Compactness and Vitali’s compactness criterion in vector-valued F-seminormed function spaces

Results of compactness for vector-valued F-seminormed function spaces and a general Vitali’s compactness criterion under the W-property are exhibited.

     

A polynomial path-following interior point algorithm for general linear complementarity problems

Linear Complementarity Problems (LCPs) belong to the class of \mathbbNP{\mathbb{NP}} -complete problems. Therefore we cannot expect a polynomial time solution method for LCPs without requiring some special property of the coefficient matrix. Our aim is to construct interior point algorithms which, according to the duality theorem in EP (Existentially Polynomial-time) form, in polynomial time either give a solution of the original problem or detects the lack of property P_*([(k)\tilde]){\mathcal{P}_*(\tilde\kappa)} , with arbitrary large, but apriori fixed [(k)\tilde]{\tilde\kappa}). In the latter case, the algorithms give a polynomial size certificate depending on parameter [(k)\tilde]{\tilde{\kappa}} , the initial interior point and the input size of the LCP). We give the general idea of an EP-modification of interior point algorithms and adapt this modification to long-step path-following interior point algorithms.     

Quasicrystalline electronic states of a one-dimensionally modulated Ag film

Ag films on GaAs(110) exhibit a one-dimensional quasiperiodic modulation, resulting in a Fibonacci sequence of parallel stripes with two different widths. Valence level photoemission shows that the Ag electronic states acquire a unique character along the quasiperiodic direction, distinctively manifested by a hierarchy of energy level replicas and avoided crossings at characteristic intervals in reciprocal space. These observations demonstrate the strong influence of the one-dimensional quasiperiodic potential on the Ag film states.     

Nonlinear Optical Properties of Benzylic Amide [2] Catenanes: A Novel Versatile Photonic Material

Abstract

Benzylic amide catenanes are a class of synthetically-accessible interlocked molecular rings which can rotate one through the other depending on the nature of the local environment. The rings contain four phenyl units each and interlocking also affords their packing in novel, highly interacting ways that may lead to unexpected properties thus opening up the possibility of developing new materials. Third harmonic generation in benzylic amide catenane solutions was measured at a wavelength of γ = 1064 nm, with the fundamental and the harmonic wavelengths in the region of transparency of the material. The thoroughly non resonant value of the hyperpolarisability γ(-3ω; ω, ω, ω) was found to be (6.5 ± 0.7) × 10^?35 esu with a negligible imaginary part, in agreement with the value of (6.8 ± 0.9) × 10^?35 esu calculated from a bond-additivity model of hyperpolarisability. The static second order hyperpolarisability predicted by a Molecular Orbital model was about a factor four less than the experimental value. Second hyperpolarizability values of several solvents were also measured at the fundamental wavelength of γ = 1064 nm.     

Understanding the mechanism of direct visible-light-activated [2 + 2] cycloadditions mediated by Rh and Ir photocatalysts: combined computational and spectroscopic studies

The mechanism of [2 + 2] cycloadditions activated by visible light and catalyzed by bis-cyclometalated Rh(iii) and Ir(iii) photocatalysts was investigated, combining density functional theory calculations and spectroscopic techniques. Experimental observations show that the Rh-based photocatalyst produces excellent yield and enantioselectivity whereas the Ir-photocatalyst yields racemates. Two different mechanistic features were found to compete with each other, namely the direct photoactivation of the catalyst–substrate complex and outer-sphere triplet energy transfer. Our integrated analysis suggests that the direct photocatalysis is the inner working of the Rh-catalyzed reaction, whereas the Ir catalyst serves as a triplet sensitizer that activates cycloaddition via an outer-sphere triplet excited state energy transfer mechanism.

The mechanism of [2 + 2] cycloadditions activated by visible light and catalyzed by bis-cyclometalated Rh(iii) and Ir(iii) photocatalysts was investigated, combining density functional theory calculations and spectroscopic techniques.     

Approaches to primary tert-alkyl amines as building blocks

Primary tert-alkyl amines include analogues of amantadine, a fragment commonly linked to pharmacophoric groups to enhance biological activity. The preparation of primary tert-alkyl amines is considered to be a difficult problem. Four synthetic procedures, some of which have been previously reported for the synthesis of amines with primary (RCH₂NH₂) or secondary (RR'CHNH₂) alkyl and/or aryl groups, were tested for the synthesis of primary tert-alkyl amines (RR′R″CNH₂) in aliphatic series including adamantane adducts. These procedures included the formation and reduction of tert-alkyl azides, the Ritter reaction in standard and modified conditions, the addition of organometallic reagents to N-tert-butyl sulfinyl ketimines and one-pot reactions between nitriles and organometallic reagents in the presence of a Lewis acid, Τi(iPrO)₄ or CeCl_3. These synthetic routes are unexplored for primary tert-alkyl amines. Studies on the synthetic routes for primary tert-alkyl amines are currently lacking. The reaction conditions and substrate limitations were studied for each procedure, with the first procedure being the most general and applicable also for compounds bearing bulky adducts.     

Universal optical conductance of graphite

We find experimentally that the optical sheet conductance of graphite per graphene layer is very close to (pi/2)e2/h, which is the theoretically expected value of dynamical conductance of isolated monolayer graphene. Our calculations within the Slonczewski-Weiss-McClure model explain well why the interplane hopping leaves the conductance of graphene sheets in graphite almost unchanged for photon energies between 0.1 and 0.6 eV, even though it significantly affects the band structure on the same energy scale. The f-sum rule analysis shows that the large increase of the Drude spectral weight as a function of temperature is at the expense of the removed low-energy optical spectral weight of transitions between hole and electron bands.     

Versatile vacuum chamber for in situ surface X‐ray scattering studies

A compact portable vacuum‐compatible chamber designed for surface X‐ray scattering measurements on beamline ID01 of the European Synchrotron Radiation Facility, Grenoble, is described. The chamber is versatile and can be used for in situ investigation of various systems, such as surfaces, nanostructures, thin films etc., using a variety of X‐ray‐based techniques such as reflectivity, grazing‐incidence small‐angle scattering and diffraction. It has been conceived for the study of morphology and structure of semiconductor surfaces during ion beam erosion, but it is also used for the study of surface oxidation or thin film growth under ultra‐high‐vacuum conditions. Coherent X‐ray beam experiments are also possible. The chamber is described in detail, and examples of its use are given.     

Development of Fish Immunity and the Role of β-Glucan in Immune Responses

Administration of β-glucans through various routes, including immersion, dietary inclusion, or injection, have been found to stimulate various facets of immune responses, such as resistance to infections and resistance to environmental stress. β-Glucans used as an immunomodulatory food supplement have been found beneficial in eliciting immunity in commercial aquaculture. Despite extensive research involving more than 3000 published studies, knowledge of the receptors involved in recognition of β-glucans, their downstream signaling, and overall mechanisms of action is still lacking. The aim of this review is to summarize and discuss what is currently known about of the use of β-glucans in fish.