Results 51 to 60 of about 516,382 (294)
Advances in Mathematical Physics, 2020 Two new orthogonal functions named the left- and the right-shifted fractional-order Legendre polynomials (SFLPs) are proposed. Several useful formulas for the SFLPs are directly generalized from the classic Legendre polynomials.
Haidong Qu, Xiaopeng Yang, Zihang She
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ChemPhysChem, Volume 26, Issue 6, March 15, 2025.The solvation structure and dynamics of the SCN− anion in mixed N, N‐Dimethylformamide (DMF)‐water liquid solvents is investigated using classical molecular dynamics simulations. A preferential solvation of SCN− by the water molecules is observed in the first hydration shell, followed by a second shell consisting by both DMF and water molecules.
Ioannis Skarmoutsos, Ilias G. Karvounis
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MathematicsIn this paper, by using the zeroth-order q-Tricomi functions, the theory of three-variable q-Legendre-based Appell polynomials is introduced.
Naeem Ahmad, Waseem Ahmad Khan
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AIMS Mathematics, 2022 A spectral collocation method is proposed to solve variable order fractional stochastic Volterra integro-differential equations. The new technique relies on shifted fractional order Legendre orthogonal functions outputted by Legendre polynomials.
Obaid Algahtani +2 more
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A Legendre Polynomial Integral [PDF]
Mathematics of Computation, 1979 Let { P n ( x ) } \{ {P_n}(x)\} be the usual Legendre polynomials. The following integral is apparently new. \[ ∫ 0 1 P n ( 2 x
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Study on fracture parameter calibration and failure characteristics of rock with hole and crack
Deep Underground Science and Engineering, EarlyView.The SIF and plastic zone equations for a single hole and crack have been derived. The model's failure state leads to the identification of four types of cracks. The plastic zone increases with increased brittleness and decreased crack length. Abstract Cracks within the surrounding rock of roadways significantly affect their stability and failure ...
Shaochi Peng, Wensong Wang
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Novel Results on Legendre Polynomials in the Sense of a Generalized Fractional Derivative
Mathematical and Computational ApplicationsIn this article, new results are investigated in the context of the recently introduced Abu-Shady–Kaabar fractional derivative. First, we solve the generalized Legendre fractional differential equation.
Francisco Martínez +2 more
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International Journal of Mathematics and Mathematical Sciences, 1985 The Legendre numbers, an infinite set of rational numbers are defined from the associated Legendre functions and several elementary properties are presented. A general formula for the Legendre numbers is given. Applications include summing certain series
Paul W. Haggard
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International Journal for Numerical Methods in Fluids, EarlyView.The proposed work implements a direct flux reconstruction method for spatial discretization and a stiffness‐resilient exponential time integration method for temporal discretization on the cube‐sphere grid. A space‐time tensor formalism is employed to provide a general representation in any curvilinear coordinate system. This combination enables highly
Stéphane Gaudreault +6 more
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Abstract and Applied Analysis, 2013 We extend the application of the Galerkin method for treating the multiterm fractional differential equations (FDEs) subject to initial conditions. A new shifted Legendre-Galerkin basis is constructed which satisfies exactly the homogeneous initial ...
A. H. Bhrawy, M. A. Alghamdi
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