Results 11 to 20 of about 4,894 (291)

Jumping with variably scaled discontinuous kernels (VSDKs) [PDF]

BIT Numerical Mathematics, 2019
AbstractIn this paper we address the problem of approximating functions with discontinuities via kernel-based methods. The main result is the construction of discontinuous kernel-based basis functions. The linear spaces spanned by these discontinuous kernels lead to a very flexible tool which sensibly or completely reduces the well-known Gibbs ...
De Marchi, S., Marchetti, F., Perracchione, E.   +2 more
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New Integral Inequalities with Weakly Singular Kernel for Discontinuous Functions and Their Applications to Impulsive Fractional Differential Systems [PDF]

Journal of Applied Mathematics, 2014
Some new integral inequalities with weakly singular kernel for discontinuous functions are established using the method of successive iteration and properties of Mittag-Leffler function, which can be used in the qualitative analysis of the solutions to ...
Jing Shao
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A Novel Method for Solving Second Kind Volterra Integral Equations with Discontinuous Kernel

Mathematics, 2021
Load leveling problems and energy storage systems can be modeled in the form of Volterra integral equations (VIE) with a discontinuous kernel. The Lagrange–collocation method is applied for solving the problem. Proving a theorem, we discuss the precision
Samad Noeiaghdam, Sanda Micula
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A Class of Generalized Differential Operators with Infinitely Many Discontinuous Points [PDF]

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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An Algorithm for Solving Phase-Lag Nonlinear Mixed Integral Equation With Discontinuous Generalized Kernel

Advances in Mathematical Physics
In this work, a nonlinear fractional integrodifferential equation (NFIo-DE) with discontinuous generalized kernel in position and time is explored in space L2Ω×C0,T ...
Abeer M. Al-Bugami, M. A. Abdou
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Homotopy Analysis Method and Physics-Informed Neural Networks for Solving Volterra Integral Equations with Discontinuous Kernels

Axioms
This paper addresses first- and second-kind Volterra integral equations (VIEs) with discontinuous kernels. A hybrid method combining the Homotopy Analysis Method (HAM) and Physics-Informed Neural Networks (PINNs) is developed.
Samad Noeiaghdam, Md Asadujjaman Miah, Sanda Micula   +2 more
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On a discussion of Volterra–Fredholm integral equation with discontinuous kernel [PDF]

Journal of the Egyptian Mathematical Society, 2020
AbstractThe purpose of this paper is to establish the general solution of a Volterra–Fredholm integral equation with discontinuous kernel in a Banach space. Banach’s fixed point theorem is used to prove the existence and uniqueness of the solution. By using separation of variables method, the problem is reduced to Volterra integral equations of the ...
M. A. Abdou, A.A. Soliman, M. A. Abdel–Aty   +2 more
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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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On a class of integral equations with discontinuous kernels [PDF]

Transactions of the American Mathematical Society, 1927
This paper is given to the discussion of the integral equation in which the kernel K(x, t) is continuous, but possesses first partial derivatives which are discontinuous along the line t = x. It is closely related to a previous papert in which the case of a discontinuous kernel has been treated.
Rudolph E. Langer, Eleanor P. Brown
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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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