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Anticipating Integral Equations
Potential Analysis, 2000The authors consider a stochastic Volterra equation of the form \[ X_t= Y_t+ \int^t_0 F_1(t,s,X_s) ds+\int^t_0 G(t,s)H (s,X_s)dW_s, \] where \(W\) is a real Brownian motion which generates the filtration \({\mathcal F}\), \(H(s,x)\) is a progressively measurable process and \(G(t,s)\) is \({\mathcal F}_t\)-measurable and smooth in Malliavin calculus ...
Jorge A. León, David Nualart
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1996
Publisher Summary This chapter illustrates a general theory of field calculation in systems having a straight optic axis. Two basic ideas, the introduction of azimuthally Fourier series expansions and the formulation of integral equations, have been described in detail, since these are particularly well adapted to the needs of electron optical field ...
Peter Hawkes, Erwin Kasper
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Publisher Summary This chapter illustrates a general theory of field calculation in systems having a straight optic axis. Two basic ideas, the introduction of azimuthally Fourier series expansions and the formulation of integral equations, have been described in detail, since these are particularly well adapted to the needs of electron optical field ...
Peter Hawkes, Erwin Kasper
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Mathematical Proceedings of the Cambridge Philosophical Society, 1963
It was pointed out by Copson(1) in 1947 that the solution of the integral equation for the electrostatic problem for a circular disc could be reduced to the solution of Abel integral equations and hence a solution obtained in a fairly elementary manner.
W. E. Williams, L. Rosenhead
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It was pointed out by Copson(1) in 1947 that the solution of the integral equation for the electrostatic problem for a circular disc could be reduced to the solution of Abel integral equations and hence a solution obtained in a fairly elementary manner.
W. E. Williams, L. Rosenhead
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Abel’s Integral Equation and Singular Integral Equations
2011Abel’s integral equation occurs in many branches of scientific fields [1], such as microscopy, seismology, radio astronomy, electron emission, atomic scattering, radar ranging, plasma diagnostics, X-ray radiography, and optical fiber evaluation. Abel’s integral equation is the earliest example of an integral equation [2].
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An overview of real‐world data sources for oncology and considerations for research
Ca-A Cancer Journal for Clinicians, 2022Donna R Rivera +2 more
exaly
On integrating the vlasov equation
Journal of Nuclear Energy. Part C, Plasma Physics, Accelerators, Thermonuclear Research, 1962A first step in analysing the stability of solutions of the Vlasov equation governing hot plasmas of low density is to solve the linearized equation for the perturbed space and velocity distribution function in terms of the perturbed electric and magnetic fields.
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The mechanisms of integral membrane protein biogenesis
Nature Reviews Molecular Cell Biology, 2021Robert J Keenan
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Solving integral equations in free space with inverse-designed ultrathin optical metagratings
Nature Nanotechnology, 2023Andrea Cordaro
exaly