We give nonequilibrium Green's function (NEGF) perspective on thermodynamics formulations for open quantum systems strongly coupled to baths. Scattering approach implying thermodynamic consideration of a super-system (system plus baths) weakly external super-baths is compared with system its analyze both approaches from the NEGF and argue that latter yields possibility formulation consistent dy...

The generalized structure of deoxyribonucleic acid (DNA) is based on the rules topological spaces. DNA recombination one most important processes within DNA, as it essential in pharmaceutical industry well gene therapy. In this paper, we are discussing relationship between rough sets, nano spaces (N), Z open (N) and recombination. We also created a new mapping using properties process. Further,...

Let R = (R,<,+, ·, . . . ) be a non-valuational weakly o-minimal real closed field, I a definable convex open subset of R and f : I → R a definable function. We prove that {x ∈ I : f ′(x) exists in R} is definable and f ′ is definable if f is differentiable.

for fr$acute{mathbf{text{e}}}$chet algebras $(a, (p_n))$ and $(b, (q_n))$, a linear map $t:arightarrow b$ is textit{almost multiplicative} with respect to $(p_n)$ and $(q_n)$, if there exists $varepsilongeq 0$ such that $q_n(tab - ta tb)leq varepsilon p_n(a) p_n(b),$ for all $n in mathbb{n}$, $a, b in a$, and it is called textit{weakly almost multiplicative} with respect to $(p_n)$ and $(q_n)$,...

The notion of -open sets in a topological space was studied by Velicko. Usha Parmeshwari et.al. and Indira introduced the concepts b# *b open respectively. Following this Ekici et. al. notions e-open e-closed mixing closure, interior, -interior -closure operators. In paper some new namely e#-open *e-open are defined their relationship with other similar concetps spaces will be investigated.