Esmail Babolian | Academic Influence

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Esmail Babolian

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Mathematics

Esmail Babolian's Degrees

PhD Mathematics University of Tehran
Masters Mathematics Sharif University of Technology
Bachelors Mathematics University of Tehran

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According to Wikipedia, Esmail Babolian is an Iranian numerical analyst, best known as the pioneer professor of numerical analysis in Iran. He has published over 60 international papers in different areas of numerical analysis. Recently he and Mohebalizadeh have developed a fast numerical method for solving differential equations with high accuracy. Babolian is member of the Institute for Research in Fundamental Sciences.

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Esmail Babolian's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Numerical solution of differential equations by using Chebyshev wavelet operational matrix of integration (2007) (236)
Numerical solution of nonlinear Fredholm integral equations of the second kind using Haar wavelets (2009) (175)
Solution of the system of ordinary differential equations by Adomian decomposition method (2004) (168)
Numerical solution of linear Fredholm fuzzy integral equations of the second kind by Adomian method (2005) (144)
Numerical solution of fractional pantograph differential equations by using generalized fractional-order Bernoulli wavelet (2017) (140)
A new operational matrix based on Bernoulli wavelets for solving fractional delay differential equations (2016) (135)
On the order of convergence of Adomian method (2002) (135)
Solution of nonlinear equations by modified adomian decomposition method (2002) (122)
The decomposition method applied to systems of Fredholm integral equations of the second kind (2004) (118)
Numerical method for solving linear Fredholm fuzzy integral equations of the second kind (2007) (116)
Solution of a system of Volterra integral equations of the first kind by Adomian method (2003) (115)
Numerical solutions of the nonlinear Volterra-Fredholm integral equations by using homotopy perturbation method (2007) (114)
Direct method to solve Volterra integral equation of the first kind using operational matrix with block-pulse functions (2008) (112)
Numerical solution of nonlinear Volterra-Fredholm integro-differential equations via direct method using triangular functions (2009) (110)
Numerical solution of linear integro-differential equation by using sine-cosine wavelets (2006) (96)
An alternate algorithm for computing Adomian polynomials in special cases (2003) (92)
Fractional-order Bernoulli wavelets and their applications (2016) (91)
Numerical computation method in solving integral equations by using Chebyshev wavelet operational matrix of integration (2007) (89)
Numerical solution of Volterra integral and integro-differential equations of convolution type by using operational matrices of piecewise constant orthogonal functions (2008) (87)
NUMERICAL SOLUTION OF NONLINEAR TWO-DIMENSIONAL INTEGRAL EQUATIONS USING RATIONALIZED HAAR FUNCTIONS (2011) (87)
New method for calculating Adomian polynomials (2004) (82)
Application of He's homotopy perturbation method to nonlinear integro-differential equations (2007) (79)
An efficient approximate method for solving delay fractional optimal control problems (2016) (72)
A numerical method for solving systems of linear and nonlinear integral equations of the second kind by hat basis functions (2011) (71)
Solution of a system of nonlinear equations by Adomian decomposition method (2004) (69)
An Augmented Galerkin Method for First Kind Fredholm Equations (1979) (68)
Two-dimensional triangular functions and their applications to nonlinear 2D Volterra-Fredholm integral equations (2010) (67)
Müntz-Legendre wavelet operational matrix of fractional-order integration and its applications for solving the fractional pantograph differential equations (2018) (66)
Some notes on using the homotopy perturbation method for solving time-dependent differential equations (2009) (66)
Analytic approximate solutions to Burgers, Fisher, Huxley equations and two combined forms of these equations (2009) (62)
Some error estimates for solving Volterra integral equations by using the reproducing kernel method (2015) (58)
