Mashallah Matinfar

Bio: Mashallah Matinfar is an academic researcher from University of Mazandaran. The author has contributed to research in topics: Homotopy analysis method & Nonlinear system. The author has an hindex of 10, co-authored 56 publications receiving 372 citations.

Three-step iterative methods with eighth-order convergence for solving nonlinear equations

Abstract: A family of eighth-order iterative methods for solution of nonlinear equations is presented. We propose an optimal three-step method with eight-order convergence for finding the simple roots of nonlinear equations by Hermite interpolation method. Per iteration of this method requires two evaluations of the function and two evaluations of its first derivative, which implies that the efficiency index of the developed methods is 1.682. Some numerical examples illustrate that the algorithms are more efficient and performs better than the other methods.

The functional variable method for solving the fractional Korteweg–de Vries equations and the coupled Korteweg–de Vries equations

Abstract: This paper presents the exact solutions for the fractional Korteweg–de Vries equations and the coupled Korteweg–de Vries equations with time-fractional derivatives using the functional variable method The fractional derivatives are described in the modified Riemann–Liouville derivative sense It is demonstrated that the calculations involved in the functional variable method are extremely simple and straightforward and this method is very effective for handling nonlinear fractional equations

GMRES implementations and residual smoothing techniques for solving ill-posed linear systems

Abstract: There are verities of useful Krylov subspace methods to solve nonsymmetric linear system of equations. GMRES is one of the best Krylov solvers with several different variants to solve large sparse linear systems. Any GMRES implementation has some advantages. As the solution of ill-posed problems are important. In this paper, some GMRES variants are discussed and applied to solve these kinds of problems. Residual smoothing techniques are efficient ways to accelerate the convergence speed of some iterative methods like CG variants. At the end of this paper, some residual smoothing techniques are applied for different GMRES methods to test the influence of these techniques on GMRES implementations.

A nonlinear Schrödinger equation describing the polarization mode and its chirped optical solitons

Abstract: A nonlinear Schrodinger equation describing the polarization mode in an optical fiber which involves different physical terms such as quintic nonlinearity, self-steepening effect, and self-frequency shift is investigated in the present paper. The study goes on by adopting a field function and effective ansatzes to arrive at a highly nonlinear ODE which is formally solved with the help of the modified Kudryashov and $$exp_{a}$$ -function methods. As a result, a series of chirped optical solitons along with nonlinear chirps is retrieved, confirming the fantastic performance of schemes.

A Tutorial Review on Fractal Spacetime and Fractional Calculus

Abstract: This tutorial review of fractal-Cantorian spacetime and fractional calculus begins with Leibniz's notation for derivative without limits which can be generalized to discontin- uous media like fractal derivative and q-derivative of quantum calculus. Fractal spacetime is used to elucidate some basic properties of fractal which is the foundation of fractional calculus, and El Naschie's mass-energy equation for the dark energy. The variational itera- tion method is used to introduce the definition of fractional derivatives. Fractal derivative is explained geometrically and q-derivative is motivated by quantum mechanics. Some effec- tive analytical approaches to fractional differential equations, e.g., the variational iteration method, the homotopy perturbation method, the exp-function method, the fractional com- plex transform, and Yang-Laplace transform, are outlined and the main solution processes are given.

Numerical methods for solving the multi-term time-fractional wave-diffusion equation

Abstract: In this paper, the multi-term time-fractional wave-diffusion equations are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], [1,2), [0,2), [0,3), [2,3) and [2,4), respectively. Some computationally effective numerical methods are proposed for simulating the multi-term time-fractional wave-diffusion equations. The numerical results demonstrate the effectiveness of theoretical analysis. These methods and techniques can also be extended to other kinds of the multi-term fractional time-space models with fractional Laplacian.

