Is U(1)H a good family symmetry?

We analyze U(1)_H as a horizontal symmetry and its possibilities to explain the known elementary-fermion masses. We find that only two candidates, in the context of SU(3)_c ? SU(2)_L ? U(1)_Y ? U(1)_H nonsuper-symmetric, are able to fit the experimental result m_b«m_t. identity, but it is a common prejudice to assume that the appropriate family symmetry may explain this fact as a consequence of (i) and (ii). In what follows we will enlarge the SM gauge group with an extra U(1)_H horizontal local gauge symmetry (the simplest multi-family continuous symmetry we can think of). We then show that the structure SU(3)_c ? SU(2)_L ? U(1)_Y ? U(1)_H by itself is able to explain (ii), and that the simplest supersymmetric (SUSY) extension of this model without a μ-term can not cope with (ii).     

Family unification inSU(6) L ⊗U(1) Y

Electroweak and horizontal interactions are unified with the groupSU(6) _L U(1) _Y for three generations. The horizontal gauge group suggested from low energy phenomenology isSU(2) _H . This model does not contain exotic quarks, but exotic leptons are needed in order to make it anomaly-free. The breaking of the symmetry gives, in a natural way, heavy masses for exotic leptons and a BCS mass matrix for the up quarks, which implies that at tree level only the top quark gets a mass of orderM _W . The see-saw mechanism generates tiny masses for the three known neutrinos. The remaining of the known fermion masses are light, because they can be generated only as radiative corrections.     

Quadratic forms for the 1-D semilinear Schrödinger equation

This paper is concerned with 1-D quadratic semilinear
Schrödinger equations. We study local well posedness in classical Sobolev space of the associated initial value problem and periodic boundary value problem. Our main interest is to obtain the lowest value of which guarantees the desired local well posedness result. We prove that at least for the quadratic cases these values are negative and depend on the structure of the nonlinearity considered.

     

Protonation and deprotonation of hydroxamic acids. An MO ab initio study

Ab initio molecular orbital calculations with 4-31G//4-31G, 6-31G^*//4-31G and 6-31+G//4-31G basis sets have been used to examine the structure, relative energy, protonation and deprotonation of a series of seven hydroxamic acids in the gas phase. The results show that hydroxamic acids are predominantly in the E-TS form and that the most probable protonation site is the carbonyl oxygen atom, while deprotonation proceeds by loss of NH hydrogen.     

Synthesis and Electronic Spectroscopy of Bromocarbazoles. Direct Bromination of N‐ and C‐Substituted Carbazoles by N‐Bromosuccinimide or a N‐Bromosuccinimide/Silica Gel System

The preparation, isolation and characterization by elemental analysis and ¹H‐NMR, ¹³C‐NMR, and MS data of the bromo derivatives of N‐substituted carbazoles, i.e., of 9‐methyl‐9H‐carbazole ( 1 ), 9‐phenyl‐9H‐carbazole ( 2 ), 9‐benzyl‐9H‐carbazole ( 3 ), 2‐methoxy‐9‐methyl‐9H‐carbazole ( 4 ), and of C‐substituted carbazoles, i.e., of 2‐(acetyloxy)‐9H‐carbazole ( 5 ) and 3‐nitro‐9H‐carbazole ( 6 ), are reported, in part for the first time. As brominating reagents, N‐bromosuccinimide (NBS) or NBS/silica gel in CH₂Cl₂, NBS in AcOH, KBrO₃/KBr in EtOH doped with a catalytic amount of H₂SO₄, or KBrO₃/KBr in AcOH were employed, and their uses were compared. Semi‐empirical PM3 calculations were performed to predict the reactivity of the N‐substituted and C‐substituted carbazoles and of their bromo derivatives and found to verify the experimental results. The UV‐absorption and fluorescence and phosphorescence emission spectra of the bromocarbazole derivatives in MeCN solution at 298 K and in a solid matrix at 77 K were compared with those of the corresponding carbazoles 1 – 6 . The dynamic properties of the lowest excited singlet and triplet states (τ_f, τ_p, ?_f, and ?_p) were measured under the same experimental conditions. The intramolecular spin–orbital‐coupling effect of the Br‐atom and NO₂ group on the spectroscopic data, photophysical parameters, and on the photo reactivity were also briefly analyzed.     

Limiting configurations allowed by the energy conditions

The energy conditions of general relativity are satisfied by all experimentally detected fields. We discuss their interpretation and application to charged spheres. It is found that they prevent the existence of naked singularities, and demand that the effective gravitational mass be everywhere non-negative. We focus on the emergence of limiting configurations-sources of the Reissner-Nordström field that have vanishing effective mass everywhere within the sphere. These configurations have a number of interesting features. Among them we find that, near the center, the limiting form of the equation of state is+3p=0. Notably this is the only equation of state consistent with the existence of zero-point electromagnetic field, and it has been considered in different contexts, in discussions of cosmic strings and in derivations of (3+1) properties of matter from (4+1) geometry. The consistency of these configurations with the Einstein-Maxwell equations is shown by means of explicit examples. These configurations can be interpreted as due to selfinteracting gravitational effects of the zero-point electromagnetic field.