NEW DIRECT METHOD TO SOLVE NONLINEAR VOLTERRA-FREDHOLM INTEGRAL AND INTEGRO-DIFFERENTIAL EQUATIONS USING OPERATIONAL MATRIX WITH BLOCK-PULSE FUNCTIONS (2008) (56)
A Chebyshev approximation for solving nonlinear integral equations of Hammerstein type (2007) (55)
Fractional-order Bernoulli functions and their applications in solving fractional FredholemVolterra integro-differential equations (2017) (55)
Numerical solution of the generalized Zakharov equation by homotopy analysis method (2009) (53)
Solution of the kinetic modeling of lactic acid fermentation using Adomian decomposition method (2003) (53)
Numerical solution of stochastic fractional integro-differential equation by the spectral collocation method (2017) (49)
Using triangular orthogonal functions for solving Fredholm integral equations of the second kind (2008) (49)
Numerically solution of fuzzy differential equations by Adomian method (2004) (48)
Restarted Adomian method for system of nonlinear Volterra integral equations (2005) (46)
On the decomposition method for system of linear equations and system of linear Volterra integral equations (2004) (45)
A modified spectral method for numerical solution of ordinary differential equations with non-analytic solution (2002) (43)
Wavelet analysis method for solving linear and nonlinear singular boundary value problems (2013) (43)
Comparison between the homotopy perturbation method and the sine-cosine wavelet method for solving linear integro-differential equations (2007) (43)
Using direct method for solving variational problems via triangular orthogonal functions (2007) (42)
Restarted Adomian method for algebraic equations (2003) (41)
A numerical method for solving Fredholm-Volterra integral equations in two-dimensional spaces using block pulse functions and an operational matrix (2011) (41)
Interpolation of fuzzy data by natural splines (1998) (40)
Solving the problem of biological species living together by Adomian decomposition method (2002) (40)
Solving generalized pantograph equations by shifted orthonormal Bernstein polynomials (2016) (40)
Numerical solution of nonlinear two-dimensional Fredholm integral equations of the second kind using Gauss product quadrature rules (2012) (39)
AN ALTERNATE ALGORITHM FOR COMPUTING ADOMIAN DECOMPOSITION METHOD IN SPECIAL CASES (2003) (36)
A Direct Method for Numerically Solving Integral Equations System Using Orthogonal Triangular Functions (2009) (36)
On numerical improvement of Gauss-Legendre quadrature rules (2005) (36)
Reducing index, and pseudospectral methods for differential-algebraic equations (2003) (33)
A numerical method for solving a class of functional and two dimensional integral equations (2008) (32)
A collocation method for fractional diffusion equation in a long time with Chebyshev functions (2018) (32)
A new computational method for Laplace transforms by decomposition method (2004) (31)
Numerical solutions of the nonlinear integro-differential equations: Wavelet-Galerkin method and homotopy perturbation method (2007) (31)
Numerical implementation of Adomian decomposition method (2004) (30)
On numerical improvement of Gauss-Lobatto quadrature rules (2005) (30)
Restarted Adomian method for integral equations (2004) (30)
Numerical implementation of Adomian decomposition method for linear Volterra integral equations of the second kind (2005) (29)
An expansion-iterative method for numerically solving Volterra integral equation of the first kind (2010) (27)
RKM for solving Bratu‐type differential equations of fractional order (2016) (27)
Solving Abel integral equations of first kind via fractional calculus (2014) (27)
Wavelet moment method for solving Fredholm integral equations of the first kind (2007) (25)
An efficient method for nonlinear fractional differential equations: combination of the Adomian decomposition method and spectral method (2014) (25)
Error analysis of reproducing kernel Hilbert space method for solving functional integral equations (2016) (24)
Numerical solutions of multi-order fractional differential equations by Boubaker polynomials (2016) (24)
Numerical solution of fuzzy max-min systems (2006) (23)
Numerical Solution of Fredholm Integro-Differential Equation by Adomian’s Decomposition Method (2009) (22)
