Ricci and Matter Collineations of Locally Rotationally Symmetric Space-Times

A new method is presented for the determination of Ricci Collineations (RC) and Matter Collineations (MC) of a given spacetime, in the cases where the Ricci tensor and the energy momentum tensor are non-degenerate and have a similar form with the metric. This method reduces the problem of finding the RCs and the MCs to that of determining the KVs whereas at the same time uses already known results on the motions of the metric. We employ this method to determine all hypersurface homogeneous locally rotationally symmetric spacetimes, which admit proper RCs and MCs. We also give the corresponding collineation vectors. These results conclude a long due open problem, which has been considered many times partially in the literature.     

Periodic hexagonal mesostructured chalcogenides based on platinum and [SnSe4]4- and [SnTe4]4- precursors. Solvent dependence of nanopore and wall organization

Mesostructured chalcogenide-based materials with long-range order and semiconducting properties can be prepared using suitable molecular building blocks, linkage metal ions and surfactant molecules. In this paper we present surfactant templated, open framework platinum tin selenide and telluride materials assembled using K4SnQ4 (Q = Se, Te) salts and K2PtCl4 as precursors and a study of pore and wall organization. We find that materials prepared in water exhibit disordered pore organization, whereas those prepared in formamide are long-range ordered with hexagonal symmetry. In formamide the [SnQ4]4- anions undergo condensation-oligomerization reactions that produce different chalcogenido molecular species, whereas in water the anions remain intact. In addition to solvent, the pore organization and overall quality of the mesostructured materials strongly depend on the surfactant molecules, i.e., chain length and headgroup size. For example, highly ordered mesostructured platinum tin selenides with hexagonal symmetry were obtained using the hydroxyl-functionalized surfactants CnH2n+1N(CH3)(CH2CH2OH)2Br (n = 16, 18, and 20), but when the headgroup was triethylammonium, hexagonal pore order was achieved only for n = 20 and not for n = 16 and 18. The experimental results imply that in order to achieve highly ordered chalcogenide frameworks a single building anionic block might be insufficient. Finally, we also report the first examples of hexagonal mesostructured Pt/Sn/Te materials based on K4SnTe4 as the precursor. The tellurides behave differently for their selenium analogues and have very low energy band gaps, in the range 0.5-0.7 eV.     

On the elastic fibre pull-out problem: asymptotic and numerical results

Summary In this paper we present some asymptotic results for the pull out of a nearly-rigid fibre from an elastic matrix. The asymptotic results are accurate toO( ²), where=(ln 2l/R)^–1, if the fibre is pull-out from a semi-infinite matrix, and toO(h ²/l ²) if the fibre is pull-out from a matrix contained in a cylindrical container of radiush. Here R andl are the fibre radius and length, respectively. An interpolation formula is suggested which yields correct asymptotic behaviour at bothh/l=0 andh/l . These asymptotic results are confirmed by numerical methods to at least an aspect ratio ofl/R9. We also report some numerical confirmation of a previous approximate result for the pull out of a rigid fibre with an enlarged spherical end.

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Zusammenfassung In der vorliegenden Arbeit geben wir einige asymptotische Ergebnisse für das Ausziehen einer beinahe starren Faser aus einer elastischen Matrix. Die asymptotischen Resultate sind aufO( ²) genau, wo=(ln 2l/R)^–1 bedeutet, falls die Faser aus einer halbunendlichen Matrix ausgezogen wird. Sie sind aufO(h ²/l ²) genau, falls die Faser aus einer Matrix ausgezogen wird, welche einen Zylinder vom Radiush füllt. Eine Interpolationsformel, die das richtige asymptotische Verhalten fürh/l=0 undh/l aufweist, wird vorgeschlagen. Diese asymptotischen Ergebnisse werden durch numerische Methoden mindestens bis geometrische Verhältnisse vonl/R9 bestätigt. Wir berichten ebenfalls über eine gewisse numerische Bestätigung eines früheren approximativen Resultats für das Ausziehen einer starren Faser mit einem vergrößerten sphärischen Kopf.

     

Water confined in two-dimensions: Fundamentals and applications

The behavior of water in close proximity to other materials under ambient conditions is of great significance due to its importance in a broad range of daily applications and scientific research. The structure and dynamics of water at an interface or in a nanopore are often significantly different from those of its bulk counterpart. Until recently, experimental access to these interfacial water structures was difficult to realize. The advent of two-dimensional materials, especially graphene, and the availability of various scanning probe microscopies were instrumental to visualize, characterize and provide fundamental knowledge of confined water. This review article summarizes the recent experimental and theoretical progress in a better understanding of water confined between layered Van der Waals materials. These results reveal that the structure and stability of the hydrogen bonded networks are determined by the elegant balance between water-surface and water-water interactions. The water-surface interactions often lead to structures that differ significantly from the conventional bilayer model of natural ice. Here, we review the current knowledge of water adsorption in different environments and intercalation within various confinements. In addition, we extend this review to cover the influence of interfacial water on the two-dimensional material cover and summarize the use of these systems in potential novel applications. Finally, we discuss emerged issues and identify some flaws in the present understanding.     

