Class number one criterion for some non-normal totally real cubic fields

Let ${\{K_m\}_{m\geq 4}}$ be the family of non-normal totally real cubic number fields defined by the irreducible cubic polynomial $f_m(x)=x^3-mx^2-(m+1)x-1$, where $m$ is an integer with $m\geq 4$. In this paper, we will give a class number one criterion for $K_m$.Comment: 9 page

METCAN simulation of candidate metal matrix composites for high temperature applications

The METCAN (Metal Matrix Composite Analyzer) computer code is used to simulate the nonlinear behavior of select metal matrix composites in order to assess their potential for high temperature structural applications. Material properties for seven composites are generated at a fiber volume ratio of 0.33 for two bonding conditions (a perfect bond and a weak interphase case) at various temperatures. A comparison of the two bonding conditions studied shows a general reduction in value of all properties (except CTE) for the weak interphase case from the perfect bond case. However, in the weak interphase case, the residual stresses that develop are considerably less than those that form in the perfect bond case. Results of the computational simulation indicate that among the metal matrix composites examined, SiC/NiAl is the best candidate for high temperature applications at the given fiber volume ratio

The Internet and democratic discourse : case studies of two humanitarian and political websites

http://www.worldcat.org/oclc/4089384

Commuting-projector Hamiltonians for chiral topological phases built from parafermions

We introduce a family of commuting-projector Hamiltonians whose degrees of freedom involve $\mathbb{Z}_{3}$ parafermion zero modes residing in a parent fractional-quantum-Hall fluid. The two simplest models in this family emerge from dressing Ising-paramagnet and toric-code spin models with parafermions; we study their edge properties, anyonic excitations, and ground-state degeneracy. We show that the first model realizes a symmetry-enriched topological phase (SET) for which $\mathbb{Z}_2$ spin-flip symmetry from the Ising paramagnet permutes the anyons. Interestingly, the interface between this SET and the parent quantum-Hall phase realizes symmetry-enforced $\mathbb{Z}_3$ parafermion criticality with no fine-tuning required. The second model exhibits a non-Abelian phase that is consistent with $\text{SU}(2)_{4}$ topological order, and can be accessed by gauging the $\mathbb{Z}_{2}$ symmetry in the SET. Employing Levin-Wen string-net models with $\mathbb{Z}_{2}$-graded structure, we generalize this picture to construct a large class of commuting-projector models for $\mathbb{Z}_{2}$ SETs and non-Abelian topological orders exhibiting the same relation. Our construction provides the first commuting-projector-Hamiltonian realization of chiral bosonic non-Abelian topological order.Comment: 29+18 pages, 25 figure

Electric-Magnetic Dualities in Non-Abelian and Non-Commutative Gauge Theories

Electric-magnetic dualities are equivalence between strong and weak coupling constants. A standard example is the exchange of electric and magnetic fields in an abelian gauge theory. We show three methods to perform electric-magnetic dualities in the case of the non-commutative $U(1)$ gauge theory. The first method is to use covariant field strengths to be the electric and magnetic fields. We find an invariant form of an equation of motion after performing the electric-magnetic duality. The second method is to use the Seiberg-Witten map to rewrite the non-commutative $U(1)$ gauge theory in terms of abelian field strength. The third method is to use the large Neveu Schwarz-Neveu Schwarz (NS-NS) background limit (non-commutativity parameter only has one degree of freedom) to consider the non-commutative $U(1)$ gauge theory or D3-brane. In this limit, we introduce or dualize a new one-form gauge potential to get a D3-brane in a large Ramond-Ramond (R-R) background via field redefinition. We also use perturbation to study the equivalence between two D3-brane theories. Comparison of these methods in the non-commutative $U(1)$ gauge theory gives different physical implications. The comparison reflects the differences between the non-abelian and non-commutative gauge theories in the electric-magnetic dualities. For a complete study, we also extend our studies to the simplest abelian and non-abelian $p$-form gauge theories, and a non-commutative theory with the non-abelian structure.Comment: 55 pages, minor changes, references adde

Dimensional Reduction of the Generalized DBI

We study the generalized Dirac-Born-Infeld (DBI) action, which describes a $q$-brane ending on a $p$-brane with a ($q$+1)-form background. This action has the equivalent descriptions in commutative and non-commutative settings, which can be shown from the generalized metric and Nambu-Sigma model. We mainly discuss the dimensional reduction of the generalized DBI at the massless level on the flat spacetime and constant antisymmetric background in the case of flat spacetime, constant antisymmetric background and the gauge potential vanishes for all time-like components. In the case of $q=2$, we can do the dimensional reduction to get the DBI theory. We also try to extend this theory by including a one-form gauge potential.Comment: 29 pages, minor change