Sentence examples for young equality from inspiring English sources

The Young equality holds.

By the Young equality, we have (4.12)  .

and the Young equality holds f ( x ) + f ∗ ( x ∗ ) = 〈 x ∗, x 〉 if and only if x ∗ ∈ ∂ f ( x ).

Moreover, by [3], Theorem 2.4.2 iii), the Young equality holds f(x)+f^{ast} bigl(x^{ast} bigr)= bigllangle x^{ast}, x bigrrangle quadLeftrightarrowquad x^{ast}in partial f(x).

By [17, Theorems 2.3.1 and 2.4.2 iii)], the Young-Fenchel inequality below holds: f(x)+f^{ast}bigl(x^{ast}bigr gebigllangle x, x^{ast}bigrrangle, quadmbox{for each pair } bigl x, x^{ast}bigr) in Xtimes X^{ast}, (2.4) and the Young equality holds: f(x)+f^bigl(x^bigr)=bigllangle x^,xbigrrangle quadmbox{if and only if}quad x^inpartial f(x).

end{aligned} (5.5) Applying the Hölder inequality and ε-Young equality, we have biglvert bigl 2Delta Vertlta^{2}vbigr)bigrvert leq2 Vert Delta vVert _{L^{2}}biglVert Delta^{2}vbigrVert _{L^{2}}leqfrac{1}{4}bigrVert Delta^{2}_{bigrVert ^{2}_{L^{2}}+4Vert Delta vVert ^{2}_{L^{2}}.

Other inmates, however, see a new equality or democracy in blindness: young and old, ugly and beautiful, all are levelled.

It also promoted lifelong learning, adult literacy, the provision of learning opportunities for old and young, gender equality and an all-round improvement in education quality.

It's time to take a long, hard look at how far we have come in offering young women genuine equality in education.

In a column in the Sunday Styles section this weekend, I look at how far toward equality young women have come, how much further they have to go, and (implicit in the conversation) what we as parents can or should be doing about it.

The polling then and now shows broad support for marriage equality among young people, including young Republicans ― well over 60percentt.