Results 41 to 50 of about 53,695 (215)
Smooth Wavelet Approximations of Truncated Legendre Polynomials via the Jacobi Theta Function
Abstract and Applied Analysis, 2014 The family of nth order q-Legendre polynomials are introduced. They are shown to be obtainable from the Jacobi theta function and to satisfy recursion relations and multiplicatively advanced differential equations (MADEs) that are analogues of the ...
David W. Pravica +2 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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Advanced Energy Materials, EarlyView.Machine learning interatomic potentials bridge quantum accuracy and computational efficiency for materials discovery. Architectures from Gaussian process regression to equivariant graph neural networks, training strategies including active learning and foundation models, and applications in solid‐state electrolytes, batteries, electrocatalysts ...
In Kee Park +19 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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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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CFD modeling and sensitivity‐guided design of silicon filament CVD reactors
AIChE Journal, EarlyView.Abstract Filament‐based chemical vapor deposition (CVD) for silicon (Si) coatings is often treated as an adaptation of planar deposition. But this overlooks fundamental shifts in transport phenomena and reaction kinetics. In filament CVD, the filament acts as a substrate, heat source, and flow disruptor simultaneously. In this work, we ask: What really
G. P. Gakis +8 more
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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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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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
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Congruences concerning Legendre polynomials II [PDF]
Journal of Number Theory, 2013 Suppose that p is an odd prime and d is a positive integer. Let x and y be integers given by p = x2+dy2 or 4p = x2+dy2. In this paper we determine x( mod p) for many values of d. For example, [Formula: see text] where x is chosen so that x ≡ 1 ( mod 3). We also pose some conjectures on supercongruences modulo p2 concerning binary quadratic forms.
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