Post-column labeling techniques in amino acid analysis by liquid chromatography

Amino acid analysis (AAA) has always presented an analytical challenge in terms of sample preparation, separation, and detection. Because of the vast number of amino acids, various separation methods have been applied taking into consideration the large differences in their chemical structures, which span from nonpolar to highly polar side chains. Numerous separation methods have been developed in the past 60 years, and impressive achievements have been made in the fields of separation, derivatization, and detection of amino acids (AAs). Among the separation methods, liquid chromatography (LC) prevailed in the AAA field using either pre-column or post-column labeling techniques in order to improve either separation of AAs or selectivity and sensitivity of AAA. Of the two approaches, the post-column technique is a more rugged and reproducible method and provides excellent AAs separation relatively free from interferences. This review considers current separations combined with post-column labeling techniques for AAA, comparison with the pre-column methods, and the strategies used to develop effective post-column methodology. The focus of the article is on LC methods coupled with post-column labeling techniques and studying the reactions to achieve optimum post-column derivatization (PCD) conditions in order to increase sensitivity and selectivity using various types of detectors (UV–Vis, fluorescence, electrochemical etc.) and illustrating the versatility of the PCD methods for practical analysis.

Lotka-Volterra equations in three dimensions satisfying the Kowalevski-Painlevé property

We examine a class of Lotka-Volterra equations in three dimensions which satisfy the Kowalevski-Painlevé property. We restrict our attention to Lotka-Volterra systems defined by a skew symmetric matrix. We obtain a complete classification of such systems. The classification is obtained using Painlevé analysis and more specifically by the use of Kowalevski exponents. The imposition of certain integrality conditions on the Kowalevski exponents gives necessary conditions. We also show that the conditions are sufficient.     

Structure of V(2)O(5)*nH(2)O xerogel solved by the atomic pair distribution function technique

A long-standing issue regarding the local and long-range structure of V(2)O(5)*nH(2)O xerogel has been successfully addressed. The full three-dimensional structure of the lamellar turbostratic V(2)O(5)*nH(2)O xerogel was determined by the atomic pair distribution function technique. We show that on the atomic scale the slabs of the xerogel can be described well as almost perfect pairs (i.e., bilayers) of single V(2)O(5) layers made of square pyramidal VO(5) units. These slabs are separated by water molecules and stack along the z-axis of a monoclinic unit cell (space group C2/m) with parameters a = 11.722(3) A, b = 3.570(3) A, c = 11.520(3) A, and beta = 88.65 degrees. The stacking sequence shows signatures of turbostratic disorder and a structural coherence limited to 50 A.     

Equilibrium points of the tilted perfect fluid Bianchi VI<Subscript><Emphasis Type="Italic">h</Emphasis></Subscript> state space

We present the full set of evolution equations for the spatially homogeneous cosmologies of type VI_h filled with a tilted perfect fluid and we provide the corresponding equilibrium points of the resulting dynamical state space. It is found that only when the group parameter satisfies h > –1 a self-similar solution exists. In particular we show that for h > – there exists a self-similar equilibrium point provided that whereas for h < – the state parameter belongs to the interval (1, . This family of new exact self-similar solutions belongs to the subclass n = 0 having non-zero vorticity. In both cases the equilibrium points have a six-dimensional stable manifold and may act as future attractors at least for the models satisfying n = 0. Also we give the exact form of the self-similar metrics in terms of the state and group parameter. As an illustrative example we provide the explicit form of the corresponding self-similar radiation model ( = ), parametrised by the group parameter h. Finally we show that there are no tilted self-similar models of type III and irrotational models of type VI_h.     

Mesostructured selenides with cubic MCM-48 type symmetry: large framework elasticity and uncommon resiliency to strong acids

The metal mesostructured Pt/Sn/Se chalcogenides with cubic MCM-48 type pore symmetry are found to be surprisingly stable in concentrated oxidizing acids. Their metal chalcogenide framework exhibits high flexibility during reversible proton exchange as it expands and contracts in an apparent breathing-like action.     

Distortion product otoacoustic emissions provide clues hearing mechanisms in the frog ear

2f1-f2 and 2 f2-f1 distortion product otoacoustic emissions (DPOAEs) were recorded from both ears of male and female Rana pipiens pipiens and Rana catesbeiana. The input-output (I/O) curves obtained from the amphibian papilla (AP) of both frog species are analogous to I/O curves recorded from mammals suggesting that, similarly to the mammalian cochlea, there may be an amplification process present in the frog AP. DPOAE level dependence on L1-L2 is different from that in mammals and consistent with intermodulation distortion expectations. Therefore, if a mechanical structure in the frog inner ear is functioning analogously to the mammalian basilar membrane, it must be more broadly tuned. DPOAE audiograms were obtained for primary frequencies spanning the animals' hearing range and selected stimulus levels. The results confirm that DPOAEs are produced in both papillae, with R. catesbeiana producing stronger emissions than R. p. pipiens. Consistent with previously reported sexual dimorphism in the mammalian and anuran auditory systems, females of both species produce stronger emissions than males. Moreover, it appears that 2 f1-f2 in the frog is generated primarily at the DPOAE frequency place, while 2 f2-f1 is generated primarily at a frequency place around the primaries. Regardless of generation place, both emissions within the AP may be subject to the same filtering mechanism, possibly the tectorial membrane.