Fractional-order Legendre wavelets and their applications for solving fractional-order differential equations with initial/boundary conditions (2017) (21)
System of linear ordinary differential and differential-algebraic equations and pseudo-spectral method (2010) (21)
APPLYING SHANNON WAVELET BASIS FUNCTIONS TO THE METHOD OF MOMENTS FOR EVALUATING THE RADAR CROSS SECTION OF THE CONDUCTING AND RESISTIVE SURFACES (2008) (21)
Radial basis functions method for solving the fractional diffusion equations (2019) (20)
Exact solutions for non-linear Duffing’s equations by He’s homotopy perturbation method (2012) (20)
Numerical Approach to Survey the Problem of Electromagnetic Scattering from Resistive Strips Based on Using a Set of Orthogonal Basis Functions (2008) (20)
CALCULATING THE RADAR CROSS SECTION OF THE RESISTIVE TARGETS USING THE HAAR WAVELETS (2008) (19)
A local reproducing kernel method accompanied by some different edge improvement techniques: application to the Burgers’ equation (2018) (19)
B-Spline collocation method for linear and nonlinear Fredholm and Volterra integro-differential equations (2013) (18)
A modification of pseudo-spectral method for solving a linear ODEs with singularity (2007) (18)
Numerical solution of linear Fredholm integral equations using sine–cosine wavelets (2007) (18)
Stable evaluations of fractional derivative of the Müntz-Legendre polynomials and application to fractional differential equations (2019) (16)
Solving differential equations by decomposition method (2005) (16)
Chebyshev reproducing kernel method: application to two-point boundary value problems (2017) (16)
Analytic Solution of the Sharma-Tasso-Olver Equation by Homotopy Analysis Method (2010) (14)
He's homotopy perturbation method: An effective tool for solving a nonlinear system of two-dimensional Volterra-Fredholm integral equations (2012) (14)
A Sinc-Galerkin technique for the numerical solution of a class of singular boundary value problems (2015) (14)
Müntz-Legendre wavelet operational matrix of fractional-order integration and its applications for solving the fractional pantograph differential equations (2017) (14)
The approximate solution of a class of Fredholm integral equations with a weakly singular kernel (2011) (13)
A Sinc-Galerkin Approximate Solution of the Reaction-Diffusion Process in an Immobilized Biocatalyst Pellet (2014) (12)
A splitting iterative method for solving second kind integral equations in reproducing kernel spaces (2017) (12)
Spline Collocation for Fredholm Integral Equations (2011) (12)
A numerical scheme for space-time fractional advection-dispersion equation (2015) (11)
Numerical method for solving arbitrary linear differential equations using a set of orthogonal basis functions and operational matrix (2016) (11)
Spline Collocation for Nonlinear Fredholm Integral Equations (2011) (11)
Spectral iterative method and convergence analysis for solving nonlinear fractional differential equation (2018) (11)
A Fast Galerkin Scheme for Linear Integro-differential Equations (1981) (11)
Numerical Solutions of Two-dimensional Linear and Nonlinear Volterra Integral Equations: Homotopy Perturbation Method and Differential Transform Method (2011) (10)
Computing the Fourier Transform via Homotopy Perturbation Method (2009) (10)
LSMR iterative method for solving one- and two-dimensional linear Fredholm integral equations (2019) (10)
New implementation of reproducing kernel Hilbert space method for solving a class of functional integral equations (2014) (10)
Application of Homotopy Perturbation Method to Some Nonlinear Problems (2009) (9)
Analytic solutions to diffusion equations (2010) (9)
A SCHEME FOR RCS DETERMINATION USING WAVELET BASIS (2010) (9)
Solving concrete examples by Adomian method (2003) (9)
A localized Newton basis functions meshless method for the numerical solution of the 2D nonlinear coupled Burgers’ equations (2017) (9)
Application of fractional-order Bernoulli functions for solving fractional Riccati differential equation (2017) (9)
An Improvement to the Homotopy Perturbation Method for Solving Nonlinear Duffing’s Equations (2015) (9)
Bernstein modal basis: Application to the spectral Petrov‐Galerkin method for fractional partial differential equations (2016) (8)
A spectral iterative method for solving nonlinear singular Volterra integral equations of Abel type (2017) (8)
