Dirac Operators on Coset Spaces

The Dirac operator for a manifold Q, and its chirality operator when Q is even dimensional, have a central role in noncommutative geometry. We systematically develop the theory of this operator when Q=G/H, where G and H are compact connected Lie groups and G is simple. An elementary discussion of the differential geometric and bundle theoretic aspects of G/H, including its projective modules and complex, Kaehler and Riemannian structures, is presented for this purpose. An attractive feature of our approach is that it transparently shows obstructions to spin- and spin_c-structures. When a manifold is spin_c and not spin, U(1) gauge fields have to be introduced in a particular way to define spinors. Likewise, for manifolds like SU(3)/SO(3), which are not even spin_c, we show that SU(2) and higher rank gauge fields have to be introduced to define spinors. This result has potential consequences for string theories if such manifolds occur as D-branes. The spectra and eigenstates of the Dirac operator on spheres S^n=SO(n+1)/SO(n), invariant under SO(n+1), are explicitly found. Aspects of our work overlap with the earlier research of Cahen et al..Comment: section on Riemannian structure improved, references adde

From spin to anyon notation: The XXZ Heisenberg model as a D3D_{3} (or su(2)4su(2)_{4}) anyon chain

We discuss a relationship between certain one-dimensional quantum spin chains and anyon chains. In particular we show how the XXZ Heisenberg chain is realised as a $D_{3}$ (alternately $su(2)_{4}$) anyon model. We find the difference between the models lie primarily in choice of boundary condition.Comment: 13 page

Research of the Power Plant Operational Modes

In this article the algorithm of the power plant operational modes research is offered. According to this algorithm the program for the modes analysis and connection power transformers choice is developed. The program can be used as educational means for studying of the power plant electric part, at the same time basic data are provided. Also the program can be used for the analysis of the working power plants modes. Checks of the entered data completeness and a choice correctness of the operational modes are provided in the program; in all cases of a deviation from the correct decisions to the user the relevant information is given

Camphor pathway redux: functional recombinant expression of 2,5- and 3,6-diketocamphane monooxygenases of Pseudomonas putida ATCC 17453 with their cognate flavin reductase catalyzing Baeyer-Villiger reactions

Whereas the biochemical properties of the monooxygenase components that catalyze the oxidation of 2,5-diketocamphane and 3,6-diketocamphane (2,5-DKCMO and 3,6-DKCMO, respectively) in the initial catabolic steps of (+) and (−) isomeric forms of camphor metabolism in Pseudomonas putida ATCC 17453 are relatively well characterized, the actual identity of the flavin reductase (Fred) component that provides the reduced flavin to the oxygenases is hitherto ill-defined. In this study, a 37-kDa Fred was purified from camphor-induced culture of P. putida ATCC 17453 and this facilitated cloning and characterization of the requisite protein. The active Fred is a homodimer with a subunit molecular mass of 18-kDa that uses NADH as electron donor (Km = 32 μM) and it catalyzes the reduction of FMN (Km = 3.6 μM; kcat = 283 s-1) in preference to FAD (Km = 19 μM; kcat = 128 s-1). Sequence determination of ∼40-kb of the camphor (CAM) degradation plasmid revealed the locations of two isofunctional 2,5-DKCMO genes (camE25-1 for 2,5-DKCMO-1, and camE25-2 for 2,5-DKCMO-2) as well as that of 3,6-DKCMO-encoding gene (camE36). In addition, by pulsed-field gel electrophoresis, the CAM plasmid was established to be linear and ∼533-kb in length. To enable functional assessment of the two-component monooxygenase system in Baeyer-Villiger oxidations, recombinant plasmids expressing Fred in tandem with the respective 2,5-DKCMO and 3,6-DKCMO encoding genes in Escherichia coli were constructed. Comparative substrate profiling of the isofunctional 2,5-DCKMOs did not yield obvious differences in Baeyer-Villiger biooxidations but they are distinct from 3,6-DKCMO in the stereoselective oxygenations with various mono- and bicyclic ketone substrates

Surprises and pitfalls arising from (pseudo)symmetry

The presence of pseudosymmetry can cause problems in structure determination and refinement. The relevant background and representative examples are presented

Detection and correction of underassigned rotational symmetry prior to structure deposition

An X-ray structural model can be reassigned to a higher symmetry space group using the presented framework if its noncrystallographic symmetry operators are close to being exact crystallographic relationships. About 2% of structures in the Protein Data Bank can be reclassified in this way