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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)
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)
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)
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)
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)
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)
In this paper, we discuss the distributed resource constrained multi-project scheduling problem (DRCMPSP) and focus on handling resource conflicts. The resource conflicts among projects are originally caused by precedence constraints and resource constraints. To reflect the influences of both constraints, this paper incorporates the critical chain concept(More)
Advanced glycation end products (AGEs)-induced vasculopathy, including oxidative stress, inflammation and apoptosis responses, contributes to the high morbidity and mortality of coronary artery diseases in diabetic patients. The present study was conducted to evaluate the protective activity of liquiritin (Liq) on AGEs-induced endothelial dysfunction and(More)