Links in a thickened surface

For a given two-dimensional surface μ, we studi invariants for oriented links in μ×[0,1] which generalize the two-variable HOMFLY polynomials when μ is the 2-disk. These invariants are connected to multiparameter quantum groups whose special properties are discussed. Si studiano gli invarianti dei nodi in spazi del tipo μ×[0,1], dove μ è una superficie. Questi invarianti generalizzano gli invarianti di HOMFLY.

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(Conferenza tenuta dal Prof. P. Cotta-Ramusino il 16 maggio 1991)     

A highly active fungal β-glucosidase

A highly active thermostable β-glucosidase was purified to homogeneity from a strain ofTrichoderma sp. The enzyme was an extracellular glycoprotein and showed hydrolytic activity toward several β-glucosides. Cellobiose was found to be the substrate of choice for this enzyme. This finding could suggest future technological applications of the purified protein.     

An algorithm for the computation of consistent initial values for differential–algebraic equations

We use boundary value methods to compute consistent initial values for fully implicit nonlinear differential-algebraic equations. The obtained algorithm uses variable order formulae and a deferred correction technique to evaluate the error. A rigorous theory is stated for nonlinear index 1, 2 and 3 DAEs of Hessenberg form. Numerical tests on classical index 1, 2 and 3 DAE problems are reported. This revised version was published online in June 2006 with corrections to the Cover Date.     

The mathematics of playing golf, or: a new class of difficult non-linear mixed integer programs

We consider a class of non-linear mixed integer programs with n integer variables and k continuous variables. Solving instances from this class to optimality is an NP-hard problem. We show that for the cases with k=1 and k=2, every optimal solution is integral. In contrast to this, for every k≥3 there exist instances where every optimal solution takes non-integral values. Received: August 2001 / Accepted: January 2002?Published online March 27, 2002     

Recursive method for building Arnold’s triangle X p (a,b)

We give a recursive method for building X _p (a,b) for each prime p. Arnold’s triangle is composed of positive integers: for a>1 and 0<b<a, X _p (a,b) is the degree of the highest power of p dividing the difference of the binomial coefficients C _pa ^pb −C _a ^b .      

Macrocyclization on the fullerene core: Direct regio- and diastereoselective multi-functionalization of [60]fullerene,and synthesis of fullerene-dendrimer derivatives

The macrocyclization between buckminsterfullerene, C₆₀, and bis-malonate derivatives in double Bingel reaction provides a versatile and simple method for the preparation of covalent bis-adducts of C₆₀ with high regio- and diastereoselectivity. A combination of spectral analysis, stereochemical considerations, and X-ray crystallography (Fig. 2) revealed that out of the possible in-in, in-out, and out-out stereoisomers, the reaction of bis-malonates linked by o-, m-, or p-xylylene tethers afforded only the out-out ones (Scheme 1). In contrast, the use of larger tethers derived from 1,10-phenanthroline also provided a first example, (±)- 19 (Scheme 2), of an in-out product. Starting from optically pure bis-malonate derivatives, the new bis-functionalization method permitted the diastereoselective preparation of optically active fullerene derivatives (Schemes 4 and 5) and, ultimately, the enantioselective preparation (enantiomeric excess ee > 97%) of optically active cis-3 bis-adducts whose chirality results exclusively from the addition pattern (Fig. 6). The macrocyclic fixation of a bis-malonate with an optically active, 9,9′-spirobi[9H-fluorene]-derived tether to C₆₀ under generation of 24 and ent- 24 with an achiral addition pattern (Scheme 4) was found to induce dramatic changes in the chiroptical properties of the tether chromophore such as strong enhancement and reversal of sign of the Cotton effects in the circular dichroism (CD) spectra (Figs. 4 and 5). By the same method, the functionafized bis-adducts 50 and 51 (Schemes 10 and 11) were prepared as initiator cores for the synthesis of the fullerene dendrimers 62 , 63 , and 66 (Schemes 12 and 13) by convergent growth. Finally, the new methodology was extended, to the regio- and diastereoselective construction of higher cyclopropanated adducts. Starting from mono-adduct 71 , a clipping reaction provided exclusively the all-cis-2 tris-adduct (±)- 72 (Scheme 14), whereas the similar reaction of bis-adduct 76 afforded the all-cis-2 tetrakis-adduct 77 (Scheme 15). Electrochemical investigations by steady-state voltammetry (Table 2) in CH₂Cl₂ (+0.1M Bu₄NPF₆) showed that all macroeyciic bis(methano)fullerenes underwent multiple reduction steps, and that regioisomerism was not much influencing the redox potentials, All cis-2 bis-adducts gave an instable dianion which decomposed during the electrochemical reduction. In CH₂Cl₂, the redox potential of the fullerene core in dendrimers 62, 63 , and 66 is not affected by differences in size and density of the surrounding poly(ether-amide) dendrons. The all-cis-2 tris- and tetrakis(meihano)fullercnes (±) -72 and 77 , respectively, are reduced at more negative potential than previously reported all-e tris- and tetrakis-adducts with methane bridges that are also located along an equatorial belt. This indicates a larger perturbation of the original fullerene π-chromophore and a larger raise in LUMO energy in the former derivatives.     

