In view of the solution representation formula (2.3), for all, we have (4.10).
Furthermore, the desired estimator parameter is obtained in view of the solution of a convex optimization problem.
The effects of pH and the organic additive, polyethylene glycol (PEG), on the trivalent chromium electroplating were investigated in view of the solution stability, electrochemical reactions and the properties of deposited layer.
Finally, in view of the symmetry result mentioned above for the solution u, that is (u(x_1,bar{x})=tilde{u}(x_1,|x|)) where (tilde{u}: mathbb {R}_+times mathbb {R}rightarrow mathbb {R}), which means that the limit above rewrites as (33).
In view of the advantages of the solution reaction route, low energy consumption, and facility, we introduce it to explore a general synthetic method for CdSe nanomaterials at low temperature.
In view of the Golomb Weinberger principle, the solution to these problems can often be obtained explicitly in the form (sum _{k=1}^M a_kphi (|circ -mathbf{x}_k|)) for a univariate function (phi ), where (|circ |) denotes the usual Euclidean norm [15, 25].
The combination of the uranium solution and chemical processing has to be optimized, especially in view of the need to recycle the solution.
We make the following obvious but essential observation: in view of the uniqueness theorem for the solutions of Hamilton's equations, the solution of (42) with initial value z 0 is the same as that of the Hamiltonian system (43) z ˙ (t ) = J ∂ z H (z (t ), t ) with z (0 ) = z 0. Denoting by (f t H z 0 ) the Hamiltonian flow determined by H z 0 we thus have f t H (z 0 ) = f t H z 0 (z 0 ).
In view of the boundedness of this solution, from the theory of impulsive differential equations in [1], it follows that the solution of system (1.1) can be defined on [ 0, + ∞ ). Lemma 2.2 Suppose that ( H 1 )-( H 6 ) are true.
Remark 2.1 In view of the boundedness of this solution in Lemma 2.1, from the theory of functional differential equations with infinite delay in [17], it follows that the solution of system (1.1) with initial conditions satisfying (2.1) can be defined on [ 0, + ∞ ). Lemma 2.2 Suppose that (H1 - H2) are true.
A definition that is relevant especially in view of the implications of ITS solutions for vulnerable road users, comes from Slater [27].
