Free Malcev algebra of rank three

We find a basis of the free Malcev algebra on three free generators over a field of characteristic zero. The specialty and semiprimity of this algebra are proved. In addition, we prove the decomposability of this algebra into subdirect sum of the free Lie algebra rank three and the free algebra of rank three of variety of Malcev algebras generated by a simple seven-dimensional Malcev algebra

Surface Plasmon Resonance Enhanced Ellipsometry for Biodetection

Biosensors enable scientists to learn more about biomolecular interactions, and are often used as detectors to indicate the presence of specific analytes. Currently, many detection methods require what are called labels, molecules that bind to an analyte of interest and can be easily detected. Radioactive isotopes are often used for this purpose, but labels such as these have the potential to interfere with the processes and molecules being studied. This poses a problem for medical screening, as labels may lead to an incorrect diagnosis. Therefore, label-free bio sensing techniques are in demand. Surface Plasmon Resonance Imaging (SPR), is one such method. A phenomenon derived from Maxwell’s Equations, SPR occurs at the interface between a dielectric and a metal thin film (Fig. 1). In the metal surface, electrons are not tied to particular atoms and are free to move throughout the material. This “sea” of free electrons can be modeled as a simple harmonic oscillator. In the presence of a drive force—in this case, the electric field in a light wave—electrons will oscillate. Unless the drive force is very close to the resonance frequency, little energy will be transferred to the oscillator. If the driving force matches the resonant frequency however, total energy transfer and SPR will occur. In other words, when a light beam has the correct wavelength to excite the plasmon, it will be absorbed by the metal. One important property of SPR is that the resonant frequencies can be found in the visible light spectrum. The particular frequency required depends largely on the dielectric constant of the metal used. Most importantly, this constant is sensitive to the refractive index of the metal’s surroundings. Consider a glass-gold interface submerged in water (Fig. 1). This system will oscillate at some frequency. If foreign particles are introduced, they raise the refractive index of the water and redshift the plasmon frequency. Thus, the plasmon surface can “detect” refractive index changes and foreign particles with high levels of sensitivity

La production d’une baladodiffusion éducative en obstétrique et gynécologie

Implication Statement: Podcasts are used in medical education to supplement conventional teaching methods such as lectures and reading. We identified a lack of Canadian medical education podcasts covering obstetrics and gynecology (Ob/Gyn) content and created a podcast specific for Canadian medical students and residents. The podcast called “OB-G in YEG” is freely available and currently has fourteen episodes that cover common topics in Ob/Gyn. We describe the process for creating a high-quality medical education resource that is widely accessible to learners that readers may be able to replicate in their own discipline.Énoncé des implications de la recherche Les baladodiffusions sont utilisées dans l’éducation médicale en complément aux méthodes d’enseignement traditionnelles comme les cours magistraux et la lecture de textes. Ayant constaté un manque de baladodiffusions d'enseignement dans les domaines de l’obstétrique et de la gynécologie (OB/GY) au Canada, nous avons créé une telle émission destinée aux étudiants et aux résidents en médecine de ce pays. La baladodiffusion, intitulée « OB-G in YEG », est disponible gratuitement et elle comporte actuellement onze épisodes sur des sujets d’intérêt général touchant à l’obstétrique et à la gynécologie. Nous décrivons le processus de création d'une ressource d'enseignement médical de qualité, qui est largement accessible aux apprenants et que les lecteurs seraient peut-être en mesure de reproduire dans leur propre discipline

Analytic Loops and Gauge Fields

In this paper the linear representations of analytic Moufang loops are investigated. We prove that every representation of semisimple analytic Moufang loop is completely reducible and find all nonassociative irreducible representations. We show that such representations are closely associated with the (anti-)self-dual Yang-Mills equations in ${\bf R}^8$Comment: 10 pages, LaTeX, no figure

Vibrational energy relaxation in proteins

An overview of theories related to vibrational energy relaxation (VER) in proteins is presented. VER of a selected mode in cytochrome c is studied using two theoretical approaches. One is the equilibrium simulation approach with quantum correction factors, and the other is the reduced model approach which describes the protein as an ensemble of normal modes interacting through nonlinear coupling elements. Both methods result in estimates of the VER time (sub ps) for a CD stretching mode in the protein at room temperature. The theoretical predictions are in accord with the experimental data of Romesberg's group. A perspective on future directions for the detailed study of time scales and mechanisms for VER in proteins is presented.Comment: 12 pages, 4 figures, accepted for publication in PNA

Improving Raman velocimetry of laser-cooled cesium atoms by spin-polarization

We study the peformances of Raman velocimetry applied to laser-cooled, spin-polarized, cesium atoms. Atoms are optically pumped into the F=4, m=0 ground-state Zeeman sublevel, which is insensitive to magnetic perturbations. High resolution Raman stimulated spectroscopy is shown to produce Fourier-limited lines, allowing, in realistic experimental conditions, atomic velocity selection to one-fiftieth of a recoil velocity.Comment: 12 pages, 6 figures, Elsevier style, to appear in Opt. Commu

On the Classification of Real Forms of Non-Abelian Toda Theories and W-algebras

We consider conformal non-Abelian Toda theories obtained by hamiltonian reduction from Wess-Zumino-Witten models based on general real Lie groups. We study in detail the possible choices of reality conditions which can be imposed on the WZW or Toda fields and prove correspondences with sl(2,R) embeddings into real Lie algebras and with the possible real forms of the associated W-algebras. We devise a a method for finding all real embeddings which can be obtained from a given embedding of sl(2,C) into a complex Lie algebra. We then apply this to give a complete classification of real embeddings which are principal in some simple regular subalgebra of a classical Lie algebra.Comment: 42 pages, LaTeX; Minor corrections to ensure consistent conventions; some references adde

Magnetic Charge in a Nonassociative Field Theory

The violation of the Jacobi identity by the presence of magnetic charge is accomodated by using an explicitly nonassociative theory of octonionic fields. It is found that the dynamics of this theory is simplified if the Lagrangian contains only dyonic charges, but certain problems in the constrained quantisation remain. The extension of these concepts to string theory may however resolve these difficulties.Comment: 10 pages, REVTeX, no figure

On n-ary Hom-Nambu and Hom-Nambu-Lie algebras

It is observed that the category of n-ary Hom-Nambu(-Lie) algebras is closed under twisting by self-weak morphisms. Constructions of ternary Hom-Nambu algebras from Hom-associative algebras, Hom-Lie algebras, ternary totally Hom-associative algebras, and Hom-Jordan triple systems are given. Every multiplicative n-ary Hom-Nambu algebra gives rise to a sequence of Hom-Nambu algebras of exponentially higher arities. Under some conditions, an n-ary Hom-Nambu(-Lie) algebra gives rise to an (n-1)-ary Hom-Nambu(-Lie) algebra.Comment: 23 page