In this article we define the tensor product of partial acts over a semigroup and prove several properties product. We also notion polite biact, which is needed to actions on acts. Finally, that certain functor left adjoint hom-functor

In this work, we investigate the classical loop models doped with monomers and dimers on a square lattice, whose partition function can be expressed as a tensor network (TN). In the thermodynamic limit, we use the boundary matrix product state technique to contract the partition function TN, and determine the thermodynamic properties with high accuracy. In this monomer-dimer-loop model, we find...

Recent results of Voevodsky and others have effectively led to the proof of the Lichtenbaum-Quillen conjectures at the prime 2, and consequently made it possible to determine the 2-local homotopy type of the K-theory spectra for various number rings. The basic case is that of BGL(Z); in this note we use these results to determine the 2-local (topological) K-theory of the space BGL(Z), which can...

Boolean network is a powerful tool in describing the genetic regulatory networks. Accompanying the development of systems biology, the analysis and control of Boolean networks have attracted much attention from biologists, physicists, and systems scientists. This paper surveys a series of recent results on Boolean (control) networks, obtained by the algebraic approach proposed by the authors. F...

In this paper, we study trellis properties of the tensor product (product code) of two linear codes, and prove that the tensor product of the lexicographically first bases for two linear codes in minimal span form is exactly the lexicographically first basis for their product code in minimal span form, also the tensor products of characteristic generators of two linear codes are the characteris...