In this paper, we will provide a simple method for starting with a given finite frame for an $n$-dimensional Hilbert space $mathcal{H}_n$ with nonzero elements and producing a frame which is $epsilon$-nearly Parseval and $epsilon$-nearly unit norm. Also, the concept of the $epsilon$-nearly equal frame operators for two given frames is presented. Moreover, we characterize all bounded invertible ...

The construction of amplitudes on curved space-times is a major challenge, particularly when the background has non-constant curvature. We give formulae for all tree-level graviton scattering in self-dual radiative space-times; these are chiral, source-free, asymptotically flat spaces determined by free characteristic data at null infinity. Such admit an elegant description terms twistor theory...

Dual topology for the function space topologies multifunctions are introduced and investigated. It is found that a T on CM(Y,Z) splitting (resp. admissible) if only its dual pair (T+,T?) admissible). Similarly, T(T+,T?)

The dual conformal box integral in Minkowski space is not fully determined by the invariants $z$ and $\bar{z}$. Depending on kinematic region its value a 'branch' of Bloch-Wigner function which occurs Euclidean case. Dual special transformations can change such way that jumps to another branch this function, encoding subtle breaking invariance for integral. We classify conformally equivalent co...