Reactions of methylaluminoxane and trimethylaluminum with zirconium and titanium tetracyclopentadienyl derivatives

Gas volumometry, gas chromatography, mass spectrometry, and ESR were used to study reactions of methylaluminoxane (MAO) and Me₃Al with Cp₄Zr, Cp₄Ti, and 2,2,6,6-tetra-methylpiperidine-1-oxyl (TEMPO). It was shown that the reaction is accompanied by evolution of methane, whose amount exceeds the initial concentration of the starting metallocene or free radical by a few hundred times, but in all the cases is no more than 15% of the starting amount of the Me??Al fragments in the organoaluminum compound. Metal-centered radicals were detected by ESR in the systems with Zr and Ti metallocene derivatives. Mechanism of the observed reactions is discussed.     

Free-radical reactions of the tris-dioximate clathrochelates: synthesis and X-ray structure of the first cyclohexyl-substituted monoribbed-functionalized macrobicyclic iron(ii) complex

Quantum chemical calculations were performed at the DFT level for the boron-capped dichloro-substituted tris-dioximate iron(II) clathrochelate and cyclohexane and 1,4-dioxane radicals. The 1,4-dioxane and cyclohexane radicals are nucleophiles towards the macrobicyclic precursor studied. The reaction of this clathrochelate with cyclohexane in the presence of a free-radical initiator resulted in substitution of a chlorine atom by a cyclohexyl fragment. The compound obtained was characterized by elemental analysis, IR spectroscopy, ¹H and ¹³C{¹H} NMR, and single-crystal X-ray diffraction data.     

Synthesis and photophysical properties of silica nanoparticles based on europium(iii) complexes

Monodisperse 280?C480 nm silica particles doped with europium complexes with thenoyltrifluoroacetylacetone and adducts with some phosphine oxides as luminophores were prepared for the first time by the optimized Stober procedure using surfactants. The size and the polydispersity of the obtained particles depend on the luminophore incorporated in the polymer template. The photophysical properties of aqueous dispersions of the europium(iii)-doped silica particles were studied by the luminescence method.     

Electrophile affinity and positional selectivity in electrophilic substitution reactions of N-substituted pyrroles

In terms of the density functional theory (DFT) using B3LYP/6-31G(d) method with full geometry optimization, gas-phase quantum chemical calculations were performed for ??-complexes formed upon the attack of electrophiles E (E = H⁺, Me⁺, Me³Si⁺, Br⁺, NO₂ ⁺, MeCO⁺, SO₃) on ??- and ??-positions of furan, thiophene, selenophene, pyrrole, and N-substituted pyrroles (NR-pyrroles, R = Me, Bu^t, SiMe₃, SiPrⁱ ₃, C₆H₄NO₂-p, SO₂Ph, CHO, COOMe) and for respective ??- and ??-substituted electrophilic substitution products. The energy differences between the ??- and ??-isomers of the ??-complexes characterize the preferred direction of the electrophilic attack, while the energy differences between the isomeric products make it possible to estimate the energy preference of a particular product. An analysis of the results obtained demonstrates the effect of the structure of heterocycle, the nature of electrophile, and thermodynamic and steric factors on the positional selectivity (??/?? ratio) in electrophilic substitution reactions of ??-electron rich five-membered heteroaromatics.     

Ligand exchange chromatography: a vital dimension for the reliable characterization of heterocycles in crude oils and refined products

In the present study, we established a statistical distribution pattern of indigenous sulfur, nitrogen, and oxygen species in Arabian Heavy crude oil and its distilled fractions: naphtha, gas oil, and vacuum gas oil (VGO) using chemical derivatization with methyl iodide and subsequent characterization by positive electrospray Fourier transform mass spectrometry. It was observed that sulfur species for naphtha and gas oil were accumulated at lower double bond equivalent values and at lower carbon numbers compared to VGO, whereas crude oil encompassed a complete range of the sulfur species detected in all distilled fractions. Moreover, the use of alumina column chromatography and ligand exchange chromatography (LEC) on a palladium-bonded silica stationary phase revealed additional structural features of sulfur heterocycles in terms of condensed and non-condensed thiophenes. During LEC separation, in addition to sulfur heterocycles, interesting results were obtained for oxygen-containing compounds. Ortho-substituted alkyl phenols were separated from meta- and para-substituted alkyl phenols on a palladium-bonded silica stationary phase.     

Relaxation of microparticles exposed to hydrodynamic forces in microfluidic conduits

The behavior of microparticles exposed to gravitational and lift forces and to the velocity gradient in flow velocity profile formed in microfluidic conduits is studied from the viewpoint of the transient period (the relaxation) between the moment at which a particle starts to be transported by the hydrodynamic flow and the time at which it reaches an equilibrium position, characterized by a balance of all active forces. The theoretical model allowing the calculation of the relaxation time is proposed. The numerical calculus based on the proposed model is compared with the experimental data obtained under different experimental conditions, namely, for different lengths of microfluidic channels, different average linear velocities of the carrier liquid, and different sizes and densities of the particles used in the study. The results are important for the optimization of microfluidic separation units such as microthermal field-flow fractionation channels in which the separation or manipulation of the microparticles of various origin, synthetic, natural, biological, etc., is performed under similar experimental conditions but by applying an additional thermodynamic force.

Extended canonical algebras and Fuchsian singularities

The authors introduce a new class of finite dimensional algebras called extended canonical, and determine the shape of their derived categories. Extended canonical algebras arise from a canonical algebra ?? by onepoint extension or coextension by an indecomposable projective module. Our main results concern the case of negative Euler characteristic of the corresponding weighted projective line ${\mathbb{X}}$ ; more specifically we establish, for a base field of arbitrary characteristic, a link to the Fuchsian singularity R of ${\mathbb{X}}$ which for the base field of complex numbers is isomorphic to an algebra of automorphic forms. By means of a recent result of Orlov we show that the triangulated category of the graded singularities of R (in the sense of Buchweitz and Orlov) admits a tilting object whose endomorphism ring is the corresponding extended canonical algebra. Of particular interest are those cases where the attached Coxeter transformation has spectral radius one. A K-theoretic analysis then shows that this happens exactly for 38 cases including Arnold??s 14 exceptional unimodal singularities. The paper is related to recent independent work by Kajiura, Saito and Takahashi.     

Foliations invariant by rational maps

We give a classification of pairs ${(\mathcal{F}, \phi)}$ where ${\mathcal{F}}$ is a holomorphic foliation on a projective surface and ${\phi}$ is a non-invertible dominant rational map preserving ${\mathcal{F}}$ .     

On q-analogues and stability theorems

In this survey recent results about q-analogues of some classical theorems in extremal set theory are collected. They are related to determining the chromatic number of the q-analogues of Kneser graphs. For the proof one needs results on the number of 0-secant subspaces of point sets, so in the second part of the paper recent results on the structure of point sets having few 0-secant subspaces are discussed. Our attention is focussed on the planar case, where various stability results are given.     

A Characterization of L-orthogonal Polynomials from?Three Term Recurrence Relations

We consider the sequence of polynomials {Q _n } satisfying the L-orthogonality ?[z ^?n+m Q _n (z)]=0, 0??m??n?1, with respect to a linear functional ? for which the moments ?[t ⁿ ]=?? _n are all complex. Under certain restriction on the moment functional these polynomials also satisfy a three term recurrence relation. We consider three special classes of such moment functionals and characterize them in terms of the coefficients of the associated three term recurrence relations. Relations between the polynomials {Q _n } associated with two of these special classes of moment functionals are also given. Examples are provided to justify this characterization.