Polynomial integrability of the Hamiltonian systems with homogeneous potential of degree − 3

In this paper, we study the polynomial integrability of natural Hamiltonian systems with two degrees of freedom having a homogeneous potential of degree k given either by a polynomial, or by an inverse of a polynomial. For k=−2,−1,…,3,4, their polynomial integrability has been characterized. Here, we have two main results. First, we characterize the polynomial integrability of those Hamiltonian systems with homogeneous potential of degree −3. Second, we extend a relation between the nontrivial eigenvalues of the Hessian of the potential calculated at a Darboux point to a family of Hamiltonian systems with potentials given by an inverse of a homogeneous polynomial. This relation was known for such Hamiltonian systems with homogeneous polynomial potentials. Finally, we present three open problems related with the polynomial integrability of Hamiltonian systems with a rational potential.     

Variable metric bundle methods: From conceptual to implementable forms

To minimize a convex function, we combine Moreau-Yosida regularizations, quasi-Newton matrices and bundling mechanisms. First we develop conceptual forms using “reversal” quasi-Newton formulae and we state their global and local convergence. Then, to produce implementable versions, we incorporate a bundle strategy together with a “curve-search”. No convergence results are given for the implementable versions; however some numerical illustrations show their good behaviour even for large-scale problems.     

Direct angle resolved photoemission spectroscopy and superconductivity of strained high-T c films

Since 1997 we systematically perform direct angle resolved photoemission spectroscopy (ARPES) on in-situ grown thin (<30 nm) cuprate films. Specifically, we probe low-energy electronic structure and properties of high-T _c superconductors (HTSC) under different degrees of epitaxial (compressive vs. tensile) strain. In overdoped and underdoped in-plane compressed (the strain is induced by the choice of substrate) ≈15 nm thin La_{2 − x} Sr _x CuO₄ (LSCO) films we almost double T _c to 40 K, from 20 K and 24 K, respectively. Yet the Fermi surface (FS) remains essentially two-dimensional. In contrast, ARPES data under tensile strain exhibit the dispersion that is three-dimensional, yet T _c drastically decreases. It seems that the in-plane compressive strain tends to push the apical oxygen far away from the CuO₂ plane, enhances the two-dimensional character of the dispersion and increases T _c, while the tensile strain acts in the opposite direction and the resulting dispersion is three-dimensional. We have established the shape of the FS for both cases, and all our data are consistent with other ongoing studies, like EXAFS. As the actual lattice of cuprates is like a ‘Napoleon-cake’, i.e. rigid CuO₂ planes alternating with softer ‘reservoir’, that distort differently under strain, our data rule out all oversimplified two-dimensional (rigid lattice) mean field models. The work is still in progress on optimized La-doped Bi-2201 films with enhanced T _c.      

Characterisation of ancient Roman wall-painting fragments using non-destructive IBA and MA-XRF techniques

Scientific investigation is very important in studies addressing issues of archaeological and historical objects. Ion beam analysis (IBA) and macro X-ray fluorescence (MA-XRF) spectroscopy are remarkable tools to obtain information about elemental composition and imaging of historical artefacts with a non-invasive character. These investigation techniques were employed in the framework of a project aimed at supporting the characterization of materials and techniques related with the Roman wall painting. The archaeological excavations at Villa della Piscina in Rome have revealed a luxury building with a large pool (about 50 m long) and thermal baths and numerous fragments of plaster, coming from intentional demolitions referable to two distinct architectural contexts of the Villa during the imperial age, have been found. This work deals with studying the interesting wall pictorial apparatus of great cultural value of the heritage inherited from the Roman age in the area of the ancient city of Rome. The colour palette of the pigments investigated, in particular, by MA-XRF and particle-induced X-ray emission (PIXE) and has revealed Fe, Cu, Pb, Si and Hg as main elements. Traces of other constituents uncover the choice of the different colours chosen by the artists who had embellished the rooms of the Villa.     

