On the reactions of methyl radicals with nitrilotris(methylenephosphonic-acid) complexes in aqueous solutions

Abstract

The reactions of methyl radicals with M^II-(ntp)(H₂O)₂ complexes were studied. The formation of an unstable intermediate (ntp)(H₂O)M^III-CH₃ is observed. This reaction is an equilibrium process, i.e. the M^III-C bond decomposes via homolysis. The (ntp)(H₂O)M^III-CH₃ complexes isomerize to a more stable form. The results compared to those obtained in analogous reactions of the M^II-(nta)(H₂O)₂ complexes were shown to be similar with one exception – for the nta complexes no isomerization process is observed.     

Alkylation of Allyl/Alkenyl Sulfones by Deoxygenation of Alkoxyl Radicals

A challenging deoxygenation of alkoxyl radicals from readily accessible alcohol derivatives was developed, affording facile synthesis of functionalized alkenes with good functional group tolerance under mild reaction conditions. Because alkoxyl radicals can easily undergo β-fragmentations or hydrogen abstractions, this new strategy for deoxygenation of alkoxyl radicals is highly valuable. Moreover, mechanistic studies revealed that the electron-neutral phosphine acts as the deoxygenation reagent.     

Rapid Interception of CnF2n+1(O)SO. Radical with Copper-Based Carbene: A Novel Access to Perfluoroalkanesulfinate Ester

In this communication, an unprecedented interception of C_nF_2n+1(O)SO^. radical with a copper-based carbene has been established. Distinguished by wide substrate scopes and mild reaction conditions, this novel radical–carbene coupling reaction (RCC reaction) provides a fundamentally different and mechanistically interesting strategy for the synthesis of perfluoroalkanesulfinate esters.     

Ideal optomechanically induced transparency generation in a cavity optoelectromechanical system

The ideal optomechanically induced transparency effects of an output probe field are investigated in a cavity optoelectromechanical system, which is composed of an optical cavity, a charged mechanical resonator, and a charged object.Although the charged mechanical resonator damping rate is nonzero, the ideal optomechanically induced transparency can still appear due to the non-rotating wave approximation effect in the system. The location of optomechanically induced transparency dip can be controlled via the Coulomb coupling strength. In addition, we find that both the transparency window width and the maximum dispersion curve slope are closely related to the optical cavity decay rate.     

On the derivation of the entropy of ideal quantum gases confined in a three-dimensional harmonic potential

In this work,the entropy functions of ideal quantum gases in a three-dimensional harmonic trap are analytically calculated using temperature as an explicit variable.Afterward,the applicability of the analytical formulas is validated by comparison with the numerical calculation.The results illustrate that the obtained functions could be applied for the whole temperature regime with a maximum relative deviation of less than 7.5%in the vicinity of the critical temperature Tcin the case of Bose gases.Meanwhile,for Fermi gases,although the analytical formula fits well at very low-and high-temperature regimes,it cannot be applied at temperature in the range[0.3-0.5]T_F,where T_F is the Fermi temperature.In addition,the consistency between our formulas and classical ones at significantly high temperatures is also discussed.     

On idempotents of a class of commutative rings

Abstract

In the present work, a procedure for determining idempotents of a commutative ring having a sequence of ideals with certain properties is presented. As an application of this procedure, idempotent elements of various commutative rings are determined. Several examples are included illustrating the main results.     

Rings whose singular ideals are nil

Abstract

It is well known that when a ring R satisfies ACC on right annihilators of elements, then the right singular ideal of R is nil, in this case, we say R is right nil-singular. Many classes of rings whose singular ideals are nil, but do not satisfy the ACC on right annihilators, are presented and the behavior of them is investigated with respect to various constructions, in particular skew polynomial rings and triangular matrix rings. The class of right nil-singular rings contains π-regular rings and is closed under direct sums. Examples are provided to explain and delimit our results.