The universal central extension of the three-point loop algebra

We consider the three-point loop algebra,

where denotes a field of characteristic 0 and is an indeterminate. The universal central extension of was determined by Bremner. In this note, we give a presentation for via generators and relations, which highlights a certain symmetry over the alternating group . To obtain our presentation of , we use the realization of as the tetrahedron Lie algebra.

     

A new construction of the Kac Jordan superalgebra

We present an elementary construction of the 10-dimensional simple Jordan superalgebra K of Kac using the 3-dimensional tiny Kaplansky superalgebra. This new realization of K enables us to derive many of its properties.

     

The Effect of the Geometry of the Particle Distribution in Ostwald Ripening

Based on [1], we derive equations for the radii and the centers that we relate to the Lifshitz-Slyozov-Wagner theory. N.D.A. and G.K. were partially supported by a ENE 99/527 interdisciplinary grant in Materials, and by a grant from the University of Athens. N.D.A. would like to thank also the people at BYU for providing extraordinary hospitality and a stimulating environment during his visit in the Fall of 2000.N.D.A. and G.K. were partially supported by a ENE 99/527 interdisciplinary grant in Materials, and by a grant from the University of Athens. N.D.A. would like to thank also the people at BYU for providing extraordinary hospitality and a stimulating environment during his visit in the Fall of 2000.     

Lie superalgebras graded by the root system B(<Emphasis Type="Italic">m,n</Emphasis>)

We determine the Lie superalgebras that are graded by the root system B(m,n) of the orthosymplectic Lie superalgebra osp(2m + 1,2n). Mathematics Subject Classification (2000) Primary 17B70, Secondary 17A70     

Crystal bases for the quantum superalgebra

A crystal base theory is introduced for the quantized enveloping algebra of the general linear Lie superalgebra , and an explicit realization of the crystal base is given in terms of semistandard tableaux.     

Cascade intramolecular N-arylation/intermolecular carboamination reactions for the construction of tricyclic heterocycles

A new method for the stereoselective synthesis of tetrahydropyrroloindoles and hexahydropyrroloquinolines of general structure 8 is described. These products are formed through cascade Pd-catalyzed coupling reactions between aryl chlorides and unsaturated amine substrates 5. A single catalyst effects an intramolecular N-arylation reaction followed by an intermolecular alkene carboamination reaction to generate two rings, three bonds, and one stereocenter with good chemoselectivity, diastereoselectivity, and chemical yield.     

Structural Characterization of Graphene Nanosheets for Miniaturization of Potentiometric Urea Lipid Film Based Biosensors

The present article describes a miniaturized potentiometric urea lipid film based biosensor on graphene nanosheets. Structural characterization of graphene nanosheets for miniaturization of potentiometric urea lipid film based biosensors have been studied through atomic force microscopy (AFM) and transmission electron microscopy (TEM) measurements. UV‐Vis and Fourrier transform IR (FTIR) spectroscopy have been utilized to study the pre‐ and postconjugated surfaces of graphene nanosheets. The presented potentiometric urea biosensor exhibits good reproducibility, reusability, selectivity, rapid response times (～4 s), long shelf life and high sensitivity of ca. 70 mV/decade over the urea logarithmic concentration range from 1×10^?6 M to 1×10^?3 M.     

Magnetic, electronic, and structural characterization of nonstoichiometric iron oxides at the nanoscale

We have investigated the structural, magnetic, and electronic properties of nonstoichiometric iron oxide nanocrystals prepared by decomposition of iron(II) and iron(0) precursors in the presence of organic solvents and capping groups. The highly uniform, crystalline, and monodisperse nanocrystals that were produced enabled a full structural and compositional survey by electron microscopy and X-ray diffraction. The complex and metastable behavior of nonstoichiometric iron oxide (wüstite) at the nanoscale was studied by a combination of Mossbauer spectroscopy and magnetic characterization. Deposition from hydrocarbon solvents with subsequent self-assembly of iron oxide nanocrystals into superlattices allowed the preparation of continuous thin films suitable for electronic transport measurements.