Topologically equivalent N-dimensional isometries

Let G be the group of isometries of the n-sphere, Euclidean n-space, or hyperbolic n-space, the group of similarities of Euclidean n-space, or the group of Möbius transformations of the n-sphere. In each case we attempt to determine the conjugacy classes in G which are amalgamated when we allow conjugation of the elements of G by homeomorphisms of the space on which G acts. We are successful modulo undetermined amalgamation among certain periodic orthogonal transformations.     

Novel synthetic route for low-cost carbon-modified TiO<Subscript>2</Subscript> with enhanced visible light photocatalytic activity: carbon content and calcination effects

The aim of this study was the development of low-cost tannin-formaldehyde xerogel/TiO₂ (XTi-w) and carbon xerogel/TiO₂ (XTiC-w) photocatalysts. The materials used as precursors were recycled titanium scraps and black wattle tannin extract, highlighting the low-cost approach employed in the synthesis. The materials were characterized by diffuse reflectance spectroscopy, scanning electron microscopy, dispersive energy spectrophotometry, X-ray diffractometry, infrared and Raman spectroscopy. X-ray diffractometry showed that the XTiC-w have tetragonal crystalline structure (anatase), whereas the XTi-w has an amorphous structure. The Raman and infrared analysis also showed the presence of titanium dioxide in the composition of both XTi-w and XTiC-w. XTi-w and XTiC-w showed photocatalytic activity at the visible wavelength. Titanium dioxide displayed no photocatalytic activity at the visible wavelength. The XTi-60 composite displayed the highest efficiency in the removal of the methylene blue from the system, as well as good reusability properties. The radicals with higher influence in the photocatalytic reaction mechanism are the photo generated electron and the singlet oxygen molecule. The effect of the heat treatment is negative on the photocatalytic properties of the hybrids produced, due to the removal of acid sites, adsorbed water and OH surface groups.

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The graphical abstract displays an illustration of the materials obtained in this work and their respective efficiency in the adsorption and photocatalytic degradation of methylene blue under visible light.

     

The midgut of Cephalotes ants (Formicidae: Myrmicinae): Ultrastructure of the epithelium and symbiotic bacteria

The ultrastructural analysis of the midgut of Cephalotes atratus, C. clypeatus, and C. pusillus reveled that the midgut epithelium lays on a basal lamina and is composed basically of three cell types: digestive cells, regenerative cells, and goblet cells. In these ants, the rough endoplasmic reticulum, in addition to producing digestive enzymes, is involved in the formation of concretions and ion storage in specialized vacuoles present in the midgut. These concretions are spherocrystals and may contribute to stabilize the pH and to maintain symbiotic bacteria found between microvilli. The ultrastructure analysis of these bacteria revealed the presence of a double envelope typical of gram-negative bacteria. For the three species examined, the ultrastructure similarities are conspicuous, suggesting that this may be the pattern for the genus Cephalotes. Details of the relationship between bacteria and microvilli were examined.     

Interface tension of silica hydroxylated nanoparticle with brine: a combined experimental and molecular dynamics study

We have used molecular dynamics simulations to calculate the interfacial tension of hydroxylated SiO(2) nanoparticles under different temperatures and solutions (helium and brine with monovalent and divalent salts). In order to benchmark the atomistic model, quartz SiO(2) interfacial tension was measured based on inverse gas chromatography under He atmosphere. The experimental interfacial tension values for quartz were found between 0.512 and 0.617 N/m. Our calculated results for the interfacial tension of silica nanoparticles within helium atmosphere was 0.676 N/m, which is higher than the value found for the system containing He∕α-quartz (0.478 N/m), but it is similar to the one found for amorphous silica surface. We have also studied the interfacial tension of the nanoparticles in electrolyte aqueous solution for different types and salts concentrations (NaCl, CaCl(2), and MgCl(2)). Our calculations indicate that adsorption properties and salt solutions greatly influence the interfacial tension in an order of CaCl(2) > MgCl(2) > NaCl. This effect is due to the difference in distribution of ions in solution, which modifies the hydration and electrostatic potential of those ions near the nanoparticle.     

