On nash theory of Arc structure of singularities

Sunto Si ha l'intenzione d'incominciare lo studio sistematico della teoria abbozzata da John Nash circa venticinque anni fa, dove si associa a una varietà algebrica singolare X spazi i cui ponti corrispondono genericamente a troncature di certi rami analitici parametrizati su X. In questo articolo si presentano accuratamente i fondamenti della teoria. Inoltre, con questi metodi (e nozioni della teoria della equisingolarità per le curve sghembe) s'introducono nuovi invarianti di una singolarità, si spera di studiarli più accuratamente in futuri lavori.     

Pomegranate By-Products as Natural Preservative to Prolong the Shelf Life of Breaded Cod Stick

This work evaluated the efficacy of pomegranate byproducts, specifically peel powder, as valid preservatives for food quality. Ready-to-cook cod sticks breaded with pomegranate peel powder were prepared. Shelf-life tests were conducted on breaded cod sticks during refrigerated storage (17 days) at 4 °C, monitoring the pH, microbiological and sensory quality. In addition, the nutritional quality of both the breaded and control samples was assessed. The results highlighted that active samples showed higher phenol and flavonoid content and higher antioxidant activity compared to the control fish, suggesting that pomegranate peel powder was responsible for a significant increase in cod stick nutritional quality. Furthermore, the cod stick active breading led to a delay in microbial growth without affecting the sensory properties; rather, it helped slow down the sensory attribute decline during the refrigerated storage. The data suggest that using pomegranate byproducts in breaded cod stick was effective in prolonging its shelf life, as well as improving its nutritional quality. Therefore, pomegranate peel powder can be considered as a potential resource as natural food preservative.     

On Some Classical Methods to Improve Algebraic Curves and Surfaces

First, a modern presentation of the theory of the Halphen transform is given. This method associates to a plane projective curve C, once a general conic has been chosen, another birationally equivalent plane curve, whose singularities are simpler than those of C. Repeating, a curve is obtained whose only singularities are nodes. Next, it is studied how to apply this process to a family of plane curves. With this technique it is possible to transform a given family (with irreducible general member) into one where, generically, the curves are nodal. Finally, it is studied a similar process, called the Halphen–Picard transformation, for surfaces in three-space. By suitably reiterating this procedure, a surface can be transformed into a birationally equivalent one (in the same projective space), such that the sections with planes in a general pencil are, generically, nodal curves.     

Arithmetic families of smooth surfaces and equisingularity of embedded schemes

This article deals with the foundations of a theory of equisingularity for families of zero-dimensional sheaves of ideals on smooth algebraic surfaces, in the arithmetic context, i.e., where one works with schemes defined over Dedekind rings. Here, different equisingularity conditions are analyzed and compared, based on one of the following requirements: 1) each member of the the family has the same desingularization tree, 2) the family admits a simultaneous desingularization, 3) a naturally associated family of curves is equisingular. Similar conditions had been investigated, in the context of Complex Local Analytic Geometry, by J. J. Risler. Received: 17 November 1997 / Revised version: 19 April 1999     

Constrained inversion of rheological data to molecular weight distribution for polymer melts

In this paper an inverse method for converting linear viscoelastic properties of polymer melts into molecular weight distribution (MWD) is presented. It relies on the use of the double reptation mixing rule and the Generalized Exponential function (GEX) describing the MWD; i.e. an a priori knowledge of the nature of the solution is postulated following previous attempts (Nobile et al. 1996b; Nobile and Cocchini 1999, 2001) where the Tuminello kernel was adopted to get analytical results. Here a MWD dependent kernel, recently proposed in the literature (Thimm et al. 1999), is applied, still obtaining analytical results but avoiding the consequences of the crude step-like approximation of the Tuminello kernel. In particular, the steady-state compliance and the elastic modulus at small frequencies do not suffer from the underestimation discussed in the cited papers. At high frequencies, the Rouse modes contribution has also been considered in the model. The present approach turns out to be simpler, more accurate and robust than the previous one. Moreover, the results can be more clearly stated in the frame of the theory. Careful and easy-to-use formulas for the zero-shear-rate viscosity, the steady-state compliance, the modulus and frequency at the G'-G' crossover, have been obtained as a function of the MW averages. As expected, the comparison among the results obtained through the two kernels explicitly confirms the minor effects of the kernel on the rheology of polydisperse polymers. Concerning the molecular weight averages values, the predictions obtained from the dynamic moduli measurements typically differ less than 10% from those obtained from the reference measurements obtained with other methods.     

Quality control of the cure process of thermosetting resins by means of differential scanning calorimetry

Calorimetric and rheological characterizations of thermosetting resin formulations containing a novalac epoxy resin hardened with 60 to 120 parts per hundred of methylated maleic acid adduct anhydride are described. The calorimetrically determined epoxy conversion has been related to the gelation limits theoretically calculated from Flory's non-linear copolymerization theory and experimentally verified in rheological tests.

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Zusammenfassung Die kalorimetrische und rheologische Charakterisierung der Ansätze von hitzhärtbarem Harz wird beschrieben. Die Ansätze enthalten ein mit 60–120% methyliertem Maleinsäure-Adduktanhydrid gehärtetes Novolackepoxidharz. Die kalorimetrisch bestimmte Epoxid-konversion wurde auf die theoretisch aus der nicht-linearen Flory'schen Kopolymerisationstheorie berechneten und experimentell durch rheologische Tests bestätigten Erstarrungsgrenzen bezogen.

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Financial and scientific support by the CNR Progetto Chimica Fine e Secondaria and the Societa Italiana Resine (SIR) is gratefully acknowledged.