Unitary Representations of the Homogeneous Lorentz Group in an O(1,1) O(2) Basis and Some Applications to Relativistic Equations

Unitary irreducible representations of the homogeneous Lorentz group O(3, 1) belonging to the principal series are reduced with respect to the subgroup O(1,1) O(2). As an application we determine the mixed basis matrix elements between O(3) and O(1,1) O(2) bases and derive recurrence relations for them. This set of functions is then used to obtain invariant expansions of solutions of the Dirac and Proca free field equations. These expansions are shown to have the correct nonrelativistic limit

Spherical functions on the de Sitter group

Matrix elements and spherical functions of irreducible representations of the de Sitter group are studied on the various homogeneous spaces of this group. It is shown that a universal covering of the de Sitter group gives rise to quaternion Euler angles. An explicit form of Casimir and Laplace-Beltrami operators on the homogeneous spaces is given. Different expressions of the matrix elements and spherical functions are given in terms of multiple hypergeometric functions both for finite-dimensional and unitary representations of the principal series of the de Sitter group.Comment: 40 page

Magnetic moment of the X-Q state with J(PC)=1(++/-) in light cone QCD sumrules

The magnetic moments of the recently observed resonance X-b(5568) by D0 Collaboration and its partner with charm quark are calculated in the framework of the light cone QCD sum rules, by assuming that these resonances are represented as tetraquark states with quantum numbers J(PC) = 1(vertical bar +/-). The magnetic moment can play a critical role in the determination of the quantum numbers, as well as give useful information about the inner structure of these mesons

Magnetic moment of the X

The magnetic moments of the recently observed resonance $X_b(5568)$ by DO Collaboration and its partner with charm quark are calculated in the framework of the light cone QCD sum rules, by assuming that these resonances are represented as tetra--quark states with quantum numbers $J^{PC}=1^{+\pm}$. The magnetic moment can play critical role in determination of the quantum numbers, as well as giving useful information about the inner structure of these mesons.Comment: 15 pages, 2 figures, LaTeX formatte

Ciliate pheromone structures and activity: a review

As in animals and other multicellular organisms, protozoan ciliates communicate via diffusible signalling pheromones. These pheromones have been identified in the culture supernatant of various species. However, their isolation and definitive structural characterization have been achieved only in species of Blepharisma and Euplotes. With the exception of the two B. japonicum pheromones represented by a tryptophan-related molecule and a glycoprotein, all the other pheromones isolated from Euplotes species are proteins that vary in extension between 38 and 109 amino acids. They form species-specific families of structurally homologous members, in full accord with their multi-allelic determination at an apparently single genetic locus. The determination of the Nuclear Magnetic Resonance (NMR) solution structures of E. raikovi and E. nobilii pheromones has provided direct evidence that, although structurally unique, Euplotes pheromones adopt a common, speciesspecific three-helix folding. This close structural homology among members of the same family well accounts for the pheromone capacity to compete with one another in cell receptor binding reactions and elicit context-dependent, autocrine (growth-promoting) or paracrine (mating-inducing) cell responses