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 Study of Highly Qualified Science Teachers' Career Trajectory in the Deep,Rural South: Examining a Link Between Deprofessionalization and Teacher Dissatisfaction

Science teacher retention, attrition, and migration continue to perplex educational scholars, political entities, as well as the general public. This study utilized an interpretive methodological design to generate assertions regarding career choice made by highly qualified science teachers in the deep, rural South through analysis of documents, interviews, focus groups, and observation. Generally considered “difficult to staff” because of location, socioeconomics, and demographics, Wilson County High School is an exemplar in science teacher retention and student achievement. Findings presented include how the science department at Wilson County improved student learning outcomes as well as the reasons why two of the highly qualified science teachers at this school were considering leaving the profession they love.     

Potential Benefits and Barriers to Integration

The rhetoric surrounding integration of mathematics and science abounds. Professional organizations’ standards and recommendations for reform in mathematics and science education each point out the need to make connections among various disciplines. However, some remain unconvinced, citing a lack of research supporting the assertion that integration improves student achievement. This article examines the current situation, discusses the growing body of related research, and examines the implementation issues related to integrated curriculum projects. The conclusion calls for mathematics and science educators to work collaboratively to address implementation issues surrounding reform of any kind and to explore further the possibilities of integration.     

Quantized enveloping algebras for Borcherds superalgebras

We construct quantum deformations of enveloping algebras of Borcherds superalgebras, their Verma modules, and their irreducible highest weight modules.

     

Functionalization of Graphene Oxide and its Biomedical Applications

Graphene oxide (GO) offers interesting physicochemical and biological properties for biomedicine due to its versatility, biocompatibility, small size, large surface area, and its ability to interact with biological cells and tissues. GO is a two-dimensional material of exceptional strength, unique optical, physical, mechanical, and electronic properties. Ease of functionalization and high antibacterial activity are two major properties identified with GO. Due to its excellent aqueous processability, amphiphilicity, surface functionalization capability, surface enhanced Raman scattering (SERS), and fluorescence quenching ability, GO chemically exfoliated from oxidized graphite is considered a promising material for biological applications. In addition, due to π-π* transitions, a low energy is required for electron movement, a property important in Biosensor and Bioimaging applications of GO. In this article, we present an overview of current advances in GO applications in biomedicine and discuss future perspectives. We conclude that GO is going to play a vital role in Biomedical applications in the near future.     

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.