Accurately approximating higher order derivatives is an inherently difficult problem. It is shown that a random variable shape parameter strategy can improve the accuracy of approximating higher order derivatives with...Accurately approximating higher order derivatives is an inherently difficult problem. It is shown that a random variable shape parameter strategy can improve the accuracy of approximating higher order derivatives with Radial Basis Function methods. The method is used to solve fourth order boundary value problems. The use and location of ghost points are examined in order to enforce the extra boundary conditions that are necessary to make a fourth-order problem well posed. The use of ghost points versus solving an overdetermined linear system via least squares is studied. For a general fourth-order boundary value problem, the recommended approach is to either use one of two novel sets of ghost centers introduced here or else to use a least squares approach. When using either ghost centers or least squares, the random variable shape parameter strategy results in significantly better accuracy than when a constant shape parameter is used.展开更多
为探究萌芽期大蒜挥发性物质的差异,采用电子鼻、捕集阱顶空-气质联用仪(Trap head space-gas chromatography-mass spectrometry,HS-Trap-GC-MS)结合正交偏最小二乘法判别分析(Orthogonal partial least squares discriminant analysis...为探究萌芽期大蒜挥发性物质的差异,采用电子鼻、捕集阱顶空-气质联用仪(Trap head space-gas chromatography-mass spectrometry,HS-Trap-GC-MS)结合正交偏最小二乘法判别分析(Orthogonal partial least squares discriminant analysis,OPLS-DA)、香气活度值、差异性热图、相关性分析分析大蒜萌芽在0、24、48、72、96 h挥发性物质的差异。电子鼻结合OPLS-DA建立预测模型其预测能力达96.00%。GC-MS分析表明:含硫化合物是不同萌芽期大蒜的主要共有挥发性物质,含硫化合物的相对含量随萌芽时间的延长而呈递减趋势,而种类呈现出递增趋势;二烯丙基二硫醚是样品在萌芽过程中含量降低最多的物质。二烯丙基四硫醚、烯丙硫醇是样品共有关键化合物。差异性热图分析显示:除共有物质含量差异外,硫化丙烯、己醛、叠氮二羧酸二叔丁酯、丙烯醇、6-甲基-2-庚炔、5-甲基噻二唑、2-亚乙基-1,3-二硫烷、2-丙-2-炔基磺酰基丙烷、2,5-二甲基噻吩、2,5-二甲基呋喃、1-戊烯-3-醇、1,3-二噻烷的缺失进一步加大了未萌芽和萌芽大蒜气味的差异。萌芽大蒜主要共有挥发性物质的种类随萌芽时间的延长呈现递增趋势。大蒜主要挥发性物质与电子鼻大多数传感器存在显著相关性。大蒜的气味强度会随萌芽时间的延长而逐步减弱。展开更多
文摘Accurately approximating higher order derivatives is an inherently difficult problem. It is shown that a random variable shape parameter strategy can improve the accuracy of approximating higher order derivatives with Radial Basis Function methods. The method is used to solve fourth order boundary value problems. The use and location of ghost points are examined in order to enforce the extra boundary conditions that are necessary to make a fourth-order problem well posed. The use of ghost points versus solving an overdetermined linear system via least squares is studied. For a general fourth-order boundary value problem, the recommended approach is to either use one of two novel sets of ghost centers introduced here or else to use a least squares approach. When using either ghost centers or least squares, the random variable shape parameter strategy results in significantly better accuracy than when a constant shape parameter is used.