A-stable Runge–Kutta methods for semilinear evolution equations

We consider semilinear evolution equations for which the linear part generates a strongly continuous semigroup and the nonlinear part is sufficiently smooth on a scale of Hilbert spaces. In this setting, we prove the existence of solutions which are temporally smooth in the norm of the lowest rung of the scale for an open set of initial data on the highest rung of the scale. Under the same assumptions, we prove that a class of implicit, A-stable Runge–Kutta semidiscretizations in time of such equations are smooth as maps from open subsets of the highest rung into the lowest rung of the scale. Under the additional assumption that the linear part of the evolution equation is normal or sectorial, we prove full order convergence of the semidiscretization in time for initial data on open sets. Our results apply, in particular, to the semilinear wave equation and to the nonlinear Schrödinger equation.     

High-frequency 263 GHz PELDOR

Pulsed electron–electron double resonance (PELDOR/DEER) at high frequencies can provide information on the relative orientation of paramagnetic centres or spin labels, if those are rigidly oriented in a host biomolecule and experiments are performed with sufficient orientation selectivity. We present the first comparative PELDOR study at 263 and 94 GHz on a model RNA system containing rigid nitroxides. We show that at 263 GHz still considerable modulation depth is observed and orientation selectivity is significant, particularly in g _x–g _y plane of the nitroxides.     

Logatom corpus for the assessment of the intelligibility in Spanish speaking environments and its relation with STI measurements

A 1000 consonant–vowel–consonant structure logatoms corpus (CVC-structure), grouped in 10 phonetically equally balanced lists of 100 words each, was developed to satisfy the need of subjective assessment of speech intelligibility in American Spanish speaking environments. This corpus was tested and correlated with the Speech Transmission Index (STI) measurements to compare its articulation intelligibility score with other lists’ scores.Through the development of this work it was determined that in two different acoustically poor rooms that have the same STI (with STI < 0.50), the intelligibility score is lower when the articulation test is performed in a quiet room with high reverberation time than when it is performed in a very noisy room with low reverberation time. The final correlation curve of the American Spanish CVC-structure corpus was around 10% points higher than the CVC_EQB curve obtained by Steeneken and Houtgast in 2002.     

Radon levels in underground workplaces – results of a nationwide survey in Italy

In Italy an extensive survey has been carried out with the aim to evaluate annual average radon concentration in underground workplaces.The survey covered 933 underground rooms located in 311 bank workplaces spread throughout in all Italian regions; at this scope the sampling was stratified random in order to be representative on national scale. The annual radon concentration was estimated by using passive radon dosemeters (NRPB/SSI type holder and CR-39 as detector): the devices were exposed for a period of about 3 months and 4 cycles were performed to cover a solar year. The radon levels in underground workplaces ranged from 27 to 4851 Bq/m³ with an overall mean value of 153 Bq/m³. As expected, radon distribution is not uniform throughout Italy: in several regions high radon annual averages have been found, confirming previous surveys.The analysis of data shows a high variability among regions and intra-region but low spread among rooms belonging to the same workplace.About 5% of underground workplaces displayed radon concentration exceeding 400 Bq/m³, and the 4.4% exceeds 500 Bq/m³, the national action level for the exposure to natural radioactivity in workplaces.     

Generalized Bosbach states: part I

States have been introduced on commutative and non-commutative algebras of fuzzy logics as functions defined on these algebras with values in [0,1]. Starting from the observation that in the definition of Bosbach states there intervenes the standard MV-algebra structure of [0,1], in this paper we introduce Bosbach states defined on residuated lattices with values in residuated lattices. We are led to two types of generalized Bosbach states, with distinct behaviours. Properties of generalized states are useful for the development of an algebraic theory of probabilistic models for non-commutative fuzzy logics.     

Weakly hyperbolic equations with non-analytic coefficients and lower order terms

In this paper we consider weakly hyperbolic equations of higher orders in arbitrary dimensions with time-dependent coefficients and lower order terms. We prove the Gevrey well-posedness of the Cauchy problem under $C^k$ -regularity of coefficients of the principal part and natural Levi conditions on lower order terms which may be only continuous. In the case of analytic coefficients in the principal part we establish the $C^\infty $ well-posedness. The proofs are based on using the quasi-symmetriser for the corresponding companion system and inductions on the order of equation and on the frequency regions. The main novelty compared to the existing literature is the possibility to include lower order terms to the equation (which have been untreatable until now in these problems) as well as considering any space dimensions. We also give results on the ultradistributional and distributional well-posedness of the problem, and we look at new effects for equations with discontinuous lower order terms.