Determination of hydroxyl groups in biorefinery resources via quantitative 31P NMR spectroscopy

Abstract: The analysis of chemical structural characteristics of biorefinery product streams (such as lignin and tannin) has advanced substantially over the past decade, with traditional wet-chemical techniques being replaced or supplemented by NMR methodologies. Quantitative 31P NMR spectroscopy is a promising technique for the analysis of hydroxyl groups because of its unique characterization capability and broad potential applicability across the biorefinery research community. This protocol describes procedures for (i) the preparation/solubilization of lignin and tannin, (ii) the phosphitylation of their hydroxyl groups, (iii) NMR acquisition details, and (iv) the ensuing data analyses and means to precisely calculate the content of the different types of hydroxyl groups. Compared with traditional wet-chemical techniques, the technique of quantitative 31P NMR spectroscopy offers unique advantages in measuring hydroxyl groups in a single spectrum with high signal resolution. The method provides complete quantitative information about the hydroxyl groups with small amounts of sample (~30 mg) within a relatively short experimental time (~30–120 min). This protocol describes a quantitative 31P NMR spectroscopy approach for the analysis and determination of hydroxyl groups on biorefinery resources such as lignins and tannins.

Real and Complex Analysis. By W. Rudin. Pp. 412. 84s. 1966. (McGraw-Hill, New York.)

Abstract: Preface Prologue: The Exponential Function Chapter 1: Abstract Integration Set-theoretic notations and terminology The concept of measurability Simple functions Elementary properties of measures Arithmetic in [0, ] Integration of positive functions Integration of complex functions The role played by sets of measure zero Exercises Chapter 2: Positive Borel Measures Vector spaces Topological preliminaries The Riesz representation theorem Regularity properties of Borel measures Lebesgue measure Continuity properties of measurable functions Exercises Chapter 3: Lp-Spaces Convex functions and inequalities The Lp-spaces Approximation by continuous functions Exercises Chapter 4: Elementary Hilbert Space Theory Inner products and linear functionals Orthonormal sets Trigonometric series Exercises Chapter 5: Examples of Banach Space Techniques Banach spaces Consequences of Baire's theorem Fourier series of continuous functions Fourier coefficients of L1-functions The Hahn-Banach theorem An abstract approach to the Poisson integral Exercises Chapter 6: Complex Measures Total variation Absolute continuity Consequences of the Radon-Nikodym theorem Bounded linear functionals on Lp The Riesz representation theorem Exercises Chapter 7: Differentiation Derivatives of measures The fundamental theorem of Calculus Differentiable transformations Exercises Chapter 8: Integration on Product Spaces Measurability on cartesian products Product measures The Fubini theorem Completion of product measures Convolutions Distribution functions Exercises Chapter 9: Fourier Transforms Formal properties The inversion theorem The Plancherel theorem The Banach algebra L1 Exercises Chapter 10: Elementary Properties of Holomorphic Functions Complex differentiation Integration over paths The local Cauchy theorem The power series representation The open mapping theorem The global Cauchy theorem The calculus of residues Exercises Chapter 11: Harmonic Functions The Cauchy-Riemann equations The Poisson integral The mean value property Boundary behavior of Poisson integrals Representation theorems Exercises Chapter 12: The Maximum Modulus Principle Introduction The Schwarz lemma The Phragmen-Lindelof method An interpolation theorem A converse of the maximum modulus theorem Exercises Chapter 13: Approximation by Rational Functions Preparation Runge's theorem The Mittag-Leffler theorem Simply connected regions Exercises Chapter 14: Conformal Mapping Preservation of angles Linear fractional transformations Normal families The Riemann mapping theorem The class L Continuity at the boundary Conformal mapping of an annulus Exercises Chapter 15: Zeros of Holomorphic Functions Infinite Products The Weierstrass factorization theorem An interpolation problem Jensen's formula Blaschke products The Muntz-Szas theorem Exercises Chapter 16: Analytic Continuation Regular points and singular points Continuation along curves The monodromy theorem Construction of a modular function The Picard theorem Exercises Chapter 17: Hp-Spaces Subharmonic functions The spaces Hp and N The theorem of F. and M. Riesz Factorization theorems The shift operator Conjugate functions Exercises Chapter 18: Elementary Theory of Banach Algebras Introduction The invertible elements Ideals and homomorphisms Applications Exercises Chapter 19: Holomorphic Fourier Transforms Introduction Two theorems of Paley and Wiener Quasi-analytic classes The Denjoy-Carleman theorem Exercises Chapter 20: Uniform Approximation by Polynomials Introduction Some lemmas Mergelyan's theorem Exercises Appendix: Hausdorff's Maximality Theorem Notes and Comments Bibliography List of Special Symbols Index