The purpose of this work is to investigate the stability property of some models which are currently used in image processing. Following L. Rudin, S.J. Osher and E. Fatemi, we decompose an image f ∈ L2(R2) as a sum u+ v where u belongs to BV(R2) and v belongs to L2(R2). The Banach space BV is aimed at modeling the objects contained in the given image. the optimal decomposition minimizes the ene...

We consider the semidiscrete upwind scheme (0.1) u(t, x)t + 1 ( f ( u(t, x) ) − f ( u(t, x− ) )) = 0. We prove that if the initial data ū of (0.1) has small total variation, then the solution u (t) has uniformly bounded BV norm, independent of t, . Moreover by studying the equation for a perturbation of (0.1) we prove the Lipschitz continuous dependence of u (t) on the initial data. Using a tec...

Skilful means is an important doctrine in Mahayana Buddhism. It gives the movement its pedagogical skill in teaching Dharma and spiritual care. This paper examines the importance of the Jyotis narrative in the Skill-in-Means Sutra, in which a monk violates celibacy for the sake of a woman’s happiness. This essay ties the idea of skill-in-means more intimately with modern Buddhism, examining its...

A dedicated test of the perturbative QCD NLO parton evolution in the very small–x region is performed. We find a good agreement with recent precision HERA–data for F p 2 (x,Q), as well as with the present determination of the curvature of F p 2 . Characteristically, perturbative QCD evolutions result in a positive curvature which increases as x decreases. Future precision measurements in the ve...

Colliding beams of 70% polarized protons at up to √ s=500 GeV, with high luminosity, L=2×10 cmsec, will represent a new and unique laboratory for studying the proton. RHIC-Spin will be the first polarized-proton collider and will be capable of copious production of jets, directly produced photons, and W and Z bosons. Features will include direct and precise measurements of the polarization of t...

Abstract We prove a Nekhoroshev type theorem for the nonlinear Schrödinger equation iut = −∆u+ V ⋆ u+ ∂ūg(u, ū) , x ∈ T, where V is a typical smooth potential and g is analytic in both variables. More precisely we prove that if the initial datum is analytic in a strip of width ρ > 0 with a bound on this strip equals to ε then, if ε is small enough, the solution of the nonlinear Schrödinger equa...

We investigate the possibility to draw conclusions on the sign of the spindependent gluon distribution, ∆G(x,Q), from existing polarized DIS data. The spin-dependent parton distributions ∆uv,∆dv ,∆ū,∆d̄,∆s, and ∆G are constructed in the framework of a phenomenological procedure taking into account some assumptions on signs of valence and sea parton distributions motivated by ’t Hooft’s mechanism...

We report on recent work concerning the effect which the change in vacuum structure (negative energy Dirac sea), in the presence of a confining scalar field, has on the nucleon structure functions and parton distributions. Using the Dirac equation in 1+1 dimensions, we show that distortions in the Dirac sea are responsible for part of the violation of the Gottfried sum rule – i.e., part of the ...