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J o u r n a l o f P r o b a b i l i t y Electron. Abstract The Parisi formula for the free energy in the spherical models with mixed even p-spin interactions was proven in Michel Talagrand [16]. In this paper we study the general mixed p-spin spherical models including p-spin interactions for odd p. We establish the Aizenman-Sims-Starr scheme and from this(More)
Structural and optical properties of thick InGaN layers with strain and composition inhomogeneities are investigated. High resolution x-ray diffractions (XRD) and reciprocal space mapping (RSM) along an asymmetric axis reveal that the In composition inhomogeneity is accompanied by strain relaxations during the growth of thick InGaN layers. According to the(More)
A hybrid patterned sapphire substrate (hybrid-PSS) was prepared using an anodic aluminum oxide etching mask to transfer nanopatterns onto a conventional patterned sapphire substrate with microscale patterns (bare-PSS). The threading dislocation (TD) suppression of light-emitting diodes (LEDs) grown on a hybrid-PSS (HP-LED) exhibits a smaller reverse leakage(More)
We study a spin system with both mixed even-spin Sherrington-Kirkpatrick (SK) couplings and Curie-Weiss (CW) interaction. Our main results are: (i) The ther-modynamic limit of the free energy is given by a variational formula involving the free energy of the SK model with a change in the external field. (ii) In the presence of a centered Gaussian external(More)
J o u r n a l o f P r o b a b i l i t y Electron. Abstract One of the remarkable applications of the cavity method in the mean field spin glasses is to prove the validity of the Thouless-Anderson-Palmer (TAP) system of equations in the Sherrington-Kirkpatrick (SK) model in the high temperature regime. This naturally leads us to the study of the limit laws(More)
The optical properties of GaAs nano-wires grown on shallow-trench-patterned Si(001) substrates were investigated by cathodoluminescence. The results showed that when the trench width ranges from 80 to 100 nm, the emission efficiency of GaAs can be enhanced and is stronger than that of a homogeneously grown epilayer. The suppression of non-radiative centers(More)
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