Two types of robust cycle bases are defined via recursively nice arrangements; complete and bipartite complete graphs are shown to have such bases. It is shown that a diagram in a groupoid is commutative up to natural equivalence (cutne) if for each cycle in a robust basis of the graph underlying the diagram, the composition of the morphisms is naturally equivalent to the identity. For a hyperc...

Commutativity of subsystems in cascade connected forms to form larger systems gets worthy to improve noise disturbance properties, stability, robustness and many other properties in system design. In this paper, another benefit of commutativity property is indicated, as far as the author knowledge for the first time, and illustrated by examples. This benefit is the gain of a new and original me...

Leading order study of direct photon production from proton–proton collisions, in the framework Minimal (Seiberg–Witten) Non-Commutative Standard Model (NCSM), taking into account Earth-rotation effects. We found that relative non-commutative contributions increase significantly at very high transverse momentum. Therefore, using Run-1 ([Formula: see text] TeV) and Run-2 ATLAS experimental data ...

in this paper, we consider the finitely presented groups $g_{m}$ and $k(s,l)$ as follows;$$g_{m}=langle a,b| a^m=b^m=1,~[a,b]^a=[a,b],~[a,b]^b=[a,b]rangle $$$$k(s,l)=langle a,b|ab^s=b^la,~ba^s=a^lbrangle;$$and find the $n^{th}$-commutativity degree for each of them. also we study the concept of $n$-abelianity on these groups, where $m,n,s$ and $l$ are positive integers, $m,ngeq 2$ and $g.c.d(s,...

We explore commutativity up to a factor for bounded operators in a complex Hilbert space.