Stability of Transonic Shocks in Steady Supersonic Flow past Multidimensional Wedges

We are concerned with the stability of multidimensional (M-D) transonic shocks in steady supersonic flow past multidimensional wedges. One of our motivations is that the global stability issue for the M-D case is much more sensitive than that for the 2-D case, which requires more careful rigorous mathematical analysis. In this paper, we develop a nonlinear approach and employ it to establish the stability of weak shock solutions containing a transonic shock-front for potential flow with respect to the M-D perturbation of the wedge boundary in appropriate function spaces. To achieve this, we first formulate the stability problem as a free boundary problem for nonlinear elliptic equations. Then we introduce the partial hodograph transformation to reduce the free boundary problem into a fixed boundary value problem near a background solution with fully nonlinear boundary conditions for second-order nonlinear elliptic equations in an unbounded domain. To solve this reduced problem, we linearize the nonlinear problem on the background shock solution and then, after solving this linearized elliptic problem, develop a nonlinear iteration scheme that is proved to be contractive.Comment: 41 pages, 10 figure

Effect of sea quarks on the single-spin asymmetries ALW±A^{W^{\pm}}_{L} in polarized pp collisions at RHIC

We calculate the single-spin asymmetries $A^{W^{\pm}}_{L}$ of $W^{\pm}$ bosons produced in polarized pp collisions with the valence part of the up and down quark helicity distributions modeled by the light-cone quark-spectator-diquark model while the sea part helicity distributions of the up and down quarks treated as parametrization. Comparing our results with those from experimental data at RHIC, we find that the helicity distributions of sea quarks play an important role in the determination of the shapes of $A^{W^{\pm}}_{L}$. It is shown that $A^{W^{-}}_{L}$ is sensitive to $\Delta \bar u$, while $A^{W^{+}}_{L}$ to $\Delta \bar d$ intuitively. The experimental data of the polarized structure functions and the sum of helicities are also important to constrain the sizes of quark helicity distributions both for the sea part and the valence part of the nucleon.Comment: 19 latex pages, 5 figures, final version for publicatio

Distant Supervision for Entity Linking

Entity linking is an indispensable operation of populating knowledge repositories for information extraction. It studies on aligning a textual entity mention to its corresponding disambiguated entry in a knowledge repository. In this paper, we propose a new paradigm named distantly supervised entity linking (DSEL), in the sense that the disambiguated entities that belong to a huge knowledge repository (Freebase) are automatically aligned to the corresponding descriptive webpages (Wiki pages). In this way, a large scale of weakly labeled data can be generated without manual annotation and fed to a classifier for linking more newly discovered entities. Compared with traditional paradigms based on solo knowledge base, DSEL benefits more via jointly leveraging the respective advantages of Freebase and Wikipedia. Specifically, the proposed paradigm facilitates bridging the disambiguated labels (Freebase) of entities and their textual descriptions (Wikipedia) for Web-scale entities. Experiments conducted on a dataset of 140,000 items and 60,000 features achieve a baseline F1-measure of 0.517. Furthermore, we analyze the feature performance and improve the F1-measure to 0.545