As wind farms are commonly installed in areas with abundant wind resources,spatial dependence of wind speed among nearby wind farms should be considered when modeling a power system with large-scale wind power.In this...As wind farms are commonly installed in areas with abundant wind resources,spatial dependence of wind speed among nearby wind farms should be considered when modeling a power system with large-scale wind power.In this paper,a novel bivariate non-parametric copula,and a bivariate diffusive kernel(BDK)copula are proposed to formulate the dependence between random variables.BDK copula is then applied to higher dimension using the pair-copula method and is named as pair diffusive kernel(PDK)copula,offering flexibility to formulate the complicated dependent structure of multiple random variables.Also,a quasi-Monte Carlo method is elaborated in the sampling procedure based on the combination of the Sobol sequence and the Rosen-blatt transformation of the PDK copula,to generate correlated wind speed samples.The proposed method is applied to solve probabilistic optimal power flow(POPF)problems.The effectiveness of the BDK copula is validated in copula definitions.Then,three different data sets are used in various goodness-of-fit tests to verify the superior performance of the PDK copula,which facilitates in formulating the dependence structure of wind speeds at different wind farms.Furthermore,samples obtained from the PDK copula are used to solve POPF problems,which are modeled on three modified IEEE 57-bus power systems.Compared to the Gaussian,T,and parametric-pair copulas,the results obtained from the PDK copula are superior in formulating the complicated dependence,thus solving POPF problems.展开更多
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
The numerical solution of linear Volterra integral equations of the second kind is discussed. The kernel of the integral equation may have weak diagonal and boundary singularities. Using suitable smoothing techniques ...The numerical solution of linear Volterra integral equations of the second kind is discussed. The kernel of the integral equation may have weak diagonal and boundary singularities. Using suitable smoothing techniques and polynomial splines on mildly graded or of the proposed algorithms is studied given. uniform grids, the convergence behavior and a collection of numerical results is give.展开更多
We reduce the initial value problem for the generalized Schroedinger equation with piecewise-constant leading coefficient to the system of Volterra type integral equations and construct new useful integral representat...We reduce the initial value problem for the generalized Schroedinger equation with piecewise-constant leading coefficient to the system of Volterra type integral equations and construct new useful integral representations for the fundamental solutions of the Schroedinger equation. We also investigate some significant properties of the kernels of these integral representations. The integral representations of fundamental solutions enable to obtain the basic integral equations, which are a powerful tool for solving inverse spectral problems.展开更多
The relationship between symmetries and Gauss kernels for the SchrSdinger equation iut = uxx ＋ f（x）u is established. It is shown that if the Lie point symmetries of the equation are nontrivial, a classical integral...The relationship between symmetries and Gauss kernels for the SchrSdinger equation iut = uxx ＋ f（x）u is established. It is shown that if the Lie point symmetries of the equation are nontrivial, a classical integral transformations of the Gauss kernels can be obtained. Then the Gauss kernels of Schroedinger equations are derived by inverting the integral transformations. Furthermore, the relationship between Gauss kernels for two equations related by an equivalence transformation is identified.展开更多
Determination of an age in a particular tree species can be considered as a vital factor in forest management.In this research we have introduced a novel scheme to determine the accurate age of the tree species in Sri...Determination of an age in a particular tree species can be considered as a vital factor in forest management.In this research we have introduced a novel scheme to determine the accurate age of the tree species in Sri Lanka.This is initially developed for the tree species called‘Hora’(Dipterocarpus zeylanicus)in wet zone of Sri Lanka.Here the core samples are extracted and further analyzed by means of the different image processing techniques such as Gaussian kernel blurring,use of Sobel filters,double threshold analysis,Hough line tran sformation and etc.The operations such as rescaling,slicing and measuring are also used in line with image processing techniques to achieve the desired results.Ultimately a Graphical user interface(GUI)is developed to cater for the user requirements in a user friendly environment.It has been found that the average growth ring identification accuracy of the proposed system is 93%and the overall average accuracy of detecting the age is 81%.Ultimately the proposed system will provide an insight and contributes to the forestry related activities and researches in Sri Lanka.展开更多
基金supported by Key-Area Research and Development Program of Guangdong Province(No.2020B010166004)the National Natural Science Foundation of China(No.52077081).
