (MeC(6)H(4)SH) and H(2)S gave Mo(2)(mu-S)(mu-SH)(PMe(3))(4)(SR)(3) (R = tol, H). Crystallographic analyses of 3Et, 3H, and 3tol indicate dinuclear species with seven terminal ligands and a Mo(2)(mu-SR)(mu-S) core (r(Mo)(-)(Mo) = 2.748(1) A). From reaction mixtures leading to 3Et from 2, we obtained the intermediate Mo(IV)(2)(mu-S)(2)(SEt)(4)(PMe(3))(2) (4), an edge-shared bis(trigonal pyramidal) structure. Compounds 3H and 3Et react further with H(2)S to give Mo(4)(mu(2)-S)(4)(mu(3)-S)(2)(PMe(3))(6)(SH)(2) (5H) and Mo(4)(mu(2)-S)(4)(mu(3)-S)(2)(PMe(3))(6)(SEt)(2) (5Et), respectively. Analogously, W(4)(mu(2)-S)(4)(mu(3)-S)(2)(PMe(3))(6)(SH)(2) was synthesized from a methanol solution of (NH(4))(2)WS(4) with H(2)S and PMe(3). A highly accurate crystallographic analysis of (NH(4))(2)MoS(4) (R(1) = 0.0193) indicates several weak NH.S interactions.