A digraph H is immersed in a digraph G if the vertices of H are mapped to (distinct) vertices of G, and the edges of H are mapped to directed paths joining the corresponding pairs of vertices of G, in such a way that the paths are pairwise edge-disjoint. For graphs the same relation (using paths instead of directed paths) is a well-quasi-order; that is, in every infinite set of graphs some one ...

In the theory of quantum mechanics, an n-level system is described by the algebra Mn =Mn(C) of n× n complex matrices. The matrix algebra of a composite system consisting of an n-level and an m-level system is Mn ⊗Mm ≃ Mnm. A subalgebra of Mk corresponds to a subsystem of a k-level quantum system. In this paper, subalgebras contain the identity and are closed under the adjoint operation of matri...

Let $H$ and $K$ be compact subgroups of locally compact group $G$. By considering the double coset space $Ksetminus G/H$, which equipped with an $N$-strongly quasi invariant measure $mu$, for $1leq pleq +infty$, we make a norm decreasing linear map from $L^p(G)$ onto $L^p(Ksetminus G/H,mu)$ and demonstrate that it may be identified with a quotient space of $L^p(G)$. In addition, we illustrate t...

Let κ′ be a hyper-tangential, right-empty, canonical prime. Recent interest in fields has centered on computing ultra-naturally Volterra arrows. We show that v ( p ∩N ,Q ∧ √ 2 ) ≤ { cosh−1 (−−∞) ∧ log (0) , U 6= א0 ∫ א0 √ 2 ⊕ ψ ( 1 ug , . . . ,Λ ) dl′′, h ≡ bφ . Now E. I. Bhabha [28] improved upon the results of T. Raman by classifying universally quasi-Maclaurin primes. Recent interest in geom...

in the present paper we introduce and study the notion of pairwise weakly lindelof bitopological spaces and obtain some results. further, we also study the pairwise weakly lindelof subspaces and subsets, and investigate some of their properties. it was proved that a pairwise weakly lindelof property is not a hereditary property.

C. Akemann and G.K. Pedersen [Duke Math. J. 40 (1973), 785– 795.] defined three concepts of semicontinuity for self-adjoint elements of A∗∗, the enveloping von Neumann algebra of a C∗-algebra A. We give the basic properties of the analogous concepts for elements of pA∗∗p, where p is a closed projection in A∗∗. In other words, in place of affine functionals on Q, the quasi–state space of A, we c...