Jacobson generators of the quantum superalgebra Uq[sl(n+1∣m)]U_q[sl(n+1|m)] and Fock representations

As an alternative to Chevalley generators, we introduce Jacobson generators for the quantum superalgebra $U_q[sl(n+1|m)]$. The expressions of all Cartan-Weyl elements of $U_q[sl(n+1|m)]$ in terms of these Jacobson generators become very simple. We determine and prove certain triple relations between the Jacobson generators, necessary for a complete set of supercommutation relations between the Cartan-Weyl elements. Fock representations are defined, and a substantial part of this paper is devoted to the computation of the action of Jacobson generators on basis vectors of these Fock spaces. It is also determined when these Fock representations are unitary. Finally, Dyson and Holstein-Primakoff realizations are given, not only for the Jacobson generators, but for all Cartan-Weyl elements of $U_q[sl(n+1|m)]$.Comment: 27 pages, LaTeX; to be published in J. Math. Phy

Higgs revised in Supersymmetric Economical 3-3-1 model with B/\mu-type terms

We re-investigate the scalar potential and the Higgs sector of the supersymmetric economical 3-3-1 model (SUSYE331) in the presence of the B/\mu type terms which has many important consequences. First, the model contains no massless Higgs fields. Second, we prove that the soft mass parameters of Higgses must be at the SU(3)_L scale. As a result, the masses of the Higgses drift toward this scale except one light real neutral Higgs with the mass of m_Z|cos(2\gamma)| at the tree level. We also show that there are some Higgses containing many properties of the Higgses in the minimal supersymmetric standard model (MSSM), especially in the neutral Higgs sector. One exact relation in the MSSM, m^2_H^{+/-}=m^2_A+m^2_W, is still true in the SUSYE331. Based on this result we make some comments on the lepton flavor violating decays of these Higgses as one of signatures of new physics in the SUSYE331 model which may be detected by present colliders.Comment: Matches version accepted for publication in EPJC. Typos are corrected. We add a new section, a new appendix, a new figure and new references to explain more clearly the properties of the lightest neutral Higgs. Results unchange

Varieties with too many rational points

We investigate Fano varieties defined over a number field that contain subvarieties whose number of rational points of bounded height is comparable to the total number on the variety.Comment: 23 page

Topologically protected surface Majorana arcs and bulk Weyl fermions in ferromagnetic superconductors

A number of ferromagnetic superconductors have been recently discovered which are believed to be in the so-called "equal spin pairing" (ESP) state. In the ESP state the Cooper pairs condense forming order parameters $\Delta_{\uparrow\uparrow}, \Delta_{\downarrow\downarrow}$ which are decoupled in the spin-sector. We show that these three-dimensional systems should generically support topologically protected surface Majorana arcs and bulk Weyl fermions as gapless excitations. Similar protected low-energy exotic quasiparticles should also appear in the recently discovered non-centrosymmteric superconductors in the presence of a Zeeman field. The protected surface arcs can be probed by angle-resolved photoemission (ARPES) as well as scanning tunneling microscope (STM) experiments.Comment: 5 pages and 2 figures; Figure 2 revised, typos correcte

Roles of Dietary Cobalt and Administration of Mixed Rumen Bacteria in Regulating Hematological Parameters of Pre-weaning Twin Lambs

Cobalt (Co) is required by rumen microorganism for vitamin B12 synthesis. Vitamin B12 is an important cofactor for methionine synthesis and gluconeogenesis. In young ruminants up to 6–8 wk old, the rumen has not been completely developed and rumen microorganisms are not ready to supply vitamin B12. The aim of this research was to determine the potency of mixed rumen bacteria and dietary supplementation of Co and its effect on plasma glucose, blood minerals (Co, Fe, and Zn) concentrations, and hematology of pre-weaning twin lambs. Twelve one month-old local twin lambs were assigned to 4 groups in a randomized complete block design. Lambs were fed cow milk at 10% body weight, adjusted weekly for 80 d. Mixed rumen bacteria were offered at 15 mL/d (8.295x1010 cfu). Dietary treatments were: 1) basal diet (Control), 2) basal diet + 1 mg/kg DM cyanocobalamin (VitB12) and 3) basal diet + 1 mg/kg DM of Co + administration of 15 mL mixed rumen bacteria (CoBac). There were no treatment effects on neither plasma glucose and blood mineral concentrations nor hematological profiles. This study demonstrated that pre-weaning twin lambs are not responsive to supplementation of Co and administration of mixed rumen bacteria