Fluorine containing phosphazene polymers

In this paper we highlighted the synthesis, characterization, and practical exploitation of different types of polyphosphazenes substituted with fluorinated groups. There are several ways in which fluorine atoms can be inserted into polyphosphazenes, all of which leading to different polymers showing a wide range of characteristics. In general it is true that the insertion of fluorine atoms into phosphazene macromolecules leads to an enhancement of the thermal stability, flame resistance, low-temperature elastomericity, and chemical inertness of the phosphazenes obtained. The contribution of Italian research groups to the preparation and exploitation of organic commercial macromolecules grafted onto fluorinated polyphosphazenes is also reviewed.     

UV‐ignited frontal polymerization of an epoxy resin

By combining frontal polymerization and radical‐induced cationic polymerization, it was possible to cure thick samples of an epoxy monomer bleached by UV light. The effect of the relative amounts of cationic photoinitiator and radical initiator was thoroughly investigated and was related to the front's velocity and its maximum temperature. The materials obtained were characterized by quantitative conversion also in the deeper layers, not reached by UV light. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 2066–2072, 2004     

Obtaining 4-vinylphenols by decarboxylation of natural 4-hydroxycinnamic acids under microwave irradiation

4-Vinylphenols, useful compounds for industrial applications, were obtained by decarboxylation of 4-hydroxycinnamic acids under microwave irradiation in the presence of 1,8-diazabicyclo[5.4.0]undec-7-ene (DBU) as base and basic aluminum oxide as solid support. The reactions were fast (15-30 min). The selective extraction of the final products with ethyl acetate avoids chromatographic purifications. The conversions are quantitative and the yields are satisfactory. Only the unstable 4-vinylcatechol was obtained in moderate yield. This procedure was successfully extended to a natural sample of ferulic acid extracted from wheat bran to get the corresponding 4-vinylguaiacol, a FEMA GRAS (Flavor and Extract Manufacturer's Association; General Regarded as Safe) approved flavoring agent.     

Normal human dermal fibroblasts: proteomic analysis of cell layer and culture medium.

Proteins present within the cell layer and those released in the cell medium from in vitro cultured normal human dermal fibroblasts were separated and characterized in terms of their isoelectric point and molecular weight, by two-dimensional (2-D) gel electrophoresis. All spots in the synthetic gel were firstly analyzed by the Melanie 3 software and compared with those of breast cancer cells, colorectal epithelial cells, HL60, lymphoma cells, and platelets, already available on-line. From the identification of 144 spots from both the cell layer and the medium, we were able to recognize 89 different proteins, since a certain number of spots represented different isoforms of the same molecule. Identifications were performed by matching with on-line 2-D databases, and by matrix assisted laser-desorption/ionization-time of flight-mass spectrometry (MALDI-TOF-MS), in order to confirm the identification by matching, or to identify new proteins. The procedure we used allows (i) to design a highly reproducible reference map of the proteome of adult human normal fibroblasts in culture, (ii) to evaluate protein species produced in the cell layer as well as those released in the culture medium, and (iii) to compare data from gel matching with those obtained by MS. This work represents an essential step for a better knowledge of mesenchymal cells, given the widespread use of this cell type in both clinical and experimental investigations.     

Entire radial solutions of elliptic systems and inequalities of the mean curvature type

In this paper we study first nonexistence of radial entire solutions of elliptic systems of the mean curvature type with a singular or degenerate diffusion depending on the solution u. In particular we extend a previous result given in [R. Filippucci, Nonexistence of radial entire solutions of elliptic systems, J. Differential Equations 188 (2003) 353-389]. Moreover, in the scalar case we obtain nonexistence of all entire solutions, radial or not, of differential inequalities involving again operators of the mean curvature type and a diffusion term. We prove that in the scalar case, nonexistence of entire solutions is due to the explosion of the derivative of every nonglobal radial solution in the right extremum of the maximal interval of existence, while in that point the solution is bounded. This behavior is qualitatively different with respect to what happens for the m-Laplacian operator, studied in [R. Filippucci, Nonexistence of radial entire solutions of elliptic systems, J. Differential Equations 188 (2003) 353-389], where nonexistence of entire solutions is due, even in the vectorial case, to the explosion in norm of the solution at a finite point. Our nonexistence theorems for inequalities extend previous results given by Naito and Usami in [Y. Naito, H. Usami, Entire solutions of the inequality div(A(|Du|)Du)?f(u), Math. Z. 225 (1997) 167-175] and Ghergu and Radulescu in [M. Ghergu, V. Radulescu, Existence and nonexistence of entire solutions to the logistic differential equation, Abstr. Appl. Anal. 17 (2003) 995-1003].     

Optimality relationships forp-cyclic SOR

Summary The optimality question for blockp-cyclic SOR iterations discussed in Young and Varga is answered under natural conditions on the spectrum of the block Jacobi matrix. In particular, it is shown that repartitioning a blockp-cyclic matrix into a blockq-cyclic form,q, results in asymptotically faster SOR convergence for the same amount of work per iteration. As a consequence block 2-cyclic SOR is optimal under these conditions.Research supported in part by the US Air Force under Grant no. AFOSR-88-0285 and the National Science Foundation under grant no. DMS-85-21154 Present address: Boeing Computer Services, P.O. Box 24346, MS 7L-21, Seattle, WA 98124-0346, USA     

A Framework for Monitoring Progress and Planning Teaching Towards the Effective Use of Computer Algebra Systems

This article suggests a framework to organise a cluster of variables that are associated with students' effective use of computer algebra systems (CAS) in mathematics learning. Based on a review of the literature and from the authors' own teaching experience, the framework identifies the main characteristics of students' interactions with CAS technology and how these may be used to monitor students' developing use of CAS; from this, the framework may be used to plan teaching in order to gain greater benefit from the availability of CAS. Four case studies describing students' development over a semester are reported. These demonstrate a variety of combinations of technical competencies and personal attributes. They indicate the importance of both the technical and personal aspects but suggest that negative attitudes rather than technical difficulties can limit the effective use of CAS. Finally practical suggestions are given for teaching strategies which may promote effective use of CAS.This revised version was published online in September 2005 with corrections to the Cover Date.     

Three solutions for a mixed boundary value problem involving the one-dimensional p-Laplacian

This paper deals with two mixed nonlinear boundary value problems depending on a parameter λ. For each of them we prove the existence of at least three generalized solutions when λ lies in an exactly determined open interval. Usefulness of this information on the interval is then emphasized by means of some consequences. Our main tool is a very recent three critical points theorem stated in [Topol. Methods Nonlinear Anal. 22 (2003) 93-104].