Abstract The orthogonality time is examined for different initial states settings interacting locally with types of spin interaction: XX , Ising and anisotropic models. It shown that the number increases, consequently decreases as environment qubits increase. shortest displayed chain model, while largest model. external field increases numbers orthogonality, Dzyaloshinsky–Moriya interaction ort...

A complex fuzzy set is a set whose membership values are vectors in the unit circle in the complex plane. This paper establishes the orthogonality relation of complex fuzzy sets. Two complex fuzzy sets are said to be orthogonal if their membership vectors are perpendicular. We present the basic properties of orthogonality of complex fuzzy sets and various results on orthogonality with respect t...

We study the norm derivatives in context of Birkhoff–James orthogonality real Banach spaces. As an application this, we obtain a complete characterization left-symmetric points and right-symmetric space terms derivatives. strong $$\ell _1^n$$ _\infty ^n$$ also relation defined by some newly introduced variation orthogonality. further orthogonality, approximate smoothness attainment bounded bili...

Atom is a powerful platform for the implementation of prooling, debugging and simulation tools. Kernel support in ATOM makes it possible to implement similar tools for the Digital UNIX kernel. We describe four non-trivial Atom kernel tools which demonstrate the support provided in Atom for kernel work as well as the range of application of Atom kernel tools. We go on to discuss some techniques ...