Tuning the electronic‐optical properties of porphyrin‐like porous C24N24 fullerene with (Li3O)n = (1–5) decoration. A computational study

Using DFT methods, the electronic properties and the first hyperpolarizabilities of porphyrin‐like porous C₂₄N₂₄ fullerene decorated with (Li₃O)_{n = (1–5)} have been systematically investigated. It is found that Li₃O molecules can effectively be adsorbed over N4 cavities of C₂₄N₂₄ with high interaction energies. This interaction is found to narrow the HOMO‐LUMO gap and work function values of C₂₄N₂₄. Thus its electronic properties are strongly sensitive to interaction with the Li₃O molecules. Indeed, compared with the sole parent C₂₄N₂₄ fullerene, (Li₃O)_{n = (1–5)}@C₂₄N₂₄ possess large first hyperpolarizabilities (β₀ ). Obviously, the Li₃O superalkali chemisorbed over C₂₄N₂₄ fullerene exhibit not only excellent stability but also large first hyperpolarizability. Therefore, they are expected to be potential innovative candidates for excellent electro‐optical materials.     

Spatial bi-stacked central configurations formed by two dual regular polyhedra

In this paper we prove the existence of two new families of spatial stacked central configurations, one consisting of eight equal masses on the vertices of a cube and six equal masses on the vertices of a regular octahedron, and the other one consisting of twenty masses at the vertices of a regular dodecahedron and twelve masses at the vertices of a regular icosahedron. The masses on the two different polyhedra are in general different. We note that the cube and the octahedron, the dodecahedron and the icosahedron are dual regular polyhedra. The tetrahedron is itself dual. There are also spatial stacked central configurations formed by two tetrahedra, one and its dual.     

Outer Trust-Region Method for Constrained Optimization

Given an algorithm A for solving some mathematical problem based on the iterative solution of simpler subproblems, an outer trust-region (OTR) modification of A is the result of adding a trust-region constraint to each subproblem. The trust-region size is adaptively updated according to the behavior of crucial variables. The new subproblems should not be more complex than the original ones, and the convergence properties of the OTR algorithm should be the same as those of Algorithm A. In the present work, the OTR approach is exploited in connection with the “greediness phenomenon” of nonlinear programming. Convergence results for an OTR version of an augmented Lagrangian method for nonconvex constrained optimization are proved, and numerical experiments are presented.     

Asymptotic normality of high level-large time crossings of a Gaussian process

We prove the asymptotic normality of the standardized number of crossings of a centered stationary mixing Gaussian process when both the level and the time horizon go to infinity in such a way that the expected number of crossings also goes to infinity.     

Optical properties of red, green and blue emitting rare earth benzenetricarboxylate compounds

Red, blue and green emitting rare earth compounds (RE³⁺=Eu³⁺, Gd³⁺ and Tb³⁺) containing the benzenetricarboxylate ligands (BTC) [hemimellitic (EMA), trimellitic (TLA) and trimesic (TMA)] were synthesized and characterized by elemental analysis, complexometric titration, X-ray diffraction patterns, thermogravimetric analysis and infrared spectroscopy. The complexes presented the following formula: [RE(EMA)(H₂O)₂], [RE(TLA)(H₂O)₄] and [RE(TMA)(H₂O)₆], except for Tb-TMA compound, which was obtained only as anhydrous. Phosphorescence data of Gd³⁺-(BTC) complexes showed that the triplet states (T) of the BTC³⁻ anions have energy higher than the main emitting states of the Eu³⁺ (⁵D₀) and Tb³⁺ (⁵D₄), indicating that BTC ligands can act as intramolecular energy donors for these metal ions. The high values of experimental intensity parameters (Ω₂) of Eu³⁺-(BTC) complexes indicate that the europium ion is in a highly polarizable chemical environment. Based on the luminescence spectra, the energy transfer from the T state of BTC ligands to the excited ⁵D₀ and ⁵D₄ levels of the Eu³⁺ and Tb³⁺ ions is discussed. The emission quantum efficiencies (η) of the ⁵D₀ emitting level of the Eu³⁺ ion have been also determined. In the case of the Tb³⁺ ion, the photoluminescence data show the high emission intensity of the characteristic transitions ⁵D₄→⁷F_J (J=0-6), indicating that the BTC ligands are good sensitizers. The RE³⁺-(BTC) complexes act as efficient light conversion molecular devices (LCMDs) and can be used as tricolor luminescent materials.     

Comprehensive investigation and optimisation of the main experimental variables in stir-bar sorptive extraction (SBSE)-thermal desorption-capillary gas chromatography (TD-CGC)

A chemometric study has been completed in order to investigate the relative contributions and interactions between the many experimental variables involved in SBSE-TD-CGC. The study was centered on data after extraction and analysis of important organophosphorous pesticides from water under different controlled conditions. An enhanced flame photometric detector was used for target compound area response. The seemingly independent operations of extraction with the stir bar followed by thermal transfer of the absorbed compounds to the chromatographic system are usually studied by independent designs for the corresponding blocks of variables. In this work all variables are treated at the same time in a single design to study the interactions and give a more robust model while requiring a lower number of experiments. The relative importance of contributing variables was clearly established and an optimum set of conditions was established for more uniform enrichment in a single analysis for a test mix of compounds with wide ranging polarities.     

Global symplectic regularization for some restricted 3-body problems on

We develop a regularization for binary collisions in some restricted 3-body problems moving in planar one-dimensional spaces with constant curvature. The main characteristic of the regularization is that it preserves the Hamiltonian structure of the equations and it regularizes all the binary collisions with just one transformation. We apply this global symplectic regularization to the 2-body problem on the unit circle and we show the global dynamics. Also, we tackle the restricted 3-body problem with one fixed center in the unit circle and we give the global dynamics for the case when it has two fixed centers.