On integral equations with discontinuous kernels [PDF]
Transactions of the American Mathematical Society, 1928 when the kernel presents certain features of finite discontinuity along the line t=-r. Kernels of this kind are typified by the Green's functions of ordinary differential equations with boundary conditions, and it was first noticed by Birkhoff that this fact might serve as a basis for the development of a theory of integral equations of this type.
J. D. Tamarkin, Rudolph E. Langer
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Optimized Realization of Sobel Edge Detection Algorithm for FT-M7002 [PDF]
Jisuanji gongcheng, 2022 Edge detection is a robust image analysis method used in image processing and computer vision.The Sobel operator is widely used in edge detection and image processing.With the development of domestic FT series high-performance Digital Signal Processors ...
FAN Mingliang, GUO Zihan, CHAI Xiaonan, SHANG Jiandong
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Robust Motion Blur Kernel Estimation by Kernel Continuity Prior
IEEE Access, 2020 The accurate kernel estimation is key to the blind motion deblurring. Many previous methods depend on the image regularization to recover strong edges in the observed image for kernel estimation.
Xueling Chen +3 more
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Kernel‐based active subspaces with application to computational fluid dynamics parametric problems using the discontinuous Galerkin method [PDF]
International Journal for Numerical Methods in Engineering, 2020 Nonlinear extensions to the active subspaces method have brought remarkable results for dimension reduction in the parameter space and response surface design. We further develop a kernel‐based nonlinear method.
F. Romor +3 more
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High energy flash X‐ray image restoration using region extrema and kernel optimization
IET Image Processing, 2021 The quality of high energy flash X‐ray images is crucial to the high‐precision diagnosis of object density. High energy flash X‐ray radiography is susceptible to the system blur, which usually causes the poor quality of static images. In response to this,
Xiaolin Wang, Qingwu Li, Jinxin Xu
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Uniform convergence of an upwind discontinuous Galerkin method for solving scaled discrete-ordinate radiative transfer equations with isotropic scattering kernel [PDF]
Mathematics of Computation, 2020 We present an error analysis for the discontinuous Galerkin method applied to the discrete-ordinate discretization of the steady-state radiative transfer equation.
Qiwei Sheng, C. Hauck
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Large Gap Asymptotics for Airy Kernel Determinants with Discontinuities [PDF]
Communications in Mathematical Physics, 2019 We obtain large gap asymptotics for Airy kernel Fredholm determinants with any number $m$ of discontinuities. These $m$-point determinants are generating functions for the Airy point process and encode probabilistic information about eigenvalues near soft edges in random matrix ensembles.
Christophe Charlier, Tom Claeys
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Sparse Support Tensor Machine with Scaled Kernel Functions
Mathematics, 2023 As one of the supervised tensor learning methods, the support tensor machine (STM) for tensorial data classification is receiving increasing attention in machine learning and related applications, including remote sensing imaging, video processing, fault
Shuangyue Wang, Ziyan Luo
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On the theory of integral equations with discontinuous kernels [PDF]
Transactions of the American Mathematical Society, 1926 This paper is concerned with the theory of the integral equation whose salient characteristic is that its kernel K(x, t) is discontinuous along the line t =x. It is closely related with the theory of the integral equation characterized by discontinuities in the partial derivatives of the kernel for t=x, of which more specific mention is made below. The
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A Class of Generalized Differential Operators with Infinitely Many Discontinuous Points
Abstract and Applied Analysis, 2014 We define a class of differential operators T which have infinitely many discontinuous points, and investigate the kernel of T in terms of operator theory.
Yurong Li, Jiong Sun, Siqin Yao
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