In this paper, the difficulties on calculation in solving singular integral equations are overcome when the restriction of curve of integration to be a closed contour is cancelled. When the curve is an open arc and th...In this paper, the difficulties on calculation in solving singular integral equations are overcome when the restriction of curve of integration to be a closed contour is cancelled. When the curve is an open arc and the solutions for singular integral equations possess singularities of higher order, the solution and the solvable condition for characteristic equations as well as the generalized Noether theorem for complete equations are given.展开更多
By dint of the stability of Cauchy-type integral with kernel density of class H＊ for an open arc, this paper discusses the stability of the solution of Riemann boundary value problem with respect to the perturbation ...By dint of the stability of Cauchy-type integral with kernel density of class H＊ for an open arc, this paper discusses the stability of the solution of Riemann boundary value problem with respect to the perturbation of boundary curve to be an open arc.展开更多
The Riemann boundary value problem with square roots in class h0 when the jumping curve is an open arc in the complex plane is considered. It is solved by reducing it to a classical Riemann boundary value problem so t...The Riemann boundary value problem with square roots in class h0 when the jumping curve is an open arc in the complex plane is considered. It is solved by reducing it to a classical Riemann boundary value problem so that its solutions are obtained in closed form. In certain cases, some auxiliary function ω（z）is introduced. With different choices of ω（z）＇s, some interesting examples are illustrated.展开更多
After choosing weight functions suitably, we define a Banach spaceH ω μ (L) and discuss the generalized inverse of singular integral operators on an open arc. Using the generalized inverse, we obtain the solutions f...After choosing weight functions suitably, we define a Banach spaceH ω μ (L) and discuss the generalized inverse of singular integral operators on an open arc. Using the generalized inverse, we obtain the solutions for the following singular integral equation展开更多
The authors examine the relation between the perturbed Cauchy singular integral with its kernel density belong to H＊ and unperturbed one and show that the Cauchy singular integral is stable under perturbation of the ...The authors examine the relation between the perturbed Cauchy singular integral with its kernel density belong to H＊ and unperturbed one and show that the Cauchy singular integral is stable under perturbation of the curve of integration.展开更多
We propose a fully discrete fast Fourier-Galerkin method for solving an integral equation of the first kind with a logarithmic kernel on a smooth open arc,which is a reformulation of the Dirichlet problem of the Lapla...We propose a fully discrete fast Fourier-Galerkin method for solving an integral equation of the first kind with a logarithmic kernel on a smooth open arc,which is a reformulation of the Dirichlet problem of the Laplace equation in the plane.The optimal convergence order and quasi-linear complexity order of the proposed method are established.A precondition is introduced.Combining this method with an efficient numerical integration algorithm for computing the single-layer potential defined on an open arc,we obtain the solution of the Dirichlet problem on a smooth open arc in the plane.Numerical examples are presented to confirm the theoretical estimates and to demonstrate the efficiency and accuracy of the proposed method.展开更多
The study of arc behavior is important to understand the dynamic phenomena concerning the interruption process in a variety of switching devices. This paper is devoted to investigate the influence of gassing material ...The study of arc behavior is important to understand the dynamic phenomena concerning the interruption process in a variety of switching devices. This paper is devoted to investigate the influence of gassing material on blow open force and arc motion. To one double- breaker model, measuring the arc current, voltage and force acting on the moving conductor, the characteristics of the ratio of the emerging blow open force over arc power FB/（ui） could be obtained. With the help of a 2-D optical fiber measurement system, to one arc chamber model, arc motion behavior was measured, too. It is demonstrated that, with the action of gassing material, FB/（ui） will increase 2.5 times, and the arc will enter the splitter plates much easier.展开更多
Influence of the initial opening speed on the characteristics of drawn vacuum arcs for axial magnetic field （AMF） vacuum interrupters （VIs） is studied using a high-speed charge- coupled device （CCD） camera. Two ...Influence of the initial opening speed on the characteristics of drawn vacuum arcs for axial magnetic field （AMF） vacuum interrupters （VIs） is studied using a high-speed charge- coupled device （CCD） camera. Two values of initial opening speed, 0.5 m/s and 1.5 m/s, were set to make a comparative study. The cup-type electrode was made of Cu-Cr （50%-50% in weight） with a diameter of 30 mm and a gap distance between electrodes of 10 mm. The results show that the transition time decreases by 0.5 ms when the initial opening speed increases from 0.5 m/s to 1.5 m/s at a peak current of 2.5 kA, while the transition time decreases by 1.0 ms when the initial opening speed increases from 0.5 m/s to 1.5 m/s at a peak current of 5.0 kA. The reason why the duration of the transition arc mode decreases is that the effect of electromagnetic force and Coulomb force among arcs is increased when the initial opening speed increases.展开更多
基金Foundation item is supported by the NNSF of China(19971064)
文摘In this paper, the difficulties on calculation in solving singular integral equations are overcome when the restriction of curve of integration to be a closed contour is cancelled. When the curve is an open arc and the solutions for singular integral equations possess singularities of higher order, the solution and the solvable condition for characteristic equations as well as the generalized Noether theorem for complete equations are given.
