Invariant functions and contractions of certain types of Lie algebras of lower dimensions

In this paper, we deal with contractions of Lie algebras. We use two invariant functions of Lie algebras as a tool, named ψ and ? function, respectively, which have a great application in Physics due to their remarkable properties. We focus the study of these functions in the frame of the filiform Lie algebras, trying to extend to these algebras some of the properties of such functions over semi-simple Lie algebras.     

Synthesis of Magnetite in Presence of Cu2+ or Cr3+

The effects of Cu or Cr ions on the formation of magnetite, which were prepared by two different methods, were studied by ⁵⁷Fe Mössbauer spectrometry. The first synthesis procedure consisted in an alkaline hydrolysis of ferrous chloride solution in accordance with literature reports. The second method, which was a variation of a reported synthetic route, consisted of a reaction of a 2:1 Fe(II)/Fe(III) solution under alkaline conditions in the presence of an oxidant agent. The samples were also prepared in the presence of chromium or copper chloride solutions. Our results showed that the magnetites obtained via the first procedure exhibits a higher degree of stoichiometry and a better crystalline quality than those prepared by the second route. It seems that the presence of chromium helped the formation of goethite, whereas the presence of copper interfered with it in agreement with other works. We observed that the magnetites obtained in the presence of copper were of poorer crystallinity than the ones obtained with chromium. Finally, the influence of Cu or Cr upon the magnetic and crystalline properties of the two series of magnetites is also presented and discussed.     

The Geometry of the First Non-zero Stekloff Eigenvalue

Let (Mⁿ, g) be a compact Riemannian manifold with boundary and dimensionn2. In this paper we discuss the first non-zero eigenvalue problem \begin{align}\Delta\varphi & = & 0\qquad & on\quad M,\\ \frac{\partial\varphi}{\partial \eta} & = & \ u_1\varphi\qquad & on\quad\partial M.\end{align}\eqno (1) Problem (1) is known as the Stekloff problem because it was introduced by him in 1902, for bounded domains of the plane. We discuss estimates of the eigenvalueν₁in terms of the geometry of the manifold (Mⁿ, g). In the two-dimensional case we generalize Payne's Theorem [P] for bounded domains in the plane to non-negative curvature manifolds. In this case we show thatν₁k₀, wherek_gk₀andk_grepresents the geodesic curvature of the boundary. In higher dimensionsn3 for non-negative Ricci curvature manifolds we show thatν₁>k₀/2, wherek₀is a lower bound for any eigenvalue of the second fundamental form of the boundary. We introduce an isoperimetric constant and prove a Cheeger's type inequality for the Stekloff eigenvalue.     

Validation of an LC–MS/MS Method for the Quantification of the CK2 Inhibitor Silmitasertib (CX-4945) in Human Plasma

Silmitasertib (CX-4945) is currently being investigated in clinical trials against various types of cancer. The U.S. Food and Drug Administration (FDA) has already granted orphan drug designation to the compound for the treatment of advanced cholangiocarcinoma, medulloblastoma, and biliary tract cancer. Silmitasertib inhibits the serine/threonine protein kinase CK2, which exerts a proliferation-promoting and anti-apoptotic effect on cancer cells. In view of current and future applications, the measurement of silmitasertib levels in plasma is expected to play an important role in the evaluation of therapeutic and toxic concentrations in cancer patients. In the present work, we therefore present an LC–MS/MS method for the quantification of silmitasertib in human plasma. Using a simple liquid–liquid extraction with ethyl acetate and a mixture of n-hexane and ethyl acetate, this method can be performed in any laboratory with mass spectrometry. The validation was carried out according to the FDA guideline.     

Mesoporous (ZrO2-TiO2)/Al2O3 ternary carriers as hydrodesulfurization catalysts support

Ternary systems at various compositions were synthesized by coprecipitating Zr and Ti (to get a ZrO₂-TiO₂ 40-60 mol%) chlorides in aqueous basic media (provided by urea thermal decomposition) over an alumina substrate. Materials characterization included N₂ physisorption, X-ray diffraction, thermal analysis, high-resolution electron microscopy and Raman and UV-vis spectroscopies. High interaction among components was clearly evidenced by various techniques. Textural properties of ternary oxides could be tuned depending on composition of formulations. Mixed oxides with 10 or 20 mol% of ZrO₂-TiO₂ (at 40-60% mol, in turn) had the most suitable combination of textural properties (surface area, average pore diameter and pore volume) for the intended application (support of catalyst for hydrodesulfurization de oil-derived middle distillates). The suitability of those ternary supports was demonstrated in the dibenzothiophene hydrodesulfurization where the corresponding supported MoS₂ catalysts (at 2.8 atom Mo nm⁻²) were much more active (on a per mass of catalyst basis) than when impregnated over either alumina or zirconia-titania oxides.     

