Second Hopf map and Yang-Coulomb system on 5d (pseudo)sphere

Using the second Hopf map, we perform the reduction of the eight-dimensional (pseudo)spherical (Higgs)oscillator to a five-dimensional system interacting with a Yang monopole. Then, using a standard trick, we obtain, from the latter system, the pseudospherical and spherical generalizations of the Yang-Coulomb system (the five dimensional analog of MICZ-Kepler system). We present the whole set of its constants of motions, including the hidden symmetry generators given by the analog of Runge-Lenz vector. In the same way, starting from the eight-dimensional anisotropic inharmonic Higgs oscillator, we construct the integrable (pseudo)spherical generalization of the Yang-Coulomb system with the Stark term.Comment: 10 pages, PACS: 03.65.-w, 02.30.Ik, 14.80.H

Anisotropic inharmonic Higgs oscillator and related (MICZ-)Kepler-like systems

We propose the integrable (pseudo)spherical generalization of the four-dimensional anisotropic oscillator with additional nonlinear potential. Performing its Kustaanheimo-Stiefel transformation we then obtain the pseudospherical generalization of the MICZ-Kepler system with linear and $\cos\theta$ potential terms. We also present the generalization of the parabolic coordinates, in which this system admits the separation of variables. Finally, we get the spherical analog of the presented MICZ-Kepler-like system.Comment: 7 page

Recoil Correction to Hydrogen Energy Levels: A Revision

Recent calculations of the order (Z\alpha)^4(m/M)Ry pure recoil correction to hydrogen energy levels are critically revised. The origins of errors made in the previous works are elucidated. In the framework of a successive approach, we obtain the new result for the correction to S levels. It amounts to -16.4 kHz in the ground state and -1.9 kHz in the 2S state.Comment: 15 pages, Latex, no figure

Nondegenerate 3D complex Euclidean superintegrable systems and algebraic varieties

A classical (or quantum) second order superintegrable system is an integrable n-dimensional Hamiltonian system with potential that admits 2n-1 functionally independent second order constants of the motion polynomial in the momenta, the maximum possible. Such systems have remarkable properties: multi-integrability and multi-separability, an algebra of higher order symmetries whose representation theory yields spectral information about the Schroedinger operator, deep connections with special functions and with QES systems. Here we announce a complete classification of nondegenerate (i.e., 4-parameter) potentials for complex Euclidean 3-space. We characterize the possible superintegrable systems as points on an algebraic variety in 10 variables subject to six quadratic polynomial constraints. The Euclidean group acts on the variety such that two points determine the same superintegrable system if and only if they lie on the same leaf of the foliation. There are exactly 10 nondegenerate potentials.Comment: 35 page

Etk/Bmx Regulates Proteinase-Activated-Receptor1 (PAR1) in Breast Cancer Invasion: Signaling Partners, Hierarchy and Physiological Significance

BACKGROUND: While protease-activated-receptor 1 (PAR(1)) plays a central role in tumor progression, little is known about the cell signaling involved. METHODOLOGY/PRINCIPAL FINDINGS: We show here the impact of PAR(1) cellular activities using both an orthotopic mouse mammary xenograft and a colorectal-liver metastasis model in vivo, with biochemical analyses in vitro. Large and highly vascularized tumors were generated by cells over-expressing wt hPar1, Y397Z hPar1, with persistent signaling, or Y381A hPar1 mutant constructs. In contrast, cells over-expressing the truncated form of hPar1, which lacks the cytoplasmic tail, developed small or no tumors, similar to cells expressing empty vector or control untreated cells. Antibody array membranes revealed essential hPar1 partners including Etk/Bmx and Shc. PAR(1) activation induces Etk/Bmx and Shc binding to the receptor C-tail to form a complex. Y/A mutations in the PAR(1) C-tail did not prevent Shc-PAR(1) association, but enhanced the number of liver metastases compared with the already increased metastases obtained with wt hPar1. We found that Etk/Bmx first binds via the PH domain to a region of seven residues, located between C378-S384 in PAR(1) C-tail, enabling subsequent Shc association. Importantly, expression of the hPar1-7A mutant form (substituted A, residues 378-384), which is incapable of binding Etk/Bmx, resulted in inhibition of invasion through Matrigel-coated membranes. Similarly, knocking down Etk/Bmx inhibited PAR(1)-induced MDA-MB-435 cell migration. In addition, intact spheroid morphogenesis of MCF10A cells is markedly disrupted by the ectopic expression of wt hPar1. In contrast, the forced expression of the hPar1-7A mutant results in normal ball-shaped spheroids. Thus, by preventing binding of Etk/Bmx to PAR(1) -C-tail, hPar1 oncogenic properties are abrogated. CONCLUSIONS/SIGNIFICANCE: This is the first demonstration that a cytoplasmic portion of the PAR(1) C-tail functions as a scaffold site. We identify here essential signaling partners, determine the hierarchy of binding and provide a platform for therapeutic vehicles via definition of the critical PAR(1)-associating region in the breast cancer signaling niche

Giant Hall effect in Ni-Mn-In Heusler alloys

We present experimental results on the giant Hall effect in the Heusler alloy Ni50 Mn50-x Inx with x=15.2. An unusual field dependence of the Hall resistivity (ρH) was observed in the vicinity of the martensitic phase transition, where ρH sharply increases up to ρH (15 kOe) =50 μΩcm. This value is comparable with the giant Hall resistivity in magnetic nanogranular alloys. Associated with ρH, the Hall angle reaches a giant value of tan-1 0.5. An explanation of the giant Hall effect in Ni50 Mn50-x Inx Heusler alloys has been suggested. © 2009 The American Physical Society