On the convergence of solutions of degenerate elliptic equations in divergence form

It is studied the convergence of solutions of Dirichlet problems for sequences of monotone operators of the type — div (a_h (x, D·)), where the functions a_h verify the following degenerate coerciveness assumption

Spectroscopic properties of the photoproducts of pyridoxal-5′-P irradiation: Catalytic site recognition of ribonuclease A

Photoproducts of pyridoxal-5-P, i.e., 4-pyridoxic-5-P and bis-pyridoxal-5-P, have been studied by spectroscopic methods. The spectroscopic properties of bis-pyridoxal-5-P (bis-PLP) resemble those of pyridoxal-5-P (PLP) under similar experimental conditions. The coupling of methylen hydrogens to the phosphorus atom has been shown by NMR spectroscopy. The singlet in the³¹P-NMR spectra and the triplet in¹H-undecoupled experiments confirm the presence of the phosphate group in the 5 position of the structure of the vitamin. The effect of pH and solvent composition on the relative distribution of species of bis-pyridoxine-5-P (bis-PNP) has been investigated by absorption and fluorescence spectroscopy. The acid-base dissociation of the phosphate group is easily detected by emission spectroscopy. Bis-PNP and bis-PLP bind to the enzyme RNase A and they behave as competitive inhibitors with respect to the substrate cytidine-2-3-cyclic phosphate. The natural forms of vitamin B₆, pyridoxine, and pyridoxine-5-P have no effect on the catalytic activity of the protein. Experimental evidence derived from fluorescence and inhibition experiments is consistent with the hypothesis that bis-PNP recognizes the catalytic site of RNase A.     

On the extreme spectral properties of Toeplitz matrices generated byL 1 functions with several minima/maxima

In this paper we are concerned with the asymptotic behavior of the smallest eigenvalue ₁ ⁽ⁿ⁾ of symmetric (Hermitian)n ×n Toeplitz matricesT _n (f) generated by an integrable functionf defined in [–, ]. In [7, 8, 11] it is shown that ₁ ⁽ⁿ⁾ tends to essinff =m _f in the following way: ₁ ⁽ⁿ⁾ –m _f 1/n ^2k . These authors use three assumptions:A1)f –m _f has a zero inx =x ₀ of order 2k.A2)f is continuous and at leastC ^2k in a neighborhood ofx ₀.A3)x =x ₀ is the unique global minimum off in [–, ]. In [10] we have proved that the hypothesis of smoothnessA2 is not necessary and that the same result holds under the weaker assumption thatf L ¹[–, ]. In this paper we further extend this theory to the case of a functionf L ¹[–, ] having several global minima by suppressing the hypothesisA3 and by showing that the maximal order 2k of the zeros off –m _f is the only parameter which characterizes the rate of convergence of ₁ ⁽ⁿ⁾ tom _f .     

A closed model category for ()-connected spaces

For each integer , we give a distinct closed model category structure to the category of pointed spaces such that the corresponding localized category is equivalent to the standard homotopy category of -connected CW-complexes. The structure of closed model category given by Quillen to is based on maps which induce isomorphisms on all homotopy group functors and for any choice of base point. For each , the closed model category structure given here takes as weak equivalences those maps that for the given base point induce isomorphisms on for .

     

V. Thioanalogues of sparteine lactams. (+)-2-Thiono-17-oxosparteine and (+)-2,17-dithionosparteine

The X-ray and spectroscopic results clearly indicate that the (+)-2-thiono-17-oxosparteine (1) and (+)-2,17-ditihionosparteine (2) are conformationally rigid. In order to analyze deviations of lactam/thiolactam groups from planarity induced by ring constraints, the Dunitz-Winkler approach has been used. The lactam and thiolactam groups are close to planarity, only the lactam group in one of the two independent molecules of 1 is markedly non-planar. The bond angles in the thiolactam and lactam groups are highly diverse. Rings A and C adopt a distorted sofa conformation in both compounds. The distortions in the molecules of 2 as compared with those in the related monothiolactams correspond to the unusual chemical shifts of H5(eq), H5(ax) and H11, as well as to the extremely low J_5ax-6 and extremely large J_5eq-6 coupling constants. Also chemical shifts show a similar regularity being extremely high and low for C2 and C17, respectively.     