Numerical implementation of the Adomian decomposition method for nonlinear Volterra integral equations of the second kind (2007) (7)
Banded operational matrices for Bernstein polynomials and application to the fractional advection-dispersion equation (2015) (7)
Numerical implementation of an expansion method for linear Volterra integral equations of the second kind with weakly singular kernels (2011) (7)
An interpolation degenerate kernel method for eigenvalue problems of a class of non-compact operators (2010) (7)
A fractional Gauss–Jacobi quadrature rule for approximating fractional integrals and derivatives (2017) (7)
Numerical solution of fuzzy differential inclusion by Euler method (2009) (6)
An improvement to the homotopy perturbation method for solving integro-differential equations (2012) (6)
Restarted Adomian method for nonlinear differential equations (2005) (6)
Convergence analysis of the Chebyshev-Legendre spectral method for a class of Fredholm fractional integro-differential equations (2018) (6)
An approximate method for solution of nonlocal boundary value problems via Gaussian radial basis functions (2019) (6)
THEORY OF BLOCK-PULSE FUNCTIONS IN NUMERICAL SOLUTION OF FREDHOLM INTEGRAL EQUATIONS OF THE SECOND KIND (2016) (5)
Improving homotopy perturbation method with optimal Lagrange interpolation polynomials (2012) (5)
ON A HOMOTOPY BASED METHOD FOR SOLVING SYSTEMS OF LINEAR EQUATIONS (2015) (5)
A fast numerical method for fractional partial differential equations (2019) (5)
Solving a Class of PDEs by a Local Reproducing KernelMethod with An Adaptive Residual SubsamplingTechnique (2015) (5)
Solving a class of singular two-point boundary value problems using new effective reproducing kernel technique (2018) (5)
A solution for Volterra Integral Equations of the First Kind Based on Bernstein Polynomials (2018) (5)
NUMERICAL SOLUTION OF VOLTERRA INTEGRO-DIFFERENTIAL EQUATION BY DIRECT METHOD VIA BLOCK-PULSE FUNCTIONS (2010) (5)
Numerical method for solving system of Fredhlom integral equations using Chebyshev cardinal functions (2014) (5)
Numerical solutions of Duffing’s oscillator problem (2012) (4)
Hybrid Fourier and block-pulse functions for applications in the calculus of variations (2006) (4)
NUMERICAL SOLVING OF GENERAL FUZZY LINEAR SYSTEMS (2009) (4)
The explicit formulas for reproducing kernel of some Hilbert spaces (2015) (4)
Error estimates of generalized spectral iterative methods with accurate convergence rates for solving systems of fractional two - point boundary value problems (2020) (4)
Automatic Augmented Galerkin Algorithms for Linear First Kind Integral Equations: Non-Singular and Weak Singular Kernels (1995) (4)
An iterative shifted Chebyshev method for nonlinear stochastic Itô-Volterra integral equations (2020) (4)
AUTOMATIC AUGMENTED GALERKIN ALGORITHMS FOR FREDHOLM INTEGRAL EQUATIONS OF THE FIRST KIND (1997) (4)
A Numerical Scheme for Solving Nonlinear Fractional Volterra Integro-Differential Equations (2018) (4)
An Euler scheme for stochastic delay differential equations on unbounded domains : pathwise convergence (2014) (4)
Numerical computation of the Riemann zeta function and prime counting function by using Gauss–Hermite and Gauss–Laguerre quadratures (2010) (4)
Application of the Homotopy Analysis Method for Solving Equal-Width Wave and Modified Equal-Width Wave Equations (2009) (4)
Numerical solution of fractional differential, integral and integro‐differential equations by using piecewise constant orthogonal functions (2007) (4)
A new algorithm for solving Van der Pol equation based on piecewise spectral Adomian decomposition method (2016) (4)
Restarted Adomian ’ s Decomposition Method for Duffing ’ s Equation (2009) (4)
On numerical integration methods with T-distribution weight function (2006) (4)
Numerical Study of Unsteady Flow of Gas Through a Porous Medium By Means of Chebyshev Pseudo-Spectral Method (2018) (3)
An extended block Golub-Kahan algorithm for large algebraic and differential matrix Riccati equations (2020) (3)
A Comparison Between Adomians Decomposition Method and the Homotopy Perturbation Method for Solving Nonlinear Differential Equations (2012) (3)
A New Approach for Solving Volterra Integral Equations Using The Reproducing Kernel Method (2017) (3)
