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.