Le V Four, 10, rue St.-Michel, (33-3) 83.32.49.48, is a sleek, modern restaurant with light and innovative food, including tiny shrimp on green peppercorn mayonnaise; smoked duck breast on mesclun; steamed merlan (whiting) with saffron couscous; creme caramel with cocoa powder.
If (u le v), (v ll w) then (u ll w).
Let (u,v in W^{2,1}(a,b)) satisfy begin{aligned} F[u] ge F[v] quad text { and } quad u le v mathrm{in} (a,bb).
Let (C = V, mathbbm {P})), (C le (V, mathbbm {P}))) and (C ge (V, mathbbm {P}))) represent the set of atomic constraints using only =, ≤ and ≥, respectively.
To show (2), we suppose to the contrary that (unot equiv v) on ([0,,R]), and note by assumption that (u le v) in ([0,,R]).
The active power generated by the wind turbine, P wt, is determined by the wind speed [32], which is formulated as: begin{gathered} P_{wt} = left{ {begin{array}{ll} 0 & quadquad { 0le v < v_{ci} } {a + bv^{3}, } & quad {, v_{ci} le v < v_{ra} } {P_{ra}, } & quad {, v_{ra} le v < v_{co} } {0, } & quad {, v > v_{co} } end{array} } right.
end{aligned} end{aligned} Then we obtain, for (tge0), the following inequalities: {{W}_{1}} bigl( biglVert phi( 0 ) bigrVert bigr)le V ( t, phi le{{W}_{2}} bigl( biglVert phi( 0 ) bigrVert bigr)+{{W}_{3}} bigl( biglvert Vert phi Vert bigrvert bigr).
The relationship between the wind power output and wind speed can be described by (22): P = left{ {begin{array}{*{20}l} 0 hfill & {v le v_{in},v ge v_{out} } hfill {P_{N} frac{{v - v_{in} }}{{v_{rated} - v_{in} }}} hfill & {v_{in} < v < v_{rated} } hfill {P_{N} } hfill & {v_{rated} le v < v_{out} } hfill end{array} } right.
By the above similar deduction steps, we know begin{gathered} M_{4} le u le M_{1},qquad M_{5} le v le M_{2},qquad M_{6} le w le M_{3}, vert u vert le max bigl{ vert M_{1} vert, vert M_{4} vert bigr} = H_{1},qquad vert v vert le max bigl{ vert M_{2} vert, vert M_{5} vert bigr} = H_{2}, vert w vert le max bigl{ vert M_{3} vert, vert M_{6} vert bigr} = H_{3}.
It follows from Lemmas 3.5 and 3.6 that there exist positive constants (g_{i}), (G_{i}), and (T^) (defined in Lemma 3.5 and Lemma 3.6, respectively) such that g_{1} le u(t),hat{u}(t) le G_{1},qquad g_{2} le v(t),hat{v}(t) le G_{2},qquad g_{3} le w(t),hat{w}(t) le G_{3}quad mbox{for } t ge T^.
The optimal solution value of the problem f n (c 1,c 2) can thus be obtained by iteratively applying the following recursive formulae: {f_{1}}left({u,v} right) = left{ {begin{array}{*{20}{c}} {{p_{1}}} & {text{for} ;{w_{1}^{1}} le u le {c_{1}},;{w_{2}^{1}} le v le {c_{2}}}, 0 & {text{otherwise}}, end{array}} right.
