The debromination of diphenyl bromomethane (Ph_2CHBr) using polymers with viologen structure as electron--transfer catalyst (ETC) afforded tetraphenylethane in good yields under het- erophase conditions.
In this note, we investigated existence and uniqueness of entropy solution for triply nonlinear degenerate parabolic problem with zero-flux boundary condition. Accordingly to the case of doubly nonlinear degenerate pa...In this note, we investigated existence and uniqueness of entropy solution for triply nonlinear degenerate parabolic problem with zero-flux boundary condition. Accordingly to the case of doubly nonlinear degenerate parabolic hyperbolic equation, we propose a generalization of entropy formulation and prove existence and uniqueness result without any structure condition.展开更多
In this article, we consider the structured condition numbers for LDU, factorization by using the modified matrix-vector approach and the differential calculus, which can be represented by sets of parameters. By setti...In this article, we consider the structured condition numbers for LDU, factorization by using the modified matrix-vector approach and the differential calculus, which can be represented by sets of parameters. By setting the specific norms and weight parameters, we present the expressions of the structured normwise, mixed, componentwise condition numbers and the corresponding results for unstructured ones. In addition, we investigate the statistical estimation of condition numbers of LDU factorization using the probabilistic spectral norm estimator and the small-sample statistical condition estimation method, and devise three algorithms. Finally, we compare the structured condition numbers with the corresponding unstructured ones in numerical experiments.展开更多
Two metal-organic coordination complexes, [Zn(2,6-ndc)(1,2-bix)]n(1) and [Zn(2,6-ndc)(1,3-bix)]n(2)(2,6-H2ndc = 2,6-naphthalenedicarboxylic acid, 1,2-bix = 1,2-bis(imidazole-1-ylmethyl)-benzene and 1,3-...Two metal-organic coordination complexes, [Zn(2,6-ndc)(1,2-bix)]n(1) and [Zn(2,6-ndc)(1,3-bix)]n(2)(2,6-H2ndc = 2,6-naphthalenedicarboxylic acid, 1,2-bix = 1,2-bis(imidazole-1-ylmethyl)-benzene and 1,3-bix = 1,3-bis(imidazole-1-ylmethyl)-benzene) have been synthesized by the hydrothermal method. Though the two complexes both crystallize in a triclinic system, space group P1 and show similar two-dimensional structures, weak intermolecular interactions(π-π packing interactions) only exist in complex 2. They are characterized by single-crystal X-ray diffraction analysis, fluorescence measurement, IR spectroscopy and TGA. Moreover, the solid-state fluorescence spectra of two complexes show maximal emission peaks at 365(λ(ex) = 329 nm) and 367 nm(λex = 344 nm), respectively.展开更多
The entropy balance equation that describes the entropy budget of atmospheric systems is derived from the Gibbs relation.The distribution of the entropy flows of a west-Pacific typhoon and a Bengal-Bay cyclone is calc...The entropy balance equation that describes the entropy budget of atmospheric systems is derived from the Gibbs relation.The distribution of the entropy flows of a west-Pacific typhoon and a Bengal-Bay cyclone is calculated and thus the dissipativity of the atmospheric systems is revealed.展开更多
Learning Bayesian network structure is one of the most exciting challenges in machine learning. Discovering a correct skeleton of a directed acyclic graph(DAG) is the foundation for dependency analysis algorithms fo...Learning Bayesian network structure is one of the most exciting challenges in machine learning. Discovering a correct skeleton of a directed acyclic graph(DAG) is the foundation for dependency analysis algorithms for this problem. Considering the unreliability of high order condition independence(CI) tests, and to improve the efficiency of a dependency analysis algorithm, the key steps are to use few numbers of CI tests and reduce the sizes of conditioning sets as much as possible. Based on these reasons and inspired by the algorithm PC, we present an algorithm, named fast and efficient PC(FEPC), for learning the adjacent neighbourhood of every variable. FEPC implements the CI tests by three kinds of orders, which reduces the high order CI tests significantly. Compared with current algorithm proposals, the experiment results show that FEPC has better accuracy with fewer numbers of condition independence tests and smaller size of conditioning sets. The highest reduction percentage of CI test is 83.3% by EFPC compared with PC algorithm.展开更多
The possibly most popular regularization method for solving the least squares problem rain ‖Ax - b‖2 with a highly ill-conditioned or rank deficient coefficient matrix A is the x Tikhonov regularization method. In ...The possibly most popular regularization method for solving the least squares problem rain ‖Ax - b‖2 with a highly ill-conditioned or rank deficient coefficient matrix A is the x Tikhonov regularization method. In this paper we present the explicit expressions of the normwise, mixed and componentwise condition numbers for the Tikhonov regularization when A has linear structures. The structured condition numbers in the special cases of nonlinear structure i.e. Vandermonde and Cauchy matrices are also considered. Some comparisons between structured condition numbers and unstructured condition numbers are made by numerical experiments. In addition, we also derive the normwise, mixed and componentwise condition numbers for the Tikhonov regularization when the coefficient matrix, regularization matrix and right-hand side vector are all perturbed, which generalize the results obtained by Chu et al. [Numer. Linear Algebra Appl., 18 (2011), 87-103].展开更多
文摘The debromination of diphenyl bromomethane (Ph_2CHBr) using polymers with viologen structure as electron--transfer catalyst (ETC) afforded tetraphenylethane in good yields under het- erophase conditions.
