We introduce a global equivariant refinement of algebraic K-theory; here ‘global equivariant’ refers to simultaneous and compatible actions all finite groups. Our construction turns specific kind categorical input data into Ω $\Omega$ -spectrum that keeps track genuine G $G$ -equivariant infinite loop spaces, for groups . The resulting K-theory spectrum is rigid way packaging the representation...

In this paper, we consider a Cahn-Hillard/Allen-Cahn equation. By using the semigroup and the classical existence theorem of global attractors, we give the existence of the global attractor in H^k(0

A gravitating global k-monopole produces a tiny gravitational field outside the core in addition to a solid angular deficit in the k-field theory. As a new feature, the gravitational field can be attractive or repulsive depending on the non-canonical kinetic term. PACS numbers: 11.27.+d, 11.10. Lm Gravitating Global k-monopole 2

Data clustering is the process of partitioning a set of data objects into meaning clusters or groups. Due to the vast usage of clustering algorithms in many fields, a lot of research is still going on to find the best and efficient clustering algorithm. K-means is simple and easy to implement, but it suffers from initialization of cluster center and hence trapped in local optimum. In this paper...

Directed graphs are commonly drawn by a four phase framework introduced by Sugiyama et al. in 1981. The vertices are placed on parallel horizontal levels. The edge routing between consecutive levels is computed by solving one-sided 2-level crossing minimization problems, which are repeated in up and down sweeps over all levels. Crossing minimization problems are generally NP-hard. We introduce ...