Hardy–Rellich inequalities with boundary remainder terms and applications

We prove a family of Hardy–Rellich inequalities with optimal constants and additional boundary terms. These inequalities are used to study the behavior of extremal solutions to biharmonic Gelfand-type equations under Steklov boundary conditions.     

Classification of Lagrangian fibrations over a Klein bottle

This paper completes the classification of regular Lagrangian fibrations over compact surfaces. Mishachev (Diff Geom Appl 6:301–320, 1996) classifies regular Lagrangian fibrations over \mathbbT²{\mathbb{T}^2}. The main theorem in Fried et al. (Comment Math Helv 56(4):487–523, 1981) is used to in order to classify integral affine structures on the Klein bottle K ² and, hence, regular Lagrangian fibrations over this space.     

A Variational Homogenization Approach to Electromechanical Hystereses Caused by Domain Wall Movement

In recent years, increasing interest in so-called smart materials such as ferroelectric polymers and ceramics has been shown. Those materials are used in various actuators, sensors, and also in medical devices. In this paper, we outline a micro-macro approach to the modeling of macroscopic hystereses which directly takes into account the microstructural evolution of electrically poled domains. To this end, an incremental variational formulation for a gradient-type phase field model is developed and exploited for the simulation of electromechanically coupled problems. The formulation determines the hysteretic response of the material in terms of an energy-enthalpy and a dissipation function which both depend on the microscopic remanent polarization treated as an order parameter. The gradient-type balance law for the phase field can be considered as a generalization of Biot's equation for standard dissipative materials and may be related to the classical Ginzburg-Landau equation. Furthermore, the variational formulation serves as natural starting point for a compact and symmetric finite element implementation of the coupled micromechanical problem covering the displacement, the electric potential, and the microscopic polarization vector. For this three-field scenario we develop a variational-based homogenization method which determines the overall macroscopic hysteretic properties of a polycrystalline aggregate. The proposed computational method can be used as a numerical laboratory for the improvement of microstructural properties. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Non Commutative Functional Calculus: Bounded Operators

In this paper we develop a functional calculus for bounded operators defined on quaternionic Banach spaces. This calculus is based on the new notion of slice-regularity, see Gentili and Struppa (Acad Sci Paris 342:741–744, 2006) and the key tools are a new resolvent operator and a new eigenvalue problem.     

Cardanol Based Matrix for Jute Reinforced Pipes

The aim of this work is the development of composite pipes using renewable resources. The pipes, manufactured by filament winding technology, were obtained using an epoxy resin crosslinked with a cardanol based novolac as matrix and jute fibres as reinforcement. Cardanol is a natural oil extracted from the shell of the cashew (Anacardium occidentale L.) nut. An amount of natural materials higher than 50% by weight was achieved in the final composites. Tensile and parallel plate compression tests were carried out on the composite pipes.     

Extrinsic Heavy Metal Atom Effect on the Solid‐State Room Temperature Phosphorescence of Cyclic Triimidazole

Four coordination compounds [Zn₃(CH₃COO)₆(H₂O)₂](TT)₂ [Cd(H₂O)₆](ClO₄)₂(TT)₂, [Cd(H₂O)₆](BF₄)₂(TT)₂, [Zn(H₂O)₆](BF₄)₂(TT)₂ ( 1 – 4 ) accommodating the crystallization induced emissive triimidazo[1,2‐a:1′,2′‐c:1′′,2′′‐e][1,3,5]triazine ( TT ) as a guest in their crystal lattice are isolated and fully photophysically and structurally characterized. Their emission properties are compared with those of afterglow TT and interpreted taking into account the heavy atom effect and crystal packing similarities and differences. In the case of 1 , due to the closeness of the TT H‐aggregates arrangement with that of the phosphor's pure phase, the observed intensification of the phosphorescent emission at the expense of the prompt one is attributed to the extrinsic heavy atom effect of Zn. In 2 and 3 , the heavier Cd atom is responsible for a decrease in the lifetimes of the afterglow emission, despite the presence of tightly overlapped H‐dimers in the crystal structure. Finally, for 4 , isostructural with 3 , the Zn atom reveals in RTUP lifetime comparable with that of 1 .     

