Results 41 to 50 of about 5,765 (234)

Müntz linear transforms of Brownian motion [PDF]

, 2014
We consider a class of Volterra linear transforms of Brownian motion associated to a sequence of Müntz Gaussian spaces and determine explicitly their kernels; the kernels take a simple form when expressed in terms of Müntz-Legendre polynomials. These are
Wu, Ching-Tang, Alili, Larbi
core   +1 more source

Multiplication polynomials and relative Manin-Mumford [PDF]

, 2015
After the introduction we prove in chapter 2 that the resultant of the standard multiplication polynomials $A_n,B_n$ of an elliptic curve in the form $y^2 = x^3+ax+b$ is
$(16\Delta)^{{n^2(n^2-1) \over 6}}$, where $\Delta=-(4a^3+27b^2)$ is the ...
Schmidt, Harry
core   +1 more source

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, Njinasoa Randriampiry, Michael J. Spurr   +2 more
doaj   +1 more source

On the multiplicative Legendre equation

Journal of Taibah University for Science, 2022
When exponentials are employed to model procedures and efficacies appearing in real life, an additive derivative of this type of function does not exist.
Sertac Goktas
doaj   +1 more source

Enhanced High Dimensionality and the Information Processing Capacity in Interfered Spin Wave‐Based Reservoir Computing, Achieved With Eight Detectors

Advanced Electronic Materials, EarlyView.
Physical reservoir computing (PRC) based on spin wave interference has demonstrated high computational performance, yet room for improvement remains. In this study, we fabricated this concept PRC with eight detectors and evaluated the impact of the number of detectors using a chaotic time series prediction task.
Sota Hikasa, Wataru Namiki, Daiki Nishioka, Maki Nishimura, Ryo Iguchi, Kazuya Terabe, Takashi Tsuchiya   +6 more
wiley   +1 more source

Numerical analysis of stochastic SIR model by Legendre spectral collocation method

Advances in Mechanical Engineering, 2019
This article represents Legendre spectral collocation method based on Legendre polynomials to solve a stochastic Susceptible, infected, Recovered (SIR) model.
Sami Ullah Khan, Ishtiaq Ali
doaj   +1 more source

Numerical solutions for fractional optimal control problems using Mü‎‎‎‎‎‎‎ntz-Legendre polynomials [PDF]

Journal of Mahani Mathematical Research
This study introduces a novel method using the Müntz-Legendre polynomials for numerically solving fractional optimal control problems. Utilizing the unique properties of Müntz-Legendre polynomials when dealing with fractional operators, these polynomials
Mohammad Sahabi, Allahbakhsh Yazdani Cherati   +1 more
doaj   +1 more source

Fast and accurate fitting and filtering of noisy exponentials in Legendre space. [PDF]

PLoS ONE, 2014
The parameters of experimentally obtained exponentials are usually found by least-squares fitting methods. Essentially, this is done by minimizing the mean squares sum of the differences between the data, most often a function of time, and a parameter ...
Guobin Bao, Detlev Schild
doaj   +1 more source

Machine Learning Interatomic Potentials for Energy Materials: Architectures, Training Strategies, and Applications

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, Saeed Pourasad, Jinhong Mun, Arunkumar Chitteth Rajan, Tae Hyeon Park, Anand Rohit, Mohammad Zafari, Tan‐Lien Pham, Eunjae Jung, Bonseung Koo, Miran Ha, Gi Beom Sim, Hyun Gyu Park, Won Woong Choi, Kwanghyeon Jo, Soohaeng Yoo Willow, David ChangMo Yang, Chang Woo Myung, Geunsik Lee, Kwang S. Kim   +19 more
wiley   +1 more source

Left- and Right-Shifted Fractional Legendre Functions with an Application for Fractional Differential Equations

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
doaj   +1 more source