Synthesis and characterization of 4-hydroxy-3-phenylprolines

4-Hydroxy-3-phenylprolines were synthesized via 1-acetyl-2,2-diethoxycarbonyl-2,3-dihydro-3-phenyl-1H-pyrrole. Reversed phase hplc resulted in the isolation of the products which were characterized by ¹H and ¹³C nmr spectroscopy.     

A stable Nyström interpolant for some Mellin convolution equations

We consider the numerical solution of second kind integral equations of the form $$u(y) - \int\limits_0^1 {k(y/x)\frac{{u(x)}}{x}dx = f(y), 0 \le y \le 1,} $$ for some given kernelk(t). These equations, usually indicated as of Mellin type, arise in a variety of applications. In particular, we examine a Nyström interpolant based on the following product quadrature rule: $$\int\limits_0^1 {k(y/x)\frac{{u(x)}}{x}dx \approx \sum\limits_{i = 0}^n {w_{ni} (y)u(x_{mi} ).} } $$ This rule is obtained by interpolatingu(x) by the Lagrange polynomial associated with the set of Gauss-Radau nodes {x _ni}. Under certain assumptions on the kernelk(t), we are able to prove the stability of our interpolant and derive convergence estimates.     

Lelong numbers of positive plurisubharmonic currents

A (k,k)-current T on an open subset of C^N is plurisubharmonic if is positive. Positive plurisubharmonic currents admit Lelong numbers; we prove here that they are independent on the coordinates system. Moreover, if Y is an analytic subset of pure dimension, then the Lelong numbers of T on Y are given by a non negative weakly plurisubharmonic function.     

The actions ofS n+1 andS n on the cohomology ring of a coxeter arrangement of typeA n−1

Let be the complexified Coxeter arrangement of hyperplanes of typeA _n−1. In this paper we construct anS _n+1 extension of the naturalS _n action on the complex cohomology ring of the complement ofA _n−1. Recurrence formulas connecting characters with respect to theS _n and theS _n+1 action are given.     

Di-2-pyridylketone semicarbazone as ligand in metal complexes: synthesis and X-ray crystal structure

A series of complexes of di-2-pyridylketone semicarbazone (Hdips) and Mn(II), Co(II), Co(III), Ni(II) and Cu(II) nitrates were synthesized and characterized by means of IR spectroscopy and for cobalt and nickel by X-ray crystal structures. The results are in agreement with the formulae: Mn(Hdips)₂(NO₃)₂·2H₂O, [Co(Hdips)₂](NO₃)₂·H₂O (I), [Ni(Hdips)₂](NO₃)₂·H₂O (II), Cu(Hdips)(NO₃)₂·2H₂O, [Co(dips)₂](NO₃)·2H₂O (III). The structure of I and II are monoclinic, space groupP2₁/c, with, I,a=15.980(4),b=11.531(2),c=16.170(2)Å;=104.20(2)°,Z=4,R=0.032; II,a=16.109(5),b=11.480(3),c=16.135(6)Å;=104.15(2)°,Z=4,R=0.069. Compound III is also monoclinic, space groupP2₁/c witha=12.173(5),b=15.619(5),c=15.338(8)Å;=111.40(4)°,Z=4,R=0.059. In these complexes the ligand is tridentate via carbonylic oxygen, semicarbazone and pyridine nitrogens forming each two five membered chelate rings with the metal in a distorted octahedral geometry.     

Intermolecular proton transfer in solid phase: a rare example of crystal-to-crystal transformation from hydroxo- to oxo-bridged iron(III) molecule-based magnet

Intermolecular proton transfer in solid phase from the hydroxo bridge to a water molecule occurs in a new mu-hydroxo iron(III) compound of formula {EtNH3[Fe2(ox)2Cl2(mu-OH)].2H2O}n leading to a still crystalline compound in which the mu-oxo bridge replaces the mu-hydroxo one. Both three-dimensional compounds exhibit magnetic ordering at Tc ca. 70 K due to a spin canting.     

Catalysis in aprotic solvents. Effect of the polarity of the catalyst.

The catalytic constants for the $\text{n}$-butylaminolysis of sultones in aprotic-apolar solvents are linearly correlated with a combination of the hydrogen-bonding parameter and the polarity parameter of the catalyst.