Some fixed-points theorems for multi-valued mappings in topological vector spaces

Sunto Si danno dei teoremi di punto fisso der trasformazioni multivoche non compatte, definite in un sottoinsieme convesso e chiuso di uno spazio lineare topologico, localmente convesso e di Hausdorff. Tali teoremi estendono alcuni noti risultati dovuti a Darbo, Sadovskij, Daneš ed altri.

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Work performed under the auspices of the National Research Council (C.N.R.).

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Entrata in Redazione il 18 maggio 1971.     

Mercury(II) dibromo-bis-(3-amino-5-mercapto-1,2,4-triazole): synthesis,crystal structure,and infrared characterization

The title compound C₄H₈N₈S₂HgBr₂ was prepared and characterized by means of X-ray crystallography, and i.r. measurements. The crystals are orthorhombic, space group Pbcn (no. 60) witha=9.707(2),b=8.609(1),c=16.128(2) Å, andZ=4. The compound exhibits discrete monometallic units with the 1,2,4-triazole molecule acting as a monodentate ligand. The structure consists of units in which the mercury atom is coordinated in a distorted tetrahedral geometry by two sulfur and two bromine atoms. The NH and NH₂ group of the 3-amino-5-mercapto-1,2,4-triazole unit are involved in intermolecular hydrogen bonds. Infrared bands are diagnostic of the coordination environment around the metal atoms.     

Simple eigenvalues for the Steklov problem in a domain with a small hole. A functional analytic approach

Let be a bounded open domain of . Let denote the outward unit normal of . We assume that the Steklov problem Δu = 0 in and on has a simple eigenvalue of . Then we consider an annular domain obtained by removing from a small‐cavity size of ε > 0, and we show that under proper assumptions there exists a real valued and real analytic function defined in an open neighborhood of (0,0) in and such that is a simple eigenvalue for the Steklov problem Δu = 0 in and on for all ε > 0 small enough, and such that . Here denotes the outward unit normal of , and δ_2,2 ≡ 1 and δ_2,n ≡ 0 if n ≥ 3. Then related statements have been proved for corresponding eigenfunctions. Copyright © 2013 John Wiley & Sons, Ltd.     

The coevolution theory of the origin of the genetic code

A review of the coevolution theory of the origin of the genetic code is presented. This theory maintains that the origin of the code should be sought in the biosynthetic relationships between amino acids. In particular, some amino acids, the precursors, occupied the structure of the genetic code early on. As the product amino acids developed from these precursors, part or all of the codon domain of the precursor amino acid was ceded to the product amino acids, which resulted in the structuring of the genetic code. This paper therefore reviews the evidence in favour of this theory. The existence of some molecular fossils representing the biosynthetic pathways on which the coevolution theory suggests biosynthetic transformations took place (precursor amino acid → product amino acid) seems to be a strong corroboration of this theory. A generalisation imposed by this theory on the ancestral metabolic state is then discussed and, finally, the main prospects that seem to stem from the coevolution theory are presented.     

Simultaneous near field imaging of electric and magnetic field in photonic crystal nanocavities

The insertion of a metal-coated tip on the surface of a photonic crystal microcavity is used for simultaneous near field imaging of electric and magnetic fields in photonic crystal nanocavities, via the radiative emission of embedded semiconductor quantum dots (QD). The photoluminescence intensity map directly gives the electric field distribution, to which the electric dipole of the QD is coupled. The magnetic field generates, via Faraday's law, a circular current in the apex of the metallized probe that can be schematized as a ring. The resulting magnetic perturbation of the photonic modes induces a blue shift, which can be used to map the magnetic field, within a single near-field scan.     

DNA damage induced by organotins on ­trout‐nucleated erythrocytes

The effect of tributyltin‐chloride (TBTC), dibutyltin‐chloride (DBTC) and monobutyltin‐chloride (MBTC) on rainbow trout (Salmo irideus) nuclear DNA, was investigated by means of single cell gel electrophoresis (‘comet’ assay). Our data show that TBTC presents a marked genotoxic effect, whereas the genotoxic effect is less pronounced for DBTC and it is completely absent for MBTC. These results could be important in evaluating the environmental risks deriving from the use of these molecules as a antifouling agents in marine paints and as agricultural biocides. Copyright © 2001 John Wiley & Sons, Ltd.

Abbreviations:

TBTC,

tributyltin‐chloride;

DBTC,

dibutyltin‐chloride;

MBTC,

monobutyltin‐chloride;

Hb,

hemoglobin.

     

On the probabilistic approach for Gaussian Berezin integrals

We present a novel approach to Gaussian Berezin correlation functions. A formula well-known in the literature expresses these quantities in terms of submatrices of the inverse matrix appearing in the Gaussian action. By using a recently proposed method to calculate Berezin integrals as an expectation of suitable functionals of Poisson processes, we obtain an alternative formula which allows one to skip the calculation of the inverse of the matrix. This formula, previously derived using different approaches (in particular by means of the Jacobi identity for the compound matrices), has computational advantages which grow rapidly with the dimension of the Grassmann algebra and the order of correlation. By using this alternative formula, we establish a mapping between two fermionic systems, not necessarily Gaussian, with short and long range interaction, respectively.