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 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.
Effective pavement maintenance and rehabilitation decisions rely on both pavement functional and structural condition data. Traditionally, state transportation agencies prioritize pavement segments based on functional...Effective pavement maintenance and rehabilitation decisions rely on both pavement functional and structural condition data. Traditionally, state transportation agencies prioritize pavement segments based on functional conditions, often neglecting structural assessments due to the time, cost, and labor involved with methods like the Falling Weight Deflectometer (FWD). The objective of this paper to develop machine learning models—Random Forest (RF) and eXtreme Gradient Boosting (XGBoost)—to predict pavement Surface Curvature Index (SCI), a key indicator of pavement structural condition, as a cost-effective alternative to frequent FWD testing. Using 3016 samples from the Long-Term Pavement Performance (LTPP) program, the models were trained and tested with variables such as surface layer condition at year 0, thickness, pavement age, environmental, and traffic data. XGBoost outperformed RF, achieving R2, RMSE, and MAE values of 0.90, 0.64, and 0.41, respectively, compared to RF’s 0.80, 0.90, and 0.51. The study highlights the importance of machine learning applications in predicting pavement structural conditions, offering precise models that can help transportation agencies optimize maintenance planning and resource allocation.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
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
Aiming at the assessment of road structural conditions,a method of combining ground penetrating radar(GPR)and falling weight deflectometer(FWD)for assessing the pavement structural integrity and strength was proposed ...Aiming at the assessment of road structural conditions,a method of combining ground penetrating radar(GPR)and falling weight deflectometer(FWD)for assessing the pavement structural integrity and strength was proposed in this study.First,3D GPR was performed to detect the thickness and internal distress of pavement structural layers using the canny edge detection and you only look once version eight(YOLOv8)detection algorithms.Results showed that the error of thickness extraction was approximately 3%,and the distress detection achieved a mean average precision(m AP)of 0.859 and an inference time of11.43 ms with a GTX 1070 GPU.Then,the extracted thickness was used for the modulus(E)inversion of pavement structure layers based on FWD test data and regression analysis.Finally,the distress ratio inside pavement structures(DRIPS)was proposed as a structural integrity index.The relationship between E and DRIPS was revealed and showed a good correlation.The greater the DRIPS value,the worse the pavement structural integrity and strength.It provides a reference for the evaluation of road structural conditions.This strategy proved to be reliable for nondestructive testing and evaluation of road structures,which could improve the comprehensiveness and effectiveness for evaluating road structural conditions.展开更多
We address the question of how the structure condition is affected when one possesses some additional information at the very beginning of the investment period.The structure condition represents essentially an altern...We address the question of how the structure condition is affected when one possesses some additional information at the very beginning of the investment period.The structure condition represents essentially an alternative to non-arbitrage conditions for the Markowitz’s portfolio optimization framework,and is crucial for the existence of the optimal portfolio in quadratic utility settings.Herein,we provide practical assumption on the initial market model and the additional information to preserve the structure condition.The stochastic tools that drive this result are a generalization of the Lazaro-Yor representation by Lazaro and Yor(1978)and optional stochastic integral.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
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
The Moore-Penrose inverse is an important tool in algebra.This paper shows that the MoorePenrose inverse is also an effcient technique in determining the minimal martingale measure if a security price follows a semi-m...The Moore-Penrose inverse is an important tool in algebra.This paper shows that the MoorePenrose inverse is also an effcient technique in determining the minimal martingale measure if a security price follows a semi-martingale which satisfies some structure condition.We extend a result of Dzhaparidze and Spreij concerning the Moore-Penrose inverse to the case that the Moore-Penrose inverse of any matrix-valued predictable process is still predictable.Furthermore,we obtain an explicit formula of the minimal martingale measure by employing the Moore-Penrose inverse.Specifically,the minimal martingale measure in a generalized Black-Scholes model is found.展开更多
We consider a modified Markov branching process incorporating with both state-independent immigration-migration and resurrection. The effect of state-independent immigration-migration is firstly in- vestigated in deta...We consider a modified Markov branching process incorporating with both state-independent immigration-migration and resurrection. The effect of state-independent immigration-migration is firstly in- vestigated in detail. The explicit expressions for the extinction probabilities and mean extinction times are presented. The ergodicity and stability properties of the process incorporating with resurrection structure are then investigated. The conditions for recurrence, ergodicity and exponential ergodicity are obtained. An explicit expression for the equilibrium distribution is also presented. As a preparation, the criteria for regularity and uniqueness for such structure are firstly established.展开更多
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 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Effective pavement maintenance and rehabilitation decisions rely on both pavement functional and structural condition data. Traditionally, state transportation agencies prioritize pavement segments based on functional conditions, often neglecting structural assessments due to the time, cost, and labor involved with methods like the Falling Weight Deflectometer (FWD). The objective of this paper to develop machine learning models—Random Forest (RF) and eXtreme Gradient Boosting (XGBoost)—to predict pavement Surface Curvature Index (SCI), a key indicator of pavement structural condition, as a cost-effective alternative to frequent FWD testing. Using 3016 samples from the Long-Term Pavement Performance (LTPP) program, the models were trained and tested with variables such as surface layer condition at year 0, thickness, pavement age, environmental, and traffic data. XGBoost outperformed RF, achieving R2, RMSE, and MAE values of 0.90, 0.64, and 0.41, respectively, compared to RF’s 0.80, 0.90, and 0.51. The study highlights the importance of machine learning applications in predicting pavement structural conditions, offering precise models that can help transportation agencies optimize maintenance planning and resource allocation.
