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Similarly, it derives a weak social preference for $B$ to $C$.
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The second step consists in performing the dynamic analysis of the gate by deriving a weak form of the equilibrium equation.
In doing so, we derive a weak formulation of this operator on which we get directly the conservation properties and the decay of the entropy as it is the case for the three-dimensional operator.
Using the asymptotic framework of Bhattacharya [Asymptotic Inference from multi-stage surveys. Journal of Econometrics 126(145 171]171], I derive a weak convergence result for the continuously-indexed Lorenz process even when the underlying density is not uniformly bounded away from zero.
We derive a weak convergence theorem for the sequences generated by the proposed scheme.
We then have derived a weak and a strong maximum principles for the linear time-fractional diffusion equation.
He derived a weak convergence result, which shows that for suitable choices of iterative paraments, the sequence of iterative algorithm solutions can converge weakly to an exact solution of the SFP.
This inequality is then employed to derive a weak and a strong maximum principles for the time-fractional diffusion equation with the Caputo fractional derivative of non-singular kernel.
He derived a weak convergence result, which shows that for suitable choices of iterative parameters (including the regularization), the sequence of iterative solutions can converge weakly to an exact solution of the SFP.
By taking (K equiv I), the identity operator in Theorem 3.1, we can derive a weak convergence result for Algorithm 3.2 in which the operator T is nonexpansive cutter, but not strongly nonexpansive as in [16].
We assume that the following coercivity condition holds: α − 1 2 ∇ ⋅ β ≥ α 0 > 0. To consider the CIP Galerkin approximation of the above optimal control problem, we first derive a weak formulation for the state equation.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com