IR multiphoton dissociation of CF3I. Pressure effect with inert and reactive gases

The IR multiphoton dissociation of CF₃I has been studied in the presence of isobutane and with isobutane and Ar and CO₂ as inert gases. The dependence of the reaction probability P(Φ) with fluence (ϕ) is confirmed. Modeling of the experimental results shows that for the energy transfer processes the average energy transferred per collision 〈†E〉_d varies with (ϕ).     

Interactions of dendrimers with selected amino acids and proteins studied by continuous wave EPR and Fourier transform EPR

Interactions of polyamidoamine dendrimers, termed Gn, where n indicates the generation (=number of amidoamine layers), at different protonation levels with selected amino acids and proteins have been investigated by means of continuous wave electron paramagnetic resonance (cw-EPR) and pulsed-EPR (electron spin-echo = ESE) analyses. A low-generation dendrimer (G2) and a high-generation one (G6) were labeled with nitroxides for the EPR measurements. Gly, Glu, Arg, and Leu were selected as representative of neutral(zwitterionic)-polar, acidic, basic, and low-polar amino acids, respectively. The water-soluble proteins alpha-chymotrypsin and albumin were selected on the basis of a basic and an acidic isoelectric point, respectively. The cw-EPR spectra were analyzed by computing the line shapes to extract information about the dendrimer-biomolecule interactions. In general, dendrimers at a high protonation level interact stronger with amino acids than those at a low level of protonation. However, even for highly protonated dendrimers, a synergistic effect between hydrophilic and hydrophobic interactions promoted the formation of stable Gn-amino acid adducts, as demonstrated by the enhanced interactions with Leu. As expected from acid-base interactions, stable adducts were formed between Arg and highly protonated dendrimers and between Glu and low level protonated dendrimers. The relatively strong dendrimer interactions with the protein chymotrypsin and the poor interactions of dendrimers with albumin demonstrated that the protonated amino groups of the dendrimers are predominantly involved in the interactions with these proteins and indicated a significant role in the interactions with the dendrimers of the hydrophobic external residues of chymotrypsin. Computer-aided analysis of the ESE experiments was consistent with the cw-EPR results and supported the conclusion of a partial complexation of the nitroxides of the dendrimer with Leu and alpha-chymotrypsin.     

High-performance liquid chromatographic determination of Levetiracetam in human plasma: comparison of different sample clean-up procedures

An accurate and precise high-performance liquid chromatographic method using diode array detection for the determination of the novel antiepileptic, Levetiracetam, has been developed. Three clean-up procedures for the analysis of Levetiracetam in human plasma were implemented and evaluated, namely solid-phase extraction, deproteinization by addition of organic solvents and formation of insoluble salts. Adenosine was used as the internal standard for all three sample pretreatment procedures. Among the several cartridges used for solid-phase extraction, the hydrophilic-lypophilic balance (Oasis) HLB) phase provides the best extraction yield of Levetiracetam, together with high precision. With the two other clean-up procedures involving plasma deproteinization by addition of methanol or zinc sulphate, lower sensitivity and precision of the assays were obtained. However, they are cheaper and faster when compared with the solid-phase extraction procedure.     

A new multi analytical approach for the identification of synthetic and natural dyes mixtures. The case of orcein-mauveine mixture in a historical dress of a Sicilian noblewoman of nineteenth century

Abstract

In this paper, the application of a multi-analytical approach for the characterisation of synthetic and natural dyes in a historical textile is presented. The work is focused on a historical dress of a Sicilian noblewoman, dating from about 1865–1870. Firstly, SERS on fibre was performed, in order to individuate the classes of dyes employed. The SERS spectra suggested the presence of two main dyes: mauveine and orcein. In order to confirm these preliminary results, two different extraction protocols were applied. The extracts obtained were analysed by ESI-MS, MALDI-ToF and UHPCL-MS analyses, confirming the SERS results. In particular, the application of the ammonia mild extraction technique allowed to selectively extract the phenoxazonic dyes, separating them already in the extraction step from the synthetic ones. Thanks to this multi-analytical approach, this dress could be considered as one of the first examples of employment of synthetic dyes in association with natural ones.