After reviewing the group structure and representation theory for dihedral $$D_{2n},$$ we consider an intertwining operator $$\varPhi _\rho $$ from algebra $$\mathbb {C}[D_{2n}]$$ into a corresponding space of semi-magic matrices. From this operator, one obtains generating function enumerating associated squares with fixed line sum extending circulant While work complements approach to $$D_{2n}...

we consider the transitive linear maps on the operator algebra $b(x)$for a separable banach space $x$. we show if a bounded linear map is norm transitive on $b(x)$,then it must be hypercyclic with strong operator topology. also we provide a sot-transitivelinear map without being hypercyclic in the strong operator topology.

-This paper discusses the ways in which automation of industrial processes may expand rather than eliminate problems with the human operator. Some comments will be made on methods of alleviating these problems within the "classic' approach of leaving the operator with responsibility for abnormal conditions, and on the potential for continued use of the human operator for on-line decision-making...

The Wilson loop with a wavy line contour is studied using integrable methods. The auxiliary problem is solved and the Lax operator is built to first order in perturbation theory, considering a small perturbation from the straight line. Finally the spectral curve of the solution is considered.

We present results on the unique reconstruction of a semi-infinite Jacobi operator from the spectra of the operator with two different boundary conditions. This is the discrete analogue of the Borg-Marchenko theorem for Schrödinger operators in the half-line. Furthermore, we give necessary and sufficient conditions for two real sequences to be the spectra of a Jacobi operator with different bou...

The long standing problem of the ordering ambiguity in the definition of the Hamilton operator for a point particle in curved space is naturally resolved by using the powerful geometric calculus based on Clifford Algebra. The momentum operator is defined to be the vector derivative (the gradient) multiplied by −i; it can be expanded in terms of basis vectors γμ as p = −iγ∂μ. The product of two ...

In this paper, the digraph valued function(digraph operator), namely the block line cut vertex digraph BLC(D) of a digraph D is defined, and the problem of reconstructing a digraph from its block line cut vertex digraph is presented. Outer planarity, maximal outer planarity, and minimally non-outer planarity properties of these digraphs are discussed.

In dimension d ≥ 5, we consider the differential operator (1.1) H0 = −∆+ τζ(x)|x|(−∆θ), ε > 0, τ > 0, where ∆θ is the Laplace-Beltrami operator on the unit sphere S = {x ∈ R : |x| = 1} and ζ is the characteristic function of the complement to the unit ball {x ∈ R : |x| ≤ 1}. The standard argument with separation of variables allows one to define this operator as the orthogonal sum of one-dimens...