Perturbation of Burkholder's martingale transform and Monge--Amp\`ere equation

Let $\{d_k\}_{k \geq 0}$ be a complex martingale difference in $L^p[0,1],$ where $1<p<\infty,$ and \{\e_k\}_{k \geq 0} a sequence in $\{\pm 1\}.$ We obtain the following generalization of Burkholder's famous result. If $\tau \in [-\frac 12, \frac 12]$ and $n \in \Z_+$ then |\sum_{k=0}^n{(\{c} \e_k \tau) d_k}|_{L^p([0,1], \C^2)} \leq ((p^*-1)^2 + \tau^2)^{\frac 12}|\sum_{k=0}^n{d_k}|_{L^p([0,1], \C)}, where $((p^*-1)^2 + \tau^2)^{\frac 12}$ is sharp and $p^*-1 = \max\{p-1, \frac 1{p-1}\}.$ For $2\leq p<\infty$ the result is also true with sharp constant for $\tau \in \R.$Comment: 45 pages, 13 figure

The Role of Action Research in Services for Deaf Alcoholics

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Bridging the Gap with Deaf Paraprofessionals

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q→Λq \to \Lambda Fragmentation Function and Nucleon Transversity Distribution in a Diquark Model

Based on a simple quark-diquark model, we propose a set of unpolarized, longitudinally polarized and transversely polarized fragmentation functions for the $\Lambda$ by fitting the unpolarized $\Lambda$ production data in $e^+ e ^-$ annihilation. It is found that the helicity structure of the obtained $\Lambda$ fragmentation functions is supported by the all available experimental data on the longitudinal $\Lambda$ polarization. Within the same framework of the diquark model, the nucleon transversity distributions are presented and consistent descriptions of the available HERMES data on the azimuthal spin asymmetries in pion electroproduction are obtained. Furthermore, the spin transfers to the transversely polarized $\Lambda$ in the charged lepton DIS on a transversely polarized nucleon target are predicted for future experiments.Comment: Talk given in a seminar of U. Santa Mari

Lambda Polarization in Polarized Proton-Proton Collisions at RHIC

We discuss Lambda polarization in semi-inclusive proton-proton collisions, with one of the protons longitudinally polarized. The hyperfine interaction responsible for the $\Delta$-$N$ and $\Sigma$-$\Lambda$ mass splittings gives rise to flavor asymmetric fragmentation functions and to sizable polarized non-strange fragmentation functions. We predict large positive Lambda polarization in polarized proton-proton collisions at large rapidities of the produced Lambda, while other models, based on SU(3) flavor symmetric fragmentation functions, predict zero or negative Lambda polarization. The effect of $\Sigma^0$ and $\Sigma^*$ decays is also discussed. Forthcoming experiments at RHIC will be able to differentiate between these predictions.Comment: 18 pages, 5 figure