Results 21 to 30 of about 369 (174)
The stability analysis of a discretized pantograph equation [PDF]
Mathematica Bohemica, 2011 Summary: The paper deals with a difference equation arising from the scalar pantograph equation via the backward Euler discretization. A case when the solution tends to zero but after reaching a certain index it loses this tendency is discussed. We analyse this problem and estimate the value of such an index.
Jánský, J., Kundrát, Petr
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Runge–Kutta methods for the multi-pantograph delay equation [PDF]
Applied Mathematics and Computation, 2005 The multi-pantograph equation is a delay differential equation of the form \(u'(t) = \lambda u(t) + \mu_1 u(q_1 t) + \mu_2 u(q_2 t) + \cdots + \mu_l u(q_l t)\), with given initial value \(u(0)\).
D. Li, M. Z. Liu
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Advances in Mechanical Engineering, 2023 During the operation of high-speed railway, the transition-point disappearance phenomenon, which is caused by the deformation of pantograph head, poses a safety threat to the pantograph-catenary system.
Junqing Chen +5 more
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Stability analysis of pantograph under frictional force
Nihon Kikai Gakkai ronbunshu, 2019 The frictional force acts to the travelling pantograph head in horizontal direction due to sliding of the pantograph head and contact wire. Therefore, vertical motion of the pantograph head is generated by link mechanism of the pantograph.
Shigeyuki KOBAYASHI +2 more
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Energies, 2020 The pantograph catenary system plays an important role in the power performance of electric mining vehicles. A pantograph catenary system combining both a pantograph and a catenary is one of the most promising solutions.
Yinping Li, Tianxu Jin, Li Liu, Kun Yuan
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The Pantograph Equation in the Complex Plane
Journal of Mathematical Analysis and Applications, 1997 The subject matter is focused on two functional differential equations. First of them is the pantograph equation with involution on the complex plane: \[ y'(z)=\sum_{k=0}^{m-1} \left[ a_k y(\omega^k z) + b_k y(r \omega^k z) + c_k y'(r \omega^k z) \right] , \] where \(a_k, b_k, c_k \in \mathbb{C}, k= 0, 1, \dots , m-1,\) are given, \(r \in (0,1)\), and \
Derfel, G., Iserles, A.
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IEEE Access, 2021 The aim of this study is to design a layer structure of feed-forward artificial neural networks using the Morlet wavelet activation function for solving a class of pantograph differential Lane-Emden models. The Lane-Emden pantograph differential equation
Kashif Nisar +7 more
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On Pantograph Integro-Differential Equations
Journal of Integral Equations and Applications, 1994 The authors study the initial value problem for pantograph integro- differential equations of the form \[ y'(t) = a y(t) + \int^ 1_ 0 y(qt) d \mu (q) + \int^ 1_ 0 y'(qt) d \nu (q),\;t > 0, \quad y(0) = y_ 0, \tag{1} \] where \(a\) is a complex constant, \(\mu (q)\) and \(\nu (q)\) are complex-valued functions of bounded variation on \([0,1]\). Denote \(
Iserles, Arieh, Liu, Yunkang
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Aeroacoustic Optimization Design of the Middle and Upper Part of Pantograph
Applied Sciences, 2022 The pantograph is the main noise source of high-speed trains, of which the middle and upper parts of the pantograph account for about 50% of the whole noise energy.
Jing Guo +5 more
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Solving a Quadratic Riccati Differential Equation, Multi-Pantograph Delay Differential Equations, and Optimal Control Systems with Pantograph Delays [PDF]
Axioms, 2020 An effective algorithm for solving quadratic Riccati differential equation (QRDE), multipantograph delay differential equations (MPDDEs), and optimal control systems (OCSs) with pantograph delays is presented in this paper. This technique is based on Genocchi polynomials (GPs). The properties of Genocchi polynomials are stated, and operational matrices
Fateme Ghomanjani, Stanford Shateyi
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