Lead(II) thiocyanate complexes with bibracchial lariat ethers: an X-ray and DFT study

Compounds of formula [Pb(L2)(NCS)2] (1) and [Pb(L4)(SCN)2] (2) (where L2 is the lariat crown ether N,N'-bis(3-aminobenzyl)-4,13-diaza-18-crown-6 and L4 is the Schiff-base lariat crown ether N,N'-bis(3-(salicylaldimino)benzyl)-4,13-diaza-18-crown-6) were isolated and structurally characterized by X-ray diffraction analyses. The X-ray crystal structures of both compounds show the metal ion coordinated to the six donor atoms of the crown moiety, leaving the corresponding pendant arms uncoordinated. The coordination sphere of lead(II) is completed by two thiocyanate groups that coordinate either through their nitrogen (1) or sulfur (2) atoms. The organic receptor adopts a syn conformation in 1, while in 2 it shows an anti conformation. To rationalize these unexpected different conformations of the L2 and L4 receptors in compounds 1 and 2, as well as the different binding modes found for the thiocyanate ligands, we have carried out theoretical calculations at the DFT (B3LYP) level. These calculations predict the syn conformation being the most stable in both 1 and 2 complexes. So, the anti conformation found for 2 in the solid state is tentatively attributed to the presence of intermolecular pi-pi interactions between phenol rings, for which the dihedral angle between the least-squares planes of both rings amounts to 2.6 degrees and the distance between the center of both rings is 3.766 A. On the other hand, the analysis of the electronic structure has revealed that the Pb-ligand bonds present highly ionic character in this family of compounds. They also suggest a greater transfer of electron density from the NCS- ligands when they coordinate through the less electronegative S atom. The Pb-SCN covalent bond formation mainly occurs due to an effective overlap of the occupied 3p z orbitals of the S atoms and the unoccupied 6p z AO of the Pb atom, while the Pb-NCS bonding interaction is primarily due to the overlap of the 6s and 7s AO of Pb with sp(1.10) hybrids of the N donor atoms. Our electronic structure calculations can rationalize the different coordination of the thiocyanate groups in compounds 1 and 2: the simultaneous formation of two Pb-SCN bonds is more favorable for S-Pb-S angles close to 180 degrees , for which the overlap between the occupied 3p z orbitals of the S atoms and the unoccupied 6 pz AO of the Pb atom is maximized.     

Reactivity of 2-halo-2H-azirines. 1. Reactions with nucleophiles.

Nucleophilic substitution reactions of 2-halo-2H-azirines 1a, 1b, 1d, and 1e with potassium phthalimide and aniline allowed the preparation of new substituted 2H-azirines 2-5. The reactions of 2-bromo-2H-azirine 1a with methylamine led to the synthesis of alpha-diimines 7 and 8. 2-Halo-2H-azirines were also established as building blocks for the synthesis of a range of heterocyclic compounds, namely, quinoxalines 10a-10d, 3-oxazoline 14, and 2H-[1,4]oxazines 18 and 20. X-ray crystal structures of alpha-diimine 7, 3-oxazoline 14, and 2H-[1,4]oxazine 18 are reported.     

Synthesis of tridimensional polymers by the copolymerization of phenylglycidylether with aromatic diglycidylethers

Copolymers from phenylglycidylether and several aromatic diglycidylethers are prepared using different ratios of difunctional comonomers and the AIP/ZnCl₂ initiator system. It is found that the percentage of incorporated comonomer depends on the nature of the aromatic moiety introduced. The copolymers are characterized by ¹³C-NMR spectroscopy and turn out to be completely regular and with a high degree of isotacticity (about 80%) that confirms the high degree of regio- and stereoselectivity of the initiator system used. The thermal characteristics of copolymer networks are investigated using differential scanning calorimetry and thermogravimetry. Two fusion endotherms are observed which vary with the degree of crosslinking. By thermogravimetric analyses the thermal stability is found to increase when the crosslinking degree does. © 1994 John Wiley & Sons, Inc.     

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.