New Homoleptic Rare‐Earth Metal Complexes Comprising the Unsymmetrically Substituted Amidinate Ligand [MeC(NEt)(NtBu)]–

New homoleptic complexes of selected rare‐earth elements containing the unsymmetrically substituted amidinate ligand [MeC(NEt)(NtBu)]^– [= (L)^–] were synthesized and fully characterized. Treatment of in situ‐prepared Li(L) ( 1 ) with anhydrous lanthanide(III) chlorides, LnCl₃ (Ln = Sc, La, Ce, Ho), afforded three different types of amidinate complexes depending on the ionic radius of the central metal atom. The large La³⁺ formed the octa‐coordinate DME solvate La(L)₃(DME) ( 2 ). Using Ce³⁺, the octa‐coordinate “ate” complex Li(THF)[Ce(L)₄] ( 3 ) was formed. Depending on the crystallization conditions, compound 3 could be crystallized in two modifications differing in the coordination environment around Li. In the case of the smaller Sc³⁺ and Ho³⁺ ions, six‐coordinate homoleptic Sc(L)₃ ( 4 ) and Ho(L)₃ ( 5 ) were isolated. The title compounds were fully characterized by spectroscopic and analytical methods as well as single‐crystal X‐ray diffraction. With Ln = La and Ce, several by‐products incorporating lithium, chlorine and/or oxygen were also isolated and structurally characterized.     

Synthesis of 5-Alkyl- and 5-Phenylamino-Substituted Azothiazole Dyes with Solvatochromic and DNA-Binding Properties

A series of new 5-mono- and 5,5′-bisamino-substituted azothiazole derivatives was synthesized from the readily available diethyl azothiazole-4,4′-dicarboxylate. This reaction most likely comprises an initial Michael-type addition by the respective primary alkyl and aromatic amines at the carbon atom C5 of the substrate. Subsequently, the resulting intermediates are readily oxidized by molecular oxygen to afford the amino-substituted azothiazole derivatives. The latter exhibit remarkably red-shifted absorption bands (λ_abs=507–661 nm) with high molar extinction coefficients and show a strong positive solvatochromism. As revealed by spectrometric titrations and circular and linear dichroism studies, the water-soluble, bis-(dimethylaminopropylamino)-substituted azo dye associates with duplex DNA by formation of aggregates along the phosphate backbone at high ligand–DNA ratios (LDR) and by intercalation at low LDR, which also leads to a significant increase of the otherwise low emission intensity at 671 nm.     

Effect of hydrothermal aging on NOx reduction performance for Sb–V–CeO2/TiO2 catalyst

Research on Chemical Intermediates - Herein, we investigated the NOx reduction performance of Sb–V–CeO2/TiO2 (SbVCT) catalyst subjected to hydrothermal aging, where 6 vol% of H2O was...     

Quadratic Integrals and Factorization of Linear Operators

We consider operators on the matrix-valued disc algebra. Weshow that any bounded linear operator to a Banach space X of cotype 2 induces a boundedoperator GX defined on some weighted Bergman space G on theunit disc. We give sufficient conditions on the weight forthe formal inclusion to be 2–C*-summing. Decompositions of T with respect to operator-valuedmeasures are obtained.     

Tractable Partially Ordered Sets Derived from Root Systems and Biased Graphs

We study new posets Q obtained by removing from a geometric lattice L ofa biased graph certain flats indexed by a simplicial complex . (One example of L is the lattice of flats of thevector matroid of a root system B _n .) We study the structureand compute the characteristic polynomial of Q. With certainchoices of L and , including ones for which Q is alattice interpolating between those of B _n and D _n , we observe curious relationships among the roots of thecharacteristic polynomials of Q, L, and .     

A -deformation of a trivial symmetric group action

Let be the arrangement of hyperplanes consisting of the reflecting hyperplanes for the root system . Let be the Varchenko matrix for this arrangement with all hyperplane parameters equal to . We show that is the matrix with rows and columns indexed by permutations with entry equal to where is the number of inversions of . Equivalently is the matrix for left multiplication on by

Clearly commutes with the right-regular action of on . A general theorem of Varchenko applied in this special case shows that is singular exactly when is a root of for some between and . In this paper we prove two results which partially solve the problem (originally posed by Varchenko) of describing the -module structure of the nullspace of in the case that is singular. Our first result is that

in the case that where Lie denotes the multilinear part of the free Lie algebra with generators. Our second result gives an elegant formula for the determinant of restricted to the virtual -module with characteristic the power sum symmetric function .