Results 21 to 30 of about 4,157,742 (220)
p-Trigonometric and p-Hyperbolic Functions in Complex Domain
Abstract and Applied Analysis, 2016 We study extension of p-trigonometric functions sinp and cosp and of p-hyperbolic functions sinhp and coshp to complex domain. Our aim is to answer the question under what conditions on p these functions satisfy well-known relations for usual ...
Petr Girg, Lukáš Kotrla
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Generalization of the Hardy-Littlewood theorem on Fourier series
Қарағанды университетінің хабаршысы. Математика сериясы, 2021 In the theory of one-dimensional trigonometric series, the Hardy-Littlewood theorem on Fourier series with monotone Fourier coefficients is of great importance.
S. Bitimkhan
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On Weighted Lp Integrability of Functions Defined by Trigonometric Series
Journal of Inequalities and Applications, 2010 We introduce a new class of sequences called GM¯θr and give a sufficient and necessary condition for weighted Lp integrability of trigonometric series with coefficients to belong to the above class.
Bogdan Szal
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Karpatsʹkì Matematičnì Publìkacìï, 2015 In this paper we prove that the condition $\sum_{k=\left[\frac{n}{2}\right] }^{2n}\frac{\lambda _{k}(p)}{(|n-k|+1)^{2-p}}=o(1)\, \left(=O(1) \right),$ is a necessary condition for the $L^{p ...
Xh.Z. Krasniqi
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Some trigonometrical series, X
Tohoku Mathematical Journal, 1953 Suppose \(m_1,\ldots, m_n\) are distinct positive integers. Put \(f(x)=-\cos m_1x - \ldots -\cos m_nx\) for real \(x\). Since \(f\) has mean-value zero, its maximum value is a positive number \(K\). Let \(T\) be the number of solutions of the equation \(m_i+m_j=m_k\) in integers \(i, j, k\) between \(1\) and \(n\) inclusive.
openaire +20 more sources
EULER–ZAGIER SUMS VIA TRIGONOMETRIC SERIES [PDF]
, 2023 In this note, we study the evaluations of Euler sums via trigonometric series. It is a commonly believed conjecture that for an even weight greater than seven, Euler sums cannot be evaluated in terms of the special values of the Riemann zeta function ...
Göral, Haydar, Çelik, Şermin Çam
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Advanced Robotics Research, EarlyView.This study explores how information processing is distributed between brains and bodies through a codesign approach. Using the “backpropagation through soft body” framework, brain–body coupling agents are developed and analyzed across several tasks in which output is generated through the agents’ physical dynamics.
Hiroki Tomioka +3 more
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Trigonometric Equations and Series by Combinatorial Geometric Series
, 2023 This paper presents the trigonometric equations and series with binomial coefficients defined in combinatorial geometric series.
Chinnaraji Annamalai
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Exponentials of general multivector in 3D Clifford algebras
Nonlinear Analysis, 2022 Closed form expressions to calculate the exponential of a general multivector (MV) in Clifford geometric algebras (GAs) Clp;q are presented for n = p + q = 3.
Adolfas Dargys, Artūras Acus
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Efficient and Robust Standing Postures of Quadruped Robots
Advanced Robotics Research, EarlyView.A calibrated static framework estimates load, optimizes torques, and adapts posture so quadruped robots stand efficiently and robustly under external payloads, achieving up to 50% lower torque demand. Inspired by the natural posture adjustments of animals under external loading, this article presents an optimization‐based framework for minimizing joint
Mohamad Kanaan +5 more
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