Some remarks on factoriality of certain hypersurfaces in \mathbb{P}^4

Let V be a reduced and irreducible hypersurface of degree k 3. In this paper we prove that if the singular locus of V consists of ₂ ordinary double points, ₃ ordinary triple points and if ₂ + 4₃ < (k – 1)², then any smooth surface contained in V is a complete intersection on V.Received: 7 January 2004     

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.     

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.     

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.     

A general framework for ADMM acceleration

Numerical Algorithms - The Alternating Direction Multipliers Method (ADMM) is a very popular algorithm for computing the solution of convex constrained minimization problems. Such problems are...     

Weyl Type Theorems for Left and Right Polaroid Operators

A bounded operator defined on a Banach space is said to be polaroid if every isolated point of the spectrum is a pole of the resolvent. In this paper we consider the two related notions of left and right polaroid, and explore them together with the condition of being a-polaroid. Moreover, the equivalences of Weyl type theorems and generalized Weyl type theorems are investigated for left and a-polaroid operators. As a consequence, we obtain a general framework which allows us to derive in a unified way many recent results, concerning Weyl type theorems (generalized or not) for important classes of operators.