Delay equations with fluctuating delay related to the regenerative chatter

The mathematical models representing machine tool chatter dynamics have been cast as differential equations with delay. In this paper, non-linear delay differential equations with periodic delays which model the machine tool chatter with continuously modulated spindle speed are studied. The explicit time-dependent delay terms, due to spindle speed modulation, are replaced by state-dependent delay terms by augmenting the original equations. The augmented system of equations is autonomous and has two pairs of pure imaginary eigenvalues without resonance. The reduced bifurcation equation is obtained by making use of Lyapunov-Schmidt Reduction method. By using the reduced bifurcation equations, the periodic solutions are determined to analyze the tool motion. Analytical results show both modest increase of stability and existence of periodic solutions near the new stability boundary.     

On classification of four-dimensional nilpotent Leibniz algebras

Leibniz algebras are certain generalization of Lie algebras. In this paper, we give the classification of four-dimensional non-Lie nilpotent Leibniz algebras. We use the canonical forms for the congruence classes of matrices of bilinear forms and some other techniques to obtain our result.     

Effects of timber skidding on chemical characteristics of herbaceous cover, forest floor and topsoil on skidroad in an oak (Quercus petrea L.) forest

This paper examines the effects of timber harvesting by skidding on some soil properties (sand, silt, clay, pH, organic carbon, bulk density and compaction), herbaceous cover (unit mass) and forest floor (unit weight) properties. Also N (%), P, K, Na, Ca, Mg, Fe, Zn, Cu and Mn (ppm) were determined in all herbaceous cover, forest floor and two soil depth (0–5 cm and 5–10 cm) on skidroad of an oak (Quercus petrea L.) stand in Istanbul Belgrad Forest – Turkey. In this study, obtained results are; the forest floor and the herbaceous cover amount on the skidroad have been found considerably lower than undisturbed area. There were some crucial changes in the characteristics of the soil which has been investigated down to 10 cm depth. Soil bulk density was found quite high in the samples taken from the skidroad subject to compaction compared to the ones on the undisturbed area. Nevertheless, no important difference had been detected between the skidroad and the undisturbed area at both soil depths in terms of organic carbon contents. Moreover, the soil acidity (pH) values showed noteworthy differences in the analysis of soil samples taken from both soil depths on the skidroad and on the undisturbed area. Fe and Cu contents of herbaceous samples on skidroad were significantly higher than undisturbed area. Forest floor on skidroad had significantly higher K content, and significantly lower Zn, Mn and N content compared to undisturbed area. P, Fe, Zn and Mn contents were found significantly lower in 0–5 cm soil depth on skidroad than undisturbed area. In 5–10 cm soil depth, concentrations of N, P, Fe, Zn and Mn were significantly lower, while Mg and Cu contents were significantly higher than undisturbed area. Results indicate that long-term harvest using skidding techniques on these sites had adversely affected soil cation concentrations, physical soil conditions and mass of herbaceous cover and forest floor.     

Communication: Identification of the molecule-metal bonding geometries of molecular nanowires

Molecular nanowires in which a single molecule bonds chemically to two metal electrodes and forms a stable electrically conducting bridge between them have been studied intensively for more than a decade. However, the experimental determination of the bonding geometry between the molecule and electrodes has remained elusive. Here we demonstrate by means of ab initio calculations that inelastic tunneling spectroscopy (IETS) can determine these geometries. We identify the bonding geometries at the gold-sulfur interfaces of propanedithiolate molecules bridging gold electrodes that give rise to the specific IETS signatures that were observed in recent experiments.     

Butylene linked palladium N-heterocyclic carbene complexes: Synthesis and catalytic properties

New bis(NHC)-Pd complexes were synthesized and characterized by elemental analysis, ¹H NMR, ¹³C NMR, and IR spectroscopy. The reaction of Pd(OAc)₂ and bis(benzimidazolium) salts in DMSO gave the monomeric palladium complex in which the N-heterocyclic carbene was bound to the metal centre. The crystal and molecular structure of the cis-dibromo{1,1′-di[2,3,4,5,6-pentamethylbenzyl]-3,3′-butylenedibenzimidazol-2,2′-diylidene}-palladium(II) complex was determined by single-crystal X-ray diffraction. The activity of the Pd(II) complexes in the direct arylation of benzothiazole with arylbromides was investigated. A preliminary catalytic study showed that these bis(NHC)-Pd complexes were highly active in the direct arylation of benzothiazole with arylbromides.     

Microcalorimetric investigation of water vapor adsorption on silica gel

In this study, the activities of four ginsenosides Rc, Re, Rd, and Rf on splenic lymphocytes growth were studied by microcalorimetry. Some qualitative and quantitative information, such as the metabolic power–time curves, growth rate constant k, maximum heat-output power of the exponential phase P _max and the corresponding appearance peak time t _max, total heat output Q _t, and promotion rate R _p of splenic lymphocytes growth affected by the four ginsenosides were calculated. In accordance with thermo-kinetic model, the corresponding quantitative relationships of k, P _max, t _max, Q _t, R _p, and c were established, . Also, the median effective concentration (EC₅₀) was obtained by quantitative analysis. Based on both the quantitative quantity–activity relationships (QQAR) and EC₅₀, the sequence of promotion activity was Rc > Re > Rd > Rf. The analysis of structure–activity relationships showed that the number, type, and position of sugar moieties on the gonane steroid nucleus had important influences on the promotion activity of Rc, Re, Rd, and Rf on splenic lymphocytes growth. Microcalorimetry can be used as a useful tool for determining the activity and studying the quantity–activity relationship of drugs on cell.     

Use of bis(benzimidazolium)–palladium system as a convenient catalyst for Heck and Suzuki coupling reactions of aryl bromides and chlorides

Six new, sterically demanding bis(benzimidazolium) salts (2a–f) as NHC precursors have been synthesized and characterized. These salts, in combination with palladium acetate, provide active catalysts for the cross‐coupling of aryl chlorides and bromides under mild conditions in aqueous media. Copyright © 2006 John Wiley & Sons, Ltd.     

The radiativeK* meson decays in QCD

ThegK ^o* K ^o _γ andgK ^+* K ⁺ _γ coupling constants and the radiative decay widths are calculated in the context of QCD sum rules. It is found that the discrepancy between the experimental data and theoretical results still exists.     

Synthèse dc la pyrido[2,3-f] phtalazine et des diformyl-6,7; -4,6; -4,7; -2,4 quinoleines

This article describes the synthesis of a new heterocycle, pyrido[2,3,f]phtalazine and three new diformylquinolincs.