Hyperbolic constant mean curvature one surfaces: Spinor representation and trinoids in hypergeometric functions

We present a global representation for surfaces in 3-dimensional hyperbolic space with constant mean curvature 1 (CMC-1 surfaces) in terms of holomorphic spinors. This is a modification of Bryant's representation. It is used to derive explicit formulas in hypergeometric functions for CMC-1 surfaces of genus 0 with three regular ends which are asymptotic to catenoid cousins (CMC-1 trinoids).Comment: 29 pages, 9 figures. v2: figures of cmc1-surfaces correcte

Classification of quantum groups and Belavin--Drinfeld cohomologies for orthogonal and symplectic Lie algebras

In this paper we continue to study Belavin-Drinfeld cohomology introduced in arXiv:1303.4046 [math.QA] and related to the classification of quantum groups whose quasi-classical limit is a given simple complex Lie algebra. Here we compute Belavin-Drinfeld cohomology for all non-skewsymmetric $r$-matrices from the Belavin-Drinfeld list for simple Lie algebras of type $B$, $C$, and $D$.Comment: 17 page

Optimization of the self-sufficient thorium fuel cycle for CANDU power reactors

The results of optimization calculations for CANDU reactors operating in the thorium cycle are presented in this paper. Calculations were performed to validate the feasibility of operating a heavy-water thermal neutron power reactor in a self-sufficient thorium cycle. Two modes of operation were considered in the paper: the mode of preliminary accumulation of 233U in the reactor itself and the mode of operation in a self-sufficient cycle. For the mode of accumulation of 233U, it was assumed that enriched uranium or plutonium was used as additional fissile material to provide neutrons for 233U production. In the self-sufficient mode of operation, the mass and isotopic composition of heavy nuclei unloaded from the reactor should provide (after the removal of fission products) the value of the multiplication factor of the cell in the following cycle K>1. Additionally, the task was to determine the geometry and composition of the cell for an acceptable burn up of 233U. The results obtained demonstrate that the realization of a self-sufficient thorium mode for a CANDU reactor is possible without using new technologies. The main features of the reactor ensuring a self-sufficient mode of operation are a good neutron balance and moving of fuel through the active core

On algebraic equations satisfied by hypergeometric correlators in WZW models. II

We give an explicit description of "bundles of conformal blocks" in Wess-Zumino-Witten models of Conformal field theory and prove that integral representations of Knizhnik-Zamolodchikov equations constructed earlier by the second and third authors are in fact sections of these bundles.Comment: 32 pp., amslate

Biocompatible Gold Nanorod Conjugates for Preclinical Biomedical Research

Gold nanorods with a peak absorption wavelength of 760 nm were prepared using a seed-mediated method. A novel protocol has been developed to replace hexadecyltrimethylammonium bromide on the surface of the nanorods with 16-mercaptohexadecanoic acid and metoxy-poly(ethylene glycol)-thiol, and the monoclonal antibody HER2. The physical chemistry properties of the conjugates were monitored through optical and zeta-potential measurements to confirm surface chemistry changes. The efficiency of the modifications was quantified through measurement of the average number of antibodies per gold nanorod. The conjugates were investigated for different cells lines: BT-474, MCF7, MCF10, MDCK, and fibroblast. The results show successful cell accumulation of the gold nanorod HER2 conjugates in cells with HER2 overexpression. Incubation of the complexes in heparinized mouse blood demonstrated the low aggregation of the metallic particles through stability of the spectral properties, as verified by UV/VIS spectrometry. Cytotoxicity analysis with LDH release and MTT assay confirms strong targeting and retention of functional activity of the antibody after their conjugation with gold nanorods. Silver staining confirms efficient specific binding to BT-474 cells even in cases where the nanorod complexes were incubated in heparinized mouse blood. This is confirmed through in vivo studies where, following intravenous injection of gold nanorod complexes, silver staining reveals noticeably higher rates of specific binding in mouse tumors than in healthy liver. The conjugates are reproducible, have strong molecular targeting capabilities, have long term stability in vivo and can be used in pre-clinical applications. The conjugates can also be used for molecular and optoacoustic imaging, quantitative sensing of biological substrates, and photothermal therapy