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.     

Elastoplastic analysis of nonlinearly hardening variable thickness annular disks under external pressure

Based on von Mises’ yield criterion, deformation theory of plasticity and Swift’s hardening law, elasto-plastic deformation of variable thickness annular disks subjected to external pressure is studied. A nonlinear shooting method using Newton’s iterations with numerically approximated tangent is designed for the solution of the problem. Considering a thickness profile in the form of a general parabolic function, the condition of occurrence of plastic deformation at the inner and outer edges of the annular disk is investigated. A critical disk profile is determined and the corresponding elastic–plastic stresses as well as the residual stress distribution upon removal of the applied pressure are computed and discussed.     

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.     

Elastoplastic deformations of rotating parabolic solid disks using Tresca''s yield criterion

Analytical solutions for the stress distribution in rotating parabolic solid disks are obtained. The analysis is based on Tresca's yield criterion, its associated flow rule and linear strain hardening. It is shown that, the deformation behavior of the convex parabolic disk is similar to that of the uniform thickness disk, but in the case of concave parabolic solid disk, it is different. In the latter, the plastic core consists of three different plastic regions with different mathematical forms of the yield criteria. Accordingly, three different stages of elastic–plastic deformation occur. All these stages of elastic–plastic deformation are studied in detail. It is also shown mathematically that in the limiting case the parabolic disk solution reduces to the solution of rotating uniform thickness solid disk.     

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.     

Tetrakis(bicyclo[2.2.2]oct‐2‐ene)‐Fused Calix[4]pyrrole

Tetrakis(bicyclo[2.2.2]oct‐2‐ene)‐fused calix[4]pyrrole, 5 , was obtained starting from (E)‐1,2‐bis(phenylsulfonyl)ethylene. This new calixpyrrole derivative is the prospective precursor of tetrabenzocalix[4]pyrrole, a potential ion‐pair receptor and an attractive species as a possible deep‐walled ‘molecular container’.     

Synthesis of Spirocyclic and Tricyclic Isoxazoline via 1,3‐Dipolar Cycloaddition Reactions

1,3‐Dipolar cycloadditions of the bicyclic monoterpenes (S)‐(?)‐camphene ( 1 ), (R)‐(+)‐a‐pinene ( 2 ), and (S)‐(?)‐b‐pinene ( 3 ) with aryl and heteroaryl nitrile oxides afforded new spirocyclic and tricyclic isoxazoline derivatives 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 whose biological activities were evaluated in bioassay studies.     

Amperometric biosensors based on deposition of gold and platinum nanoparticles on polyvinylferrocene modified electrode for xanthine detection

In this study, new xanthine biosensors, XO/Au/PVF/Pt and XO/Pt/PVF/Pt, based on electroless deposition of gold(Au) and platinum(Pt) nanoparticles on polyvinylferrocene(PVF) coated Pt electrode for detection of xanthine were presented. The amperometric responses of the enzyme electrodes were measured at the constant potential, which was due to the electrooxidation of enzymatically produced H₂O₂. Compared with XO/PVF/Pt electrode, XO/Au/PVF/Pt and XO/Pt/PVF/Pt exhibited excellent electrocatalytic activity towards the oxidation of the analyte. Effect of Au and Pt nanoparticles was investigated by monitoring the response currents at the different deposition times and the different concentrations of KAuCl₄ and PtBr₂. Under the optimal conditions, the calibration curves of XO/Au/PVF/Pt and XO/Pt/PVF/Pt were obtained over the range of 2.5 × 10^?3 to 0.56 mM and 2.0 × 10^?3 to 0.66 mM, respectively. The detection limits were 7.5 × 10^?4 mM for XO/Au/PVF/Pt and 6.0 × 10^?4 mM for XO/Pt/PVF/Pt. The effects of interferents, the operational and the storage stabilities of the biosensors and the applicabilities of the proposed biosensors to the drug samples analysis were also evaluated.     

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.