文摘As wind farms are commonly installed in areas with abundant wind resources,spatial dependence of wind speed among nearby wind farms should be considered when modeling a power system with large-scale wind power.In this paper,a novel bivariate non-parametric copula,and a bivariate diffusive kernel(BDK)copula are proposed to formulate the dependence between random variables.BDK copula is then applied to higher dimension using the pair-copula method and is named as pair diffusive kernel(PDK)copula,offering flexibility to formulate the complicated dependent structure of multiple random variables.Also,a quasi-Monte Carlo method is elaborated in the sampling procedure based on the combination of the Sobol sequence and the Rosen-blatt transformation of the PDK copula,to generate correlated wind speed samples.The proposed method is applied to solve probabilistic optimal power flow(POPF)problems.The effectiveness of the BDK copula is validated in copula definitions.Then,three different data sets are used in various goodness-of-fit tests to verify the superior performance of the PDK copula,which facilitates in formulating the dependence structure of wind speeds at different wind farms.Furthermore,samples obtained from the PDK copula are used to solve POPF problems,which are modeled on three modified IEEE 57-bus power systems.Compared to the Gaussian,T,and parametric-pair copulas,the results obtained from the PDK copula are superior in formulating the complicated dependence,thus solving POPF problems.
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Acknowledgements The authors are grateful to the referees for many helpful remarks and suggestions. This work was supported by the Estonian Science Foundation （Grant No. 9104）.
文摘The numerical solution of linear Volterra integral equations of the second kind is discussed. The kernel of the integral equation may have weak diagonal and boundary singularities. Using suitable smoothing techniques and polynomial splines on mildly graded or of the proposed algorithms is studied given. uniform grids, the convergence behavior and a collection of numerical results is give.
文摘We reduce the initial value problem for the generalized Schroedinger equation with piecewise-constant leading coefficient to the system of Volterra type integral equations and construct new useful integral representations for the fundamental solutions of the Schroedinger equation. We also investigate some significant properties of the kernels of these integral representations. The integral representations of fundamental solutions enable to obtain the basic integral equations, which are a powerful tool for solving inverse spectral problems.
基金supported by the National Natural Science Foundation of China for Distinguished Young Scholars (Grant No.10925104)the National Natural Science Foundation of China (Grant No.11001220)the Ph.D.Program Foundation of the Ministry of Education of China (Grant No.20106101110008)
文摘The relationship between symmetries and Gauss kernels for the SchrSdinger equation iut = uxx ＋ f（x）u is established. It is shown that if the Lie point symmetries of the equation are nontrivial, a classical integral transformations of the Gauss kernels can be obtained. Then the Gauss kernels of Schroedinger equations are derived by inverting the integral transformations. Furthermore, the relationship between Gauss kernels for two equations related by an equivalence transformation is identified.
文摘Determination of an age in a particular tree species can be considered as a vital factor in forest management.In this research we have introduced a novel scheme to determine the accurate age of the tree species in Sri Lanka.This is initially developed for the tree species called‘Hora’(Dipterocarpus zeylanicus)in wet zone of Sri Lanka.Here the core samples are extracted and further analyzed by means of the different image processing techniques such as Gaussian kernel blurring,use of Sobel filters,double threshold analysis,Hough line tran sformation and etc.The operations such as rescaling,slicing and measuring are also used in line with image processing techniques to achieve the desired results.Ultimately a Graphical user interface(GUI)is developed to cater for the user requirements in a user friendly environment.It has been found that the average growth ring identification accuracy of the proposed system is 93%and the overall average accuracy of detecting the age is 81%.Ultimately the proposed system will provide an insight and contributes to the forestry related activities and researches in Sri Lanka.
