In this paper, we deal with Molaei’s generalized groups. We definethe notion of a fuzzy generalized subgroup with respect to a t-norm (orT-fuzzy generalized subgroup) and give some related properties. Especially,we state and prove the Representation Theorem for these fuzzy generalizedsubgroups. Next, using the concept of continuity of t-norms we obtain a correspondencebetween TF(G), the set of ...

The purpose of this paper is to show that an isomorphism between the lattices of all closed sets of two topological spaces induces an isomorphism on the lattices of their zero-sets. This is achieved by showing that any continuous real-valued function on a space X can be transferred to any space latticeequivalent to X. Several topological properties are shown to be lattice-invariant.

We report a direct observation of surface dominated conduction in an intrinsic Bi(2)Se(3) thin film with a thickness of six quintuple layers grown on lattice-matched CdS (0001) substrates by molecular beam epitaxy. Shubnikov-de Haas oscillations from the topological surface states suggest that the Fermi level falls inside the bulk band gap and is 53 ± 5 meV above the Dirac point, which is in ag...

The recently developed families index theory for the overlap lattice Dirac operator is applied to demonstrate an interplay between topological features of the space of SU(N) lattice gauge fields on the 4-torus and the existence question for G0 gauge fixings which do not have the Gribov problem. The continuum version of our considerations leads to topological obstructions to the existence of suc...

Twists are defects in the lattice which can be utilized to perform computations on encoded data. have been studied various classes of topological codes like qubit and qudit surface codes, color subsystem codes. They known exhibit projective non-Abelian statistics is exploited gates. In this paper, we initiate study twists over odd prime alphabet. To best our knowledge, first Specifically, prese...

We study the renormalization group evolution up to the xed point of the lattice topological susceptibility in the 2{d O(3) non{linear {model. We start with a discretization of the continuum topological charge by a local charge density, polynomial in the lattice elds. Among the diierent choices we propose also a Symanzik{improved lattice topological charge. We check step by step in the renormali...

We propose an experimental implementation of a topological superfluid with ultracold fermionic atoms. An optical superlattice is used to juxtapose a 1D gas of fermionic atoms and a 2D conventional superfluid of condensed Feshbach molecules. The latter acts as a Cooper pair reservoir and effectively induces a superfluid gap in the 1D system. Combined with a spin-dependent optical lattice along t...

On the lattice some of the salient features of pure gauge theories and of gauge theories with fermions in complex representations of the gauge group seem to be lost. These features can be recovered by considering part of the theory in the continuum. The prerequisite for that is the construction of continuum gauge fields from lattice gauge fields. Such a construction, which is gauge covariant an...

A novel feature of a Ginsparg-Wilson lattice Dirac operator is discussed. Unlike the Dirac operator for massless fermions in the continuum, this lattice Dirac operator does not possess topological zero modes for any topologically-nontrivial background gauge fields, even though it is exponentially-local, doublers-free, and reproduces correct axial anomaly for topologically-trivial gauge configur...