Reconstructing pluricanonical embeddings of general k-gonal curves via odd theta-characteristics

Abstract Here we investigate r-canonical embeddings of general k-gonal curves of genus g from the point of view of Caporaso–Sernesi’s reconstruction procedure via odd theta-characteristics. Keywords: Theta-characteristic, general k-gonal curve, trigonal curve, pluricanonical embedding, Hilbert scheme Mathematics Subject Classification (2000): 14H50, 14N05     

Numerical detection of instability regions for delay models with delay-dependent parameters

In this paper we are interested in gaining local stability insights about the interior equilibria of delay models arising in biomathematics. The models share the property that the corresponding characteristic equations involve delay-dependent coefficients. The presence of such dependence requires the use of suitable criteria which usually makes the analytical work harder so that numerical techniques must be used. Most existing methods for studying stability switching of equilibria fail when applied to such a class of delay models. To this aim, an efficient criterion for stability switches was recently introduced in [E. Beretta, Y. Kuang, Geometric stability switch criteria in delay differential systems with delay dependent parameters, SIAM J. Math. Anal. 33 (2002) 1144–1165] and extended [E. Beretta, Y. Tang, Extension of a geometric stability switch criterion, Funkcial Ekvac 46(3) (2003) 337–361]. We describe how to numerically detect the instability regions of positive equilibria by using such a criterion, considering both discrete and distributed delay models.     

Ion-pair reversed-phase high-performance liquid chromatography for trace metal preconcentration followed by ion-interaction chromatography

Ion-interaction chromatography of Plasmocorinth B (a disulphonated azo dye) complexes of Co(III), Cu(II), Fe(III), Ga(III), In(III), Ni(II), V(V) and Zr(IV) was studied. The behaviour of two different reversed-phase C₁₈ columns (5 and 10 μm) was compared and an on-line enrichment procedure was developed following the optimization of eluent (pH, ligand concentration, ionic strength and organic modifier). The described technique, applied to the analysis of metal ions at μg/1 levels in natural waters, gave satisfactory precision and accuracy in comparison with inductively coupled plasma atomic emission spectroscopic results.     

On the stability of certain higher rank bundles on P N

Here we prove the stability of several higher rank bundles on ? ⁿ strongly related with the postulation of projective varieties. As a particular case, we give another proof of the stability of ? ⁿ      

Synthesis and Ruthenium-Catalyzed Enantioselective Hydrogenation of 3-O-Substituted 1,3-Dihydroxypropan-2-ones. Part 2

A number of 3-O-substituted 1,3-dihydroxypropan-2-ones have been synthesized in view of their potential use as prochiral precursors of optically active glycerols. Indeed, the oxo-ethers have been reduced to the corresponding 3-O-substituted glycerols via chiral Ru complexes derived from (S)-binap, ( =(?)-(S)-2,2′-bis(diphenylphosphino)-1,1′-binaphthalene) with enantiomeric excesses up to 93%. The steric course of the catalytic reduction appears to be essentially dependent on the steric encumbrance of the substituents; indeed, a dramatic increase of the enantiomeric excess is observed when the bulky trityl group is substituted by the less encumbering benzyl or octadecyl groups.     

Some remarks on continuous dependence and uniqueness in finite elastostatics for unbounded domains

Summary In connection with a foregoing paper, in the present note we establish some continuous dependence and uniqueness theorems for classical solutions to the equilibrium problem of finite elasticity. The elastic body is supposed to fill an unbounded domain of the physical space. We employ the weight function method and a suitable extension to the non-linear case of a method previously introduced by other authors for the linear case.

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Sommario In connessione con un precedente lavoro, si dimostrano nella presente nota alcuni teoremi di dipendenza continua ed unicità per soluzioni classiche del problema statico non lineare relativo ad un corpo elastico occupante un dominio illimitato dello spazio fisico. Vengono adoperati il metodo della funzione peso e l'estensione al caso non lineare di un metodo precedentemente introdotto da altri autori per il caso lineare.

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Work performed under the auspices of G.N.F.M. of the Italian Research Council (C.N.R.).     

Structure of sodium glycodeoxycholate micellar aggregates from small-angle X-ray scattering and light-scattering techniques

Small-angle X-ray scattering (SAXS) and dynamic light scattering (DLS) measurements were accomplished on sodium glycodeoxycholate (NaGDC) aqueous electrolyte solutions as a function of NaGDC and NaCl concentrations with the aim to determine with satisfactory approximation the NaGDC micellar aggregate structure at a gross molecular level, assuming monodispersity. Different conditions of interparticle interactions by varying ionic strength (NaCl concentration from 0 to 0.70 M) and NaGDC concentration (from 0.02 to 0.10 M) were studied. Smeared scattering intensities and electron pair distance distribution functions, radii of gyration, and aggregate heights are in satisfactory agreement with the corresponding functions calculated using a 2(1) helix as model. It is formed by trimers, each one composed by three NaGDC and nine H2O molecules related by a 3-fold rotation axis, and can be described by a hollow cylinder, probably filled by water molecules, characterized by a conventional radius of 23.7 A and a trimer repeat along the helical axis of 3.6 A. The helix is considerably inhomogeneous since the volume of the cylinder occupied by NaGDC molecules is less than one-third of the total. On the other hand, calculations performed with the average radial electronic density of the helix without water molecules or totally filled by water molecules (a NaGDC/H2O molecular ratio of about 1/50) or by using a three-shell average radial electronic density, independently evaluated on absolute scale, do not show significant differences, thus supporting the helical model. The aggregate size increases for all the samples by increasing either the NaCl or NaGDC concentration. The NaGDC low concentration (0.02 M) samples with NaCl within the range 0.30-0.70 M are characterized by short cylindrical aggregates that do not give rise to sensible interference effects. This assertion is supported by the satisfactory fit between the observed apparent mean hydrodynamic radii and the calculated ones by means of the method of Ortega and Garcia de la Torre (J. Chem. Phys. 2003, 119, 9914), valid for rods with a length-to-diameter ratio > or = 0.1 in dilute solution (noninteracting rods). The NaGDC moderate concentration (0.10 M) samples with NaCl within the range 0.20-0.60 M are characterized by cylindrical aggregates that, in the presence of repulsive Coulombic interactions progressively more and more screened, produce interference effects, due to the hard-body repulsion and attractive forces, but the agreement between observed and calculated SAXS data is satisfactory. The results of the low and moderate NaGDC concentration samples seem to indicate that the aggregation number increase, produced by adding 0.10 M NaCl, is constant within an ionic strength range and occurs by the addition of oligomers formed by trimers. The samples with a variable NaGDC concentration (0.02-0.10 M) at a fixed and high NaCl concentration (0.6 M) contain cylindrical aggregates that give rise to an attractive term effect prevailing on the hard-body repulsive one. The same situation seems to occur in the NaGDC moderate concentration samples.     

The dual geometry of Hermitian two-point codes

In this paper, we study the algebraic geometry of any two-point code on the Hermitian curve and reveal the purely geometric nature of their dual minimum distance. We describe the minimum-weight codewords of many of their dual codes through an explicit geometric characterization of their supports. In particular, we show that they appear as sets of collinear points in many cases.