Subbundles of maximal degree of the normal bundle of algebraic space curves almost complete intersection of special type

Summary LetX⊂P ³ be an irreducible smooth curve which is not a complete intersection. The main result of this paper shows that whenX is an a.c.i. of special type, i.e. its homogeneous ideal is generated by three polynomial of the same degreem, and additionallym>2, the subbundles of maximal degree of the normal bundle ofX inP ³ correspond to the singular points of maximal multiplicity of a plane curve which is the image ofX by a map (the linear system of the surfaces of minimal degree throughX). In particular this normal bundle is stable. The initial case of this family of curves, i.e. form=3, has been studied by E. Ballico-Ph. Ellia with different methods.

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Riassunto SiaX⊂P ³ una curva irriducibile e liscia che non è una completa intersezione. Il risultato principale di questa Nota mostra che quandoX è una almost completa intersezione di tipo speciale, cioè il suo ideale omogeneo è generato minimamente da 3 polinomi dello stesso gradom, e, inoltre,m>2, i sottofibrati di grado massimo del fibrato normale diX inP ³ corrispondono ai punti singolari di molteplicità massima di una curva piana che è l’immagine diX tramite una mappa (il sistema lineare delle superficie di grado minimo passanti perX). In particolare questo fibrato normale è stabile. Il caso iniziale di questa famiglia di curve, i.e. perm=3, è stato studiato da E. Ballico-Ph. Ellia con differenti metodi.

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This research is supported by GNSAGA (Italy).

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The main results of this paper have been the object of a talk at the meeting on ?Curves in Projective Space? held at Rocca di Papa in june 1985.     

Frequency‐dependent NMR relaxation of liquids confined inside porous media containing an increased amount of magnetic impurities

Frequency‐dependent NMR relaxation studies have been carried out on water (polar) and cyclohexane (nonpolar) molecules confined inside porous ceramics containing variable amounts of iron oxide (III). The porous ceramics were prepared by compression of powders mixed with iron oxide followed by thermal treatment. The pore size distribution was estimated using a technique based on diffusion in internal fields that exposed a narrow distribution of macropore sizes with an average pore dimension independent of iron oxide content. The relaxation dispersion curves were obtained at room temperature using a fast field cycling NMR instrument. They display an increase of the relaxation rate proportional to the iron oxide concentration. This behavior is more prominent at low Larmor frequencies and is independent of the polar character of the confined molecules. The results reported here can be fitted well with a relaxation model considering exchange between molecules in the close vicinity of the paramagnetic centers located in the surface and bulk‐like molecules inside the pores. This model allows the extraction of the transverse diffusional correlation time that can be related to the polar character of the confined molecules. Copyright © 2013 John Wiley & Sons, Ltd.     

On the spectral norm of algebraic numbers

In this paper we continue to study the spectral norms and their completions ([4]) in the case of the algebraic closure $ \overline {\mathbb Q} $ of ? in ?. Let $ \widetilde{\overline{\mathbb{Q}}} $ be the completion of $ \overline {\mathbb Q} $ relative to the spectral norm. We prove that $ \widetilde{\overline{\mathbb{Q}}} $ can be identified with the R‐subalgebra of all symmetric functions of C(G), where C(G) denotes the ?‐Banach algebra of all continuous functions defined on the absolute Galois group G = Gal$ {\overline {\mathbb Q}} / {\mathbb Q} $. We prove that any compact, closed to conjugation subset of ? is the pseudo‐orbit of a suitable element of $ \widetilde{\overline{\mathbb{Q}}} $. We also prove that the topological closure of any algebraic number field in $ \widetilde{\overline{\mathbb{Q}}} $ is of the form $\widetilde{\mathbb{Q}[x]}$ with x in $ \widetilde{\overline{\mathbb{Q}}} $.     

