scholarly journals Commentary to: Generalized derivations of Lie triple systems

2016 ◽  
Vol 14 (1) ◽  
pp. 543-544 ◽  
Author(s):  
Ivan Kaygorodov ◽  
Yury Popov
Keyword(s):  
Generalized Derivations ◽  
Triple Systems

scholarly journals Generalized derivations of Lie triple systems

2016 ◽  
Vol 14 (1) ◽  
pp. 260-271 ◽  
Author(s):  
Jia Zhou ◽  
Liangyun Chen ◽  
Yao Ma
Keyword(s):  
Triple System ◽  
Generalized Derivation ◽  
Generalized Derivations ◽  
Lie Triple System ◽  
Triple Systems ◽  
Basic Properties ◽  
Derivation Algebra ◽  
The Relationship

AbstractIn this paper, we present some basic properties concerning the derivation algebra Der (T), the quasiderivation algebra QDer (T) and the generalized derivation algebra GDer (T) of a Lie triple system T, with the relationship Der (T) ⊆ QDer (T) ⊆ GDer (T) ⊆ End (T). Furthermore, we completely determine those Lie triple systems T with condition QDer (T) = End (T). We also show that the quasiderivations of T can be embedded as derivations in a larger Lie triple system.

Catalytic Activity of Binary and Triple Systems Based on Redox Inactive Metal Compound, LiSt and Additives of Monodentate Ligands-Modifiers: DMF, HMPA and PhOH, in Selective Ethylbenzene Oxidation with Dioxygen

2016 ◽  
Vol 10 (3) ◽  
pp. 259-270
Author(s):  
Ludmila Matienko ◽  
◽  
Larisa Mosolova ◽  
Vladimir Binyukov ◽  
Gennady Zaikov ◽  
...  
Keyword(s):  
Catalytic Activity ◽  
Triple System ◽  
Metal Compound ◽  
Ethylbenzene Oxidation ◽  
Catalytic Systems ◽  
Triple Systems ◽  
Lithium Compound ◽  
Mechanism Of Catalysis ◽  
Monodentate Ligands

Mechanism of catalysis with binary and triple catalytic systems based on redox inactive metal (lithium) compound {LiSt+L2} and {LiSt+L2+PhOH} (L2=DMF or HMPA), in the selective ethylbenzene oxidation by dioxygen into -phenylethyl hydroperoxide is researched. The results are compared with catalysis by nickel-lithium triple system {NiII(acac)2+LiSt+PhOH} in selective ethylbenzene oxidation to PEH. The role of H-bonding in mechanism of catalysis is discussed. The possibility of the stable supramolecular nanostructures formation on the basis of triple systems, {LiSt+L2+PhOH}, due to intermolecular H-bonds, is researched with the AFM method.

scholarly journals Formation rate of LB-1-like systems through dynamical interactions

2020 ◽  
Vol 72 (3) ◽  
Author(s):  
Ataru Tanikawa ◽  
Tomoya Kinugawa ◽  
Jun Kumamoto ◽  
Michiko S Fujii
Keyword(s):  
Open Cluster ◽  
Formation Rate ◽  
Open Clusters ◽  
Type Star ◽  
Dynamical Mechanism ◽  
Milky Way Galaxy ◽  
Triple Systems ◽  
Stellar Collisions ◽  
Solar Metallicity ◽  
Helium Star

Abstract We estimate formation rates of LB-1-like systems through dynamical interactions in the framework of the theory of stellar evolution before the discovery of the LB-1 system. The LB-1 system contains a ∼70 ${M_{\odot}}$ black hole (BH), a so-called pair instability (PI) gap BH, and a B-type star with solar metallicity, and has nearly zero eccentricity. The most efficient formation mechanism is as follows. In an open cluster, a naked helium star (with ∼20 ${M_{\odot}}$) collides with a heavy main sequence star (with ∼50 ${M_{\odot}}$) which has a B-type companion. The collision results in a binary consisting of the collision product and the B-type star with a high eccentricity. The binary can be circularized through the dynamical tide with radiative damping of the collision product envelope. Finally, the collision product collapses to a PI-gap BH, avoiding pulsational pair instability and pair instability supernovae because its He core is as massive as the pre-colliding naked He star. We find that the number of LB-1-like systems in the Milky Way galaxy is ∼0.01(ρoc/104 ${M_{\odot}}$ pc−3), where ρoc is the initial mass densities of open clusters. If we take into account LB-1-like systems with O-type companion stars, the number increases to ∼0.03(ρoc/104 ${M_{\odot}}$ pc−3). This mechanism can form LB-1-like systems at least ten times more efficiently than the other mechanisms: captures of B-type stars by PI-gap BHs, stellar collisions between other types of stars, and stellar mergers in hierarchical triple systems. We conclude that no dynamical mechanism can explain the presence of the LB-1 system.

Sign in / Sign up

Export Citation Format

Share Document