Proof. Let C be a binary code with minimum relative distance δ. Suppose x ∈ {0, 1} is arbitrary and c1, c2, . . . , cL ∈ C are codewords such that for all i, ∆ (x, ci) < ρn. Since each ci is a codeword, we have that ∆ (ci, cj) ≥ δn for all i 6= j. Let Φ : {0, 1} → Rn be the map sending 0 to 1 and 1 to −1. Define u = Φ (x), and, for all i, define vi = Φ (ci). Let ū = 1 √ n u denote the normaliza...

The approach on the left does not work for merely statistically periodic microstructures because periodic boundary conditions cannot be prescribed. Instead, macroscopic strains (ū) are imposed on the boundary ∂Ω of the bounding box and the stress response σ̄ is computed on a proper interior subset Ω#β := {x ∈ Ω | dist(x, ∂Ω) > β} shown in red on the far left. This avoids boundary artifacts (stif...

The study presented in this paper shows that accounting for the relativistic structure of the deuteron allows to explain the ratio of the Drell-Yan pair production cross-section at the low Bjorken x off the deuteron and the proton. Thus, the sea quark distributions in the nucleon should be studied with accounting for the effects of the relativistic structure of the deuteron. The suggested appro...

We present a comprehensive analysis of the recent data from the E866 experiment at Fermilab on Drell-Yan production in pD and pp collisions, which indicates a non-trivial x-dependence for the asymmetry between ū and d̄ quark distributions in the proton. The relatively fast decrease of the asymmetry at large x suggests the important role played by the chiral structure of the nucleon, in particula...

The STAR collaboration aims to study polarized proton-proton collisions at RHIC. The emphasis of the spin run this year is on transverse single spin asymmetries. Beyond 2001, we aim to determine directly and precisely the gluon polarization, as well as the polarizations of the u, ū, d and d̄ quarks in the proton by measuring in addition longitudinal and double spin asymmetries. Furthermore, we a...

Consider the Cauchy problem for a strictly hyperbolic, N×N quasilinear system in one space dimension ut + A(u)ux = 0, u(0, x) = ū(x), (1) where u 7→ A(u) is a smooth matrix-valued map, and the initial data u is assumed to have small total variation. We investigate the rate of convergence of approximate solutions of (1) constructed by the Glimm scheme, under the assumption that, letting λk(u), r...

The interpretation of Drell-Yan production in terms of the antiquark densities depends on NLO corrections. Besides the NLO corrections to the familiar annihilation qq̄ → γ∗ → ll, there is a substantial contribution from the QCD Compton subprocesses gq → qγ∗ → qll and gq̄ → qγ∗ → qll. The beam and target dependence of the two classes of corrections is different. We discuss the impact of this diffe...

Pontryagin’s maximum principle in its infinite dimensional version provides (separate) necessary and su cient conditions for both time and norm optimality for the system y0 = Ay + u (A the infinitesimal generator of a strongly continuous semigroup); in particular it provides a costate z(t) for every time or norm optimal control ū(t) hitting a target ȳ 2 D(A). This paper shows that for the right...

Experiment E04-113 at Jefferson Lab Hall C plans to measure the beam-target double-spin asymmetries in semi-inclusive deep-inelastic ~ p(e, eh)X and ~ d(e, eh)X reactions (h = π, π,K orK) with a 6 GeV polarized electron beam and longitudinally polarized NH3 and LiD targets. The high statistic data will allow a spin-flavor decomposition in the region of x = 0.12 ∼ 0.41 at Q = 1.21 ∼ 3.14 GeV. Es...

Let us work on the numerator. The aim is to rewrite it as a linear combination of γ piece, iσqν piece and q μ piece. The reason is the following. It is only γ piece which receives the wave function renormalization at this order, as we will see later. Therefore, iσqν piece is finite by itself. Furthermore, this is the piece which generates the anomalous magnetic moment, and hence it is useful to...