Structural and optical properties of MOCVD AllnN epilayers

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Mean Value from Representation of Rational Number as Sum of Two Egyptian Fractions

For given positive integers $n$ and $a$, let $R(n;\,a)$ denote the number of positive integer solutions $(x,\,y)$ of the Diophantine equation $${a\over n}={1\over x}+{1\over y}.$$ Write $$S(N;\,a)=\sum_{\substack{n\leq N (n,\,a)=1}}R(n;\,a).$$ Recently Jingjing Huang and R. C. Vaughan proved that for $4\leq N$ and $a\leq 2N$, there is an asymptotic formula $$S(N;\,a)={3\over \pi^2a}\prod_{p|a}{p-1\over p+1}\cdot N(\log^2N+c_1(a) \log N+c_0(a))+\Delta(N;\,a).$$ In this paper, we shall get a more explicit expression with better error term for $c_0(a)$

2-D Prony-Huang Transform: A New Tool for 2-D Spectral Analysis

This work proposes an extension of the 1-D Hilbert Huang transform for the analysis of images. The proposed method consists in (i) adaptively decomposing an image into oscillating parts called intrinsic mode functions (IMFs) using a mode decomposition procedure, and (ii) providing a local spectral analysis of the obtained IMFs in order to get the local amplitudes, frequencies, and orientations. For the decomposition step, we propose two robust 2-D mode decompositions based on non-smooth convex optimization: a "Genuine 2-D" approach, that constrains the local extrema of the IMFs, and a "Pseudo 2-D" approach, which constrains separately the extrema of lines, columns, and diagonals. The spectral analysis step is based on Prony annihilation property that is applied on small square patches of the IMFs. The resulting 2-D Prony-Huang transform is validated on simulated and real data.Comment: 24 pages, 7 figure

Optimization and resilience of complex supply-demand networks

Acknowledgments This work was supported by NSF under Grant No. 1441352. SPZ and ZGH were supported by NSF of China under Grants No. 11135001 and No. 11275003. ZGH thanks Prof Liang Huang and Xin-Jian Xu for helpful discussions.Peer reviewedPublisher PD

Halpern-Huang directions in effective scalar field theory

Halpern and Huang recently showed that there are relevant directions in the space of interactions at the Gaussian fixed point. I show that their result can be derived from Polchinski's form of the Wilson renormalization group. The derivation shows that the existence of these directions is independent of the cutoff function used.Comment: 6 pages, plain Te