This article addresses the nonlinear state estimation problem where the conventional Gaussian assumption is completely relaxed.Here,the uncertainties in process and measurements are assumed non-Gaussian,such that the ...This article addresses the nonlinear state estimation problem where the conventional Gaussian assumption is completely relaxed.Here,the uncertainties in process and measurements are assumed non-Gaussian,such that the maximum correntropy criterion(MCC)is chosen to replace the conventional minimum mean square error criterion.Furthermore,the MCC is realized using Gaussian as well as Cauchy kernels by defining an appropriate cost function.Simulation results demonstrate the superior estimation accuracy of the developed estimators for two nonlinear estimation problems.展开更多
In this paper, we set up and discuss a kind of singular integral differential equation with convolution kernel and Canchy kernel. By Fourier transform and some lemmas, we turn this class of equations into Riemann boun...In this paper, we set up and discuss a kind of singular integral differential equation with convolution kernel and Canchy kernel. By Fourier transform and some lemmas, we turn this class of equations into Riemann boundary value problems, and obtain the general solution and the condition of solvability in class {0}.展开更多
The solutions of the nonlinear singular integral equation , t 6 L, are considered, where L is a closed contour in the complex plane, b ≠ 0 is a constant and f(t) is a polynomial. It is an extension of the results obt...The solutions of the nonlinear singular integral equation , t 6 L, are considered, where L is a closed contour in the complex plane, b ≠ 0 is a constant and f(t) is a polynomial. It is an extension of the results obtained in [1] when f(t) is a constant. Certain special cases are illustrated.展开更多
This article, first gives the estimaties of two modulus, namely, generalized Lebesgue constant and modulus of generalized singular integral quadrature formulas, then applies them to obtain the error bounds of the oper...This article, first gives the estimaties of two modulus, namely, generalized Lebesgue constant and modulus of generalized singular integral quadrature formulas, then applies them to obtain the error bounds of the operator BL^Pm to the operator B.展开更多
In this paper, two kinds of convolution integral equations with both Cauchy kernel and reflection are discussed. Using Fourier transformation theory they can be transformed into Riemann boundary value problems with bo...In this paper, two kinds of convolution integral equations with both Cauchy kernel and reflection are discussed. Using Fourier transformation theory they can be transformed into Riemann boundary value problems with both discontinuous coefficients and reflection. And we give a new method, by which the general solution and the condition of solvability are obtained respectively.展开更多
The fracture mechanics of cortical bone has received much attention in biomedical engineering.It is a fundamental question how the material constants and the geometric parameters of the cortical bone affect the fractu...The fracture mechanics of cortical bone has received much attention in biomedical engineering.It is a fundamental question how the material constants and the geometric parameters of the cortical bone affect the fracture behavior of the cortical bone.In this work,the plane problem for cortical bone with a microcrack located in the interstitial tissue under tensile loading was considered.Using the solution for the continuously distributed edge dislocations as Green ’ s functions,the problem was formulated as singular integral equations with Cauchy kernels.The numerical results suggest that a soft osteon promotes microcrack propagation,while a stiff osteon repels it,but the interaction effect between the microcrack and the osteon is limited near the osteon.This study not only sheds light on the fracture mechanics behavior of cortical bone but also offers inspiration for the design of bioinspired materials in biomedical engineering.展开更多
基金Rahul Radhakrishnan received the B.Tech.degree in Applied Electronics and Instrumentation from the Government Engineering College,Calicut,India,in 2010 and the M.Tech.degreein Control Systems from the Department of Electrical Engineering,National Institute of Technology Kurukshetra,India,in 2013.He received the Ph.D.degree from the Department of Electrical Engineering,Indian Institute of Technology Patna,India,in 2018.Currently,he is workingasan Assistant Professor in the Department of Electrical Engineering,Sardar Vallabhbhai National Institute of Technology,Surat,Gujarat,India.His main research interests include nonlinear filtering,aerospace,and underwater target tracking.
文摘This article addresses the nonlinear state estimation problem where the conventional Gaussian assumption is completely relaxed.Here,the uncertainties in process and measurements are assumed non-Gaussian,such that the maximum correntropy criterion(MCC)is chosen to replace the conventional minimum mean square error criterion.Furthermore,the MCC is realized using Gaussian as well as Cauchy kernels by defining an appropriate cost function.Simulation results demonstrate the superior estimation accuracy of the developed estimators for two nonlinear estimation problems.
基金Supported by the Qufu Normal University Youth Fund(XJ201218)
文摘In this paper, we set up and discuss a kind of singular integral differential equation with convolution kernel and Canchy kernel. By Fourier transform and some lemmas, we turn this class of equations into Riemann boundary value problems, and obtain the general solution and the condition of solvability in class {0}.
文摘The solutions of the nonlinear singular integral equation , t 6 L, are considered, where L is a closed contour in the complex plane, b ≠ 0 is a constant and f(t) is a polynomial. It is an extension of the results obtained in [1] when f(t) is a constant. Certain special cases are illustrated.
文摘This article, first gives the estimaties of two modulus, namely, generalized Lebesgue constant and modulus of generalized singular integral quadrature formulas, then applies them to obtain the error bounds of the operator BL^Pm to the operator B.
文摘In this paper, two kinds of convolution integral equations with both Cauchy kernel and reflection are discussed. Using Fourier transformation theory they can be transformed into Riemann boundary value problems with both discontinuous coefficients and reflection. And we give a new method, by which the general solution and the condition of solvability are obtained respectively.
基金Supported by the National Natural Science Foundation of China(82060331,12062021,12062022)the Natural Science Foundation of Ningxia(2021AAC03028,2022AAC03001)。
文摘The fracture mechanics of cortical bone has received much attention in biomedical engineering.It is a fundamental question how the material constants and the geometric parameters of the cortical bone affect the fracture behavior of the cortical bone.In this work,the plane problem for cortical bone with a microcrack located in the interstitial tissue under tensile loading was considered.Using the solution for the continuously distributed edge dislocations as Green ’ s functions,the problem was formulated as singular integral equations with Cauchy kernels.The numerical results suggest that a soft osteon promotes microcrack propagation,while a stiff osteon repels it,but the interaction effect between the microcrack and the osteon is limited near the osteon.This study not only sheds light on the fracture mechanics behavior of cortical bone but also offers inspiration for the design of bioinspired materials in biomedical engineering.
