We show that there exist no proper warped product semi-invariant submanifolds in almost paracontact Riemannian manifolds such that totally geodesic submanifold and totally umbilical submanifold of the warped product are invariant and anti-invariant, respectively. Therefore, we consider warped product semi-invariant submanifolds in the form N N⊥×fNT by reversing two factor manifolds NT and N⊥. W...

The direct product of two Fibonacci tilings can be described as a genuine stone inflation rule with four prototiles. This admits various modifications, which lead to 48 different rules, known the variations. They all result in that are measure-theoretically isomorphic by Halmos–von Neumann theorem. cut and project sets characteristic windows two-dimensional Euclidean internal space. Here, we an...

The purpose of this study is to construct the concept direct product bitonic algebras, and investigate some respective features. Also, commutative homomorphism are studied. Then notion algebras expanded finite family their qualifications practised.

We propose a generalization of the external direct product concept to polyadic algebraic structures which introduces novel properties in two ways: arity can differ from that constituents, and elements different multipliers be \textquotedblleft entangled\textquotedblright\ such is no longer componentwise. The main property we want preserve associativity, gained by using associativity quiver tech...

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 ...

In this paper we present a new proof to generalize the Fubini's Theorem for even index subgroup of compact Lie group, using recent result on semi-direct product groups. We also some applications invariant theory.