On k-symmetries of hyperbolic spaces

We determine all the possible pointwise k-symmetric spaces of negative constant curvature. In general, such spaces are not k-symmetric.In fact we show that, for all $n?3$, $k\ne 2$, $H^n$ is not k-symmetric, i.e., for any set of selected k-symmetries, one for each point of $H^n$, the regularity condition does not hold.     

Fluorescence Spectroscopy of Porphyrins and Phthalocyanines: Some Insights into Supramolecular Self-Assembly,Microencapsulation, and Imaging Microscopy

The molecular interactions of anionic tetrasulfonate phenyl porphyrin (TPPS) with poly(amido amine) (PAMAM) dendrimers of generation 2.0 and 4.0 (G2 and G4, respectively) forming H- or J-aggregates, as well as with human and bovine serum albumin proteins (HSA and BSA), were reviewed in the context of self-assembly molecular complementarity. The spectroscopic studies were extended to the association of aluminum phthtalocyanine (AlPCS₄) detected with a PAMAM G4 dendrimer with fluorescence studies in both steady state and dynamic state, as well as due to the fluorescence quenching associated to electron-transfer with a distribution of lifetimes. The functionalization of TPPS with peripheral substituents enables the assignment of spontaneous pH-induced aggregates with different and well-defined morphologies. Other work reported in the literature, in particular with soft self-assembly materials, fall in the same area with particular interest for the environment. The microencapsulation of TPPS studies into polyelectrolyte capsules was developed quite recently and aroused much interest, which is well supported and complemented by the extensive data reported on the Imaging Microscopy section of the Luminescence of Porphyrins and Phthalocyanines included in the present review.     

A New Hybrid Evolutionary Multiobjective Algorithm Guided by Descent Directions

Hybridization of local search based algorithms with evolutionary algorithms is still an under-explored research area in multiobjective optimization. In this paper, we propose a new multiobjective algorithm based on a local search method. The main idea is to generate new non-dominated solutions by adding a linear combination of descent directions of the objective functions to a parent solution. Additionally, a strategy based on subpopulations is implemented to avoid the direct computation of descent directions for the entire population. The evaluation of the proposed algorithm is performed on a set of benchmark test problems allowing a comparison with the most representative state-of-the-art multiobjective algorithms. The results show that the proposed approach is highly competitive in terms of the quality of non-dominated solutions and robustness.     

On rotated D n -lattices constructed via totally real number fields

In this paper we construct families of rotated D _n -lattices, which may be suitable for signal transmission over both Gaussian and Rayleigh fading channels via subfields of cyclotomic fields. These constructions exhibit full diversity and good minimum product distance, which are important parameters related to the signal transmission error probability. It is also shown that for some Galois extensions ${\mathbb{K}|\mathbb{Q}}$ , it is impossible to construct rotated D _n -lattices via fractional ideals of ${\mathcal{O}_{\mathbb{K}}}$ .     

On projections of arbitrary lattices

In this paper we prove that given any two point lattices _Λ1⊂Rⁿ${\Lambda }_1\subset {\mathbb{R}}^n$ and _Λ2⊂R^n−k${\Lambda }_2\subset {\mathbb{R}}^{n-k}$, there is a set of k   vectors {_v1,…,_vk}⊂_Λ1$\{{\mathit{v}}_1,\dots ,{\mathit{v}}_k\}\subset {\Lambda }_1$ such that _Λ2${\Lambda }_2$ is, up to similarity, arbitrarily close to the projection of _Λ1${\Lambda }_1$ onto the orthogonal complement of the subspace spanned by {_v1,…,_vk}$\{{\mathit{v}}_1,\dots ,{\mathit{v}}_k\}$. This result extends the main theorem of Sloane et al. (2011) [1] and has applications in communication theory.     

Scaling invariance for the escape of particles from a periodically corrugated waveguide

The escape dynamics of a classical light ray inside a corrugated waveguide is characterised by the use of scaling arguments. The model is described via a two-dimensional nonlinear and area preserving mapping. The phase space of the mapping contains a set of periodic islands surrounded by a large chaotic sea that is confined by a set of invariant tori. When a hole is introduced in the chaotic sea, letting the ray escape, the histogram of frequency of the number of escaping particles exhibits rapid growth, reaching a maximum value at np and later decaying asymptotically to zero. The behaviour of the histogram of escape frequency is characterised using scaling arguments. The scaling formalism is widely applicable to critical phenomena and useful in characterisation of phase transitions, including transitions from limited to unlimited energy growth in two-dimensional time varying billiard problems.     

