Families of curves with ordinary singular points on regular surfaces

Sunto Fissata una superficie algebrica liscia X sopra un campo algebricamente chiuso e di caratteristica 0, e una curva ridotta C su X, si introduce, per ogni -upla di numeri naturali m₁,..., m, uno schema W=W(C, m₁,..., m), parametrizzante le curve del sistema lineare ¦C¦ con punti multipli ordinari di molteplicità almeno m₁,..., m. Si studia W in relazione con la configurazione delie singolarità e delle componenti irriducibili di C. Si prova in particolare un teorema di «virtuale connessione», che permette di stabilire l'esistenza di curve irriducibili in alcuni di tali schemi W.

---

---

Membro del G.N.S.A.G.A. del C.N.R.     

1H and31P ENDOR of the isotropic CO2 − signal atg=2.0007 in the EPR spectra of precipitated carbonated apatites

The isotropic EPR signal atg=2.0007 in X-irradiated carbonated apatites, precipitated from aquaeous solutions and dried at 25°C, is investigated with Electron Nuclear Double Resonance (ENDOR). The²³Na,³¹P and¹H ENDOR results indicate that the precursor of this radical is most probably located in an aqueous phase entrapped between the crystallites (the so-called occluded water). Other experimental features, such as the correlation between the appearance of the signal in the EPR spectrum and the presence of some residual (adsorbed and/or occluded) water in the sample seem to strengthen our hypothesis.     

Facets for the cut cone I

We study facets of the cut coneC _n , i.e., the cone of dimension 1/2n(n – 1) generated by the cuts of the complete graph onn vertices. Actually, the study of the facets of the cut cone is equivalent in some sense to the study of the facets of the cut polytope. We present several operations on facets and, in particular, a lifting procedure for constructing facets ofC _n+1 from given facets of the lower dimensional coneC _n . After reviewing hypermetric valid inequalities, we describe the new class of cycle inequalities and prove the facet property for several subclasses. The new class of parachute facets is developed and other known facets and valid inequalities are presented.     

Strengthened semidefinite programming bounds for codes

We give a hierarchy of semidefinite upper bounds for the maximum size A(n,d) of a binary code of word length n and minimum distance at least d. At any fixed stage in the hierarchy, the bound can be computed (to an arbitrary precision) in time polynomial in n; this is based on a result of de Klerk et al. (Math Program, 2006) about the regular ∗-representation for matrix ∗-algebras. The Delsarte bound for A(n,d) is the first bound in the hierarchy, and the new bound of Schrijver (IEEE Trans. Inform. Theory 51:2859–2866, 2005) is located between the first and second bounds in the hierarchy. While computing the second bound involves a semidefinite program with O(n ⁷) variables and thus seems out of reach for interesting values of n, Schrijver’s bound can be computed via a semidefinite program of size O(n ³), a result which uses the explicit block-diagonalization of the Terwilliger algebra. We propose two strengthenings of Schrijver’s bound with the same computational complexity. Supported by the Netherlands Organisation for Scientific Research grant NWO 639.032.203.     

The cut cone III: On the role of triangle facets

The cut polytopeP _n is the convex hull of the incidence vectors of the cuts (i.e. complete bipartite subgraphs) of the complete graph onn nodes. A well known class of facets ofP _n arises from the triangle inequalities:x _ij +x _ik +x _jk ≤ 2 andx _ij -x _ik -x _jk ≤ 0 for 1 ≤i,j, k ≤n. Hence, the metric polytope M_n, defined as the solution set of the triangle inequalities, is a relaxation ofP _n . We consider several properties of geometric type for P_n, in particular, concerning its position withinM _n . Strengthening the known fact ([3]) thatP _n has diameter 1, we show that any set ofk cuts,k ≤ log₂ n, satisfying some additional assumption, determines a simplicial face ofM _n and thus, also, ofP _n . In particular, the collection of low dimension faces ofP _n is contained in that ofM _n . Among a large subclass of the facets ofP _n , the triangle facets are the closest ones to the barycentrum of P_n and we conjecture that this result holds in general. The lattice generated by all even cuts (corresponding to bipartitions of the nodes into sets of even cardinality) is characterized and some additional questions on the links between general facets ofP _n and its triangle facets are mentioned.     

Assessing weak intramolecular donor-acceptor interactions using 1H-117Sn J-HMQC spectroscopy

It is demonstrated that long-range nJ(1H,117Sn) coupling constants down to 0.3 Hz, can be accurately quantified from non-linear fitting of the sine modulation of the associated 1H-117Sn correlation cross-peak intensities sampled as a function of the heteronuclear antiphase coherence preparation time in the 1H-117Sn J-HMQC pulse sequence. The contribution of additional, undesired modulations is illustrated and assessed using the product operator formalism, and is traced back to contributions that arise from miss-setting of the wandering 180 degrees pulse angle in the constant time period. The power of the method and its use in the characterization of weak intramolecular donor-acceptor interactions are illustrated by the determination of long-range nJ(1H,117Sn) coupling constants of bis[3-(dimethylamino)propyl]tin derivatives, [Me2N(CH2)3]2SnR2 (', R = Me; 3, R = Ph; 4, R = t-Bu). By comparing these with the values found for the corresponding bis(4-methylpentyl)tin derivatives, [Me2CH(CH2)3]2SnR2 (2', R = Me; 3', R = Ph), which lack such interactions, the use of long-range coupling constants to detect intramolecular donor-acceptor interactions is evaluated. It is concluded that nJ(1H,117Sn) couplings up to six bonds through an organic carbon chain can be quantified, whether donor-acceptor interactions are present or not. Furthermore, evidence is presented that, when two scalar coupling pathways co-exist, the pathway involving an intramolecular donor-acceptor interaction can have opposite sign, thus decreasing the overall coupling constant to a value smaller than that actually measured in the absence of a donor-acceptor interaction, where only one coupling pathway is active. There is nevertheless clear numerical value discrimination in the series of compounds investigated between long-range couplings in derivatives without weak intramolecular donor-acceptor interactions and those where such interactions can exist.     

