Virtual processes and virtual particles: real or fictitious?

The notions of a virtual process and a virtual quantum, central in current field theories, are usually justified by means of the so-called fourthindeterminacy relation between energy and time. But since the latter formula is meaningless in quantum theory, virtual processes and virtual quanta turn out to be fictions. A number of consequences follow.     

On minimum problems for families of functionals

Sommario Per una famiglia { | λ ∈ ⁁} di funzionali reali definiti in uno spazio metricoX e dipendenti da un parametro λ ∈ ⁁, dove ⁁ è uno spazio topologico, si pone il problema di come si comporta, al variare di λ, l'insieme dei punti di minimo di I_λ. Lo studio di tale problema è l'oggetto del presente lavoro e il risultato principale è dato dal Teorema1.

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Entrata in Redazione il 3 marzo 1970.     

Sulle corrispondenze fra tre piani

Sunto In una corrispondenza puntualeC fra tre piani proiettivi, considerata una terna ordinaria O₁, O₂, O₃ di punti corrispondenti, in generale, a due E₂ di centri O₁, O₂ non corrisponde inC un E₂. Orbene, nel presente lavoro, si ricercano le terne di E₂ corrispondenti inC. Fra siffatte terne si considerano poi quelle per cui uno dei tre E₂ è di flesso, pervenendo così, in ciascuno dei tre piani, a nove direzioni particolari (chiamatecaratteristiche odinflessionali) e a sei E₂ intrinsecamente determinati. Le direzioni caratteristiche si distinguono in tre terne e si indica nna proprietà dell'involuzione da esse determinata. Si ottengono anche altri E₂ intrinsecamente determinati daC e una proprietà di essi. Infine si considerano, in ciascuno dei tre piani, certe cubiche che, quando i piani siano euclidei, sono intrinsecamente determinate daC. Alla memoria di Guido Castelnuovo, nel primo centenario della nascita.     

Smooth quasiregular mappings with branching

We give an example of a -smooth quasiregular mapping in 3-space with nonempty branch set. Moreover, we show that the branch set of an arbitrary quasiregular mapping in n-space has Hausdorff dimension quantitatively bounded away from n. By using the second result, we establish a new, qualitatively sharp relation between smoothness and branching.     

Sectional Curvature Rigidity of Asymptotically Locally Hyperbolic Manifolds

This paper presents a rigidity result of real hyperbolic quotients inanalogy to Min-Oo's result in Math. Ann. 285(4) (1989),527–539, but without the spin condition. In order to prove this,we use special Killing forms on the exterior form bundle. Moreover, wemake an assumption on the sectional curvature to obtain the necessaryeigenvalue estimates of the curvature endomorphism in theBochner–Weitzenböck formula of ^k M.     

Ultrarapid capillary electrophoresis method for the determination of reduced and oxidized glutathione in red blood cells

We describe a very rapid high-performance capillary electrophoresis method for the separation and quantification of reduced (GSH) and oxidized (GSSG) glutathione in red blood cells. Two procedures for sample preparation have been compared, Microcon-10 membrane filtration and acid precipitation. The separation is obtained in an uncoated capillary using a high ionic strength borate buffer at pH 7.8. The intra-assay coefficients of variation (CVs%) are 1.53 and 1.66 for GSH and GSSG, respectively. The run is shorter than 90 s and the migration time is highly reproducible both for GSH (CV% 0.22) and GSSG (CV% 0.17). When the filtration step is used only GSH is found, whereas both GSH and GSSG are detectable after acid precipitation, suggesting that GSSG revealed after acid treatment may be an artefact due to GSH oxidation. Because of its good analytical performance this method could be used for routine red blood cell glutathione measurement in healthy or pathological conditions.     

A versatile approach to affinitychromic polythiophenes

The preparation of both postfunctionalizable and chromic poly[3-(N-succinimido-p-phenylcarboxylate(tetraethoxy)oxy)-4-methylthiophene] is reported. The N-hydroxysuccinimide ester side group can easily react with different amine-bearing molecules in the solid state to yield a library of new polythiophene derivatives. The resulting polymers can be dissolved in various solvents, and interactions between the side chains (ligands) and different analytes (targets) can be detected from modifications of both the side-chain and the backbone conformations resulting in important color changes (i.e., affinitychromism). This colorimetric polymeric transducer could therefore lead to highly valuable, versatile, and inexpensive tools for highthroughput screening and drug discovery.