Duality and multiplication operators

We describe a space of functions contained inxxLx (D)C(D G) but not necessarily inU. We give a representation of these functions as bounded multiplication operators on the Bergman spacexxLx _a ² and identify the subspace consisting of functions which induce compact multiplication operators. We also describe a newC ^*-subalgebra ofxxLx (D) which we conjecture to be a proper super-set ofU.Most of this research was done while the second author was visiting Cleveland State University. He would like to thank the Mathematics Department for its hospitality. He would also like to thank the NNSFC for partial support.     

Synthesis of bridgedhead azolo[3,2-a]pyrimidines and imidazo[2,1-b]thiazines through ring transformation of 2H-pyran-2-ones

Suitably functionalized 3-carbomethoxy/cyano-2H-pyran-2-ones are excellent synthons for the synthesis of arenes and heteroarenes of therapeutic importance. The compounds 6-aryl-3-cyano-4-methylsulfanyl-2H-pyran-2-ones have been transformed into bridgedhead azolopyrimidines and imidazothiazines through thermal and base-induced ring transformation reactions with aminoazoles and imidazolidin-2-thiones, respectively.     

Solution-processed electrochemical synthesis of ZnFe2O4 photoanode for photoelectrochemical water splitting

Journal of Solid State Electrochemistry - Herein, we report the synthesis of ZnO nanorod films onto FTO (fluorine-doped tin oxide) substrates using the solution-processed electrodeposition method....     

Concise Enantioselective Synthesis of Naturally Active (S)-3-Hydroxypiperidine

A short and efficient enantioselective synthesis of natural product (S)-3-hydroxypiperidine has been achieved starting from commercially available raw materials employing two catalytic routes: (i) cocatalyzed hydrolytic kinetic resolution (HKR) of racemic methyl-3-(oxiran-2-yl)propanoate; (ii) proline-catalyzed α-aminooxylation followed by Horner–Wardsworth–Emmons olefination in high enantiomeric purity (97% ee) and high overall yield (38%).     

Synthesis of Metal‐Free Phthalocyanines in Functionalized Ammonium Ionic Liquids

A convenient, fast, efficient, and ecofriendly synthesis of metal‐free phthalocyanines from various substituted phthalonitriles in different hydroxyalkylammonium ionic liquids in the presence of 1,8‐diazabicyclo‐[5,4,0]‐undec‐7‐ene (DBU) is reported in moderate yields. The effect of concentration of DBU and temperature on the synthesis of phthalocyanine in N‐(2‐hydroxyethyl)‐N,N‐dimethylbutylammonium bromide ionic liquid has been examined, and the ionic liquid has been recovered and reused conveniently.     

Optoelectronic and biological quantification of semi-conducting,crimson europium chelates with fluorinated β-keto acid and N-donor ancillary ligands

Research on Chemical Intermediates - Five luminescent ternary and one binary Europium(III) complexes were synthesised with β-keto acid as primary ligand and neocuproine(neo),...     

Michael addition of ethyl anthranilate and phenyl monothioanthranilate to acetylenic esters: experimental and theoretical results

Structural Chemistry - The reaction of ethyl anthranilate with DMAD and with methyl propiolate in dichloromethane in the presence of ethylaluminium dichloride as catalyst at room temperature gives...     

Ag NPs decked GO composite as a competent and reusable catalyst for ‘ON WATER’ chemoselective synthesis of pyrano[2,3-c:6,5-c′]dipyrazol]-2-ones

We have synthesized and characterized Ag NPs decked GO composite and studied its role as reusable catalyst for the ‘ON WATER’ chemoselective synthesis of pyranodipyrazolones via the reaction of different carbonyl compounds with 3-methyl-1-phenyl-1H-pyrazol-5(4H)-one. This method illustrates significant selectivity for pyranodipyrazolones over arylmethylene bispyrazolols and arylmethylenepyrazolones. Synergistic effect of heterogenic nature of water with reactants and Ag NPs/GO had profuse outcome on reaction as indicated by high TOF (18.03 × 10^?5 mol g^?1 min^?1). Furthermore, catalyst was recycled for 7-times without significant loss of activity.