Numerical Solution of Fractional Partial Differential Equations with Normalized Bernstein Wavelet Method (2019) (3)
Fractional pseudospectral integration/differentiation matrix and fractional differential equations (2019) (3)
A COMPUTATIONAL METHOD FOR SOLVING OPTIMAL CONTROL PROBLEM OF TIME-VARYING SINGULAR SYSTEMS USING THE HAAR WAVELETS (2012) (3)
A computational approach for solving fractional integral equations based on Legendre collocation method (2019) (3)
MODIFIED VARIATIONAL ITERATION METHODFOR SOLVING DUFFING EQUATIONS (2014) (2)
A DIRECT METHOD TO SOLVE LINEAR TWO-DIMENSIONAL INTEGRAL EQUATIONS USING A FAMILY OF OPERATIONAL MATRICES WITH BLOCK-PULSE FUNCTIONS (2011) (2)
WITHDRAWN: An analytical solution of nonlinear infiltration equation using modified Adomian Decomposition Method (2008) (2)
Augmented Subspaces in the LSQR Krylov Method (2020) (2)
An adaptive weak continuous Euler-Maruyama method for stochastic delay differential equations (2015) (2)
An efficient approximate method for solution of the heat equation using Laguerre-Gaussians radial functions (2016) (2)
THE SPECTRAL ITERATIVE METHOD FOR SOLVING FRACTIONAL-ORDER LOGISTIC EQUATION (2016) (2)
A comparison between the Homotopy Perturbation Method and Adomian's Decomposition Method for Solving Nonlinear (2011) (2)
An Augmented Galerkin Method for Singular Integral Equations with Hilbert Kernel (1997) (2)
A set of multi-dimensional orthogonal basis functions and its application to solve integral equations (2010) (2)
Reproducing kernel method to solve non-local fractional boundary value problem (2021) (2)
Chain least squares method and ill-posed problems (2014) (2)
An adaptive wavelet collocation method for the optimal heat source problem (2021) (2)
An automatic augmented galerkin method for singular integral equations with Hilbert kernel (2001) (2)
RESTARTED ADOMIANS DECOMPOSITION METHOD FOR DUNGS EQUATION (2009) (1)
A computational method for solving weakly singular Fredholm integral equation in reproducing kernel spaces (2018) (1)
New fractional pseudospectral methods with accurate convergence rates for fractional differential equations (2021) (1)
Modified chain least squares method and some numerical results (2015) (1)
A degenerate kernel method for eigenvalue problems of non-compact operators with applications in electromagnetism and continuum-of-alleles models (2008) (1)
An efficient approximate solution of Riesz fractional advection-diffusion equation (2021) (1)
About solving stochastic Itô-Volterra integral equations using the spectral collocation method (2021) (1)
Application of Gauss quadrature rule in finding bounds for solution of linear systems of equations (2006) (1)
A Petrov–Galerkin spectral method for the numerical simulation and analysis of fractional anomalous diffusion (2020) (1)
Parallel solution of Fredholm integral equations (1989) (1)
A New Fast Numerical Method for One-Dimensional Nonlinear Sine-Gordon Equation Using Multivariate Pad\'e approximation (2014) (1)
An efficient collocation method with convergence rates based on Müntz spaces for solving nonlinear fractional two-point boundary value problems (2020) (1)
Pseudospectral operational matrix for numerical solution of single and multiterm time fractional diffusion equation (2016) (1)
Stability and Convergence of Spectral Approach for Fractional Integral-Differential Equation based on Legendre Basis (2016) (1)
On integral equations with Weakly Singular kernel by using Taylor series and Legendre polynomials (2015) (1)
A Study on Functional Fractional Integro-Differential Equations of Hammerstein type (2020) (1)
Application of the Homotopy–Pad$$\acute{\mathrm{e}}$$e´ technique in the prediction of optimal convergence-control parameter (2015) (1)
The convergence of operational Tau method for solving a class of nonlinear Fredholm fractional integro-differential equations on Legendre basis (2017) (0)
Numerical Solution of Functional Volterra–Hammerstein Integro-differential Equations of Order Two (2019) (0)
An Effective Numerical Technique for Solving Second Order Linear Two-Point Boundary Value Problems with Deviating Argument (2019) (0)
Application of the Homotopy–Pad ´ e technique in the prediction of optimal convergence-control parameter (2015) (0)
The Application of Homotopy Perturbation Method to Solve the Higher Order KdV Equations (2012) (0)