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.
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sponsored by the National Key Research and Development Program of China(No.2021YFC3000074)the Xizang Autonomous Region 2024 Major Science and Technology Special Project(No.XZ202402ZD0008)the Xizang Autonomous Region 2024 Key Research and Development Plan(No.XZ202401ZY0082)。
文摘Aiming at the assessment of road structural conditions,a method of combining ground penetrating radar(GPR)and falling weight deflectometer(FWD)for assessing the pavement structural integrity and strength was proposed in this study.First,3D GPR was performed to detect the thickness and internal distress of pavement structural layers using the canny edge detection and you only look once version eight(YOLOv8)detection algorithms.Results showed that the error of thickness extraction was approximately 3%,and the distress detection achieved a mean average precision(m AP)of 0.859 and an inference time of11.43 ms with a GTX 1070 GPU.Then,the extracted thickness was used for the modulus(E)inversion of pavement structure layers based on FWD test data and regression analysis.Finally,the distress ratio inside pavement structures(DRIPS)was proposed as a structural integrity index.The relationship between E and DRIPS was revealed and showed a good correlation.The greater the DRIPS value,the worse the pavement structural integrity and strength.It provides a reference for the evaluation of road structural conditions.This strategy proved to be reliable for nondestructive testing and evaluation of road structures,which could improve the comprehensiveness and effectiveness for evaluating road structural conditions.
基金supported by the Natural Sciences and Engineering Research Council of Canada (Grant No. G121210818)National Natural Science Foundation of China (Grant No. 11501105)
文摘We address the question of how the structure condition is affected when one possesses some additional information at the very beginning of the investment period.The structure condition represents essentially an alternative to non-arbitrage conditions for the Markowitz’s portfolio optimization framework,and is crucial for the existence of the optimal portfolio in quadratic utility settings.Herein,we provide practical assumption on the initial market model and the additional information to preserve the structure condition.The stochastic tools that drive this result are a generalization of the Lazaro-Yor representation by Lazaro and Yor(1978)and optional stochastic integral.
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].
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 (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)
文摘The Moore-Penrose inverse is an important tool in algebra.This paper shows that the MoorePenrose inverse is also an effcient technique in determining the minimal martingale measure if a security price follows a semi-martingale which satisfies some structure condition.We extend a result of Dzhaparidze and Spreij concerning the Moore-Penrose inverse to the case that the Moore-Penrose inverse of any matrix-valued predictable process is still predictable.Furthermore,we obtain an explicit formula of the minimal martingale measure by employing the Moore-Penrose inverse.Specifically,the minimal martingale measure in a generalized Black-Scholes model is found.
基金supported by National Natural Science Foundations of China (Grant Nos. 10771216 and 11071259)
文摘We consider a modified Markov branching process incorporating with both state-independent immigration-migration and resurrection. The effect of state-independent immigration-migration is firstly in- vestigated in detail. The explicit expressions for the extinction probabilities and mean extinction times are presented. The ergodicity and stability properties of the process incorporating with resurrection structure are then investigated. The conditions for recurrence, ergodicity and exponential ergodicity are obtained. An explicit expression for the equilibrium distribution is also presented. As a preparation, the criteria for regularity and uniqueness for such structure are firstly established.
