Discontinuous Solutions to Unbounded Differential Inclusions under State Constraints. Applications to Optimal Control Problems

We consider a nonconvex and unbounded differential inclusion derived from a control system whose control sets are time and space-dependent. We extend the inclusion in order to allow discontinuous trajectories. We prove that the set of solutions of the original inclusion is dense in the set of solutions of the extended inclusion and, moreover, these last solutions are stable with respect to the initial data. Both of these results are also proven in the presence of state and integral constraints (assuming suitable conditions at the boundary of the constraining set). As an application, the value function of a Mayer problem is shown to be continuous and the unique viscosity solution of a Hamilton–Jacobi equation with suitable boundary conditions.     

Multiecho multimoment refocussing of motion in magnetic resonance imaging: MEM-MO-RE

Gradient moment nulling techniques for refocussing of spin dephasing resulting from movement during application of magnetic resonance imaging gradients have gained widespread application. These techniques offer advantages over conventional imaging gradients by reducing motion artifacts due to intraview motion, and by recovering signal lost from spin dephasing. This paper presents a simple technique for designing multiecho imaging gradient waveforms that refocus dephasing from the interaction of imaging gradients and multiple derivatives of position. Multiple moments will be compensated at each echo. The method described relies on the fact that the calculation of time moments for nulled moment gradient waveforms is independent of the time origin chosen. Therefore, waveforms used to generate the second echo image for multiple echo sequences with echo times given by TEn = TE1 + (n - 1) * (TE2 - TE1) may also be used for generation of the third and additional echo images. All echoes will refocus the same derivatives of position. Multiecho, multimoment refocussing (MEM-MO-RE) images through the liver in a patient with ampullary adenocarcinoma metastatic to the liver demonstrate the application of the method in clinical scanning.     

Photophysical Properties and Conformational Effects on the Circular Dichroism of an Azobenzene–Cyclodextrin [1]Rotaxane and Its Molecular Components

The photophysical properties of a multicomponent [1]rotaxane bearing a β‐cyclodextrin ring covalently connected to an axle comprising an azobenzene photoisomerisable moiety and a naphthalimide‐type fluorescent stopper are investigated by a combined experimental and computational study. The absorption and fluorescence spectra, and particularly the induced circular dichroism (ICD) signal, are determined. The latter shows a sign relation that cannot be rationalised in terms of the simple general rules commonly employed to analyse the ICD spectra of achiral guests encircled by chiral hosts. To assist the interpretation of experimental results, DFT and time‐dependent (TD) DFT calculations are performed to explore the availability of low‐energy conformations and to model their spectroscopic response. Molecular dynamics simulations performed in water show the interconversion of a number of conformers, the contribution of which to the ICD signal is in agreement with the observation.     

Effect of oxygen on the electronic structure of highly crystalline picene films

The electronic structure of highly crystalline picene films with a standing-up orientation grown epitaxially on the Ag(110) surface was investigated. Upon exposure to oxgen gas, O(2) molecules incorporate at the interstitial sites within the a-b plane of the film. Features related to the highest three occupied molecular orbitals shift toward a lower binding energy which results in the inactivation of traps and the reduction of the charge injection barrier by about 1 eV. It is suggested that the highest two picene orbitals are inverted due to the strong interactions between the singly occupied oxygen π orbital and the highest occupied orbital of picene.     

EXAFS of the superconducting oxide BaPb1−xBixO3

The two-valence state Bi³⁺ and Bi⁵⁺ of Bi in the semiconductor BaBiO₃ and in the BaPb_1?xBi_xO₃ (x = 0, 0.25, 0.6 and 1) system has been determined from the EXAFS spectra above the L_III-edges of Ba, Pb and Bi. Peaks in the radial distribution function up to 5 Å from the absorber have been identified through a model calculation using theoretical amplitudes and phase shifts and the interatomic distances from neutron diffraction measurements. We found indication of local disorder in the Pb-Bi sublattice for the mixed compound.     

Study of variables for optimization of the dye indosol adsorption process using red mud and clay as adsorbents

The effluents from the textile industry, which not properly treated or discharged directly into water bodies, are a serious environmental problem. In order to find options to solve this problem, in this study, it was evaluate two alternative adsorbents: red mud and smectite clay, to remove the dye Indosol dark-blue SF-BL SGR 240. Assays were performed in batch using the experimental design to optimize the process and evaluate the influence of pH, mass and agitation speed on the adsorption capacity of dye by each material. The results showed that the adsorption process was influenced by the amount of mass of the adsorbent, by the pH and the by interaction between pH and mass, thereby obtaining a removal of approximately 0.110 and 0.119 mg g^?1 with red mud and smectite clay respectively.     

DC(13)PC bilayers from anomalous swelling to main transition: an X-ray scattering investigation

We have performed small-angle (SAXS) and wide-angle X-ray scattering (WAXS) measurements on the lamellar phase and on large unilamellar vesicles (LUVs) of DC(13)PC in the temperature range corresponding to the anomalous swelling regime of multibilayer systems, adjacent to the chain melting transition, and across the transition. Our SAXS measurements indicate that on cooling from the L(alpha) phase, a uniform progressive swelling of the lamellar system to anomalous distances, starting approximately 2 degrees C above the main transition, is followed by a region of coexistence, covering the width of the transition ( approximately 0.6 degrees C). Across the transition region, a progressively increasing volume fraction of gel phase with a constant P (beta') interlamellar distance coexists with a decreasing amount of nongel phase that keeps on swelling to longer distances. Along both the swelling and the transition regions, anomalies in the specific heat are observed revealing a two-step process. Simultaneous WAXS experiments show a progressive "density" increase along the swelling region, constituting a direct spectroscopic evidence of an "evolving membrane" approaching the transition in a bulk real system. Calorimetric and densitometric measurements on LUVs are also presented, together with WAXS results, that show the existence of a double step main transition in a single component nanosized closed bilayer.