Janus-like squaramide-based hosts: dual mode of binding and conformational transitions driven by ion-pair recognition

New tripodal squaramide-based hosts have been synthesised and structurally characterised by spectroscopic methods. In 2.5?% (v/v) [D(6)]DMSO in CDCl(3), compound 4 formed dimeric assemblies [log?K(dim)=3.68(8)] as demonstrated by (1)H?NMR spectroscopy and UV dilution experiments. AFM and SEM analyses revealed the formation of a network of bundled fibres, which indicates a preferential mechanism for aggregation. These C(3)-symmetric tripodal hosts exhibited two different and mutually exclusive modes of binding, each one easily accessible by simultaneous reorientation of the squaramide groups. In the first, a convergent disposition of the NH squaramide protons allowed the formation of an array of N-H???X(-) hydrogen bonds with anions. In the second mode, reorientation of carbonyl squaramide groups allowed multiple C=O???H interactions with ammonium cations. The titration of 4 with different tetraalkylammonium iodides persistently showed the formation of 1:1 complexes, as well as 1:2 and 1:3 complexes. The corresponding stoichiometries and binding affinities of the complexes were evaluated by multi-regression analysis. The formation of high-order complexes, supported by ROESY, NOESY and mass spectrometry experiments, has been attributed to the insertion of NR(4)I ion pairs between the carbonyl and NH protons of the squaramide groups located in adjacent arms of 4. The observed effects reflect the induction of significant conformational changes in the hosts, mainly in relation to the relative orientation of the squaramide groups adapting their geometries to incoming ion-pair complementary substrates. The results presented herein identify and fully describe two different modes of ion-pair recognition aimed at directing conformational transitions in the host, therefore establishing a base for controlling more elaborate movements of molecular devices through ion-pair recognition.     

Ultra-high pressure LC determination of glucosamine in shrimp by-products and migration tests of chitosan films

Chitosan, a multiple applications molecule, was isolated from shrimp by-products by fermentation. The amount of chitosan in the solid fraction of the fermented extract was measured after its conversion in the respective glucosamine units. The procedure includes an acid hydrolysis (110 °C, 4 h with HCl 8 M) and a derivatization with 9-fluorenylmethyl chloroformate (Fmoc-Cl). Ultra-high-pressure liquid chromatography method was developed and optimized. Excellent peaks resolution was achieved in just 10 min. The method was evaluated in what concerns to validation parameters such as linearity, repeatability, quantification limit, and recovery. Migration tests of films prepared with chitosan were carried out in two simulants: ultrapure water and ethanol 95% (v/v).     

Force Field Benchmark of Organic Liquids: Density, Enthalpy of Vaporization, Heat Capacities, Surface Tension, Isothermal Compressibility, Volumetric Expansion Coefficient, and Dielectric Constant

The chemical composition of small organic molecules is often very similar to amino acid side chains or the bases in nucleic acids, and hence there is no a priori reason why a molecular mechanics force field could not describe both organic liquids and biomolecules with a single parameter set. Here, we devise a benchmark for force fields in order to test the ability of existing force fields to reproduce some key properties of organic liquids, namely, the density, enthalpy of vaporization, the surface tension, the heat capacity at constant volume and pressure, the isothermal compressibility, the volumetric expansion coefficient, and the static dielectric constant. Well over 1200 experimental measurements were used for comparison to the simulations of 146 organic liquids. Novel polynomial interpolations of the dielectric constant (32 molecules), heat capacity at constant pressure (three molecules), and the isothermal compressibility (53 molecules) as a function of the temperature have been made, based on experimental data, in order to be able to compare simulation results to them. To compute the heat capacities, we applied the two phase thermodynamics method (Lin et al. J. Chem. Phys.2003, 119, 11792), which allows one to compute thermodynamic properties on the basis of the density of states as derived from the velocity autocorrelation function. The method is implemented in a new utility within the GROMACS molecular simulation package, named g_dos, and a detailed exposé of the underlying equations is presented. The purpose of this work is to establish the state of the art of two popular force fields, OPLS/AA (all-atom optimized potential for liquid simulation) and GAFF (generalized Amber force field), to find common bottlenecks, i.e., particularly difficult molecules, and to serve as a reference point for future force field development. To make for a fair playing field, all molecules were evaluated with the same parameter settings, such as thermostats and barostats, treatment of electrostatic interactions, and system size (1000 molecules). The densities and enthalpy of vaporization from an independent data set based on simulations using the CHARMM General Force Field (CGenFF) presented by Vanommeslaeghe et al. (J. Comput. Chem.2010, 31, 671) are included for comparison. We find that, overall, the OPLS/AA force field performs somewhat better than GAFF, but there are significant issues with reproduction of the surface tension and dielectric constants for both force fields.     

Measurement of interchain and intrachain exciton hopping barriers in luminescent polymer

The integrated photoluminescence intensity in thin films of 'Super Yellow' copolymer has been analyzed using a Mott-like temperature dependence. This has enabled us to observe contributions from two emission channels, indicative of exciton recombination proceeding from two distinct origins. At high temperature, interchain thermally activated exciton energy transfer and migration dominates, resulting in large scale quenching of the integrated emission intensity and hence the photoluminescence quantum yield. However, at relatively low temperature, an additional increase of the integrated emission intensity occurs. This new channel of emission has been attributed to recombination from excitons where intrachain exciton energy transfer between adjacent subunits of the copolymer backbone becomes hindered. The activation energy barriers that control both of these emission channels have been obtained and are correlated with chain backbone degrees of freedom.