In this paper, we set up a general framework of parallel matrix mullisplitting relaxation methods for solving large scale system of linear equations. We investigate the convergence properties of this framework and giv...In this paper, we set up a general framework of parallel matrix mullisplitting relaxation methods for solving large scale system of linear equations. We investigate the convergence properties of this framework and give several sufficient conditions ensuring it to converge as well as diverge. At last, we conclude a necessary and sufficient condition for the convergence of this framework when the coefficient matrix is an L-matrix.展开更多
Internet services and web-based applications play pivotal roles in various sensitive domains, encompassing e-commerce, e-learning, e-healthcare, and e-payment. However, safeguarding these services poses a significant ...Internet services and web-based applications play pivotal roles in various sensitive domains, encompassing e-commerce, e-learning, e-healthcare, and e-payment. However, safeguarding these services poses a significant challenge, as the need for robust security measures becomes increasingly imperative. This paper presented an innovative method based on differential analyses to detect abrupt changes in network traffic characteristics. The core concept revolves around identifying abrupt alterations in certain characteristics such as input/output volume, the number of TCP connections, or DNS queries—within the analyzed traffic. Initially, the traffic is segmented into distinct sequences of slices, followed by quantifying specific characteristics for each slice. Subsequently, the distance between successive values of these measured characteristics is computed and clustered to detect sudden changes. To accomplish its objectives, the approach combined several techniques, including propositional logic, distance metrics (e.g., Kullback-Leibler Divergence), and clustering algorithms (e.g., K-means). When applied to two distinct datasets, the proposed approach demonstrates exceptional performance, achieving detection rates of up to 100%.展开更多
The concept of the divergence is fundamental in electromagnetic field theory, yet they are especially difficult mathematical concepts. Understanding this concept requires strong spatial and abstract thinking. When tea...The concept of the divergence is fundamental in electromagnetic field theory, yet they are especially difficult mathematical concepts. Understanding this concept requires strong spatial and abstract thinking. When teaching, through the graphical and quantitative methods presented herein, the significance of the divergence is displayed by a quantitative method for the first time. Through these methods, the concepts of the divergence can be grasped more easily. These explanations will be helpful for students to strengthen the understanding of this concept and has a certain reference significance.展开更多
A partial Runge-Kutta Discontinuous Galerkin(RKDG)method which preserves the exactly divergence-free property of the magnetic field is proposed in this paper to solve the two-dimensional ideal compressible magnetohydr...A partial Runge-Kutta Discontinuous Galerkin(RKDG)method which preserves the exactly divergence-free property of the magnetic field is proposed in this paper to solve the two-dimensional ideal compressible magnetohydrodynamics(MHD)equations written in semi-Lagrangian formulation on moving quadrilateral meshes.In this method,the fluid part of the ideal MHD equations along with zcomponent of the magnetic induction equation is discretized by the RKDG method as our previous paper[47].The numerical magnetic field in the remaining two directions(i.e.,x and y)are constructed by using the magnetic flux-freezing principle which is the integral form of the magnetic induction equation of the ideal MHD.Since the divergence of the magnetic field in 2D is independent of its z-direction component,an exactly divergence-free numerical magnetic field can be obtained by this treatment.We propose a new nodal solver to improve the calculation accuracy of velocities of the moving meshes.A limiter is presented for the numerical solution of the fluid part of the MHD equations and it can avoid calculating the complex eigen-system of the MHD equations.Some numerical examples are presented to demonstrate the accuracy,non-oscillatory property and preservation of the exactly divergence-free property of our method.展开更多
The concept of divergence is the basis of electromagnetic field theory, and has been a special difficulty in mathematical theory. In this paper, the connotation of divergence itself is truly displayed by quantitative ...The concept of divergence is the basis of electromagnetic field theory, and has been a special difficulty in mathematical theory. In this paper, the connotation of divergence itself is truly displayed by quantitative method for the first time. Through these methods, the concepts of divergence can be grasped more easily. The explanation of divergence is helpful to strengthen the understanding of the concept and has a certain reference significance.展开更多
基金Supported by Natural Science Fundations of China and Shanghai.
文摘In this paper, we set up a general framework of parallel matrix mullisplitting relaxation methods for solving large scale system of linear equations. We investigate the convergence properties of this framework and give several sufficient conditions ensuring it to converge as well as diverge. At last, we conclude a necessary and sufficient condition for the convergence of this framework when the coefficient matrix is an L-matrix.
文摘Internet services and web-based applications play pivotal roles in various sensitive domains, encompassing e-commerce, e-learning, e-healthcare, and e-payment. However, safeguarding these services poses a significant challenge, as the need for robust security measures becomes increasingly imperative. This paper presented an innovative method based on differential analyses to detect abrupt changes in network traffic characteristics. The core concept revolves around identifying abrupt alterations in certain characteristics such as input/output volume, the number of TCP connections, or DNS queries—within the analyzed traffic. Initially, the traffic is segmented into distinct sequences of slices, followed by quantifying specific characteristics for each slice. Subsequently, the distance between successive values of these measured characteristics is computed and clustered to detect sudden changes. To accomplish its objectives, the approach combined several techniques, including propositional logic, distance metrics (e.g., Kullback-Leibler Divergence), and clustering algorithms (e.g., K-means). When applied to two distinct datasets, the proposed approach demonstrates exceptional performance, achieving detection rates of up to 100%.
文摘The concept of the divergence is fundamental in electromagnetic field theory, yet they are especially difficult mathematical concepts. Understanding this concept requires strong spatial and abstract thinking. When teaching, through the graphical and quantitative methods presented herein, the significance of the divergence is displayed by a quantitative method for the first time. Through these methods, the concepts of the divergence can be grasped more easily. These explanations will be helpful for students to strengthen the understanding of this concept and has a certain reference significance.
基金supported by National Natural Science Foundation of China(Nos.12071046,11671049,91330107,11571002 and 11702028)China Postdoctoral Science Foundation(No.2020TQ0013).
文摘A partial Runge-Kutta Discontinuous Galerkin(RKDG)method which preserves the exactly divergence-free property of the magnetic field is proposed in this paper to solve the two-dimensional ideal compressible magnetohydrodynamics(MHD)equations written in semi-Lagrangian formulation on moving quadrilateral meshes.In this method,the fluid part of the ideal MHD equations along with zcomponent of the magnetic induction equation is discretized by the RKDG method as our previous paper[47].The numerical magnetic field in the remaining two directions(i.e.,x and y)are constructed by using the magnetic flux-freezing principle which is the integral form of the magnetic induction equation of the ideal MHD.Since the divergence of the magnetic field in 2D is independent of its z-direction component,an exactly divergence-free numerical magnetic field can be obtained by this treatment.We propose a new nodal solver to improve the calculation accuracy of velocities of the moving meshes.A limiter is presented for the numerical solution of the fluid part of the MHD equations and it can avoid calculating the complex eigen-system of the MHD equations.Some numerical examples are presented to demonstrate the accuracy,non-oscillatory property and preservation of the exactly divergence-free property of our method.
文摘The concept of divergence is the basis of electromagnetic field theory, and has been a special difficulty in mathematical theory. In this paper, the connotation of divergence itself is truly displayed by quantitative method for the first time. Through these methods, the concepts of divergence can be grasped more easily. The explanation of divergence is helpful to strengthen the understanding of the concept and has a certain reference significance.
