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Theoretical Model for Ostwald Ripening of Nanoparticles with Size-Linear Capture Coefficients. [PDF]

Nanomaterials (Basel)
Dubrovskii VG, Leshchenko ED.
europepmc   +1 more source

Coherent multiple scattering in small-angle scattering experiments: modeling approximations based on the Born expansion. [PDF]

J Appl Crystallogr
Frielinghaus H, Gommes CJ.
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On Fuzzy Integral Equations

Fundamenta Informaticae, 1999
Using the embedding method, the fuzzy integral is represented as a parametric Riemann integral. An algorithm which approximates this integral uniformly, is incorporated to design a soft computing tool for solving a fuzzy Fredholm integral equation of the second kind with arbitrary kernel, using a uniformly convergent iterative procedure.
Friedman, Menahem, Ming, Ma, Kandel, Abraham   +2 more
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Anticipating Integral Equations

Potential Analysis, 2000
The 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 ...
León, Jorge A., Nualart, David
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On integrating the vlasov equation

Journal of Nuclear Energy. Part C, Plasma Physics, Accelerators, Thermonuclear Research, 1962
A 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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On an Abstract Integral Equation

SIAM Journal on Mathematical Analysis, 1979
The existence of solutions of the nonlinear Volterra equation \[u(t) + \int_0^t {k(t - s)} gu(s)ds \ni f(t)\] is studied in a real Hilbert space. The nonlinear operator g is assumed to be the subdifferential of a convex function. The results obtained extend earlier ones by Barbu (SIAM J. Math. Anal., 1975), Londen (SIAM J. Math. Anal., 1977) and Londen
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An Integral Equation Technique

SIAM Journal on Applied Mathematics, 1974
This paper deals with an integral equation technique to reduce the solution of $n(n\geqq 2)$ simultaneous Fredholm integral equations of the first kind to that of $2n$ Volterra integral equations of the first kind and n simultaneous Fredholm integral equations of the second kind.
Vaid, B. K., Jain, D. L.
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Abel’s Integral Equation and Singular Integral Equations

2011
Abel’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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Singular Integral Equations

Journal of Mathematical Physics, 1966
The integral equation P ∫ cK(ζ′,ζ)ζ′−ζφ(ζ′) dζ′=h(ζ)φ(ζ)+f(ζ)is shown to have simple solutions obtained by standard and elementary methods if h and K have appropriate analytic properties.
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A Stochastic Integral Equation

SIAM Journal on Applied Mathematics, 1970
We investigate a stochastic integral equation of the form $x'(s) = y'(s) + \int_0^\alpha {K(s,t)dx(t)} $, where $y( s )$ is a process with orthogonal increments on the interval $T_\alpha = [0,\alpha ]$ and $K(s,t)$ is a continuous Fredholm or Volterra kernel on $T_\alpha \times T_\alpha $.
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