This paper introduces some concepts such as q- process in random environment, Laplace transformation, ergodic potential kernel, error function and some basic lemmas.We study the continuity and Laplace transformation o...This paper introduces some concepts such as q- process in random environment, Laplace transformation, ergodic potential kernel, error function and some basic lemmas.We study the continuity and Laplace transformation of random transition function. Finally, we give the sufficient condition for the existence of ergodic potential kernel for homogeneous q- processes in random environments.展开更多
针对局部线性嵌入(Locally Linear Embedding,LLE)算法在挖掘数据结构时未考虑特征权重且仅局限于数据的线性拟合关系,导致特征提取效果不佳的问题,提出一种基于熵权距离的图正则局部线性嵌入(Graph Regular Local Linear Embedding Alg...针对局部线性嵌入(Locally Linear Embedding,LLE)算法在挖掘数据结构时未考虑特征权重且仅局限于数据的线性拟合关系,导致特征提取效果不佳的问题,提出一种基于熵权距离的图正则局部线性嵌入(Graph Regular Local Linear Embedding Algorithm Based on Entropy Weight Distance,EWD-GLLE)算法。首先,采用信息熵加权的余弦距离划分样本邻域,减小不重要特征对邻域划分的影响,提高了邻域划分的准确性;然后,利用融合热核权重与余弦权重的拉普拉斯图约束低维嵌入,以保留更多的原始数据信息,进而提取到更显著的特征。在两种轴承数据集上的实验结果表明:EWD-GLLE算法的特征提取性能明显优于LLE、LTSA、LDA算法。展开更多
Before going further with fractional derivative which is constructed by Rabotnov exponential kernel,there exist many questions that are not addressed.In this paper,we try to recapitulate all the fundamental calculus,w...Before going further with fractional derivative which is constructed by Rabotnov exponential kernel,there exist many questions that are not addressed.In this paper,we try to recapitulate all the fundamental calculus,which we can obtain with this new fractional operator.The problems in this paper are to determine the solutions of the fractional differential equations where the second members are constant functions,polynomial functions,exponential functions,trigonometric functions,or Mittag-Leffler functions.For all the fractional differential equations,the obtained solutions are represented graphically.The Laplace transform of the fractional derivative with Rabotnov exponential kernel is the primary tool in the investigations.Finally,we give the fundamental solution to the nonlinear time-fractional modified Degasperis-Procesi equation by considering the fractional operator with Rabotnov exponential kernel.展开更多
基金Supported by the National Natural Science Foundation of China (10371092)
文摘This paper introduces some concepts such as q- process in random environment, Laplace transformation, ergodic potential kernel, error function and some basic lemmas.We study the continuity and Laplace transformation of random transition function. Finally, we give the sufficient condition for the existence of ergodic potential kernel for homogeneous q- processes in random environments.
基金The National Science & Technology of the Key Projects(2008ZX50443-14)Natural Science Key Projects of the Sichuan Education Bureau of China(12ZA164)Innovation Fund of Xihua University(YCJJ2009-16)
文摘针对局部线性嵌入(Locally Linear Embedding,LLE)算法在挖掘数据结构时未考虑特征权重且仅局限于数据的线性拟合关系,导致特征提取效果不佳的问题,提出一种基于熵权距离的图正则局部线性嵌入(Graph Regular Local Linear Embedding Algorithm Based on Entropy Weight Distance,EWD-GLLE)算法。首先,采用信息熵加权的余弦距离划分样本邻域,减小不重要特征对邻域划分的影响,提高了邻域划分的准确性;然后,利用融合热核权重与余弦权重的拉普拉斯图约束低维嵌入,以保留更多的原始数据信息,进而提取到更显著的特征。在两种轴承数据集上的实验结果表明:EWD-GLLE算法的特征提取性能明显优于LLE、LTSA、LDA算法。
基金TUBITAK(The Scientific and Technological Research Council of Turkey).
文摘Before going further with fractional derivative which is constructed by Rabotnov exponential kernel,there exist many questions that are not addressed.In this paper,we try to recapitulate all the fundamental calculus,which we can obtain with this new fractional operator.The problems in this paper are to determine the solutions of the fractional differential equations where the second members are constant functions,polynomial functions,exponential functions,trigonometric functions,or Mittag-Leffler functions.For all the fractional differential equations,the obtained solutions are represented graphically.The Laplace transform of the fractional derivative with Rabotnov exponential kernel is the primary tool in the investigations.Finally,we give the fundamental solution to the nonlinear time-fractional modified Degasperis-Procesi equation by considering the fractional operator with Rabotnov exponential kernel.
