Abstract The deep theory of approximate subgroups establishes three-step product growth for subsets finite simple groups $G$ Lie type bounded rank. In this paper, we obtain two-step results representations such (including those unbounded rank), where products are replaced by tensor representations. Let be a group and $\chi $ character $G$. $|\chi |$ denote the sum squares degrees all (distinct)...

Since the 1930s, topological counting on finite sets has been an interesting work so as to enumerate number of corresponding order relations sets. Starting from semi-tensor product (STP), we give expression relationship between subsets perspective algebra. Firstly, using STP matrices, present algebraic representation subset and complement structure matrices. Then, investigate respectively inter...

We construct a classification of coherent sheaves with an integrable log connection, or, more precisely, sheaves with an integrable connection on a smooth log analytic space X over C. We do this in three contexts: sheaves and connections which are equivariant with respect to a torus action, germs of holomorphic connections, and finally global log analytic spaces. In each case, we construct an e...

Abstract. The main purpose of this paper is to present a kneading theory for two-dimensional triangular maps. This is done by defining a tensor product between the polynomials and matrices corresponding to the one-dimensional basis map and fiber map. We also define a Markov partition by rectangles for the phase space of these maps. A direct consequence of these results is the rigorous computati...

A rank 3 tensor product network has 3 dimensions of size p, q, and r, say. Its processing units include pqr Networks Using Distributed binding units, and input/output units grouped into 3 Representations vectors of length p, q and r. Typically one of the I/O vectors represents a predicate, and the other two represent William H. Wilson a pair of arguments. The information represented in the Comp...