Sentence examples for tin Jbigr} from inspiring English sources
Let (E=C(J)) be the standard Banach space with the maximum norm and P be the typical cone of nonnegative continuous functions in the form P=bigl{ uin E u(t geqgamma(t)|u|, tin Jbigr}.
Define the set of selections of F by S_{F,u}:=bigl{ vin L^{1}(J,mathbb{R}): v(t)in Fbigl t, u(t), u'(t), u t), ^{mathrm{c}}D^{p}u(t) bigr) mbox{ for almost all } tin Jbigr}.
Define the multifunction (U: J rightarrow {mathcal{P}}(mathbb{R})) by begin{aligned} U t) =&bigl{ zinmathbb{R} : biglvert v_{1}(t -zbigrvert leq m(t -zbigrvertleqrt u(t)-w(t)bigrvert +biglvert u'(t)-w'(t) bigrvert + biglvert u"(t)-w"(t) bigrvert &+ biglvert ^{mathrm{c}}D^{p} u(t)-^{mathrm{c}}D^{p} w(t)biglvert biglvertox{ for almost all } tin Jbigr}.
(2.14) Let C be a cone in E which is defined as C=bigl{ xin E: xgeq0, x t geqdelta|x|, tin Jbigr}, where delta=frac{rho_{1}}{rho_{2}}.
Set begin{aligned} &P=bigl{ xin X:x mbox{ is nonnegative, concave and } x t geq GammalVert{x}lVert, tin Jbigr}, &overline{P_{r}}=bigl{ x in P:lVert{x}lVertleq rbigr}, end{aligned} (4.1) where Γ is defined as in Lemma 2.4.
It is well known that (mathrm{PC}(J,E)) is a Banach space endowed with the Chebyshev PC-norm: Vert x Vert _{mathrm{PC}(J,E)}=maxbigl{ biglVert x t) bigrVert :t in Jbigr}, or the Bielecki PCB-norm: Vert x Vert _{mathrm{PCB}(J,E)}=maxbigl{ e^{-Lt} biglVert x t) bigrVert : tin Jbigr},quad Lin[ 0,infty).
Consider the multifunction (U Jto{mathcal{P}}(mathbb{R})) by U t)=bigl{ sinmathbb{R}: biglvert v_{1}(t -sbigrvert leq m(t -sbigrvert{ for aleqst all } tin Jbigr}, where begin{aligned} g(t) =& Biggl[ biglvert u(t) -w(t) bigrvert + biglvert u'(t) -w'(t) bigrvert + biglvert u"(t)-w"(t)bigrvert &+ sum_{i=1}^{k} biglvert g{c}D^{q_{i}} u(t)-^{c}D^{q_{i}}w(t) bigrvert Biggr].
RIN TIN TIN, by Susan Orlean.
