A phenomenological ansatz for the flavor–asymmetry of the light sea distributions of the nucleon, based on the Pauli exclusion principle, is proposed. This ansatz is compatible with the measured flavor–asymmetry of the unpolarized sea distributions, d̄ > ū, of the nucleon. A prediction for the corresponding polarized flavor–asymmetry is presented and shown to agree with predictions of (chiral qu...

We study the Cauchy problem for a strictly hyperbolic n×n system of conservation laws in one space dimension: ut + f(u)x = 0, u(0, x) = ū(x). The initial data ū is a small BV perturbation of a single rarefaction wave with an arbitrary strength. All characteristic fields are assumed to be genuinely nonlinear or linearly degenerate in the vicinity of the reference rarefaction curve. We prove that...

In this paper we prove that there exists a random sequence θi for the Glimm scheme such that the approximate solution u (t) converges to the exact semigroup solution Stū of the strictly hyperbolic system of conservation laws ut + f(u)x = 0, u(t = 0) = ū as follows: for all T ≥ 0 it holds lim ε→0 ‖uε(T )− ST ū √ ε| log ε| = 0. This result is the extension of the analysis of [9] to the general ca...

The HERMES experiment has measured double spin asymmetries of inclusive and semi–inclusive cross sections for the production of charged hadrons in deep– inelastic scattering of polarised positrons on polarised hydrogen and deuterium targets, in the kinematic range 0.023 < x < 0.6, and 1 GeV < Q < 15 GeV. For the data taken on the deuterium target, a RICH detector provides the complete identific...

Flavor asymmetry is investigated in polarized light-antiquark distributions by a meson-cloud model. In particular, ρ meson contributions to ∆ū−∆d̄ are calculated. We point out that the g2 part of ρ contributes to the structure function g1 of the proton in addition to the ordinary longitudinally polarized distributions in ρ. This kind of contribution becomes important at medium x (> 0.2) with sma...

We consider the special Jin-Xin relaxation model (0.1) ut + A(u)ux = 2(uxx − utt), We assume that the initial data (u0, 2u0,t) are sufficiently smooth and close to (ū, 0) in L∞ and have small total variation. Then we prove that there exists a solution (u2(t), 2ut(t)) with uniformly small total variation for all t ≥ 0, and this solution depends Lipschitz continuously in the L1 norm w.r.t. the in...

Theorem 4.3 Let the initialization u0 be sufficiently close to the solution ū of P. Then the iterates uk of Algorithm 1 converge superlinearly to ū in L2(Ω). Moreover, the corresponding states yk converge superlinearly to ȳ in H1 0 (Ω). Proof To apply Theorem 4.1, it remains to show that the generalized derivative (4.7) is invertible and that the norms of the inverse linear mappings are bounded...

Proof. Define a map U → μn by u 7→ u/ū; this gives a well-defined map by exercise 2 of homework 5. Compose with the quotient μn → μn/μ 2 n, and denote the resulting map by φ : U → μn/μ 2 n. It is enough to show that ker φ = μnU , since μn/μ 2 n has order 2. Certainly μnU + ⊂ kerφ, since φ(ζu) = [ζ] = 0 in μn/μ 2 n for u + ∈ U and ζ ∈ μn. Conversely, suppose φ(u) = 0 for some u ∈ U : then u/ū = ...

For a continuous self-similar solution to a system of conservation laws, genuine nonlinearity yields Lipschitz continuity at points where the type of the governing system changes. This is a well-known fact in one space dimension, where a constant state ū bifurcates towards a rarefaction wave at a point x/t that equals an eigenvalue λj(ū). We extend this observation to several space dimensions. ...