Structural and optical properties of MOCVD AllnN epilayers

7] M.-Y. Ryu, C.Q. Chen, E. Kuokstis, J.W. Yang, G. Simin, M. Asif Khan, Appl. Phys. Lett. 80 (2002) 3730. [8] D. Xu, Y. Wang, H. Yang, L. Zheng, J. Li, L. Duan, R. Wu, Sci. China (a) 42 (1999) 517. [9] H. Hirayama, A. Kinoshita, A. Hirata, Y. Aoyagi, Phys. Stat. Sol. (a) 188 (2001) 83. [10] Y. Chen, T. Takeuchi, H. Amano, I. Akasaki, N. Yamada, Y. Kaneko, S.Y. Wang, Appl. Phys. Lett. 72 (1998) 710. [11] Ig-Hyeon Kim, Hyeong-Soo Park, Yong-Jo Park, Taeil Kim, Appl. Phys. Lett. 73 (1998) 1634. [12] K. Watanabe, J.R. Yang, S.Y. Huang, K. Inoke, J.T. Hsu, R.C. Tu, T. Yamazaki, N. Nakanishi, M. Shiojiri, Appl. Phys. Lett. 82 (2003) 718

Some estimates of Wang-Yau quasilocal energy

Given a spacelike 2-surface $\Sigma$ in a spacetime $N$ and a constant future timelike unit vector $T_0$ in $\R^{3,1}$, we derive upper and lower estimates of Wang-Yau quasilocal energy $E(\Sigma, X, T_0)$ for a given isometric embedding $X$ of $\Sigma$ into a flat 3-slice in $\R^{3,1}$. The quantity $E(\Sigma, X, T_0)$ itself depends on the choice of $X$, however the infimum of $E(\Sigma, X, T_0)$ over $T_0$ does not. In particular, when $\Sigma$ lies in a time symmetric 3-slice in $N$ and has nonnegative Brown-York quasilocal mass \mby(\Sigma), our estimates show that $\inf\limits_{T_0}E(\Sigma, X, T_0)$ equals \mby (\Sigma). We also study the spatial limit of $\inf\limits_{T_0}E(S_r,X_r,T_0)$, where $S_r$ is a large coordinate sphere in a fixed end of an asymptotically flat initial data set $(M, g, p)$ and $X_r$ is an isometric embeddings of $S_r$ into $\mathbb{R}^3 \subset \mathbb{R}^{3,1}$. We show that if $(M, g, p)$ has future timelike ADM energy-momentum, then $\lim\limits_{r\to\infty}\inf\limits_{T_0}E(S_r,X_r,T_0)$ equals the ADM mass of $(M, g, p)$.Comment: 17 page

Cayley graphs generated by small degree polynomials over finite fields

We improve upper bounds of F. R. K. Chung and of M. Lu, D. Wan, L.-P. Wang, X.-D. Zhang on the diameter of some Cayley graphs constructed from polynomials over finite fields