Bifurcation of limit cycles from a 4-dimensional center in 1:n resonance

We study the bifurcation of limit cycles from the periodic orbits of a linear differential system in R⁴ in resonance 1:n perturbed inside a class of piecewise linear differential systems, which appear in a natural way in control theory. Our main result shows that at most 1 limit cycle can bifurcate using expansion of the displacement function up to first order with respect to a small parameter. This upper bound is reached. For proving this result we use the averaging theory in a form where the differentiability of the system is not needed.     

Optical absorption of tetraphenylporphyrin thin films in UV-vis-NIR region

The optical absorption of thermally-evaporated tetraphenylporphyrin (TPP), in the UV-vis-NIR region has been studied. The absorption spectra recorded in the UV-vis region for the as-deposited and annealed films showed different absorption bands, namely the Soret, B, at region 360-490 nm, Q-band region consist of four bands in the region 500-720 nm and two other bands labeled N and M in UV region. The Soret band always shows splitting in all the TPP thin films and the effect of annealing on the intensities of these components have been observed. The spectra of the infrared absorption allow characterization of vibrational modes for the powder, as deposited and annealed thin films. Some of the optical absorption parameters, namely molar extinction coefficient (epsilon), half band width (Deltalambda), electronic dipole strength (q2), and oscillator strength (f), of the principal optical transitions have also been evaluated.     

Co3O4/SiO2 nanocomposites for supercapacitor application

In this study, Co₃O₄/SiO₂ nanocomposites have been successfully synthesized by citrate–gel method by utilizing SiO₂ matrix for Co₃O₄ embedment. Spectroscopy analyses confirm the formation of high crystalline Co₃O₄ nanoparticles; meanwhile, microscopy findings reveal that the Co₃O₄ nanoparticles are embedded in SiO₂ matrix. Electrochemical properties of the Co₃O₄/SiO₂ nanocomposites were carried out using cyclic voltammetry (CV), galvanostatic charge–discharge, and electrochemical impedance spectroscopy (EIS) in 5 M KOH electrolyte. The findings show that the charge storage of Co₃O₄/SiO₂ nanocomposites is mainly due to the reversible redox reaction (pseudocapacitance). The highest specific capacitance of 1,143 F g ^?1 could be achieved at a scan rate of 2.5 mV s^?1 in the potential region between 0 and 0.6 V. Furthermore, high-capacitance retention (>92 %) after 900 continuous charge–discharge tests reveals the excellent stability of the nanocomposites. It is worth noting from the EIS measurements that the nanocomposites have low ESR value of 0.33 Ω. The results manifest that Co₃O₄/SiO₂ nanocomposites are the promising electrode material for supercapacitor application.     

Electron paramagnetic resonance and computational studies of radicals derived from boron-substituted N-heterocyclic carbene boranes

Fifteen second-generation NHC-ligated boranes with aryl and alkyl substituents on boron were prepared, and their radical chemistry was explored by electron paramagnetic resonance (EPR) spectroscopy and calculations. Hydrogen atom abstraction from NHC-BH(2)Ar groups produced boryl radicals akin to diphenylmethyl with spin extensively delocalized across the NHC, BH, and aryl units. All of the NHC-B·HAr radicals studied abstracted Br-atoms from alkyl bromides. Radicals with bulky N,N'-dipp substituents underwent dimerization about 2 orders of magnitude more slowly than first-generation NHC-ligated trihydroborates. The evidence favored head-to-head coupling yielding ligated diboranes. The first ligated diboranyl radical, with a structure intermediate between that of ligated diboranes and diborenes, was spectroscopically characterized during photolysis of di-t-butyl peroxide with N,N'-di-t-butyl-imidazol-2-ylidene phenylborane. The reactive site of B-alkyl-substituted NHC-boranes switched from the boron center to the alkyl substituent for both linear and branched alkyl groups. The β-borylalkyl radicals obtained from N,N'-dipp-substituted boranes underwent exothermic β-scissions with production of dipp-Imd-BH(2)· radicals and alkenes. The reverse additions of NHC-boryl radicals to alkenes are probably endothermic for alkyl-substituted alkenes, but exothermic for conjugated alkenes (addition of an NHC-boryl radical to 1,1-diphenylethene was observed). A cyclopropylboryl radical was observed, but, unlike other α-cyclopropyl-substituted radicals, this showed no propensity for ring-opening.     

Solutions of magnetohydrodynamic problems based on a conventional computational fluid dynamics code

It is pointed out that there exists a hidden analogy between magnetohydrodynamic (MHD) and conventional computational fluid dynamic (CFD) equations. This allows the generalization of any conventional CFD code so that the effects of MHD can be accounted for. This generalization is actually made for the FLUENT CFD code. Although this generalized FLUENT code can easily be adjusted to any MHD environment, it has been specifically designed for metallurgical applications. Predictions of the code are validated against the analytical solutions for the Poiseuille-Hartmann flow and for the shielding of magnetic field oscillations by a conducting medium (skin effect).     

Alginate polyelecrtolyte ionotropic gels. Part IX: Diffusion control effects on the relaxation time of sol-gel transformation for transition-divalent metal alginate ionotropic gel complexes

The rate of gel growth for spherical ionotropic metal alginate gel complexes has been measured. The experimental results show that the stability of these complexes increases in the order Mn相似文献