粗糙子群和粗糙子环

文[1]研究了半群中的理想,首次提出了粗半群和粗理想的概念.本文继续研究了群中的粗糙子群和粗正规子群.同时,在环中引入了粗子环的概念.最后,研究了粗糙集的同态问题.     

平均非扩张映射的公共不动点性质

研究了平均非扩张型映射T:‖Tx-Ty‖≤a‖x-y‖+b‖x-Tx‖+c‖x-Ty‖,(x,y∈K,a,b,c≥0,a+b+c≤1)的公共不动点的存在性和唯一性.得到平均非扩张型映射T1和T2满足T1T2=T2T1,则T1T2存在唯一的不动点,并且T1和T2存在唯一的公共不动点.本文结果是近期相关文献结果的推广.     

A theoretical study of antioxidant activity of some Schiff bases derived from biologically important phenolic aldehydes and phenylenediamines

Because of their numerous biological as well as industrial importance, the study of Schiff bases is an emerging field for the researchers, in recent time. In this study, we have designed some Schiff bases derived from biologically important precursors. The antioxidant activities of the designed compounds are thoroughly studied theoretically using density functional theory taking various parameters like bond dissociation enthalpy, ionization enthalpy, proton dissociation enthalpy, and electron transfer enthalpy followed by the study of effects of solvent, spin density, and molecular orbital on antioxidant activity of the compounds. The comparison of antioxidant activity of the compounds with that of phenol and their parent aldehydes reveals the superior antioxidant activity of the designed compounds. This study contributes towards the information of an important bridge between bioorganic and computational chemistry.     

Solution for One-Dimensional Quantum Oscillator with Time-Dependent Frequency and Mass

Based on the generalized linear quantum transformation theory, we present a normal ordering evolution operator for onedimensional quant urn oscillator with time-dependent frequency and mass, then give the exact expression of the evolution matrix elements, wave function and expectation value of arbitrary observable.     

Mössbauer study of the vibrational anisotropy and of the light-induced population of metastable states in single-crystalline guanidinium nitroprusside

M?ssbauer studies were performed on single crystals of guanidinium nitroprusside with different orientations of their principal crystallographic axes (a, b, c) with respect to the incident radiation. The markedly anisotropic Lamb-M?ssbauer factor f _LM , i.e. f _LM ^(a) = 0.118(8), f _LM ^(b) = 0.174(8), f _LM ^(c) = 0.202(8) is in contrast to that of nitroprussides with inorganic anions. The observed anisotropy is ascribed to the anisotropic vibrational mean-square displacement of the nitroprusside anions as a whole which is due to the specific packing of both, anions and cations, as well as the very weak chemical bonding between the ions, typical only for guanidinium nitroprusside. The vibrational anisotropy of iron atoms in barium nitroprusside that has been observed by X-ray structural investigations has a different origin and therefore does not result in an anisotropic Lamb-M?ssbauer factor. We have also investigated metastable states in guanidinium nitroprusside that have been populated by means of incoherent irradiation from light-emitting diodes. With a specific orientation of the guanidinium nitroprusside single crystal a population of the metastable states up to 26% could be achieved. Populations of comparable size on lithium, sodium and potassium nitroprussides have only been reached using coherent laser irradiation. Received 15 December 1998 and Received in final form 3 March 1999     

Asymmetric Reactions involving Lewis Base Catalyst Tethered Dearomatized Intermediates

Numerous protocols have been developed for the functionalization of aromatic substances. Among them, the strategy by which aromatic substrates are activated in situ to generate dearomatized intermediates is highly efficient but challenging, especially in the field of asymmetric catalysis. In this Concept article, the application of some well-established chiral Lewis base catalysis, including primary/secondary amines and N-heterocyclic carbenes, that can covalently form catalyst-tethered dearomatized ortho/para-quinodimethane species with diverse heteroaryl and aryl carbonyl substrates is summarized in a number of asymmetric cycloaddition and addition reactions with diverse reagents generally having electrophilic properties. As a result, a variety of enantioenriched aromatic products with higher molecular complexity are constructed effectively through a rearomatization process.     

Octaboraneyl Complexes of Nickel: Monomers for Redox-Active Coordination Polymers

Herein, we establish the preparation, characterization, and reactivity of a new diphosphine ligand, 1,2-bis(di(3-dicyclohexylboraneyl)propylphosphino)ethane (P₂B^Cy₄), a scaffold that contains four pendant boranes. An entryway into the coordination chemistry of P₂B^Cy₄ is established by using nickel, providing the octaboraneyl complex [Ni(P₂B^Cy₄)₂]—this species contains a boron-rich secondary coordination sphere that reacts readily with Lewis bases. In the case of 4,4′-bipyridine, an air-sensitive coordination polymer is obtained. Characterization of this material by solid-state NMR and EPR spectroscopy reveals the presence of a charge-transfer polymer, which forms as a function of intramolecular Ni→4,4′-bpy electron transfer (ET), providing an array of oxidized nickel sites and reduced 4,4′-bpy radical anion sites. Notably, the related intermolecular reaction between the model fragments [Ni(dnppe)₂] (dnppe=1,2-bis(di-n-propylphosphino)ethane) and a bis(boraneyl)-protected 4,4′-bpy, provides no ET. Overall, the P₂B^Cy₄ fragment provides a unique opportunity for Lewis base activation, in one case allowing for the facile construction of monomers for incorporation into redox-active macromolecules.     

A Mechanistically and Operationally Simple Route to Metal–N-Heterocyclic Carbene (NHC) Complexes

We have been puzzled by the involvement of weak organic and inorganic bases in the synthesis of metal–N-heterocyclic carbene (NHC) complexes. Such bases are insufficiently strong to permit the presumed required deprotonation of the azolium salt (the carbene precursor) prior to metal binding. Experimental and computational studies provide support for a base-assisted concerted process that does not require free NHC formation. The synthetic protocol was found applicable to a number of transition-metal- and main-group-centered NHC compounds and could become the synthetic route of choice to form M–NHC bonds.     

Are Hetero-metallapentalenes Aromatic or Not? A DFT Investigation

Aromaticity is one of the most basic concepts in organic chemistry. The planar Möbius aromatic metallapentalynes and metallapentalenes have attracted considerable attention in the past few years. However, the aromaticity of metallapentalenes containing heteroatoms (such as B, N, and O), termed as hetero-metallapentalenes, is rarely studied. Herein, the stability and aromaticity of a series of hetero-metallapentalenes are theoretically investigated. The results reveal lower aromaticity in metallaborapentalene, comparable aromaticity in metallazapentalene, and nonaromaticity in metalloxapentalene relative to that of metallapentalene. Moreover, the effect of Lewis bases on the aromaticity and stability of metallaborapentalene is discussed. These results provide useful information for experimental chemists to realize more hetero-metallapentalenes.     

New construction of special Lagrangian submanifolds in T^＊R^n equipped with the standard metric

A class of twisted special Lagrangian submanifolds in T~*R~n and a kind of austere submanifold from conormal bundle of minimal surface of R~3 are constructed.