DNA-assisted decoration of single-walled carbon nanotubes with gold nanoparticles for applications in surface-enhanced Raman scattering imaging of cells

Single-walled carbon nanotubes (SWNTs) are 1D nanostructures with distinct physical and chemical properties that have shown great promise for applications in many fields, including biomedicine. Since for biomedical application the water solubility is crucial and SWNTs have low solubility, various methods (including polymer and biopolymer wrapping, chemical modifications) have been developed to solubilize and disperse them in water. Due to their unique optical properties such as photoluminescence in the NIR and strong resonant Raman signatures, they can be used as nanoprobes in biomedical imaging and phototherapies. Furthermore, decoration of SWNTs with noble metal nanoparticles will induce an excellent surface-enhanced Raman scattering (SERS) effect of the nanoparticles-SWNTs composites, with applications in cell imaging. Herein, we present a new and facile strategy for the DNA-assisted decoration of SWNTs with gold nanoparticles (AuNPs) and their application in SERS imaging. By ultrasonication at room temperature of SWNTs with AuNPs functionalized with synthetic DNA, SWNT-AuNPs nanocomposites with enhanced Raman signal were obtained. Among the important advantages of the proposed method are the presence of the free DNA overhangs around the SWNT-AuNPs suitable for post-synthetic modification of nanocomposite through hybridization of complementary DNA strands containing molecules of interest attached by well-developed bio-conjugation chemistry.

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Probing the Pore Size of Porous Ceramics with Controlled Amount of Magnetic Impurities via Diffusion Effects on the CPMG Technique

In our work, we will explore the possibility of implementing the well-known Carr–Purcell–Meiboom–Gill pulse sequence to determine the pore size of porous ceramics with magnetic impurities. The proposed approach exploits the diffusion dependence of the spin-echo signal in the presence of internal gradients occurring as a result of susceptibility contrast between the porous matrix and the confined liquid. For calibrating the technique, a comparison of the pore size data with those extracted from the so-called DDIF technique (DDIF, decay due to diffusion in the internal fields) is performed. This approach can be applied for nondestructive in situ characterization of soils, concrete, biological tissues or other structures with micrometer pore size.     

Existence and asymptotic results for a system of integro-partial differential equations

A non-Fourier phase field model is considered. A global existence result for a Dirichlet, or generalized Neumann, initial-boundary value problem is obtained, followed by a discussion of the regularity and asymptotic properties of solutions ast.This research was supported in part by the National Science Foundation under Grant DMS 91-11794 and in part by the Italian M.U.R.S.T. project Problemi non lineari...Part of this author's work was done while visiting Ohio University.     

Enhanced quantum well infrared photodetector focal plane arrays for space applications

A 30 months European Space Agency project started in March 2008, whose overall purpose is to expand and assess the performance of broadband (11–15 μm) quantum detectors for spectro-imaging applications: Dispersive Spectrometers and Fourier Transform Spectrometers. We present here the technical requirements, the development approach chosen as well as preliminary experimental results. Our approach is fully compatible with the final array format (1024 × 256, pitch 50–60 μm). We expect the requested uniformity, operability and SNR levels to be achieved at temperatures close to the goal values. The performance level will be demonstrated on 256 × 256, 50 μm pitch arrays. Also, operability and uniformity issues will be addressed on large mechanical 1024 × 256 hybrid arrays.     

Curve flows in Lagrange–Finsler geometry,bi-Hamiltonian structures and solitons

Methods in Riemann–Finsler geometry are applied to investigate bi-Hamiltonian structures and related mKdV hierarchies of soliton equations derived geometrically from regular Lagrangians and flows of non-stretching curves in tangent bundles. The total space geometry and nonholonomic flows of curves are defined by Lagrangian semisprays inducing canonical nonlinear connections (N$N$-connections), Sasaki type metrics and linear connections. The simplest examples of such geometries are given by tangent bundles on Riemannian symmetric spaces G/SO(n)$G/SO\left(n\right)$ provided with an N$N$-connection structure and an adapted metric, for which we elaborate a complete classification, and by generalized Lagrange spaces with constant Hessian. In this approach, bi-Hamiltonian structures are derived for geometric mechanical models and (pseudo) Riemannian metrics in gravity. The results yield horizontal/vertical pairs of vector sine-Gordon equations and vector mKdV equations, with the corresponding geometric curve flows in the hierarchies described in an explicit form by nonholonomic wave maps and mKdV analogs of nonholonomic Schrödinger maps on a tangent bundle.