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. ...

The 1/Nc–expansion of QCD suggests large flavor asymmetries of the polarized antiquark distributions in the nucleon. This is confirmed by model calculations in the large–Nc limit (chiral quark–soliton model), which give sizable results for ∆ū(x)−∆d̄(x) and ∆ū(x)+∆d̄(x)−2∆s̄(x). We compute the contributions of these flavor asymmetries to the spin asymmetries in hadron production in semi-inclusive d...

In this study, the proton is taken as an ensemble of quark-gluon Fock states. Using the principle of detailed balance, the probabilities of finding every Fock states of the proton are obtained without any parameter. A new origin of the light flavor sea quark asymmetry, i.e., ū 6= d̄, is given as a pure statistical effect. It is found that d̄− ū ≈ 0.124, which is in surprisingly agreement with the...

The paper is concerned with the Cauchy problem for a nonlinear, strictly hyperbolic system with small viscosity: ut +A(u)ux = ε uxx, u(0, x) = ū(x). (∗) We assume that the integral curves of the eigenvectors ri of the matrix A are straight lines. On the other hand, we do not require the system (∗) to be in conservation form, nor do we make any assumption on genuine linearity or linear degenerac...

“The NURBS Book” [L. Piegl, W. Tiller, The NURBS Book, second edn, Springer, 1997] is very popular in the fields of computer aided geometric design (CAGD) and geometric modeling. In Section 9.5.2 of the book, the well-known problem of the local cubic spline approximation is discussed. The key in local cubic spline approximation is cubic polynomial interpolation. In this short paper, we present ...

We present an improved determination of the upand down-quark distributions in the proton using recent data on charged lepton asymmetries from W± gauge-boson production at the LHC and Tevatron. The analysis is performed in the framework of a global fit of parton distribution functions. The fit results are consistent with a non-zero iso-spin asymmetry of the sea, x(d̄ − ū), at small values of Bjor...

Quark masses are shown to play an important role in the nucleon sea. Our analysis using massive QCD splitting functions demonstrates the existence of two Feynman-x sea regimes. For small x the strange sea is larger while at large x the non-strange light sea is dominant. This crossover effect has been observed in a phenomenological analysis by the CTEQ Collaboration. We also investigate the char...

Let b ≤ |z|. We wish to extend the results of [16] to algebras. We show that τ ≡ |ES |. Therefore it is not yet known whether K ( Ḡ ) < ⊕ m̃∈ŝ ∫ V ( 1 ρ , . . . , ū ∨ |w| ) djD, although [16] does address the issue of solvability. Next, the groundbreaking work of K. Euclid on left-universally singular elements was a major advance.

We present the ultraviolet poles and finite terms of two-loop vertex corrections for diagrams with massive partons in the eikonal approximation. We discover and prove that the results for a set of the corrections generalize to n-loop eikonal diagrams. These results will enhance theoretical understanding and allow greater calculational accuracy for the many partonic processes where the eikonal a...