Silica aerogel–iron oxide nanocomposites: recoverable catalysts for the oxidation of alcohols with hydrogen peroxide

Various aerogels of silica gel doped with Fe₂O₃ were prepared by sol–gel method. They were calcined to produce nanoparticle solids. The nanosized mixed oxides were active in the oxidation of alcohols and produced carbonyl compounds in very good to excellent yields using hydrogen peroxide.     

Common properties of table algebras and association schemes

The concept of table algebra in the title is a real nonsingular generalized table algebra in the sense of [Z. Arad, E. Fisman, M. Muzychuk, Generalized table algebras, Israel J. Math. 114 (1999) 29–60]. In this paper we first give some definitions and facts about table algebras. It is well known that every association scheme gives a Hecke-algebra which is a table algebra too. This leads to the natural question which properties of association schemes stay valid for table algebras. For instance, we prove the Second Isomorphism Theorem and the Jordan–Holder's theorem for standard table algebras.     

A necessary condition for the existence of periodic solutions of certain three dimensional autonomous systems

In this article, we give a necessary condition for the existence of periodic solutions of certain three dimensional autonomous systems. This may become useful in further investigations. Our claims are proved and supported by certain examples for the third order autonomous systems.     

Phase-controlled atom-photon entanglement in a three-level Λ-type closed-loop atomic system

We study the entanglement of dressed atom and its spontaneous emission in a three-level Λ-type closed-loop atomic system in a multi-photon resonance condition and beyond it.It is shown that the von Neumann entropy in such a system is phase-dependent,and it can be controlled by either the intensity or relative phase of applied fields.It is demonstrated that for the special case of the Rabi frequency of applied fields,the system is disentangled.In addition,we take into account the effect of Doppler broadening on the entanglement and it is found that a suitable choice of laser propagation direction allows us to obtain the steady state degree of entanglement(DEM) even in the presence of the Doppler effect.     

Olefin epoxidation with H2O2 in the presence of Mn(II) dicarboxylate coordination polymer catalysts

Abstract  

The Mn(II) dicarboxylate coordination polymers [Mn(μ-terephthalate)(H₂O)₂] _n , [Mn(μ-oxalate)(H₂O)₂] _n , and [Mn(μ-d-(−)-tartrate)] _n were prepared in water and characterized by FT-IR spectroscopy and CHN analysis. Particles of the terephthalate catalyst were also synthesized, by reaction of terephthalic acid and MnCl₂·4H₂O by a sonochemical method. The catalytic potential of these coordination polymers as slow-release sources of catalytically active Mn species was tested in the oxidation of cyclooctene to its epoxide in acetonitrile, using hydrogen peroxide as oxygen source. For the terephthalate species the catalytic activity was found to increase with increasing dielectric constant and dipole moment of the solvent (being highest in acetonitrile), with reaction temperature to a maximum at 60 °C, and with an imidazole co-catalyst (highest activity found for a imidazole-to-catalyst molar ratio of 20:1). Good activity with more than 64% conversion in 24 h was obtained for epoxidation of cyclooctene and cyclohexene, whereas low yields only were obtained from aryl-substituted olefins. Some exo versus endo regioselectivity was found for norbornene.     

A handy proof of Gay's theorem

In 1979, Gay proved that Broyden's methods, when used for n‐square linear systems, terminate in at most 2n iterations (SIAM J. Numer. Anal. 1979; 16 :623–630). Also, the ABS methods were introduced in 1984 (Numer. Math. 1984; 45 :1361–1376). In this paper we show another (handy) proof of Gay's theorem by these algorithms. Copyright © 2008 John Wiley & Sons, Ltd.     

Definition of the feasible solution set in multicriteria optimization problems with continuous,discrete, and mixed design variables

Engineering optimization problems are multicriteria with continuous, discrete, and mixed design variables. Correct definition of the feasible solution set is of fundamental importance in these problems. It is quite difficult for the expert to define this set. For this reason, the results of searching for optimal solutions frequently have no practical meaning. Furthermore, correct definition of this set makes it possible to significantly reduce the time of searching for optimal solutions. This paper describes construction of the feasible solution set with continuous, discrete, and mixed design variables on the basis of Parameter Space Investigation (PSI) method.     

Manganese(II) complexes of hydrazone based NNO-donor ligands and their catalytic activity in the oxidation of olefins

The reaction between tridentate NNO donor hydrazone ligands, (E)-2-cyano-N′-(phenyl(pyridin-2-yl)methylene)acetohydrazide (HL¹) and (E)-2-cyano-N′-(1-(pyridin-2-yl)ethylidene)acetohydrazide (HL²), with MnCl₂·4H₂O in methanol resulted in [Mn(HL¹)Cl₂(CH₃OH)] (1) and [Mn(HL²)Cl₂(CH₃OH)] (2). Molecular structures of the complexes were determined by single-crystal X-ray diffraction. All of the investigated compounds were further characterized by elemental analysis, FT-IR, TGA, and UV–Vis spectroscopy. These complexes were used as catalysts for olefin oxidation in the presence of tert-butylhydroperoxide (TBHP) as an oxidant. Under similar experimental conditions with equal manganese loading, the presence of [Mn(HL²)Cl₂(CH₃OH)] (2) resulted in higher conversion than [Mn(HL¹)Cl₂(CH₃OH)] (1).