The conservativity of a minimal quantum dynamical semigroup is proved whenever there exists a "generalized" subharmonic operator bounded from below by the dissipative part of the infinitesimal generator.
In this paper, we investigate whenever there exists Λ such that {e−2πiλx}λ∈Λ is an orthonormal basis for L2(μρ,{ak,bk}).
For any nonempty subset of a metric space, the diameter of is denoted and defined by = sup A mapping has diminishing orbital diameters [19, 20] if for each and whenever there exists such that.
A point x ∈ X is called an interior point of a set A ⊆ X whenever there exists 0 ≺ r ∈ C such that B ( x, r ) : = { y ∈ X : d ( x, y ) ≺ r } ⊆ A, where B ( x, r ) is an open ball.
(tin Asubsetmathbb{T}) or △-a.e. on (Asubsetmathbb{T}) whenever there exists a set (Esubset A) with the null Lebesgue △-measure such that this property holds for every (tin Asetminus E).
For two tree monomials α and β, say that α is divisible by β whenever there exists a subtree of the underlying tree of α for which the corresponding tree monomial α ′ is equal to α.
Throughout the paper, we say that the expressions A and B are equivalent, and write A ≈ B whenever there exist positive constants C 1 and C 2 such that C 1 A ≤ B ≤ C 2 A. As usual, the letter C denotes a positive constant, possibly different on each occurrence.
This paper addresses the makespan minimization problem in scheduling flexible job shops whenever there exist separable sequence-dependent setup times.
This shows that AMD is able to quickly disseminate messages whenever there exist end-to-end connectivity to one of the fixed vehicles responsible for gathering data messages.
The selfmap T on X is called a generalized convex contraction whenever there exist a mapping α : X × X → [ 0, ∞ ) and a, b ∈ [ 0, 1 ), with a + b < 1, such that α ( x, y ) d ( T 2 x, T 2 y ) ≤ a d ( T x, T y ) + b d ( x, y ). for all x, y ∈ X. We say that α is the based mapping.
To this end, let us recall, according to [6], that an extended quasi-metric space ((X,d)) is said to be balanced if, given (r,s>0) and (x,yin X) we have (d x,y leq r+s) whenever there exist sequences ((x_{n})_{ninmathbb{N}}), and ((y_{n})_{ninmathbb{N}}) with (lim_{n,mrightarrowinfty }d y_{m},x_{n})=0) and such that (d x,x_{n})leq r) and (d y_{n},y leq s) for all (ninmathbb{N}).