Intermolecular interactions of substituted benzenes on multi-walled carbon nanotubes grafted on HPLC silica microspheres and interaction study through artificial neural networks

Purified multi-walled carbon nanotubes (MWCNTs) grafted onto silica microspheres by gamma-radiation were applied as a HPLC stationary phase for investigating the intermolecular interactions between MWCNTs and substituted benzenes. The synthetic route, simple and not requiring CNTs derivatization, involved no alteration of the nanotube original morphology and physical–chemical properties. The affinity of a set of substituted benzenes for the MWCNTs was studied by correlating the capacity factor (k′) of each probe to its physico-chemical characteristics (calculated by Density Functional Theory). The correlation was found through a theoretical approach based on feedforward neural networks. This strategy was adopted because today these calculations are easily affordable for small molecules (like the analytes), and many critical parameters needed are not known. This might increase the applicability of the proposed method to other cases of study. Moreover, it was seen that the normal linear fit does not provide a good model. The interaction on the MWCNT phase was compared to that of an octadecyl (C18) reversed phase, under the same elution conditions. Results from trained neural networks indicated that the main role in the interactions between the analytes and the stationary phases is due to dipole moment, polarizability and LUMO energy. As expected for the C18 stationary phase correlation, is due to dipole moment and polarizability, while for the MWCNT stationary phase primarily to LUMO energy followed by polarizability, evidence for a specific interaction between MWCNTs and analytes. The CNT-based hybrid material proved to be not only a chromatographic phase but also a useful tool to investigate the MWCNT-molecular interactions with variously substituted benzenes.     

Reaction of Nitrogen‐Radicals with Organometallics Under Ni‐Catalysis: N‐Arylations and Amino‐Functionalization Cascades

Herein, we report a strategy for the generation of nitrogen‐radicals by ground‐state single electron transfer with organyl–Ni^I species. Depending on the philicity of the N‐radical, two types of processes have been developed. In the case of nucleophilic aminyl radicals direct N‐arylation with aryl organozinc, organoboron, and organosilicon reagents was achieved. In the case of electrophilic amidyl radicals, cascade processes involving intramolecular cyclization, followed by reaction with both aryl and alkyl organometallics have been developed. The N‐cyclization–alkylation cascade introduces a novel retrosynthetic disconnection for the assembly of substituted lactams and pyrrolidines with its potential demonstrated in the short total synthesis of four venom alkaloids.     

Kernel method for nonlinear granger causality

Important information on the structure of complex systems can be obtained by measuring to what extent the individual components exchange information among each other. The linear Granger approach, to detect cause-effect relationships between time series, has emerged in recent years as a leading statistical technique to accomplish this task. Here we generalize Granger causality to the nonlinear case using the theory of reproducing kernel Hilbert spaces. Our method performs linear Granger causality in the feature space of suitable kernel functions, assuming arbitrary degree of nonlinearity. We develop a new strategy to cope with the problem of overfitting, based on the geometry of reproducing kernel Hilbert spaces. Applications to coupled chaotic maps and physiological data sets are presented.     

PRESS-MAG-O: A new facility to probe materials and phenomena under extreme conditions

In the recent years, several experiments performed under high magnetic fields (HMFs), at high pressure (HP) and/or at low temperature (LT) have led to spectacular discoveries in condensed matter. In many new systems, although challenging, it is strategic to perform a magneto-optical analysis, to investigate the phonon behavior in the far infrared (IR) domain. By combining HMF and HP in a wide temperature (T) range to perform concurrently IR magneto-optics and ac-magneto-dynamic experiments, it will be possible to achieve unique information on systems and/or new phenomena, almost impossible to obtain with standard spectroscopic methods. Here we present PRESS-MAG-O, a new facility under construction that will perform HP experiments under HMF in a wide T range. The system is expected to be operational by the end of 2008 and will be tested at SINBAD, the IR synchrotron radiation beamline operational since 2001 at DAΦNE (Double Annular Φ-factory for Nice Experiments), the storage ring of the INFN Frascati National Laboratory (LNF). While for IR experiments an interferometer will be used, for the magneto-dynamic experiments a SQUID magnetometer in the 10 Hz-2 KHz frequency range will be utilized. HP will be applied to samples by a Cu-Be diamond anvil cell (DAC), so that the device will be able to collect FTIR spectra and high harmonic ac susceptibility data in a dc magnetic field up to 8 T and to about 20 GPa in a wide temperature range (4.2-200 K).