Biomimetic membrane arrays on cast hydrogel supports

Lipid bilayers are intrinsically fragile and require mechanical support in technical applications based on biomimetic membranes. Tethering the lipid bilayer membranes to solid substrates, either directly through covalent or ionic substrate-lipid links or indirectly on substrate-supported cushions, provides mechanical support but at the cost of small molecule transport through the membrane-support sandwich. To stabilize biomimetic membranes while allowing transport through a membrane-support sandwich, we have investigated the feasibility of using an ethylene tetrafluoroethylene (ETFE)/hydrogel sandwich as the support. The sandwich is realized as a perforated surface-treated ETFE film onto which a hydrogel composite support structure is cast. We report a simple method to prepare arrays of lipid bilayer membranes with low intrinsic electrical conductance on the highly permeable, self-supporting ETFE/hydrogel sandwiches. We demonstrate how the ETFE/hydrogel sandwich support promotes rapid self-thinning of lipid bilayers suitable for hosting membrane-spanning proteins.     

Elimination of Listeria inoculated in ready-to-eat carrots by combination of antimicrobial coating and γ-irradiation

A combined treatment of an edible coating composed of trans-cinnamaldehyde (TCN; 0.5% p/p) with γ-irradiation was investigated against Listeria inoculated in peeled mini-carrots. First, the D₁₀ value (γ-irradiation dose required to eliminate 90% of the bacterial population) of TCN was evaluated under air. This treatment resulted in a 3.66-fold increase in relative bacterial radiosensitivity (RBR) as compared to the control without antimicrobial coating. Secondly, the shelf life of mini-carrots during 21 day of storage at 4 °C was studied. Antimicrobial coating containing TCN was assayed in combination with two irradiation doses (0.25 and 0.5 kGy). Results suggested that the inactive coating did not have any antimicrobial effect against Listeria while the coating containing TCN resulted in a 1.29 log reduction in carrots packed under air after 21 days of storage. Hence, these observations indicated that the combination of irradiation with antimicrobial coating played an important role in enhancing the radiosensitization of Listeria to γ-irradiation.     

simple and mixed ligand complexes of copper(II) with polyfunctional phenolic compounds as models of natural substances

In order to analyse metal complexation with polyfunctional phenolic compounds as ligand models of natural substances, a detailed examination is described for five simple binary complexes and three ternary mixed ligand complexes at 25°C (μ = 0.1 M NaClO₄). The ligands are tyrosine, 4,5-dihydroxy-1,3-benzene disulfonic acid, disodium salt (tiron), 3,4-dihydroxycinnamic acid (caffeic acid), 3,4,5-trihydroxy-1 -cyclohexene-1 -carboxylic acid (shikimic acid) and 1,3,4,5-tetrahydroxycyclohexanecarboxylic acid 3-(3,4-dihydroxycinnamate) (chlorogenic acid). The ternary systems are Cu(II)/H_qA/tiron, where H_qA is tyrosine, caffeic or chlorogenic acids. Potentiometric data were used successively to evaluate the protonation of each individual ligand, to detect simple and mixed complexes (including protonated species) and to determine their stability constants (a set of 33 values of constants with several original data is provided). The calculated distribution (speciation) of each species as a function of pH is indicated. Mixed coordination enhances the stability of complexes and the stabilization is expressed in terms of various parameters. The results emphasize that mixed ligand complex formation is essential to studies of multiple equilibria.     

AgNP-decorated SBA-15 for MWCNT Paste Modified Electrode: A Sensor for Simultaneous Voltammetric Determination of Paracetamol and Sulfamethoxazole

A new electrochemical sensor based on a carbon nanotube paste electrode modified with a Santa Barbara Amorphous material (SBA-15) decorated with silver nanoparticles, namely CNT/SBA/Ag-PE, was developed. It was successfully applied for individual and simultaneous determination of both paracetamol (PC) and sulfamethoxazole (SMZ) medicines. The electrode exhibited a linear dynamic range of 0.12–110 μmol L⁻¹ for paracetamol and 0.06–70 μmol L⁻¹ for sulfamethoxazole, and detection limits of 38 and 19 nmol L⁻¹, respectively. The proposed sensor offered high sensitivity, fast response time and the potential for detecting both drugs simultaneously. The CNT/SBA/Ag-PE enabled the simultaneous determination of PC and SMZ in urine samples with high recovery rates.