Primitive Cohomology of Hopf algebras

Primitive cohomology of a Hopf algebra is defined by using a modification of the cobar construction of the underlying coalgebra. Among many of its applications, two classifications are presented. Firstly we classify all non locally PI, pointed Hopf algebra domains of Gelfand-Kirillov dimension two; and secondly we classify all pointed Hopf algebras of rank one. The first classification extends some results of Brown, Goodearl and others in an ongoing project to understand all Hopf algebras of low Gelfand-Kirillov dimension. The second generalizes results of Krop-Radford and Wang-You-Chen which classified Hopf algebras of rank one under extra hypothesis. Properties and algebraic structures of the primitive cohomology are discussed

Gabor Shearlets

In this paper, we introduce Gabor shearlets, a variant of shearlet systems, which are based on a different group representation than previous shearlet constructions: they combine elements from Gabor and wavelet frames in their construction. As a consequence, they can be implemented with standard filters from wavelet theory in combination with standard Gabor windows. Unlike the usual shearlets, the new construction can achieve a redundancy as close to one as desired. Our construction follows the general strategy for shearlets. First we define group-based Gabor shearlets and then modify them to a cone-adapted version. In combination with Meyer filters, the cone-adapted Gabor shearlets constitute a tight frame and provide low-redundancy sparse approximations of the common model class of anisotropic features which are cartoon-like functions.Comment: 24 pages, AMS LaTeX, 4 figure

Projective non-Abelian Statistics of Dislocation Defects in a Z_N Rotor Model

Non-Abelian statistics is a phenomenon of topologically protected non-Abelian Berry phases as we exchange quasiparticle excitations. In this paper, we construct a Z_N rotor model that realizes a self-dual Z_N Abelian gauge theory. We find that lattice dislocation defects in the model produce topologically protected degeneracy. Even though dislocations are not quasiparticle excitations, they resemble non-Abelian anyons with quantum dimension sqrt(N). Exchanging dislocations can produces topologically protected projective non-Abelian Berry phases. The dislocations, as projective non-Abelian anyons can be viewed as a generalization of the Majorana zero modes.Comment: 4 pages + refs, 4 figures. RevTeX

Connected Hopf algebras and iterated Ore extensions

We investigate when a skew polynomial extension T = R[x; {\sigma}, {\delta}] of a Hopf algebra R admits a Hopf algebra structure, substantially generalising a theorem of Panov. When this construction is applied iteratively in characteristic 0 one obtains a large family of connected noetherian Hopf algebras of finite Gelfand-Kirillov dimension, including for example all enveloping algebras of finite dimensional solvable Lie algebras and all coordinate rings of unipotent groups. The properties of these Hopf algebras are investigated

Doping a spin-orbit Mott Insulator: Topological Superconductivity from the Kitaev-Heisenberg Model and possible application to (Na2/Li2)IrO3

We study the effects of doping a Mott insulator on the honeycomb lattice where spins interact via direction dependent Kitaev couplings J_K, and weak antiferromagnetic Heisenberg couplings J. This model is known to have a spin liquid ground state and may potentially be realized in correlated insulators with strong spin orbit coupling. The effect of hole doping is studied within a t-J-J_K model, treated using the SU(2) slave boson formulation, which correctly captures the parent spin liquid. We find superconductor ground states with spin triplet pairing that spontaneously break time reversal symmetry. Interestingly, the pairing is qualitatively different at low and high dopings, and undergoes a first order transition with doping. At high dopings, it is smoothly connected to a paired state of electrons propagating with the underlying free particle dispersion. However, at low dopings the dispersion is strongly influenced by the magnetic exchange, and is entirely different from the free particle band structure. Here the superconductivity is fully gapped and topological, analogous to spin polarized electrons with px+ipy pairing. These results may be relevant to honeycomb lattice iridates such as A2IrO3 (A=Li or Na) on doping.Comment: 8 pages + 6 pages supplementary material; 5 figures, 3 tabl

Ultrathin MgB2 films fabricated on Al2O3 substrate by hybrid physical-chemical vapor deposition with high Tc and Jc

Ultrathin MgB2 superconducting films with a thickness down to 7.5 nm are epitaxially grown on (0001) Al2O3 substrate by hybrid physical-chemical vapor deposition method. The films are phase-pure, oxidation-free and continuous. The 7.5 nm thin film shows a Tc(0) of 34 K, which is so far the highest Tc(0) reported in MgB2 with the same thickness. The critical current density of ultrathin MgB2 films below 10 nm is demonstrated for the first time as Jc ~ 10^6 A cm^{-2} for the above 7.5 nm sample at 16 K. Our results reveal the excellent superconducting properties of ultrathin MgB2 films with thicknesses between 7.5 and 40 nm on Al2O3 substrate.Comment: 7 pages, 4 figures, 2 table

Effects of direct injection timing of ethanol fuel on engine knock and lean burn in a port injection gasoline engine

Ethanol is a promising alternative fuel for internal combustion engines due to its renewable feature. To make the use of ethanol fuel more effective and efficient, ethanol direct injection plus gasoline port injection (EDI + GPI) has been investigated in recent years. By directly injecting ethanol into the engine, the advantages of ethanol fuel such as high latent heat of vaporization, fast laminar flame speed, wide flammability and better low temperature combustion stability can be well utilized to enhance engine anti-knock ability and improve lean burn performance. For an engine equipped with direct injection (DI) system, start of injection (SOI) timing is an important control parameter which directly affects the engine performance. This paper reports the investigation to the effect of ethanol fuel SOI timing on knock mitigation and lean burn. Experiments were conducted on a 250 cc single cylinder spark ignition (SI) engine equipped with EDI + GPI system. Ethanol fuel SOI timing before and after the inlet valve closing, defined as early and late injection timings (EEDI and LEDI) were investigated in engine conditions at knock limited spark advance (KLSA) and lean burn limit. The experimental results showed that LEDI was effective on suppressing engine knock and permitting more advanced spark timing. EEDI was less effective than LEDI on mitigating knock due to the increased heat transfer from cylinder wall to gases. The mixture quality may be deteriorated in LEDI conditions which resulted in low engine efficiency and high emissions. Volumetric efficiency was increased and combustion duration was reduced in EEDI conditions. The combined effects of improved volumetric efficiency, reduced combustion duration and moderately advanced spark timing resulted in increased engine thermal efficiency in EEDI conditions. In lean burn, EEDI was more effective on extending lean burn limit. The maximum lambda achieved in EEDI condition was 1.29 when ethanol energy ratio (EER) was 24% and SOI timing was 290 CAD BTDC. LEDI only slightly increased lean burn limit which was just over stoichiometric air-fuel ratio (AFR). In EEDI conditions, IMEP was greater and combustion stability (COV) was better than that in LEDI conditions. The emissions in EEDI conditions were also lower than that in LEDI conditions. © 2014 Elsevier Ltd. All rights reserved