The number of limit cycles bifurcating from the periodic orbits of an isochronous center

This paper concerns the bifurcation of limit cycles for a quartic system with an isochronous center. By using the averaging theory, it shows that under any small quintic homogeneous perturbations, at most 14 limit cycles birfucate from the period annulus of the considered system.     

Production of Graphite During the Extinguishing Arc with New SF6 Alternative Gases

Most high voltage circuit breakers in operation use SF₆ as the arc interruption medium because of its high dielectric strength and good arc interruption properties. However SF₆ also displays a high global warming potential which motivates the investigation of possible alternatives such as CO₂–Novec?4710 and N₂–Novec?5110 mixtures proposed by different HVCB manufacturers. CB power test comparison between pure CO₂ and CO₂–Novec?4710 mixture shows that the latter created a large amount of graphite and reduced CB performances after several current breaking shots. Using Gibbs free energy method, a theoretical study has been conducted on SF₆ replacement candidates listed above. Aiming to understand graphite formation, several parameters impact were discussed: carrier gas such as CO₂ and N₂, pressure and O₂ initial mixture proportions. The study focuses on graphite condensation temperature and graphite production amount evolutions in respect to the study parameters as well as in respect to CB inter-contacts space condition in terms of pressure and temperature at current-zero. It has been shown that a high percentage of CO₂ in the mixture reduces graphite condensation temperature by 2600 K while adding N₂ do not make such an impact. Pressure increases graphite condensation temperature and O₂ reduces it. The amount of graphite produced is pressure independent but decreases with the increase of O₂ proportion in the initial mixture. It has been shown that adding a sufficient O₂ amount can prevent graphite production at all.

     

Reactivity of N-substituted alkenylidene hydrazinecarbothioamides toward tetracyanoethylene,an efficient synthesis stereoselective 1,3-thiazole compounds

Research on Chemical Intermediates - The reaction between N-substituted alkenylidene hydrazinecarbothioamides and two molar amounts of tetracyanoethylene (TCNE) in anhydrous THF at room temperature...     

Synthesis and reactions of N-heterocyclic carbene boranes

Boranes are widely used Lewis acids and N-heterocyclic carbenes (NHCs) are popular Lewis bases, so it is remarkable how little was known about their derived complexes until recently. NHC-boranes are typically readily accessible and many are so stable that they can be treated like organic compounds rather than complexes. They do not exhibit "borane chemistry", but instead are proving to have a rich chemistry of their own as reactants, as reagents, as initiators, and as catalysts. They have significant potential for use in organic synthesis and in polymer chemistry. They can be used to easily make unusual complexes with a broad spectrum of functional groups not usually seen in organoboron chemistry. Many of their reactions occur through new classes of reactive intermediates including borenium cations, boryl radicals, and even boryl anions. This Review provides comprehensive coverage of the synthesis, characterization, and reactions of NHC-boranes.     

LIMIT CYCLES OF QUARTIC AND QUINTIC POLYNOMIAL DIFFERENTIAL SYSTEMS VIA AVERAGING THEORY

We study the maximum number of limit cycles that can bifurcate from the period annulus surrounding the origin of a class of cubic polynomial differential systems using the averaging theory. More precisely,we prove that the perturbations of the period annulus of the center located at the origin of a cubic polynomial differential system,by arbitrary quartic and quintic polynomial differential systems,there respectively exist at least 8 and 9 limit cycles bifurcating from the periodic orbits of the period annu...     

Cohomology of Hom-Lie superalgebras and q-deformed Witt superalgebra

Hom-Lie algebra (superalgebra) structure appeared naturally in q-deformations, based on σ-derivations of Witt and Virasoro algebras (superalgebras). They are a twisted version of Lie algebras (superalgebras), obtained by deforming the Jacobi identity by a homomorphism. In this paper, we discuss the concept of α ^k -derivation, a representation theory, and provide a cohomology complex of Hom-Lie superalgebras. Moreover, we study central extensions. As application, we compute derivations and the second cohomology group of a twisted osp(1, 2) superalgebra and q-deformed Witt superalgebra.     

Utilization of 2-ylidene-4-thiazolidinones in the synthesis of heterocyclic compounds. Part I: Synthesis of pyrazoles

2-Ylidene and 2,5-diylidene-4-thiazolidinones 2a–d were synthesized and converted into pyrazole derivatives 4a–d by reaction with hydrazine hydrate. A mechanism of this novel conversion is suggested.     

Cohomology of q-Deformed Witt–Virasoro Superalgebras of the Hom Type

Ukrainian Mathematical Journal - We study Virasoro-type extensions of the q-deformed Witt Hom–Lie superalgebras. Moreover, we provide the cohomology of q-deformed Witt–Virasoro...