A Hardy's Uncertainty Principle Lemma in Weak Commutation Relations of Heisenberg-Lie Algebra

In this article we consider linear operators satisfying a generalized commutation relation of a type of the Heisenberg-Lie algebra. It is proven that a generalized inequality of the Hardy's uncertainty principle lemma follows. Its applications to time operators and abstract Dirac operators are also investigated

Trions in a periodic potential

The group-theoretical classification of trion states is presented. It is based on considerations of products of irreducible representations of the 2D translation group. For a given BvK period N degeneracy of obtained states is N^2. Trions consist of two identical particles so the symmetrization of states with respect to particles transposition is considered. Completely antisymmetric states can be constructed by introducing antisymmetric spin functions. Two symmetry adapted bases are considered. The third possibility is postponed for the further investigations.Comment: revtex, 5 p., sub. to Physica

Non-Abelian Vortices on Cylinder -- Duality between vortices and walls

We investigate vortices on a cylinder in supersymmetric non-Abelian gauge theory with hypermultiplets in the fundamental representation. We identify moduli space of periodic vortices and find that a pair of wall-like objects appears as the vortex moduli is varied. Usual domain walls also can be obtained from the single vortex on the cylinder by introducing a twisted boundary condition. We can understand these phenomena as a T-duality among D-brane configurations in type II superstring theories. Using this T-duality picture, we find a one-to-one correspondence between the moduli space of non-Abelian vortices and that of kinky D-brane configurations for domain walls.Comment: 33 pages, 17 figures, v2: references added, typos corrected, the final version published in PR

Global Structure of Moduli Space for BPS Walls

We study the global structure of the moduli space of BPS walls in the Higgs branch of supersymmetric theories with eight supercharges. We examine the structure in the neighborhood of a special Lagrangian submanifold M, and find that the dimension of the moduli space can be larger than that naively suggested by the index theorem, contrary to previous examples of BPS solitons. We investigate BPS wall solutions in an explicit example of M using Abelian gauge theory. Its Higgs branch turns out to contain several special Lagrangian submanifolds including M. We show that the total moduli space of BPS walls is the union of these submanifolds. We also find interesting dynamics between BPS walls as a byproduct of the analysis. Namely, mutual repulsion and attraction between BPS walls sometimes forbid a movement of a wall and lock it in a certain position; we also find that a pair of walls can transmute to another pair of walls with different tension after they pass through.Comment: 42 pages, 11 figures; a few comments adde

Properties of hyperkahler manifolds and their twistor spaces

We describe the relation between supersymmetric sigma-models on hyperkahler manifolds, projective superspace, and twistor space. We review the essential aspects and present a coherent picture with a number of new results.Comment: 26 pages. v2: Sign mistakes corrected; Kahler potential explicitly calculated in example; references added. v3: Published version--several small clarifications per referee's reques

NaV2O4: a Quasi-1D Metallic Antiferromagnet with Half-Metallic Chains

NaV2O4 crystals were grown under high pressure using a NaCl flux, and the crystals were characterized with X-ray diffraction, electrical resistivity, heat capacity, and magnetization. The structure of NaV2O4 consists of double chains of edge-sharing VO6 octahedra. The resistivity is highly anisotropic, with the resistivity perpendicular to the chains more than 20 times greater than that parallel to the chains. Magnetically, the intrachain interactions are ferromagnetic and the interchain interactions are antiferromagnetic; 3D antiferromagnetic order is established at 140 K. First principles electronic structure calculations indicate that the chains are half metallic. Interestingly, the case of NaV2O4 seems to be a quasi-1D analogue of what was found for half-metallic materials.Comment: 14 pages, including 4 figures and 1 table, accepted for publication in PR

N = 2 supersymmetric sigma-models and duality

For two families of four-dimensional off-shell N = 2 supersymmetric nonlinear sigma-models constructed originally in projective superspace, we develop their formulation in terms of N = 1 chiral superfields. Specifically, these theories are: (i) sigma-models on cotangent bundles T*M of arbitrary real analytic Kaehler manifolds M; (ii) general superconformal sigma-models described by weight-one polar supermultiplets. Using superspace techniques, we obtain a universal expression for the holomorphic symplectic two-form \omega^{(2,0)} which determines the second supersymmetry transformation and is associated with the two complex structures of the hyperkaehler space T*M that are complimentary to the one induced from M. This two-form is shown to coincide with the canonical holomorphic symplectic structure. In the case (ii), we demonstrate that \omega^{(2,0)} and the homothetic conformal Killing vector determine the explicit form of the superconformal transformations. At the heart of our construction is the duality (generalized Legendre transform) between off-shell N = 2 supersymmetric nonlinear sigma-models and their on-shell N = 1 chiral realizations. We finally present the most general N = 2 superconformal nonlinear sigma-model formulated in terms of N = 1 chiral superfields. The approach developed can naturally be generalized in order to describe 5D and 6D superconformal nonlinear sigma-models in 4D N = 1 superspace.Comment: 31 pages, no figures; V2: reference and comments added, typos corrected; V3: more typos corrected, published versio

Metabolomics of carotenoids: The challenges and prospects – A review

Considerable progress in carotenoids research has been made to understand the carotenoid metabolism in animals including human. Epidemiological and clinical studies have correlated with dietary intake of carotenoids on reduction of vitamin A deficiency, age-related macular degeneration, cancer and cardiovascular diseases. Recent findings demonstrate the existence of carotenoid metabolites in vivo and their efficacy have made greater insight on prospecting carotenoid metabolites. Owing to their biological activity, exploration of analytical methods for the characterization of carotenoid metabolites is considered to be important before addressing the stability and bioactivity. Although few studies are available on carotenoid metabolites, their structural characterization in biological samples require a substantial refining of analytical protocols like isolation, purification, prerequisite of equipment parameters and robustness in hyphenated techniques. Recently, researchers have focused on biotransformation of carotenoids and made an attempt to screen their metabolites by high-throughput analytical strategies. However, till date there is no detailed analytical techniques available to fingerprint carotenoid metabolites, due to interference with complex biological matrices. This review highlights the carotenoid metabolism, possible bioconversion and available bio-analytical techniques to characterize metabolites in vivo. Further, advancement in sensitivity, mode of ionization and fragmentation patterns of metabolites were also discussed. The identification of carotenoid metabolites in system specific will have further insight in the emerging field of nutritional metabolomics

Review

The chalcogen elements oxygen, sulfur, and selenium are essential constituents of side chain functions of natural amino acids. Conversely, no structural and biological function has been discovered so far for the heavier and more metallic tellurium element. In the methionine series, only the sulfur-containing methionine is a proteinogenic amino acid, while selenomethionine and telluromethionine are natural amino acids that are incorporated into proteins most probably because of the tolerance of the methionyl-tRNA synthetase; so far, methoxinine the oxygen analogue has not been discovered in natural compounds. Similarly, the chalcogen analogues of tryptophan and phenylalanine in which the benzene ring has been replaced by the largely isosteric thiophene, selenophene, and more recently, even tellurophene are fully synthetic mimics that are incorporated with more or less efficiency into proteins via the related tryptophanyl- and phenylalanyl-tRNA synthetases, respectively. In the serine/cysteine series, also selenocysteine is a proteinogenic amino acid that is inserted into proteins by a special translation mechanism, while the tellurocysteine is again most probably incorporated into proteins by the tolerance of the cysteinyl-tRNA synthetase. For research purposes, all of these natural and synthetic chalcogen amino acids have been extensively applied in peptide and protein research to exploit their different physicochemical properties for modulating structural and functional properties in synthetic peptides and rDNA expressed proteins as discussed in the following review