Results 41 to 50 of about 53,539 (221)
Polynomially Interpolated Legendre Multiplier Sequences [PDF]
Computational Methods and Function Theory, 2017 We prove that every multiplier sequence for the Legendre basis which can be interpolated by a polynomial has the form $\{h(k^2+k)\}_{k=0}^{\infty}$, where $h\in\mathbb{R}[x]$. We also prove that a non-trivial collection of polynomials of a certain form interpolate multiplier sequences for the Legendre basis, and we state conjectures on how to extend ...
Chasse, Matthew +2 more
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Advanced Intelligent Systems, Volume 7, Issue 3, March 2025.This review aims to provide a broad understanding for interdisciplinary researchers in engineering and clinical applications. It addresses the development and control of magnetic actuation systems (MASs) in clinical surgeries and their revolutionary effects in multiple clinical applications.
Yingxin Huo +3 more
wiley +1 more source
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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Engineering Science and Technology, an International Journal, 2023 This work develops a new Legendre delay operational matrix based on Legendre polynomial features that are integrated with regard to the Legendre fractional derivative operational matrix in order to solve the issues.
Mays Basim +3 more
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Rocky Mountain Journal of Mathematics, 2010 We introduce a new class of polynomials $\{P_{n}\}$, that we call polar Legendre polynomials, they appear as solutions of an inverse Gauss problem of equilibrium position of a field of forces with $n+1$ unit masses. We study algebraic, differential and asymptotic properties of this class of polynomials, that are simultaneously orthogonal with respect ...
Cabrera, H. Pijeira +2 more
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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
wiley +1 more source
Delannoy numbers and Legendre polytopes [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 We construct an $n$-dimensional polytope whose boundary complex is compressed and whose face numbers for any pulling triangulation are the coefficients of the powers of $(x-1)/2$ in the $n$-th Legendre polynomial.
Gábor Hetyei
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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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Adaptive Back-stepping Stability Control Strategy for MMC Based on Legendre Polynomial
Zhongguo dianli, 2022 In view of the poor stability control performance and frequent operation faults of the flexible HVDC transmission system due to the parameter changes of system dynamic model structure caused by serious signal interference or device temperature rise ...
Lei XU +5 more
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