An efficient method for nonlinear fractional differential equations: combination of the Adomian decomposition method and spectral method (2014) (0)
An Improvement to the Homotopy Perturbation Method for Solving Nonlinear Duffing’s Equations (2015) (0)
A Computational Meshless Method for Solving Multivariable Integral Equations (2007) (0)
$(n D+1)$ Pad\'e approximation (2014) (0)
Pseudo-Hessian and Taylor's expansion for vector-valued functions (2010) (0)
A local reproducing kernel method accompanied by some different edge improvement techniques: application to the Burgers’ equation (2016) (0)
An adaptive weak continuous Euler-Maruyama method for stochastic delay differential equations (2014) (0)
Direct method for solving convection-diffusion by block pulse functions with error analysis (2012) (0)
TCHEBYCHEV MULTI-WAVELET BASIS FOR SOLVING BOUNDARY INTEGRAL EQUATION (2009) (0)
Some notes on convergence of homotopy based methods for functional equations (2013) (0)
Constructing General Chebyshev Multiwavelets by Orthonormality and Vanishing Moments Conditions (2008) (0)
Local Annihilation Method and Some Stiff Problems (2020) (0)
Bernstein modal basis: application to spectral Petrov-Galerkin method for higher-order differential equations (2016) (0)
An Augmented Galerkin Algorithms for First Kind Integral Equations of Hammerstein type (1996) (0)
SOLVING DIFFERENTIAL EQUATIONS USING MODIFIED VIM (2014) (0)
A degenerate kernel method for eigenvalue problems of a class of non-compact operators (2008) (0)
A Comparative Study of Numerical Methods for Solving the Riccati Equation (2012) (0)
The Chebychev best approximation for unsolvable systems of Max-Min fuzzy equations (2006) (0)
Aninterpolationdegeneratekernelmethodforeigenvalueproblemsofa classofnon-compactoperators (2010) (0)
Direct methods for solving time-varying delay systems (2020) (0)
Erratum to: An adaptive weak continuous Euler-Maruyama method for stochastic delay differential equations (2015) (0)
A Sinc-Galerkin technique for the numerical solution of a class of singular boundary value problems (2013) (0)
Direct methods for solving time-varying delay systems (2020) (0)
An efficient method for solving strongly nonlinear oscillators: combination of the multi-step homotopy analysis and spectral method (2015) (0)
Bernstein Multi-Scaling Operational Matrix Method for Nonlinear Matrix Differential Models of Second-Order (2019) (0)
On Some Nonlinear Generalizations of Growall ’ s Inequality and their Applications (2011) (0)
A Nyström Method for the Eigenvalue Problem of a Class of Noncompact Operators (2010) (0)
THE ANALYTICAL SOLUTION OF THE FLOW OF GAS THROUGH A MICRO-NANO POROUS MEDIUM (2014) (0)
The Legendre Spectral-Collocation method for a class of fractional integral equations (2018) (0)
Chebyshev reproducing kernel method: application to two-point boundary value problems (2017) (0)
Analytical Treatment of Volterra Integro-Diﬀerential Equations of Fractional Derivatives (2016) (0)
A numerical method for one-dimensional nonlinear Sine-Gordon equation using (nD + 1) Padé approximation (2014) (0)
Solving Dierential Equations Using Modied VIM (2014) (0)
Exact solutions for non-linear Duffing’s equations by He’s homotopy perturbation method (2012) (0)
A General Approach for Applying Homotopy Perturbation Method for Differential and Systems of Differential Equations (2011) (0)
Numerical solution of sigularly perturbed parabolic problems by a local kernel-based method with an adaptive algorithm (2019) (0)
Normalized Bernstein polynomials in solving space-time fractional diffusion equation (2017) (0)
Pseudo-spectral matrix and normalized Grunwald approximation for numerical solution of time fractional Fokker-Planck equation (2019) (0)
Chebyshev-Legendre Spectral Approach in Fractional Integro-Differential Equations (2016) (0)
Dynamical analysis, stability and discretization of fractional-order predator-prey model with negative feedback on two species (2021) (0)
Operational Matrix for two Dimensional Haar and WAlsh Functions and Applications to solve Volterra-fredholm Integral Equations using Direct Method (2012) (0)
Erratum to: An adaptive weak continuous Euler-Maruyama method for stochastic delay differential equations (2015) (0)

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