Tensor Calculus in the Free Lie Algebra

In this Letter we characterize Lie elements and the elements of the kernel of the Lie bracketing from right to left mapping, using tensor calculus tools.     

A Homotopy in the Usual Cochain Complex of Free Lie Algebras

In this Letter, we construct a natural contracting homotopy in the usual cochain complex of free Lie algebras. As a consequence, we prove that the triple cohomology of Lie algebras coincides with a slightly different form of the standard cohomology theory.     

Mild olefin formation via bio-inspired vitamin B12 photocatalysis

Dehydrohalogenation, or elimination of hydrogen-halide equivalents, remains one of the simplest methods for the installation of the biologically-important olefin functionality. However, this transformation often requires harsh, strongly-basic conditions, rare noble metals, or both, limiting its applicability in the synthesis of complex molecules. Nature has pursued a complementary approach in the novel vitamin B₁₂-dependent photoreceptor CarH, where photolysis of a cobalt–carbon bond leads to selective olefin formation under mild, physiologically-relevant conditions. Herein we report a light-driven B₁₂-based catalytic system that leverages this reactivity to convert alkyl electrophiles to olefins under incredibly mild conditions using only earth abundant elements. Further, this process exhibits a high level of regioselectivity, producing terminal olefins in moderate to excellent yield and exceptional selectivity. Finally, we are able to access a hitherto-unknown transformation, remote elimination, using two cobalt catalysts in tandem to produce subterminal olefins with excellent regioselectivity. Together, we show vitamin B₁₂ to be a powerful platform for developing mild olefin-forming reactions.

Terminal or subterminal olefins can be selectively formed from alkyl electrophiles via bio-inspired vitamin B₁₂ photocatalysis.     

On complementary decompositions of the complete graph

We consider decompositionsK _n H, whereH is eitherP ₃ (the path with 3 edges) or the complete bipartite graphK _{1, 3}, with the property that upon taking the complement of each graph in the decomposition one obtains a new decompositionK _n H ^c .Research supported in part by an NSERC postgraduate Scholarship.     

A family of hexanuclear Mn(III) single-molecule magnets

In an attempt to employ salicylic acid (HOsalH), 2,6-dihydroxy benzoic acid {(HO)₂PhCO₂H}, and naphthalene-1,8-dicarboxylic acid {1,8-naph(CO₂H)₂} in Mn(III) salicylaldoximate chemistry as a means to alter the structural identity of the hexanucluear clusters usually obtained from this reaction system, we have isolated a family of hexanuclear Mn(III) complexes based on salicyladloxime (saoH₂) and 2-hydroxy-1-naphthaldehyde oxime (naphthsaoH₂). Five hexanuclear clusters, [Mn₆O₂(sao)₆(HOsal)₂(EtOH)₄]·EtOH (1·EtOH), [Mn₆O₂(sao)₆{1,8-naph(CO₂Me)(CO₂)}₂(MeOH)₆]·3MeOH (2·3MeOH), [Mn₆O₂(naphthsao)₆{1,8-naph(CO₂Et)(CO₂)}₂(EtOH)₆] (3·2MeOH), [Mn₆O₂(naphthsao)₆(MeCO₂)₂(EtOH)₄]·2H₂O (4·2H₂O), and [Mn₆O₂(naphthsao)₆{(HO)₂PhCO₂}₂(EtOH)₄]·4EtOH (5·4EtOH), have been synthesized and characterized by single-crystal X-ray crystallography. The magnetic properties of 3, 4, and 5 are discussed.     

Formal synthesis of the piperidine alkaloid (±)-prosophylline using polymer-supported dihydro-2H-pyridin-3-one

The use of polymer-supported 2,6-disubstituted-dihydro-2H-pyridin-3-one, as the ‘polymorphic’ core molecule for the formal synthesis of the piperidine alkaloid (±)-prosophylline is presented.     

Microwave Assisted Synthesis of Sodium Sulfonates Precursors of Sulfonyl Chlorides and Fluorides

We describe the use of a microwave reaction for the conversion of various bromides to sodium sulfonates that have been further elaborated to sulfonyl chlorides. This new approach leads to much improved yields and shorter reaction times. Representative sulfonyl chlorides serve as precursors for the respective sulfonyl fluorides that are potent inhibitors of the fatty acid amide hydrolase.     

Surface plasmon resonance as a tool for the estimation of adsorbed polymeric layer characteristics: Theoretical considerations and experiment

The potential application of Surface Plasmon Resonance (SPR) spectroscopy in evaluating the thickness and volume fraction of adsorbed macromolecular layers is discussed in this work. The sensitivity of SPR spectroscopy to different layer concentration and to the layer extension normal to the surface (thickness) is theoretically illustrated. A new approach for the interpretation of SPR data is presented, which is applicable whenever the functional form of the density profile is known. The use of the proposed procedure for the fitting of experimental results from PS‐PEO brush self‐assembly on alumina surface has allowed the determination of the layer parameters, which have been found to be in accordance with theoretical mean‐field and scaling predictions, being also in good agreement with previous results from neutron reflectivity experiments. Furthermore, it has been confirmed that the dependence of the brush layer thickness d on the molecular weight M_w obeys the scaling law d ～ M_w^0.63. Since surface plasmon measurements can be acquired quite fast, it is suggested that under the present analysis scheme, the technique may be implemented to probe the average conformational properties of adsorbed macromolecular layers during their formation or under external stimuli. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 2060–2070, 2007     

Amphiphilic diblock copolymer‐based multiagent photonic sensing scheme

Efficient functionalization of polymer optical fibers' (POF) surface by a novel block copolymer material toward the development of low‐cost multiagent sensors is presented. The employed poly(styrene sulfonate‐b‐tert‐butylstyrene) (SPS‐b‐PtBS) diblock copolymer possesses two blocks of distinctively different polarity and charge, the hydrophilic SPS which is sensitive to polar substances and the hydrophobic PtBS which is sensitive to organic solvents. The coexistence of two different blocks allows for the detection of a wide variety of agents, ranging from ammonia, and organic solvents, to biomolecules like lysozyme, at room temperature as opposed to alternative usually more complicated techniques, all with the sole use of one sensing medium. Copolymers' high glass transition temperature enables the formation of stable and environmentally robust overlayers. The sensing performance of the material is evaluated experimentally on the customizable platform of POFs, demonstrating fast response, high operational reversibility, and also reusability in successively different testing agents. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2014 , 52, 46–54     

Optimizing silicon-plasmonic waveguides for chi ^{(3)} nonlinear applications

Hybrid silicon-plasmonic waveguides constitute an appealing platform for integrated photonic circuitry. They merge the technical maturity and prevalence of the SOI platform with the subwavelength confinement of plasmonic waveguides, essential for accessing enhanced nonlinear response at micron length-scales. Employing full-wave numerical simulations complemented with Schrödinger equation techniques, we propose nonlinear waveguide designs for Kerr-effect applications exhibiting minimized impairments due to free-carrier effects, thus raising the power-ceiling imposed on standard silicon waveguides.