A Lower Bound for the Height of a Rational Function at S-unit Points

Let a,b be given, multiplicatively independent positive integers and let >0. In a recent paper jointly with Y. Bugeaud we proved the upper bound exp(n) for g.c.d.(aⁿ–1, bⁿ–1); shortly afterwards we generalized this to the estimate g.c.d.(u–1,v–1)<>u,v) for multiplicatively independent S-units u,vZ. In a subsequent analysis of those results it turned out that a perhaps better formulation of them may be obtained in terms of the language of heights of algebraic numbers. In fact, the purposes of the present paper are: to generalize the upper bound for the g.c.d. to pairs of rational functions other than {u–1,v–1} and to extend the results to the realm of algebraic numbers, giving at the same time a new formulation of the bounds in terms of height functions and algebraic subgroups of G_m².     

Variations on Weyl's theorem

In this note we study the property (w), a variant of Weyl's theorem introduced by Rako?evi?, by means of the localized single-valued extension property (SVEP). We establish for a bounded linear operator defined on a Banach space several sufficient and necessary conditions for which property (w) holds. We also relate this property with Weyl's theorem and with another variant of it, a-Weyl's theorem. We show that Weyl's theorem, a-Weyl's theorem and property (w) for T (respectively T^*) coincide whenever T^* (respectively T) satisfies SVEP. As a consequence of these results, we obtain that several classes of commonly considered operators have property (w).     

Hermitian matrices and cohomology of Kähler varieties

We give some upper bounds on the dimension of the kernel of the cup product map $H^{1}(X,\mathbb{C}) \otimes H^{1}(X,\mathbb{C}) \to H^{2}(X,\mathbb{C})We give some upper bounds on the dimension of the kernel of the cup product map , where X is a compact K?hler variety without Albanese fibrations.     

Capillary electrophoresis–electrospray mass spectrometry and HR–ICP–MS for the detection and quantification of 10B-boronophenylalanine (10B–BPA) used in boron neutron capture therapy

Boron neutron capture therapy (BNCT) is a bimodal radiotherapeutic treatment based on the irradiation of neoplastic tissues with neutrons after the tissues have selectively accumulated molecules loaded with nuclides with large neutron capture cross-sections (such boron-10). Boron-10 carriers have been tested to a limited extent, and clinical trials have been conducted on sulfhydryl borane (¹⁰B-BSH) and boronophenylalanine (¹⁰B-BPA). However, precise and accurate measurements of boron-10 concentrations (0.1–100 μg/g) in specimens and samples of limited size (μg scale) are needed in order to be able to biologically characterise new compounds in predictive tissue dosimetry, toxicology and pharmacology studies as well as in clinical investigations. A new approach based on fast separation and detection of ¹⁰B-BPA performed by coupling capillary electrophoresis to electrospray mass spectrometry is reported. This method allows the quantitative analysis and characterisation of ¹⁰B-BPA in a short time with a high separation efficiency. Detection limits of 3 μM for ¹⁰B-BPA and 30 ng/mL for ¹⁰B were obtained with CE–ESI–MS. A quantification limit of 10 μM for ¹⁰B-BPA (100 ng/mL for ¹⁰B) was attained. The total boron-10 concentration was determined by high-resolution inductively coupled mass spectrometry in order to validate the method. Boron-10 isotope measurements were carried out by HR–ICP–MS at medium resolution (R=4000) due to the presence of an isobaric interference at mass 10. Good agreement was obtained between the values from CE–ESI–MS and those from HR–ICP–MS. The method has been successfully used to determine the ¹⁰B-BPA in two lines of cultured cells.     

Phenol production in benzene/air plasmas at atmospheric pressure. Role of radical and ionic routes

Benzene can be efficiently converted into phenol when it is treated by either corona or dielectric barrier discharge (DBD) plasmas operating at atmospheric pressure in air or mixtures of N(2) and O(2). Phenol produced by corona discharge in an atmospheric pressure chemical ionization source (APCI) has been detected as the corresponding radical cation C(6)H(5)OH(+*) at m/z 94 by an ion trap mass spectrometer. On the other hand, phenol has been observed also as neutral product by gas chromatography-mass spectrometry analysis (GC-MS) after treatment in a DBD plasma. Experiments aimed at shading light on the elementary processes responsible for benzene oxidation were carried out (i) by changing the composition of the gas in the corona discharge source; (ii) by using isotopically labeled reagents; and (iii) by investigating some relevant ion-molecule reactions (i.e. C(6)H(6)(+*) + O(2), C(6)H(5)(+) + O(2)) via selected guided ion beam measurements and with the help of ab initio calculations. The results of our approach show that ionic mechanisms do not play a significant role in phenol production, which can be better explained by radical reactions resulting in oxygen addition to the benzene ring followed by 1,2 H transfer.     

C2C12 myoblast sensitivity to different apoptotic chemical triggers

Apoptosis is a form of cell death crucial for normal development and tissue homeostasis. Its typical features include chromatin changes, nuclear breakdown, plasma membrane blebbing and splitting of cellular content into apoptotic bodies, that progressively undergo phagocytosis.Apoptosis is considered essential for skeletal muscle development, where defective cells are deleted during differentiation. In addition, it plays a relevant role in several muscle myopathies, as well as in denervation and disuse.The aim of this study was to evaluate muscle cell sensitivity to different apoptotic triggers, acting through different mechanisms of action. Chemical agents, active against distinct intracellular targets, such as mitochondrial respiratory chain and DNA, have been chosen to better highlight cell death mechanisms. To induce apoptosis, C2C12 myoblasts have been exposed to H₂O₂, staurosporine, cisplatin and etoposide, at different doses and incubation times, and they have been analysed by flow cytometry, scanning and transmission electron microscopy.Flow cytometry analysis revealed a certain subdiploid peak after all treatments. The best apoptotic effect was observable, as confirmed at reverted microscope, at minimum doses and after the major exposure time.At ultrastructural level programmed cell death has been observed. Characteristic chromatin condensation and margination, as well as apoptotic bodies, frequently appeared, even if in the presence of secondary necrosis; surface blebs were also observed during scanning microscopic observation.In particular, exposure to H₂O₂ or staurosporine showed the largest number of myoblasts in late apoptotic stages and in secondary necrosis. Cisplatin treatments revealed few early apoptotic cells. The analysis of etoposide-induced apoptosis was in agreement with data obtained from flow cytometry, indicating a significant increase of apoptotic cell number.These results suggest that all conditions are able to induce apoptosis in C2C12 myoblasts, which occurs, considering trigger mechanisms of action, mostly following the mitochondrial pathway, if not excluding that due to DNA damage. Therefore, mitochondria permeability alteration is an important step in skeletal muscle programmed cell death. This last conclusion seems to have a significant relevance in understanding the mechanisms involved in muscle disorders, denervation and chronic muscle disuse, conditions frequently characterized by a decline in mitochondrial content and by an increase of mitochondrial apoptosis susceptibility.     

Controllability of quasi-linear Hamiltonian NLS equations

We prove internal controllability in arbitrary time, for small data, for quasi-linear Hamiltonian NLS equations on the circle. We use a procedure of reduction to constant coefficients up to order zero and HUM method to prove the controllability of the linearized problem. Then we apply a Nash–Moser–Hörmander implicit function theorem as a black box.