A spectral quadrilateral multidomain penalty method model for high Reynolds number incompressible stratified flows

A two‐dimensional quadrilateral spectral multidomain penalty method (SMPM) model has been developed for the simulation of high Reynolds number incompressible stratified flows. The implementation of higher‐order quadrilateral subdomains renders this model a nontrivial extension of a one‐dimensional subdomain SMPM model built for the simulation of the same type of flows in vertically nonperiodic domains (Diamessis et al., J. Comp. Phys, 202 :298‐322, 2005). The nontrivial aspects of this extension consist of the implementation of subdomain corners, the penalty formulation of the pressure Poisson equation (PPE), and, most importantly, the treatment of specific challenges that arise in the iterative solution of the SMPM‐discretized PPE. The two primary challenges within the framework of the iterative solution of the PPE are its regularization to ensure the consistency of the associated linear system of equations and the design of an appropriate two‐level preconditioner. A qualitative and quantitative assessment of the accuracy, efficiency, and stability of the quadrilateral SMPM solver is provided through its application to the standard benchmarks of the Taylor vortex, lid‐driven cavity, and double shear layer. The capacity of the flow solver for the study of environmental stratified flow processes is shown through the simulation of long‐distance propagation of an internal solitary wave of depression in a manner that is free of numerical dispersion and dissipation. The methods and results presented in this paper make it a point of reference for future studies oriented toward the reliable application of the quadrilateral SMPM model to more complex environmental stratified flow process studies. Copyright © 2014 John Wiley & Sons, Ltd.     

Molecular mobility in biodegradable poly( $ \varepsilon$ -caprolactone)/poly(hydroxyethyl acrylate) networks

Poly( e \varepsilon -caprolactone)/poly(hydroxyethyl acrylate) networks have been investigated by thermally stimulated depolarization currents (TSDC) and differential scanning calorimetry (DSC). The introduction of hydrophilic units (HEA) in the system aiming at tailoring the hydrophilicity of the system results in a series of copolymer networks with microphase separation into hydrophobic/hydrophilic domains. Polycaprolactone (PCL) crystallization is prevented by the topological constraints HEA units imposed in such heterogeneous domains. Moreover, the mobility of the amorphous PCL chains is enhanced as revealed by the main relaxation process which becomes faster. The glass transition of PHEA-rich domains shifts to lower temperatures, as the total amount of PCL in the copolymer increases, due to the presence of PCL units within the same region. The behaviour of the copolymer networks swollen with different content of water has been investigated to analyze the interaction between water molecules and hydrophobic/hydrophilic domains and provide further insights into the molecular structure of the system.     

Synthesis of 1,5-Benzodiazepines with Unusual Substitution Pattern from Chalcones Under Solvent-Free Microwave Irradiation Conditions

1,5-Benzodiazepines have been synthesized from the corresponding 2′-hydroxychalcones [1-(2-hydroxyphenyl)-3-aryl-2-propen-1-ones] and o-phenylenediamine, both in methanol, under reflux and under solvent-free microwave irradiation conditions on alumina. The latter method proved to be advantageous.     

2‐(4′‐Pyridyl‐N‐oxide)‐Substituted Hemithioindigos as Photoresponsive Guests for a Super Aryl‐Extended Calix[4]pyrrole Receptor

We report the synthesis of two 2‐(4′‐pyridyl‐N‐oxide)‐substituted hemithioindigos (HTIs). We probed their photoisomerization by using UV/Vis and ¹H NMR spectroscopy techniques. Light irradiation at λ=450 nm provoked the isomerization of the HTI Z isomer to the E counterpart to a large extent (≈80 % at the photostationary state). ¹H NMR titration experiments revealed the formation of thermodynamically and kinetically stable 1:1 inclusion complexes of the (Z)‐HTI isomers with a super aryl‐extended host (association constant>10⁴ m ^?1). Photoirradiation at λ=450 nm of the inclusion complexes induced the isomerization of the bound HTI N‐oxide to afford the (E)‐HTI?calix[4]pyrrole complex. We determined accurate association constant values for the 1:1 inclusion complexes of the (Z)‐ and (E)‐HTI isomers by using isothermal titration calorimetry experiments. The results showed that the stability constants of the (E)‐HTI complexes were 2.2–2.8‐fold lower than those of the (Z)‐HTI counterparts, which explains the lack of light‐induced release of the former to the bulk solution.