文摘In this note, we investigated existence and uniqueness of entropy solution for triply nonlinear degenerate parabolic problem with zero-flux boundary condition. Accordingly to the case of doubly nonlinear degenerate parabolic hyperbolic equation, we propose a generalization of entropy formulation and prove existence and uniqueness result without any structure condition.
基金Supported by the National Natural Science Foundation of China(11671060).
文摘In this article, we consider the structured condition numbers for LDU, factorization by using the modified matrix-vector approach and the differential calculus, which can be represented by sets of parameters. By setting the specific norms and weight parameters, we present the expressions of the structured normwise, mixed, componentwise condition numbers and the corresponding results for unstructured ones. In addition, we investigate the statistical estimation of condition numbers of LDU factorization using the probabilistic spectral norm estimator and the small-sample statistical condition estimation method, and devise three algorithms. Finally, we compare the structured condition numbers with the corresponding unstructured ones in numerical experiments.
基金Supported by the National Natural Science Foundation of China for Young Scholars(No.21201087)Natural Science Foundation of Jiangsu Province(No.BK20131244)+1 种基金Jiangsu Overseas Research & Training Program for University Prominent Young & Middle-aged Teachers and Presidents,a start-up grant from Jiangsu University of Science and Technology,and Jiangsu Innovation Program for Graduate Student(No.KYZZ15-0300)Innovation Program for Graduate Student from Jiangsu University of Science and Technology,China
文摘Two metal-organic coordination complexes, [Zn(2,6-ndc)(1,2-bix)]n(1) and [Zn(2,6-ndc)(1,3-bix)]n(2)(2,6-H2ndc = 2,6-naphthalenedicarboxylic acid, 1,2-bix = 1,2-bis(imidazole-1-ylmethyl)-benzene and 1,3-bix = 1,3-bis(imidazole-1-ylmethyl)-benzene) have been synthesized by the hydrothermal method. Though the two complexes both crystallize in a triclinic system, space group P1 and show similar two-dimensional structures, weak intermolecular interactions(π-π packing interactions) only exist in complex 2. They are characterized by single-crystal X-ray diffraction analysis, fluorescence measurement, IR spectroscopy and TGA. Moreover, the solid-state fluorescence spectra of two complexes show maximal emission peaks at 365(λ(ex) = 329 nm) and 367 nm(λex = 344 nm), respectively.
文摘The entropy balance equation that describes the entropy budget of atmospheric systems is derived from the Gibbs relation.The distribution of the entropy flows of a west-Pacific typhoon and a Bengal-Bay cyclone is calculated and thus the dissipativity of the atmospheric systems is revealed.
基金Supported by the National Natural Science Foundation of China(61403290,11301408,11401454)the Foundation for Youths of Shaanxi Province(2014JQ1020)+1 种基金the Foundation of Baoji City(2013R7-3)the Foundation of Baoji University of Arts and Sciences(ZK15081)
文摘Learning Bayesian network structure is one of the most exciting challenges in machine learning. Discovering a correct skeleton of a directed acyclic graph(DAG) is the foundation for dependency analysis algorithms for this problem. Considering the unreliability of high order condition independence(CI) tests, and to improve the efficiency of a dependency analysis algorithm, the key steps are to use few numbers of CI tests and reduce the sizes of conditioning sets as much as possible. Based on these reasons and inspired by the algorithm PC, we present an algorithm, named fast and efficient PC(FEPC), for learning the adjacent neighbourhood of every variable. FEPC implements the CI tests by three kinds of orders, which reduces the high order CI tests significantly. Compared with current algorithm proposals, the experiment results show that FEPC has better accuracy with fewer numbers of condition independence tests and smaller size of conditioning sets. The highest reduction percentage of CI test is 83.3% by EFPC compared with PC algorithm.
基金Supported by the National Natural Science Foundation of China (No.10871064)the Key Laboratory of Computational and Stochastic Mathematics and It's Applications,Universities of Hunan Province,Hunan Normal University and the Soft Scientific Research Funds of Hunan Provincial Science & Technology Department of China (No.2009ZK4021)
基金The authors would like to thank the anonymous referees for their valu- able suggestions and comments. This work was supported by the National Natural Science Foundation of China (No. 11571004 and No. 11171371).
文摘The possibly most popular regularization method for solving the least squares problem rain ‖Ax - b‖2 with a highly ill-conditioned or rank deficient coefficient matrix A is the x Tikhonov regularization method. In this paper we present the explicit expressions of the normwise, mixed and componentwise condition numbers for the Tikhonov regularization when A has linear structures. The structured condition numbers in the special cases of nonlinear structure i.e. Vandermonde and Cauchy matrices are also considered. Some comparisons between structured condition numbers and unstructured condition numbers are made by numerical experiments. In addition, we also derive the normwise, mixed and componentwise condition numbers for the Tikhonov regularization when the coefficient matrix, regularization matrix and right-hand side vector are all perturbed, which generalize the results obtained by Chu et al. [Numer. Linear Algebra Appl., 18 (2011), 87-103].