Dynamic behaviour modelling of a flexible gear system by the elastic foundation theory in presence of defects

In this paper a novel approach for modelling a spur gear system using finite element method combined with elastic foundation theory is developed. The pinion is modelled by shaft finite element and the wheel by a three-dimensional finite element. Elastic foundation is utilized to model the gearmesh. The modal analysis showed the presence of lower natural frequency for thin rimmed gear cases susceptible to be excited by the operating running condition. The transmission error is affected by the wheel shape and by the presence of lower natural frequencies. Eccentricity error and tooth crack are also modelled to observe their influence on the dynamics behaviour of the system. It was found that they are responsible of the apparition of an amplitude modulation.     

On the stability of the Kalman–Bucy filter with stationary time varying parameters

Linear filtering systems with stationary parameters are considered in continuous time. We generalize the conditionally Gaussian result of Lipster – Shiryaev and Haussmann – Pardoux. Moreover, we show that the Kalman – Bucy filter is exponentially stable under weak conditions of stabile ability and detect ability. This filter will have a well defined asymptotic behaviour     

A one-step procedure for the monoacylation of symmetrical 1,2-diols

A series of lanthanide (III) salts have been shown to catalyze the monoacylation of symmetrical 1,2-diols by carboxylic acid anhydrides with surprisingly high selectivity.     

Synthesis of pyrroles from alkyl trans-2-methyoxycyclopropyl ketones

2-Alkylpyrroles were obtained by the reaction of alkyl trans-2-methoxycyclopropyl ketones with ammonium hydroxide. N-Substituted 2-alkylpyrroles were synthesized by the reaction of the indicated ketones with methylamine or aniline in acetic acid or methanol-acetic acid.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 10, pp. 1335–1336, October, 1990.     

Convenient method of preparing 3-substituted 2,2′-furyl(thienyl)pyrroles

2,2-Furyl(thienyl)pyrroles and their 3-decylthio derivatives were synthesized by the Paal-Knorr reaction from the corresponding 3-unsubstituted or 3-decylthio-substituted dimethylacetals of 4-(2-furyl)- and 4-(2-thienyl)-4-oxobutanal. The starting materials were synthesized in three stages from methyl-2-furan- and -2-thiophenecarboxylates. The latter were treated with 1-bromo-2-ethoxycyclopropyllithium via acid-catalyzed methanolysis of the 1-bromo-2-ethoxyketones formed and farther reaction with zinc powder or sodium decylthiolate.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 8, pp. 1141–1143, August, 1991.     

Synthesis, structure, and characterization of hybrid materials: [Ce(H2O)]2[O2C(CH2)2CO2]3 and [Sm(H2O)]2[O2C(CH2)2CO2]3·H2O

The rare-earth dicarboxylate hybrid materials [Ce(H₂O)]₂[O₂C(CH₂)₂CO₂]₃ ([Ce(Suc)]) and [Sm(H₂O)]₂[O₂C(CH₂)₂CO₂]₃·H₂O ([Sm(Suc)]) have been hydrothermally synthesized (200°C, 3 days) under autogenus pressure. [Ce(Suc)] is triclinic, a=7.961 (3) Å, b=8.176 (5) Å, c=14.32 (2) Å, α=97.07° (7), β=96.75° (8), γ=103.73° (6), and z=2. The crystal structure of this compound has been determined using 3120 unique single crystal data. The final refinements let the agreement factors R₁ and wR₂(F²) converge to 0.0138 and 0.0363, respectively. [Ce(Suc)] is built up from infinite chains of edge-sharing nine-fold coordinated cerium atoms running along [100]. These chains are interconnected by the carbon atoms of the succinate anions, leading to a three-dimensional hybrid framework. The cell constants of [Sm(Suc)], isotypic with monoclinic C2/c [Pr(H₂O)]₂[O₂C(CH₂)₂CO₂]₃·H₂O ([Pr(Suc)]), were refined starting from X-ray powder data: a=20.275 (3) Å, b=7.919 (6) Å, c=14.130 (3) Å, and β=121.45° (1). Despite its lower symmetry, [Ce(Suc)] presents an important structural filiation with [Sm(Suc)]     

Preparative separation of quinolines by centrifugal partition chromatography with gradient elution

Centrifugal partition chromatography has been successfully applied to the separation of 2-alkylquinolines from liquid combinatorial synthesis crude samples. Original gradient elution using the ternary two-phase solvent systems heptane-water-acetonitrile and heptane-acetonitrile-methanol were used to separate them with high purity degrees. Part of the effluent was monitored with evaporative light scattering detection, for direct control, and the collected fractions were analyzed by thin-layer chromatography, GC, nuclear magnetic resonance spectroscopy and MS. It was thus possible to purify in one run more than 3 g of crude mixture using only 1.31 of solvents to obtain more than 300 mg of several alkylquinolines homologues with 99% purity and in less than 7 h.     

A Stereodivergent Approach to the Synthesis of gem-Diborylcyclopropanes

We report a designed stereodivergent strategy for the synthesis of gem-diborylcyclopropanes. The reaction provides a highly modular approach to prepare cyclopropane ring variants bearing gem-(Bpin,Bpin), gem-(Bpin,Bdan), and gem-(Bpin,BF₃K), with outstanding levels of stereocontrol. This was achieved by diastereoselective Pd-catalyzed cyclopropanation reactions of gem-diborylalkenes with α-diazoarylacetates and α-diazoaryl-trifluoromethyl. The key to the success of this general protocol was the diastereoselective trifluorination reaction of gem-diborylcyclopropanes, followed by the stereospecific interconversion of the trifluoroborate salts into the Bdan group.