On the Convergence of a Weak Greedy Algorithm for the Multivariate Haar Basis

We define a family of weak thresholding greedy algorithms for the multivariate Haar basis for L ₁[0,1] ^d (d≥1). We prove convergence and uniform boundedness of the weak greedy approximants for all f∈L ₁[0,1] ^d .     

Inscribing a regular m-gon in a regular n-gon

We find necessary and sufficient conditions on m and n for inscribing a regular m-gon in a regular n-gon.     

Recent developments in the coordination chemistry of technetium

TMC Literature Highlights-23;Transition Met. Chem.,15, 330 (1990).     

Isolation and Crystal Structure of Novel by-products Observed During the Formation of bis(thiosemicarbazones)

During the condensation of 4-methyl-4-phenyl-3-thiosemicarbazide (3) with 2,3-butanedione an unexpected by-product, 8a-methyl-6,8a-dihydro-8-methyl-2-[N-methyl-N-phenylamino]-5H-1,3,4-thiadiazolo[3,2-d][1,2,4]triazine-5-thione, (5) was obtained in addition to the desired bis(thiosemicarbazone) (4). An X-ray crystal structure was obtained and is presented together with a proposed mechanism for its formation. A brief investigation of the coordination chemistry of bicycle (5) was carried out. The formation of cyclic compounds during the synthesis of analogues with extended backbones is also described.     

Designing Zn(II) and Cu(II) derivatives as probes for in vitro fluorescence imaging

New M(II) bis(thiosemicarbazonato) complexes (M = Ni(II), Cu(II) and Zn(II)) featuring allyl groups at the exocyclic nitrogens have been synthesised. The complexes were characterised in solution by spectroscopic methods and their solid state structures determined by single crystal X-ray diffraction using synchrotron radiation. The Zn(II) complex was found to be intrinsically fluorescent and soluble in biocompatible media. The uptake of this Zn(II) complex in HeLa, MCF-7 and IGROV cancer cells was monitored by fluorescence microscopies (epi- and confocal fluorescence imaging). The radiolabelling to (64)Cu(II) bis(thiosemicarbazonato) complex was performed cleanly by transmetallation from the corresponding Zn(II) species using (64)Cu(OAc)(2).     

Gold complexes with potentially tri- and tetradentate phosphinothiolate ligands

Reactions of [Au(PPh3)Cl], (Bu4N)[AuCl4] and the organometallic gold complex [Au(damp-C1,N)Cl2] (damp- = 2-(N,N-dimethylaminomethyl)phenyl) with the potentially tri- and tetradentate proligands PhP(C6H3-SH-2-R-3)2 (H2L1a, R = SiMe3; H2L1b, R = H) and P(C6H4-SH-2)3 (H3L2) result in the formation of mono- or dinuclear gold complexes depending on the precursor used. Monomeric complexes of the type [AuL1Cl] are formed upon the reaction with [Au(damp-C1,N)Cl2], but small amounts of dinuclear [AuL1]2 complexes with gold in two different oxidation states, +1 and +3, have been isolated as side-products. The dinuclear compounds are obtained in better yields from [AuCl4]-. A dinuclear complex having two Au(III) centers can be isolated from the reaction of [Au(PPh3)Cl] with H3L2, whereas from the reaction with H2L1b the mononuclear [Au(Ph3P)HL1b] is obtained, which contains a three-coordinate gold atom. Comparatively short gold-gold distances have been found in the dinuclear complexes (2.978(2) and 3.434(1) A). They are indicative of weak gold-gold interactions, which is unusual for gold(III).