Lp空间Kantorovich-Vertesi算子逼近的Jackson型估计

考虑了Kantorovich-Vertesi有理插值型算子L^*n,s（f,X,x）对L^p[-1,1]（1≤p≤∞）空间函数逼近的Jackson型估计。并获得了如下逼近阶：‖L^*n,s(f,X,x)-f(x)‖L^p[-1,1]≤Cp,sw(f,1/n 2)L^p[-1,1] （s＞2）。     

Charge-transfer spectra of structurally characterized mixed-valence thiolate-bridged Cu(I)/Cu(II) cluster complexes

A series of Cu(II) and Cu(I)/Cu(II) complexes containing the cis-N(amine)(2)S(thiolate)(2) copper complex rac-2 has been synthesized to provide a basis for understanding the charge-transfer spectra of mixed-valence thiolate-bridged Cu(I)/Cu(II) complexes. In combination with Cu(Me(2)-13-N(4)ane), rac-2 yields a monobridged dinuclear homovalent adduct, rac-5, while reaction with CuCl yields the mixed-valance pentanuclear complex rac-6. In the presence of Cu(II)(acac)(2), chiral R,R-1 reacts to form a mixed-valence pentanuclear cation R,R-7. rac-6 exhibits a relatively short Cu(I). Cu(II) contact [2.8231(9) A] and associated structural features that suggest the presence of a weak Cu(I).Cu(II) interaction in a valence-trapped system. Additional structural features in rac-6 and R,R-7 include singly and doubly bridging thiolates, three- and four-coordinated Cu(I) ions, and varying Cu(I) ligand sets. These features extend the types and complexities of electronic absorptions significantly. Spectra of rac-6 and R,R-7 exhibit multiple overlapping absorptions over the entire visible and ultraviolet spectral regions studied, consonant with these observations. Trends resulting from variations in structure type and oxidation state permit a first approach toward developing a detailed assignment of the individual ligand Rydberg, LF, LMCT, MLCT, and possible MMCT absorptions in these complexes.     

Structural and spectroscopic features of mono- and binuclear nickel(II) complexes with tetradentate N(amine)2S(thiolate)2 ligation

Three complexes containing Ni(II)N(amine)2S(thiolate)2 units have been prepared and characterized. Both (R,R)-N,N'-bis(1-carboxy-2-mercaptoethyl)-1,2-diaminoethane [(R,R)-1] and N,N'-bis(2-methyl-2-mercaptoprop-1-yl)-1,3-diamino-2,2-dimethylpropane (4) act as tetradentate S-N-N-S ligands to form complexes Ni((R,R)-1) and Ni4 with nearly planar cis-NiN2S2 units. The N-Ni-N and S-Ni-S angles differ significantly in the two complexes yet are very nearly supplementary. The 1,3-disubstituted cyclohexane species rac-N,N'-bis(2-mercapto-2-methylprop-1-yl)-1,3-cyclohexanediamine (6) behaves as a bis(bidentate-N,S) ligand to form an unexpectedly intense-blue dinickel complex (1S,3R,1'S,3'R)-7, which contains two trans-NiN2S2 units bridged by 1,3-disubstituted cyclohexane groups. The coordination geometry in (1S,3R,1'S,3'R)-7 is distorted 15 degrees toward tetrahedral, most likely as a result of steric crowding, suggested by several short contacts between the NiS2 units and both the cyclohexyl and gem-dimethyl groups of the N,S-chelate rings. The complexes exhibit rich UV-vis spectra, whose deconvoluted bands are now fully assigned, from low to high energy, as ligand field (LF), pi(S) --> Ni(II) ligand-to-metal charge transfer (LMCT), sigma(S) --> Ni(II) LMCT, sigma(N) --> Ni(II) LMCT, localized S, and S,N Rydberg transitions. The unusually intense LF absorptions shown by (1S,3R,1'S,3'R)-7 are thought to result from relaxation of the Laporte restriction arising from the 15 degrees tetrahedral twist.     

Copper(II) and nickel(II) complexes of binucleating macrocyclic bis(disulfide)tetramine ligands

Novel macrocyclic bis(disulfide)tetramine ligands and several Cu(II) and Ni(II) complexes of them with additional ligands have been synthesized by the oxidative coupling of linear tetradentate N2S2 tetramines with iodine. Facile demetalation of the Ni(II) oxidation products affords the free 20-membered macrocycles meso-9 and rac-9 and the 22-membered macrocycle 16, all of which are potentially octadentate N4S4 ligands. X-ray structure analyses reveal distinctly different conformations for the two isomers of 9; meso-9 shows a stepped conformation in profile with the disulfide groups corresponding to the rise of the step, whereas rac-9 exhibits a V conformation with the disulfide groups near the vertex of the V. No metal complexes of rac-9 have been isolated. Crystallographic studies of three Cu(II) complexes reveal that depending upon the size of the macrocyclic ligand and the nature of the additional ligands (I-, NCO-, and CH3CN), the Cu(II) coordination geometry shows considerable variation (plasticity), with substantial changes in the Cu(II)-disulfide bonding. Thus, a diiodide salt contains six-coordinate Cu(II) to which all four bridging disulfide sulfur atoms form strong equatorial bonds. In contrast, isocyanato complexes of the 20- and 22-membered macrocycles exhibit trigonal-bipyramidal Cu(II) and distorted cis-octahedral Cu(II) geometries, respectively, having only one and no short equatorially bound sulfur atoms. The coordination geometry of the latter complex can also be described as four-coordinate seesaw with two semicoordinated S(disulfide) ligands. Disulfide-->Cu(II) ligand-to-metal charge transfer absorptions of both isocyanato-containing Cu(II) species appear too weak to observe, probably because of poor overlap of the sulfur orbitals with the Cu(II) d-vacancy. The dual disulfide-bridged Ni(II) units of the crystallographically characterized octahedral Ni(II) complex of meso-9 with axial iodide and acetonitrile ligands promote substantial antiferromagnetic coupling (J = -13.0(2) cm-1).