基金supported by Natural Science Foundation of China (10071016)the Natural Science Foundation of Fujian Province (2008J0187)the Science and Technology Foundation of Education Department of Fujian Province (JA08255), China
文摘By dint of the stability of Cauchy-type integral with kernel density of class H＊ for an open arc, this paper discusses the stability of the solution of Riemann boundary value problem with respect to the perturbation of boundary curve to be an open arc.
基金Supported by the National Natural Science Foundation of China (10161009)
文摘The Riemann boundary value problem with square roots in class h0 when the jumping curve is an open arc in the complex plane is considered. It is solved by reducing it to a classical Riemann boundary value problem so that its solutions are obtained in closed form. In certain cases, some auxiliary function ω（z）is introduced. With different choices of ω（z）＇s, some interesting examples are illustrated.
基金Supported by the National Natural Science Foundation of China( No.2 0 1980 6 33)
文摘After choosing weight functions suitably, we define a Banach spaceH ω μ (L) and discuss the generalized inverse of singular integral operators on an open arc. Using the generalized inverse, we obtain the solutions for the following singular integral equation
基金Supported by the Natural Science Foundation of Fujian Province（2008J0187）
文摘The authors examine the relation between the perturbed Cauchy singular integral with its kernel density belong to H＊ and unperturbed one and show that the Cauchy singular integral is stable under perturbation of the curve of integration.
基金supported by the President Fund of GUCAS and the US National Science Foundation(Grant No.CCR-0407476,DMS-0712827)National Natural Science Foundation of China(Grant No.10371122,10631080)
文摘We propose a fully discrete fast Fourier-Galerkin method for solving an integral equation of the first kind with a logarithmic kernel on a smooth open arc,which is a reformulation of the Dirichlet problem of the Laplace equation in the plane.The optimal convergence order and quasi-linear complexity order of the proposed method are established.A precondition is introduced.Combining this method with an efficient numerical integration algorithm for computing the single-layer potential defined on an open arc,we obtain the solution of the Dirichlet problem on a smooth open arc in the plane.Numerical examples are presented to confirm the theoretical estimates and to demonstrate the efficiency and accuracy of the proposed method.
基金National Natural Science Foundation of China (NSFC) (No.50507016)
文摘The study of arc behavior is important to understand the dynamic phenomena concerning the interruption process in a variety of switching devices. This paper is devoted to investigate the influence of gassing material on blow open force and arc motion. To one double- breaker model, measuring the arc current, voltage and force acting on the moving conductor, the characteristics of the ratio of the emerging blow open force over arc power FB/（ui） could be obtained. With the help of a 2-D optical fiber measurement system, to one arc chamber model, arc motion behavior was measured, too. It is demonstrated that, with the action of gassing material, FB/（ui） will increase 2.5 times, and the arc will enter the splitter plates much easier.
文摘Influence of the initial opening speed on the characteristics of drawn vacuum arcs for axial magnetic field （AMF） vacuum interrupters （VIs） is studied using a high-speed charge- coupled device （CCD） camera. Two values of initial opening speed, 0.5 m/s and 1.5 m/s, were set to make a comparative study. The cup-type electrode was made of Cu-Cr （50%-50% in weight） with a diameter of 30 mm and a gap distance between electrodes of 10 mm. The results show that the transition time decreases by 0.5 ms when the initial opening speed increases from 0.5 m/s to 1.5 m/s at a peak current of 2.5 kA, while the transition time decreases by 1.0 ms when the initial opening speed increases from 0.5 m/s to 1.5 m/s at a peak current of 5.0 kA. The reason why the duration of the transition arc mode decreases is that the effect of electromagnetic force and Coulomb force among arcs is increased when the initial opening speed increases.
