In this paper, we first present a new type of the concept of open sets by expressing some properties of arbitrary mappings on a power set. With the generalization of the closure spaces in categorical topology, we introduce the generalized topological spaces and the concept of generalized continuity and become familiar with weak and strong structures for generalized topological spaces. Then, int...

In this paper we define an order structure on the $p$-operator projective tensor product of Herz algebras and we show that the canonical isometric isomorphism between $A_p(Gtimes H)$ and $A_p(G)widehat{otimes}^p A_p(H)$ is an order isomorphism for amenable groups $G$ and $H$.

In this paper an algebraic star product and differential one defined on a regular coadjoint orbit of a compact semisimple group are compared. It is proven that there is an injective algebra homomorphism between the algebra of polynomials with the algebraic star product and the algebra of differential functions with the differential star product structure. Investigation supported by the Universi...

Let g be a simple simply laced Lie algebra. In this paper two families of varieties associated to the Dynkin graph of g are described: tensor product and multiplicity varieties. These varieties are closely related to Nakajima’s quiver varieties and should play an important role in the geometric constructions of tensor products and intertwining operators. In particular, it is shown that the set ...

In this paper, we characterize w -Noetherian rings and SM rings. More precisely, in terms of the id="M3"> u -operation on a commutative ring id="M4"> R , prove that id="M5"> is id="M6"> if only direct limit id="M7"> r GV -torsion-free injective id="M8"> -modules id="M9"> SM, whic...

SUMMARY This paper proposes a novel signal estimation method that uses a tensor product expansion. When a bivariable function, which is expressed by two-dimensional matrix, is subjected to conventional tensor product expansion, two single variable functions are calculated by minimizing the mean square error between the input vector and its outer product. A tensor product expansion is useful for...

An injective map from the vertex set of a graph G—its order may not be finite—to the set of all natural numbers is called an arithmetic (a geometric) labeling of G if the map from the edge set which assigns to each edge the sum (product) of the numbers assigned to its ends by the former map, is injective and the range of the latter map forms an arithmetic (a geometric) progression. A graph is c...

The properties and applications of kronecker product in quantum theory is studied thoroughly. The use of kronecker product in quantum information theory to get the exact spin Hamiltonian is given. The proof of non-commutativity of matrices, when kronecker product is used between them is given. It is shown that the non-commutative matrices after kronecker product are similar or they are similar ...

4 Derived Tensor 15 4.1 Tensor Product of Complexes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 4.2 Hoflat Complexes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 4.3 Derived Tensor Product . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 4.4 Change of Rings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...

This article is dedicated to the study of quasinormable injective tensor products of locally convex spaces and quasinormable spaces of continuous linear operators. The stability of the quasinormability is obtained in the frame of the class of spaces which are quasinormable by operators; this class, introduced and studied here, contains many function spaces. The problems considered in the articl...