First-return integrals

Properties of first-return integrals of real functions defined on the unit interval are explored. In particular, first-return integrals are shown to be continuous but not absolutely continuous.     

On the validity of the Euler-Lagrange equation

The purpose of the present paper is to establish the validity of the Euler-Lagrange equation for the solution to the classical problem of the calculus of variations.     

High energy radiation fluences in the ISS-USLab: Ion discrimination and particle abundances

The ALTEA (Anomalous Long Term Effects on Astronauts) detector was used to characterize the radiation environment inside the USLab of the International Space Station (ISS), where it measured the abundances of ions from Be to Fe. We compare the ALTEA results with Alteino results obtained in the PIRS module of the Russian segment of the ISS, and normalize to the high energy Si abundances given by Simpson. These are the first particle spectral measurements, which include ions up to Fe, performed in the USLab. The small differences observed between those made inside the USLab and the Simpson abundances can be attributed to the transport through the spacecraft hull. However, the low abundance of Fe cannot be attributed to only this process.     

Preparation and photoactivity of nanostructured anatase, rutile and brookite TiO2 thin films

Photoactive films consisting of pure anatase, brookite or rutile TiO2 were prepared by dip coating from water dispersions obtained by using TiCl4 as the precursor under similar mild experimental conditions.     

Using a factored dual in augmented Lagrangian methods for semidefinite programming

In the context of augmented Lagrangian approaches for solving semidefinite programming problems, we investigate the possibility of eliminating the positive semidefinite constraint on the dual matrix by employing a factorization. Hints on how to deal with the resulting unconstrained maximization of the augmented Lagrangian are given. We further use the approximate maximum of the augmented Lagrangian with the aim of improving the convergence rate of alternating direction augmented Lagrangian frameworks. Numerical results are reported, showing the benefits of the approach.     

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.     

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.