the bft approach is used to formulate the electronic states in graphene through a non-commutative space in the presence of a constant magnetic field b for the first time. in this regard, we introduce a second class of constrained system, which is not gauge symmetric but by applying bft method and extending phase space, the second class constraints  converts  to the first class constraints so th...

‎let $pa$ be a commutative banach algebra and $ex$ be a left banach $pa$-module‎. ‎we study the set‎ ‎$dec_{pa}(ex)$ of all elements in $pa$ which induce a decomposable multiplication operator on $ex$‎. ‎in the case $ex=pa$‎, ‎$dec_{pa}(pa)$ is the well-known apostol algebra of $pa$‎. ‎we show that $dec_{pa}(ex)$ is intimately related with the largest spectrally separable subalgebra of $pa$ and...

An ω-tree-automatic structure is a relational structure whose domain and relations are accepted by Muller or Rabin tree automata. We investigate in this paper the isomorphism problem for ω-tree-automatic structures. We prove first that the isomorphism relation for ω-treeautomatic boolean algebras (respectively, partial orders, rings, commutative rings, non commutative rings, non commutative gro...

An ideal I in the free associative algebra k〈X1, . . . ,Xn〉 over a field k is shown to have a finite Gröbner basis if the algebra defined by I is commutative; in characteristic 0 and generic coordinates the Gröbner basis may even be constructed by lifting a commutative Gröbner basis and adding commutators.

Amethod developed by Polychronakos to study singular gauge transformations in 1+2 dimensional non-commutative Chern-Simons gauge theory is generalized from U(1) group to U(2) group. The method clarifies the singular behavior of topologically non-trivial gauge transformations in non-commutative gauge theory, which appears when the gauge transformations are viewed from the commutative gauge theor...

We rst develop a notion of quadratic form on a locally compact abelian group. Under suitable hypotheses, we construct a probability measure on the set of closed maximal isotropic subspaces of a locally compact quadratic space over Fp. A random subspace chosen with respect to this measure is discrete with probability 1, and the dimension of its intersection with a xed compact open maximal isotro...

We consider the implications of the equivalence of commutative semifields of odd order and planar Dembowski-Ostrom polynomials. This equivalence was outlined recently by Coulter and Henderson. In particular, following a more general statement concerning semifields we identify a form of planar Dembowski-Ostrom polynomial which must define a commutative semifield with the nuclei specified. Since ...

Lincoln, Scedrov and Shankar proved undecidability of intuitionistic second order multiplicative commutative linear logic by embedding LJ2 into this logic. Emms did the same for intuitionistic second order non-commutative linear logic. Recently, Lafont and Scedrov demonstrated undecidability of classical second order multiplicative commutative linear logic. As for classical second order non-com...

Linear network coding over finite fields is a wellstudied problem. We consider the more general setting of linear coding for directed acyclic networks with finite commutative ring alphabets. Our results imply that for scalar linear network coding over commutative rings, fields can always be used when the alphabet size is flexible, but other rings may be needed when the alphabet size is fixed. W...