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- ROWAN KILLIP, XIAOYI ZHANG
- 2008

We establish global well-posedness and scattering for solutions to the mass-critical nonlinear Schrödinger equation iut +∆u = ±|u| 4/d u for large spherically symmetric L 2 x (R d) initial data in dimensions d ≥ 3. In the focusing case we require that the mass is strictly less than that of the ground state. As a consequence, we obtain that in the focusing… (More)

- XIAOYI ZHANG
- 2006

We consider the minimal mass m 0 required for solutions to the mass-critical nonlinear Schrödinger (NLS) equation iut + ∆u = µ|u| 4/d u to blow up. If m 0 is finite, we show that there exists a minimal-mass solution blowing up (in the sense of an infinite spacetime norm) in both time directions, whose orbit in L 2 x (R d) is compact after quotienting out by… (More)

- TERENCE TAO, XIAOYI ZHANG
- 2008

We establish global well-posedness and scattering for solutions to the defocusing mass-critical (pseudoconformal) nonlinear Schrödinger equation iut + ∆u = |u| 4/n u for large spherically symmetric L 2 x (R n) initial data in dimensions n ≥ 3. After using the reductions in [32] to reduce to eliminating blowup solutions which are almost periodic modulo… (More)

- Zhenyu Hu, Xiling Bian, +5 authors Yinye Wang
- Brain research
- 2013

Honokiol, a major bioactive constituent of the bark of Magnolia officinalis has been confirmed to have the neuroprotective effect on ischemic stroke in rats. This study was designed to observe the therapeutic time window of honokiol microemulsion on cerebral ischemia-reperfusion injury to support its potential for future clinical trials and further explore… (More)

- XIAOYI ZHANG
- 2005

We undertake a comprehensive study of the nonlinear Schrödinger equation iut + ∆u = λ 1 |u| p 1 u + λ 2 |u| p 2 u, where u(t, x) is a complex-valued function in spacetime Rt × R n x , λ 1 and λ 2 are nonzero real constants, and 0 < p 1 < p 2 ≤ 4 n−2. We address questions related to local and global well-posedness, finite time blowup, and asymptotic… (More)

- Shancheng Zhao, Xiao Ma, Xiaoyi Zhang, Baoming Bai
- IEEE Trans. Communications
- 2013

- Ming-Chun Huang, Xiaoyi Zhang, Wenyao Xu, Jason J. Liu, Majid Sarrafzadeh
- CHI Extended Abstracts
- 2014

Sleep quality affects people's work performance, mood, safety, and quality of life. Poor sleep quality reduces short-term memory, cognitive abilities, and motor skills for all age groups. We introduce EZwakeup, a system that extracts sleep quality indicators with an eTextile-based sensing system and applies feedback-guided external stimuli to smoothly wake… (More)

- Kai Lu, Yinghua Shu, +6 authors Wenqing Zhang
- Journal of insect physiology
- 2015

Vitellogenin receptors (VgRs), members of the low-density lipoprotein receptor (LDLR) superfamily, are responsible for taking vitellogenin (Vg) into developing oocytes. Here the first full-length VgR cDNA from a hemipteran insect, the brown planthopper (Nilaparvata lugens), was cloned and sequenced. The complete mRNA sequence was 6174 bp in length with an… (More)

- Rowan Killip, Dong Li, Monica Visan, Xiaoyi Zhang
- SIAM J. Math. Analysis
- 2009

Let d ≥ 4 and let u be a global solution to the focusing mass-critical nonlinear Schrödinger equation iut + ∆u = −|u| 4 d u with spherically symmetric H 1 x initial data and mass equal to that of the ground state Q. We prove that if u does not scatter then, up to phase rotation and scaling, u is the solitary wave e it Q. Combining this result with that of… (More)

- ROWAN KILLIP, XIAOYI ZHANG
- 2006

We consider the defocusing ˙ H 1-critical nonlinear Schrödinger equation in all dimensions (n ≥ 3) with a quadratic potential V (x) = ± 1 2 |x| 2. We show global well-posedness for radial initial data obeying ∇u 0 (x), xu 0 (x) ∈ L 2. In view of the potential V , this is the natural energy space. In the repulsive case, we also prove scattering. We follow… (More)