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 .     

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.     

Enantioselective synthesis of 1-deoxy-d-gulonojirimycin from a phenylglycinol-derived lactam

Cyclocondensation of (R)-phenylglycinol with appropriately γ-substituted δ-oxo acid derivatives provides bicyclic lactams from which the enantioselective synthesis of 1-deoxy-d-gulonojirimycin has been reported.     

Establishing the synthetic origin of amphetamines by 2H NMR spectroscopy

Nine samples of N-acetyl-3,4-methylenedioxyamphetamine (N-acetyl-MDA), prepared according to the most common synthetic procedures, are submitted to (2)H NMR spectroscopy. The relative deuterium content at the various sites of the molecule is shown to depend on its synthetic history. The technique provides a chemical fingerprint of N-acetyl-MDAs and it can be used to trace back the precursor materials and the synthetic pathways employed in the preparation of the samples.     

Preparation of the Enantiomerically Enriched Isomers of the Odorous Cyclic Ethers Clarycet ®, Florol ®, and Rhubafuran ® by Enzymatic Catalysis

All the enantiomerically enriched stereoisomers of Clarycet ^® ( 1 ), Florol ^® ( 2 ), and Rhubafuran ^® ( 3 ) were prepared by biocatalysis routes. Their absolute configurations were established, and their olfactory properties were fully evaluated.     

New glycidyl ester compounds containing a preformed imide ring—I

The synthesis of the new esterglycidyl compounds produced by condensation of bis-carboxyimides with a large excess of epichlorohydrin were reported. To define the optimal conditions of condensation the process with monofunctional compounds were studied at first. For all synthesis, yield and epoxide and chlorine contents were found. The structure of glycidyl esters was determined by elementary analysis, IR and ¹H and ¹³C NMR spectra. The physical properties were also defined.     

Synthesis, characterization and electrochemical studies of the heterometallic diclusters [{Fe2(μ-CO)(CO)6(μ-PPh2)Au}2(diphosphine)] (diphosphine=dppm, dppip, dppe, dppp)

Treatment of [(ClAu)₂(diphosphine)] {diphosphine=bis(diphenylphosphino)methane (dppm), bis(diphenylphosphino)isopropane (dppip), 1,2-bis(diphenylphosphino)ethane (dppe), 1,3-bis(diphenylphosphino)propane (dppp)} with two equivalents of the anion [Fe₂(μ-CO)(CO)₆(μ-PPh₂)]⁻ in the presence of TlBF₄ gives the new heterometallic diclusters [{Fe₂(μ-CO)(CO)₆(μ-PPh₂)Au}₂(diphosphine)] that have been isolated and characterized. Their ³¹P-NMR spectra show different patterns as a function of the diphosphine ligand. The electrochemical behavior of these compounds has been investigated and compared with that of the mono- [Fe₂(μ-CO)(CO)₆(μ-PPh₂)(μ-AuPPh₃)] and tricluster [{Fe₂(μ-CO)(CO)₆(μ-PPh₂)Au}₃(triphos)] derivatives.     

Crystal and Molecular Structure of (BzlMe3N) 2 + [Fe2OCl6]2-

The crystal and molecular structure of (BzlMe₃N) ₂ ⁺ [Fe₂OCl₆]^2- has been determined. The asymmetric unit contains two benzyltrimethylammonium cations and two half -oxo-bis(trichloro-iron(III)) anions. The bridging -oxygen atoms of these anions are located over crystallographic symmetry elements. Therefore, the two anions resulting from the symmetry operations correspond to two different conformers presenting angular and linear dispositions of the Fe-O-Fe bond angle. Mössbauer spectrum consists of two asymmetric lines that are adequately simulated by two equally populated quadrupole doublets associated with the two iron sites.     

Staphylococcus aureus bicomponent gamma-hemolysins, HlgA, HlgB, and HlgC, can form mixed pores containing all components

Staphylococcal gamma-hemolysins are bicomponent toxins forming a protein family with leucocidins and alpha-toxin. Two active toxins (AB and CB) can be formed combining one of the class-S components, HlgA or HlgC, with the class-F component HlgB. These two gamma-hemolysins form pores with marked similarities to alpha-toxin in terms of conductance, nonlinearity of the current-voltage curve, and channel stability in the open state. AB and CB pores, however, are cation-selective, whereas alpha-toxin is anion-selective. gamma-Hemolysins' pores are hetero-oligomers formed by three or four copies of each component (indicated as 3A3B and 3C3B or 4A4B and 4C4B). Point mutants located on a beta-strand of the class-S component that forms part of the protomer-protomer contact region can prevent oligomer assembly. Interestingly, these mutants inhibit growth of pores formed not only by their natural components but also by nonstandard components. This lead to the hypothesis that mixed ABC pores could also be formed. By studying the conductance of pores, assembled in the presence of all three components (in different ratios), it was observed that the magnitudes expected for mixed pores were, indeed, present. We conclude that the gamma-hemolysin/leucocidin bicomponent toxin family may form a larger than expected number of active toxins by cross-combining various S and F components.     

Biogenetically inspired enantioselective approach to Indolo[2,3-a]- and benzo[a]quinolizidine alkaloids from a synthetic equivalent of secologanin

[reaction: see text] Racemic oxodiester 1 undergoes stereoselective cyclocondensation with (S)-tryptophanol, (S)-(3,4-dimethoxyphenyl)alaninol, or the corresponding amino acids, in a process involving a tandem dynamic kinetic resolution/desymmetrization of diastereotopic groups, to give bicyclic lactams, which are cyclized to substituted indolo[2,3-a]- and benzo[a]quinolizidines.