Simulation-aided design and synthesis of hierarchically porous membranes

Free-standing silica membranes with hierarchical porosity (ca. 300 nm macropores surrounded by 6-8 nm mesopores) and controllable mesopore architecture were prepared by a dual-templating method, with the structural design aided by mesoscale simulation. To create a two-dimensional, hexagonal macropore array, polymeric colloidal hemisphere arrays were synthesized by a two-step annealing process starting with non-close-packed polystyrene sphere arrays on silicon coated with a sacrificial alumina layer. A silica precursor containing a poly(ethylene) oxide-poly(propylene oxide)-poly(ethylene) oxide (PEO-PPO-PEO) triblock-copolymer surfactant as template for mesopore creation was spin-coated onto the support and aged and then converted into the free-standing membranes by dissolving both templates and the alumina layer. To test the hypothesis that the mesopore architecture may be influenced by confinement of the surfactant-containing precursor solution in the colloidal array and by its interactions with the polymeric colloids, the system was studied theoretically by dissipative particle dynamics (DPD) simulations and experimentally by examining the pore structures of silica membranes via electron microscopy. The DPD simulations demonstrated that, while only tilted columnar structure can be formed through tuning the interaction with the substrate, perfect alignment of 2D hexagonal micelles perpendicular to the plane of the membrane is achievable by confinement between parallel walls that interact preferentially with the hydrophilic components (PEO blocks, silicate, and solvent). The simulations predicted that this alignment could be maintained across a span of up to 10 columns of micelles, the same length scale defined by the colloidal array. In the actual membranes, we manipulated the mesopore alignment by tuning the solvent polarity relative to the polar surface characteristics of the colloidal hemispheres. With methanol as a solvent, columnar mesopores parallel to the substrate were observed; with a methanol-water mixed solvent, individual spherical mesopores were present; and with water as the only solvent, twisted columnar structures were seen.     

Inclusion complex of usnic acid with β-cyclodextrin: characterization and nanoencapsulation into liposomes

In this study β-cyclodextrin (β-CD) was used to improve usnic acid (UA) solubility and the inclusion complex (UA:β-CD) was incorporated into liposomes in order to produce a targeted drug delivery system for exploiting the antimycobacterial activity of UA. A phase-solubility assay of UA in β-CD at pH 7.4 was performed. An apparent stability constant of K_1:1 = 234.5 M^?1 and a complexation efficiency of 0.005 was calculated. In the presence of 16 mM of β-CD the solubility of UA (7.3 μg/mL) increased more than 5-fold. The UA:β-CD complex was prepared using the freeze-drying technique and characterized through infrared and ¹HNMR spectroscopy, X-ray diffraction and thermal analyses. The UA:β-CD inclusion complex presented IR spectral modifications when compared with UA and β-CD spectra. ¹HNMR spectrum of UA:β-CD inclusion complex showed significant chemical shifts in proton H5 located inside the cavity of β-CD (Δδ = 0.127 ppm), suggesting that phenyl ring moiety of UA would be expected to be included within the β-CD cavity, interacting with the H-5 proton. A change in UA from its crystalline to amorphous form was observed on X-ray, suggesting the formation of a drug inclusion complex. DSC analysis showed the disappearance of the UA fusion peak UA:βCD complex. No differences between the antimicrobial activity of free UA and UA:βCD were found, supporting the hypothesis that the complexation with cyclodextrin did not interfere with drug activity. Liposomes containing UA:βCD were prepared using hydration of a thin lipid film method with subsequent sonication. Formulations of liposomes containing UA:βCD exhibited a drug encapsulation efficiency of 99.5% and remained stable for four months in a suspension form. Interestingly, the encapsulation of UA:βCD into the liposomes resulted in a modulation of in vitro kinetics of release of UA. Indeed, liposomes containing UA:β-CD presented a more prolonged release profile of free usnic acid compared to usnic acid-loaded liposomes.     

Conformational polymorphism of the antidiabetic drug chlorpropamide

In this paper, the main features of Raman spectroscopy, one of the first choice methods in the study of polymorphism in pharmaceuticals, are presented taking chlorpropamide as a case of study. The antidiabetic drug chlorpropamide (1‐[4‐chlorobenzenesulphonyl]‐3‐propyl urea), which belongs to the sulfonylurea class, is known to exhibit, at least, six polymorphic phases. These forms are characterized not only by variations in their molecular packing but also in their molecular conformation. In this study, the polymorphism of chlorpropamide is discussed on the basis of Raman scattering measurements and quantum mechanical calculations. The main spectroscopic features that fingerprint the crystalline forms are correlated with the corresponding crystalline structures. Using a theoretical approach on the energy dependence of the conformers, simulated molecular torsion angles are plotted versus the formation energy, which provides a satisfactory agreement between the torsion angles at the energy minima and the experimental values observed in the different solid forms of chlorpropamide. Copyright © 2011 John Wiley & Sons, Ltd.