Covalent modification of calcium hydroxyapatite surface by grafting phenyl phosphonate moieties

The reaction between phenyl phosphonic dichloride (C₆H₅P(O)Cl₂) and synthetic calcium hydroxy- and fluorapatite has been investigated. The presence of mono- or polymeric (C₆H₅PO) fragment bound to hydroxyapatite was evidenced by IR, and solid-state ³¹P NMR spectroscopy. X-ray powder analysis has shown that the apatitic structure remains unchanged during the reaction. In contrast, no reaction was found using fluorapatite. According to the results found for these two different apatites a mechanism was proposed for the formation of covalent P-O-P bonds as the result of a reaction between the C₆H₅P(O)Cl₂ organic reagent and (HPO₄)⁻ and/or OH⁻ ions of the hydroxyapatite.     

Darstellung und Charakterisierung der Trisilylphosphane (Ph 3Si) n P(SiMe 3)3−n,n=1,2,3

A simple preparation of the title compounds is achieved by reacting Na₃P/K₃P with stoichiometric mixtures of chlorotriphenylsilane and chlorotrimethylsilane.³¹P- and²⁹Si-NMR-Data as well as Ir and Raman spectra of the compounds are reported.

     

Experimental and DFT study of the aza-Diels-Alder reaction between cyclopentadiene and protonated benzylimine derivated from glyoxylates

The Diels-Alder reaction of protonated N-benzyl imine of methyl glyoxylate with cyclopentadiene in different solvents gave mixtures of exo/endo adducts. The exo/endo selectivity of the reaction was elucidated by NMR experiments. Theoretical calculations by means of density functional theory (DFT) at the B3LYP/6-31G(d) level have also been performed to elucidate the molecular mechanism of this reaction. The DFT results suggest a highly asynchronous concerted mechanism, which in turn can explain the preferred exo stereoselectivity of the reaction. Inclusion of solvent effects enhances the exo selectivity, and this effect increases with the polarity of the solvent, in good agreement with the experimental findings.     

Styrene oxide DNA adducts: quantitative determination using <Superscript>31</Superscript>P monitoring

The reaction of styrene oxide, a potential carcinogen in humans, with DNA constituents has been used to develop an improved method for quantification of DNA adducts. To enable monitoring of DNA adducts caused by xenobiotics at physiological relevant levels, a robust, reliable and powerful method based on monitoring of phosphorus in nucleotides is described. An efficient enzymatic digestion step and a sample-preconcentration procedure are essential, and enable separation of alkylated nucleotides from the large excess of native nucleotides. The adducts are detected by means of the phosphorus signal measured at mass m/z=31 with an inductively-coupled-plasma mass spectrometer. Bis(4-nitrophenyl)phosphate (BNPP) serves as internal standard for quantification of the adducts. The absolute limit of detection, 45 fmol, corresponds to detection of three modified nucleotides among 10⁷ native nucleotides (the calculation is based on use of 50 g calf thymus DNA). An adduct formation ratio at the DNA of 3.6 adducts per 1000 nucleotides was measured, which is 75% lower than for reaction with monomeric 2-deoxy-nucleotides. In addition, a substantial amount of phosphate adducts were detected, but in DNA the rate of phosphate formation was lower than with monomeric nucleotides. Most probably these adducts escaped unnoticed when ³¹P-post-labelling was employed.     

Symmetric Skorohod topology onn-variable functions and hierarchical Markov properties ofn-parameter processes

Summary We introduce a new Skorohod topology for functions of several variables. Since ann-variable function may be viewed as a one-variable function with values in the set of (n–1)-variable functions, this topology is defined by induction from the classical Skorohod topology for one-variable functions. This allows us to define the notion of completen-parameter symmetric Markov processes: Such processes are, for any 1pn, rawp-parameter Markov processes (in the sense of our previous paper [17]) with values in the space of (n–p)-variable functions. We prove, for these processes and their Bochner subordinates, a maximal inequality which implies the continuity of additive functionals associated with finite energy measures. We finally present several important examples.     

On extension theory inL 2-spaces

We present the first steps towards a general extension theory inL ²-spaces. By this theory it is possible to construct all perturbations of the Laplacian supported by a closed setN even if the classical capacity ofN equals zero.     

An indexed set of density bounds on lattice packings

It has long been known that the admissibility of a lattice with respect to a symmetric convex bodyB is equivalent to being a packing lattice for 1/2B. This fact is the basis of the interplay between the classical theory of the arithmetic minima of positive definite quadratic forms, on the one hand, and the dense lattice packing of spheres inR ⁿ , on the other.We give an indexed set of bounds _L (B) a _j , where 0 j n/2, on the lattice packing density ofB. The casej=0 reduces to the aforementioned long-known fact, andj=1 was proved by Elkies, Odlyzko, and Rush, and was used to obtain record high packing densities for various superballs. The new cases make possible the use of smaller primes in the construction of these dense packings.Supported by National Science Foundation grant DMS-9103233.     

Sur le comportement asymptotique des potentiels d'une chaîne de Markov sur ℝ d

Résumé Dans cet article j'étudie le comportement à l'infini des potentiels des chaînes de Markov sur ^d (d3) proches du mouvement brownien, tout spécialement le cas des marches aléatoires, ainsi que des critères de transience et de récurrence inspirés de la méthode utilisée.

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We study the asymptotic behaviour of potentials of Markov chains on ^d (d3), closed to Brownian motion, and particularly the case of random walks. Following a similar approach, we give transience and recurrence criteria.

     

Finely holomorphic functions and quasi-analytic classes

We study the set of functions in quasi-analytic classes and the set of finely holomorphic functions. We show that no one of these two sets is contained in the other.LetI denote the set of complex functionsf: for which there exists a quasi-analytic classC{M _n} containingf. Let denote the set of complex functionsf: for which there exist a fine domainU containing the real line and a function finely holomorphic onU satisfyingf(x)= (x) for allx . The power of unique continuation is incomparable in these two cases (I\ is non-empty, \I is non-empty).Research supported by the grant No. 201/93/2174 of Czech Grant Agency and by the grant No. 354 of Charles University.     

Conformal capacities and conformally invariant functions on Riemannian manifolds

This paper develops the theory of conformal invariants initiated inJ. Differential Geom 8 (1973), 487–510 for a Riemannian manifoldM with dimensionn2. We construct and study four conformally invariant functions M, M, M, M resp. depending on 4, 3 or 2 points onM, defined as extremal capacities for condensers associated with those points. These functions have similarities with the classical invariants onS ⁿ ,R ⁿ orH ⁿ . Their properties, and especially their continuity, are efficient tools for solving some problems of conformal geometry in the large.