On a pp-Laplacian type of evolution system and applications to the Bean model in the type-II superconductivity theory

We study the Cauchy problem for an $p$-Laplacian type of evolution system {\mathbf H}_{t}+\g [ | \g {\mathbf H}|^{p-2} \g {\mathbf H}|]={\mathbf F}. This system governs the evolution of a magnetic field ${\bf H}$, where the current displacement is neglected and the electrical resistivity is assumed to be some power of the current density. The existence, uniqueness and regularity of solutions to the system are established. Furthermore, it is shown that the limit solution as the power $p\rightarrow \infty$ solves the problem of Bean's model in the type-II superconductivity theory. The result provides us information about how the superconductor material under the external force to become the normal conductor and vice visa. It also provides an effective method to find numerical solutions to Bean's model

Measuring dark matter-neutrino relative velocity on cosmological scales

We present a new method to measure neutrino masses using the dark matter-neutrino relative velocity. The relative motion between dark matter and neutrinos results in a parity-odd bispectrum which can be measured from cross-correlation of different cosmic fields. This new method is not affected by most systematics which are parity even and not limited by the knowledge of optical depth to the cosmic microwave background. We estimate the detectability of the relative velocity effect and find that the minimal sum of neutrino masses could be detected at high significance with upcoming surveys.Comment: 6 pages, 2 figures, 1 table, published versio

When Globalization Meets Urbanization: Labor Market Reform, Income Inequality, and Economic Growth in the People's Republic of China

The development path that the People's Republic of China (PRC) has been following during the past thirty years has led to both internal and external economic imbalances, and is now greatly challenged by the global crisis. This unbalanced growth path was primarily a result of the PRC's labor market reform which took the years of the mid-1990s as its turning point. Before the mid-1990s, the scale of rural-to-urban migration was limited, but it has grown dramatically since then. 1996 also saw drastic employment restructuring in urban areas of the PRC. Labor market reform, accompanied by the foreign exchange system reform in 1994, confirmed the PRC's comparative advantage of low labor cost, and therefore further increased the PRC's reliance on exports. However, the increased income disparity that resulted from the labor market reform may jeopardize sustainable growth if no adjustment is made. To sustain the high economic growth, especially in face of the current crisis, the PRC needs to adjust its reform and development strategies to promote income equality.china labor market unemployment; china income inequality; china economic growth crisis

A flexible and adaptive Simpler GMRES with deflated restarting for shifted linear systems

In this paper, two efficient iterative algorithms based on the simpler GMRES method are proposed for solving shifted linear systems. To make full use of the shifted structure, the proposed algorithms utilizing the deflated restarting strategy and flexible preconditioning can significantly reduce the number of matrix-vector products and the elapsed CPU time. Numerical experiments are reported to illustrate the performance and effectiveness of the proposed algorithms.Comment: 17 pages. 9 Tables, 1 figure; Newly update: add some new numerical results and correct some typos and syntax error