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Kolmogorov GAM Networks Are All You Need! [PDF]
Entropy (Basel)Polson S, Sokolov V.
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Focused reservoir characterization: analysis of selected sand units using well log and 3-D seismic data in 'Kukih' field, Onshore Niger Delta, Nigeria. [PDF]
Sci RepFagbemi OI +3 more
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Photoelectron imaging of substituted benzenes in aqueous aerosol droplets.
Phys Chem Chem PhysHeitland J +7 more
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Regularisation of Abel's integral equation
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1987SynopsisConsider the Abel integral operatorwhere 0 < α < 1. Supposeuis inH1(0, 1) ofH1-norm ≦E, andfis an element ofL2(0, 1) such that ∥Au–f∥L−2< ε. We give a regularised approximate solutionuβ(f) of the equationwhich satisfiesand can be computed simply by performing some integrations.
Dang Dinh Hai, Dang Dinh Ang
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Interval Abel integral equation
Soft Computing, 2016The authors study the solvability of the interval Abel integral equation of the form: \[ \frac{1}{\Gamma(\alpha)} \int\limits_a^t (t-s)^{\alpha-1} X(s) \text{d}s = Y(t) ,\, t \in [a, b] \tag{1} \] where \(\alpha \in (0, 1)\), \(K\) is the set of any nonempty compact intervals of the real line \(\mathbb{R}\), \(Y(\cdot) : [a, b] \to K\) being a given ...
Lupulescu, Vasile, Van Hoa, Ngo
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1990
Even though they have a rather specialized structure, Abel equations form an important class of integral equations in applications. This happens because completely independent problems lead to the solution of such equations. After an initial survey of Abel integral equations, this chapter focuses on the numerical solution of these equations when the ...
R. S. Anderssen, F. R. Hoog
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Even though they have a rather specialized structure, Abel equations form an important class of integral equations in applications. This happens because completely independent problems lead to the solution of such equations. After an initial survey of Abel integral equations, this chapter focuses on the numerical solution of these equations when the ...
R. S. Anderssen, F. R. Hoog
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Numerical solution of the abel integral equation
BIT, 1973A numerical method for the solution of the Abel integral equation is presented. The known function is approximated by a sum of Chebyshev polynomials. The solution can then be expressed as a sum of generalized hypergeometric functions, which can easily be evaluated, using a simple recurrence relation.
Piessens, R., Verbaeten, P.
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1995
The following Volterra integral equation of the first kind is due to Abel (1823): $$g(x) = \int\limits_a^x {\frac{{f(y)}} {{\sqrt {x - y} }}dy\;for\;x \geqslant a}$$ (6.1.1) . Since the denominator \(\sqrt {x - y} \) has a zero at y=x, the integral in (1) is to be understood in the improper sense (cf.
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The following Volterra integral equation of the first kind is due to Abel (1823): $$g(x) = \int\limits_a^x {\frac{{f(y)}} {{\sqrt {x - y} }}dy\;for\;x \geqslant a}$$ (6.1.1) . Since the denominator \(\sqrt {x - y} \) has a zero at y=x, the integral in (1) is to be understood in the improper sense (cf.
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A nonlinear Abel integral equation
2006For the general nonlinear Abel integral equation $$\frac{1}{{\Gamma (\alpha )}}\int\limits_0^x {(x - t)^{\alpha - 1} K(x,t,u(t))dt = f(x),{\text{ 0}} \leqslant x \leqslant 1,0 < \alpha < 1,}$$ some theorems on existence and uniqueness of solutions in L P , 1≤p≤∞, and in C[0, 1] are established.
Dang Dinh Ang, Rudolf Gorenflo
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