Sentence examples for conjugate index from inspiring English sources

Define the conjugate index by.

is the Sobolev conjugate index of q.

For (p>1), let (p') be its conjugate index.

And (p') is the conjugate index of p, namely, (1/p+1/p'=1/p+1/p

Throughout this paper, let (p') denote the conjugate index of p, that is, (1/p+1/p'=1/p+1/p

For any index (qin[1, infty]), (q') denotes the conjugate index of q, namely, (1/q+1/{q'}=1).

If (sgeq4), (q=frac{s}{2}), and p is the index conjugate to q, then int_{mathbb{R} } bigglvert biggl( frac{sinpixi}{pixi} biggr) biggrvert ^{s},dxileq sqrt{ frac{2}{s}} biggl( frac{2sqrt{p}}{p+1} biggr) ^{q/p}< sqrt{ frac{2}{s}}.

(b) If (sgeq4), (q=frac{s}{2}), and p is the index conjugate to q, then int_{mathbb{R} } bigglvert biggl( frac{sinpixi}{pixi} biggr) biggrvert ^{s},dxileq sqrt{ frac{2}{s}} biggl( frac{2sqrt{p}}{p+1} biggr) ^{q/p}< sqrt{ frac{2}{s}}.  .

Applying the sharp Hausdorff-Young inequality [3], (Vert hat{chi} Vert _{s} leq C_{p}Vert chi Vert _{p}), where (sgeq2), (p=s ^{prime}), the index conjugate to s, and (C_{p}) is given by (C_{p}^{2}=p^{1/p}(s)^{-1/s}), we obtain int_{R} bigglvert frac{sinpixi}{pixi} biggrvert ^{s},dxileq bigl( p^{1/p}s ^{-1/s} bigr) ^{s/2}.

BMI, body mass index; CEE, conjugated equine estrogens; MPA, medroxyprogesterone acetate.

AI: Atherogenic index; CLA: Conjugated linoleic Acid; DGV: Direct genetic value; LCFA: Long chain fatty acid; MCFA: Medium chain fatty acid; MCMC: Markov chain monte carlo; MUFA: Mono-unsaturated fatty acid; PPI: Posterior probability of inclusion; PUFA: Polyunsaturated fatty acids; QTL: Quantitative trait loci; SFA: Saturated fatty acid.