Spectral distributions of adjacency and Laplacian matrices of random graphs

In this paper, we investigate the spectral properties of the adjacency and the Laplacian matrices of random graphs. We prove that: (i) the law of large numbers for the spectral norms and the largest eigenvalues of the adjacency and the Laplacian matrices; (ii) under some further independent conditions, the normalized largest eigenvalues of the Laplacian matrices are dense in a compact interval almost surely; (iii) the empirical distributions of the eigenvalues of the Laplacian matrices converge weakly to the free convolution of the standard Gaussian distribution and the Wigner's semi-circular law; (iv) the empirical distributions of the eigenvalues of the adjacency matrices converge weakly to the Wigner's semi-circular law.Comment: Published in at http://dx.doi.org/10.1214/10-AAP677 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Comment on " a unified scheme for flavored mesons and baryons"

We would comment on the results of the paper "a unified scheme for flavored mesons and baryons" (P.C.Vinodkumar, J.N.Panandya, V.M.Bannur, and S.B.Khadkikar Eur. Phys. J. A4(1999)83), and point out some inconsistencies and mistakes in the work for solving the Dirac equation. In terms of an example for a single particle we investigate the reliability of the perturbative method for computing the Coulomb energy and discuss the contribution to the wavefunction at origin from the Coulomb potential. We conclude that the accuracy of their numerical results needs to be reconsidered.Comment: Latex file, 11page

The Current State and Characteristics of Parental Educational Anxiety and Contributing Factors

The study focused on the parents of compulsory education students in Shanghai city. Through a large-scale survey and subsequent data analysis, it aimed to the status quo and characteristics of educational anxiety among parents of compulsory education students; analyze the factors in parental educational anxiety from the standpoints of educational policies, schools, families, and students; and propose recommendations on improving the education policy system from the perspective of policy design

A Platinum Nanowire Network as a Highly Effective Current Collector for Intermediate Temperature Solid Oxide Fuel Cells

We report the fabrication and evaluation of a platinum nanowire network as a highly efficient current collector for solid oxide fuel cells (SOFCs). The ink of carbon-black supported platinum nanoparticles was sprayed onto the cathode. After firing, the carbon black was oxidized and disappeared as carbon dioxide gas while the platinum nanoparticles connect with one another, forming a tree-branch-like nanowire network. The diameters of the nanowires range from 100 nm to 400 nm. Compared to a conventional platinum paste current collector, the polarization resistance of the PrBaCo2O5+δ (PBCO) cathode with a nanowire current collector was reduced by 44% at 650 °C (from 0.18 Ω cm2 to 0.1 Ω cm2). The peak power density of the button cells was improved at different degrees of 31.8–59.6% under temperatures 650–550 °C for typical cathode materials of PBCO, La0.6Sr0.4Co0.2Fe0.8O3−δ (LSCF), and Ba0.5Sr0.5Co0.8Fe0.2O3−δ(BSCF). The nanowire network did not show obvious changes after long term testing (400 h)