Suppose that the vector-valued functions f and g in the primal problem (CLFP) can be parameterized as the vector-valued functions (mathbf{f}_{epsilon}) and (mathbf{g}_{epsilon}) for (epsilon>0) in which (mathbf{f}_{epsilon}) and (mathbf{g}_{epsilon}) are assumed to be continuous functions on ([0,T]) and (mathbf{g}_{epsilon}(t geqmathbf{0}) for all (tin[0,T]).
where f ( x ) ∈ L q 2 for some q > n, and the coefficients a i j ( i, j = 1, …, n ) are assumed to be measurable functions on Ω, and there exist positive constants λ and Λ such that a i j ( x ) ξ i ξ j ≥ λ | ξ | 2, ∀ x ∈ Ω, ξ ∈ R n (4.2). and Σ | a i j ( x ) | 2 ≤ Λ 2. (4.3).
The deleted regions were assumed to have crucial functions, on the basis of our novel observations of the reduced genome, along with the previous reports of its advantages in various applications [ 17, 21, 23] but its limited evolvability [ 20].
This function is assumed to depend on the saturation and fluid properties but not on the flow regime (or Reynolds number).
The size of criticality is modelled by a distribution function and assumed to be independent on location.
The observation that recreational use of cocaine is associated with impairments in response inhibition, cognitive flexibility, and IOR all functions that are assumed to rely on dopaminergic pathways [9], [15], [16] suggests that recreational use is sufficient to hamper the dopaminergic support of cognitive control functions.
The gene expression function g is here assumed to depend on the ultimate metabolite only, the latter acting on the synthesis of the first enzyme.
The elasticity tensor is assumed to depend linearly on the design function (density) as in the variable thickness sheet problem.
Since the vector-valued function g is assumed to be nonnegative on ([0,T]), it is easy to see that the primal problem (CLFP) is feasible with the trivial feasible solution (mathbf{x}(t)=mathbf{0}) for all (tin[0,T]).
Thus, the approximate sequence ({ X^{n}(t) }) uniformly converges to (X t)) (where (X t)) is assumed to be the sum function) on ([t_{0} - tau,T]), and it is (mathsf{F}_{t} -adapted.
