Let B(X) be the algebra of all bounded linear operators on the Banach space X, and let N (X) be the set of nilpotent operators in B(X). Suppose φ : B(X)→ B(X) is a surjective map such that A,B ∈ B(X) satisfy AB ∈ N (X) if and only if φ(A)φ(B) ∈ N (X). If X is infinite dimensional, then there exists a map f : B(X)→ C \ {0} such that one of the following holds: (a) There is a bijective bounded li...

theoretically, in order to describe the behavior of a spectrum, a mathematical model whichcould predict the spectrum characteristics is needed. since in this study a two-state system has beenused like models which was introduced previously past and could couple with the environment, theformer ideas have been extended in this study. we use the second quantized version for writing thishamiltonian...

We numerically study the superconductor-insulator phase transition in a model disordered two-dimensional 2D superconductor as a function of applied magnetic field. The calculation involves quantum Monte Carlo calculations of the 2+1 D XY model in the presence of both disorder and magnetic field. The XY coupling is assumed to have the form −J cos i− j −Aij , where Aij has a mean of zero and a st...

We introduce a family of kernels on graphs based on the notion of regularization operators. This generalizes in a natural way the notion of regularization and Greens functions, as commonly used for real valued functions, to graphs. It turns out that diffusion kernels can be found as a special case of our reasoning. We show that the class of positive, monotonically decreasing functions on the un...

the object of this paper is to establish certain generalized fractional integration and differentiation involving generalized mittag-leffler function defined by salim and faraj [25]. the considered generalized fractional calculus operators contain the appell's function $f_3$ [2, p.224] as kernel and are introduced by saigo and maeda [23]. the marichev-saigo-maeda fractional calculus operat...

Theoretically, in order to describe the behavior of a spectrum, a mathematical model whichcould predict the spectrum characteristics is needed. Since in this study a Two-state system has beenused like models which was introduced previously past and could couple with the environment, theformer ideas have been extended in this study. we use the second quantized version for writing thisHamiltonian...