We investigate sharp conditions for boundary and interior gradient estimates of continuous viscosity solutions to fully nonlinear, uniformly elliptic equations under Dirichlet boundary conditions. When these condition...We investigate sharp conditions for boundary and interior gradient estimates of continuous viscosity solutions to fully nonlinear, uniformly elliptic equations under Dirichlet boundary conditions. When these conditions are violated, there can be blow up of the gradient in the interior or on the boundary of the domain. In particular we de- rive sharp results on local and global Lipschitz continuity of continuous viscosity solutions under more general growth conditions than before. Lipschitz regularity near the boundary allows us to predict when the Dirichlet condition is satisfied in a classical and not just in a viscosity sense, where detachment can occur. Another consequence is this： if interior gra- dient blow up occurs, Perron-type solutions can in general become discontinuous, so that the Dirichlet problem can become unsolvable in the class of continuous viscosity solutions.展开更多
This paper reprots that with Ni-based catalyst/solvent and with a dopant of NAN3, large green single crystal diamonds with perfect shape are successfully synthesized by temperature gradient method under high pressure ...This paper reprots that with Ni-based catalyst/solvent and with a dopant of NAN3, large green single crystal diamonds with perfect shape are successfully synthesized by temperature gradient method under high pressure and high temperature in a China-type cubic anvil high-pressure apparatus （SPD-6 × 1200）, and the highest nitrogen concentration reaches approximately 121-1257 ppm calculated by infrared absorption spectra. The synthesis conditions are about 5.5 CPa and 1240-1300 ℃. The growth behaviour of diamond with high-nitrogen concentration is investigated in detail. The results show that, with increasing the content of NaN3 added in synthesis system, the width of synthesis temperature region for growth high-quality diamonds becomes narrower, and the morphology of diamond crystal is changed from cube-octahedral to octahedral at same temperature and pressure, the crystal growth rate is slowed down, nevertheless, the nitrogen concentration doped in synthetic diamond increases.展开更多
This paper considers online classification learning algorithms for regularized classification schemes with generalized gradient. A novel capacity independent approach is presented. It verifies the strong convergence o...This paper considers online classification learning algorithms for regularized classification schemes with generalized gradient. A novel capacity independent approach is presented. It verifies the strong convergence of sizes and yields satisfactory convergence rates for polynomially decaying step sizes. Compared with the gradient schemes, this al- gorithm needs only less additional assumptions on the loss function and derives a stronger result with respect to the choice of step sizes and the regularization parameters.展开更多
目的研究慢性胃炎腻苔患者的口腔微生物菌群组成特征,探索腻苔的形成机制。方法收集40例慢性胃炎患者舌苔样本(腻苔组20例,非腻苔组20例)和20名正常人舌苔样本(健康对照组)。利用16SrRNA基因变性梯度凝胶电泳(denatured gradient gel el...目的研究慢性胃炎腻苔患者的口腔微生物菌群组成特征,探索腻苔的形成机制。方法收集40例慢性胃炎患者舌苔样本(腻苔组20例,非腻苔组20例)和20名正常人舌苔样本(健康对照组)。利用16SrRNA基因变性梯度凝胶电泳(denatured gradient gel electrophoresis,DGGE)技术检测各组舌苔微生物菌群,得到舌苔样本细菌DGGE图谱,将其数字化后进行主成分分析(PCA)和偏最小二乘判别法分析(PLS-DA)。结果慢性胃炎腻苔组、非腻苔组与健康对照组舌苔的微生物组成存在差异。(1)腻苔组与非腻苔组之间有5条具有显著差异的条带,PLS判别模型的预报准确率达到97.5%;腻苔组和健康对照组之间有8条具有显著差异的条带,PLS判别模型的预报准确率达到95.0%;非腻苔组和健康对照组之间的条带差异不明显。(2)腻苔组的8号条带亮度高于非腻苔组和健康对照组,测序结果显示其最近邻居为Moraxella ca-tarrhalis(黏膜炎莫拉氏菌/卡他莫拉菌),但两者相似度仅为96.2%,可能是目前尚未报道的一个新菌种;10号条带亮度为健康对照组>非腻苔组>腻苔组,测序结果显示其与Rothia mucilaginosa(黏滑罗斯菌)相似度达到100.0%。结论 8号条带的菌种可能与慢性胃炎腻苔的形成有密切关系,10号条带的菌种可能与慢性胃炎非腻苔形成有一定的关系,提示口腔微生物菌群的变化可能是腻苔的形成机制之一。展开更多
基金financed by the Alexander von Humboldt Foundationcontinued in March 2009 at the Mathematisches Forschungsinstitut Oberwolfach in the "Research in Pairs"program
文摘We investigate sharp conditions for boundary and interior gradient estimates of continuous viscosity solutions to fully nonlinear, uniformly elliptic equations under Dirichlet boundary conditions. When these conditions are violated, there can be blow up of the gradient in the interior or on the boundary of the domain. In particular we de- rive sharp results on local and global Lipschitz continuity of continuous viscosity solutions under more general growth conditions than before. Lipschitz regularity near the boundary allows us to predict when the Dirichlet condition is satisfied in a classical and not just in a viscosity sense, where detachment can occur. Another consequence is this： if interior gra- dient blow up occurs, Perron-type solutions can in general become discontinuous, so that the Dirichlet problem can become unsolvable in the class of continuous viscosity solutions.
基金Project supported by the National Natural Science Foundation of China (Grant No. 50572032)
文摘This paper reprots that with Ni-based catalyst/solvent and with a dopant of NAN3, large green single crystal diamonds with perfect shape are successfully synthesized by temperature gradient method under high pressure and high temperature in a China-type cubic anvil high-pressure apparatus （SPD-6 × 1200）, and the highest nitrogen concentration reaches approximately 121-1257 ppm calculated by infrared absorption spectra. The synthesis conditions are about 5.5 CPa and 1240-1300 ℃. The growth behaviour of diamond with high-nitrogen concentration is investigated in detail. The results show that, with increasing the content of NaN3 added in synthesis system, the width of synthesis temperature region for growth high-quality diamonds becomes narrower, and the morphology of diamond crystal is changed from cube-octahedral to octahedral at same temperature and pressure, the crystal growth rate is slowed down, nevertheless, the nitrogen concentration doped in synthetic diamond increases.
文摘This paper considers online classification learning algorithms for regularized classification schemes with generalized gradient. A novel capacity independent approach is presented. It verifies the strong convergence of sizes and yields satisfactory convergence rates for polynomially decaying step sizes. Compared with the gradient schemes, this al- gorithm needs only less additional assumptions on the loss function and derives a stronger result with respect to the choice of step sizes and the regularization parameters.
