In topological phases of matter, the interplay between intrinsic order and global symmetry is an interesting task. study orders with discrete symmetry, important systematic approach construction exactly soluble lattice models. However, for continuous in particular electromagnetic U(1), has been less systematically developed. this paper, we introduce a effective theories large class abelian on t...

By adding a proper term to the Lagrangian density of a real non-linear KG system with a proposed non-topological unstable solitary wave solution, its stability guaranteed appreciably. This additional term in the new modified Lagrangian density behaves like a strong internal force which stands against any arbitrary small deformation in the proposed non-topological solitary wave solution.

Notions and techniques of enriched category theory can be used to study topological structures, like metric spaces, topological spaces and approach spaces, in the context of topological theories. Recently in [D. Hofmann, Injective spaces via adjunction, arXiv:math.CT/0804.0326] the construction of a Yoneda embedding allowed to identify injectivity of spaces as cocompleteness and to show monadic...

The topological semantics for modal logic interprets a standard modal propositional language in topological spaces rather than Kripke frames: the most general logic of topological spaces becomes S4. But othermodal logics can be given a topological semantics by restricting attention to subclasses of topological spaces: in particular, S5 is logic of the class of almost discrete topological spaces...

Description PathNet uses topological information present in pathways and differential expression levels of genes (obtained from microarray experiment) to identify pathways that are 1) significantly enriched and 2) associated with each other in the context of differential expression. The algorithm is described in: PathNet: A tool for pathway analysis using topological information.

Notions and techniques of enriched category theory can be used to study topological structures, like metric spaces, topological spaces and approach spaces, in the context of topological theories. Recently in [D. Hofmann, Injective spaces via adjunction, arXiv:math.CT/0804.0326] the construction of a Yoneda embedding allowed to identify injectivity of spaces as cocompleteness and to show monadic...

In this paper, the new concept of non-autonomous iterated function system is introduced and also shown that non-autonomous iterated function system IFS(f_(1,∞)^0,f_(1,∞)^1) is topologically transitive for the metric space of X whenever the system has average shadowing property and its minimal points on X are dense. Moreover, such a system is topologically transitive, whenever, there is a point ...

We give sufficient conditions for the existence of a Quillen model structure on small categories enriched in a given monoidal model category. This yields a unified treatment for the known model structures on simplicial, topological, dgand spectral categories. Our proof is mainly based on a fundamental property of cofibrant enriched categories on two objects, stated below as the Interval Cofibra...

The Lieb-Schultz-Mattis theorem and its higher-dimensional generalizations by Oshikawa and Hastings require that translationally invariant 2D spin systems with a half-integer spin per unit cell must either have a continuum of low energy excitations, spontaneously break some symmetries, or exhibit topological order with anyonic excitations. We establish a connection between these constraints and...