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The Heaviside Step Function and MATLAB [PDF]
, 2008 Mathematical software enables to solve in a very simple way differential equations arisen from casual systems. In this note we point out that the solutions provided by MATLAB may occasionally neglect Heaviside step functions in the output when instant impulses or piecewise continuous functions appear in the input.
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Recursive Heaviside step functions and beginning of the universe
New Astronomy, 2017Abstract This article introduces recursive Heaviside step functions, as a potential of the known universe, for the first time in the history of mathematics, science, and engineering. In modern cosmology, various bouncing models have been suggested based on the postulation that the current universe is the result of the collapse of a previous universe.
Changsoo Shin, Seongjai Kim
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International Journal of Computational Methods, 2021
In the framework of the extended finite element method, a two-dimensional four-node quadrilateral element enriched with only the Heaviside step function is formulated for stationary and propagating crack analyses. In the proposed method, two types of signed distance functions are used to implicitly express crack geometry, and finite elements, which ...
Toshio Nagashima, Chenyu Wang
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In the framework of the extended finite element method, a two-dimensional four-node quadrilateral element enriched with only the Heaviside step function is formulated for stationary and propagating crack analyses. In the proposed method, two types of signed distance functions are used to implicitly express crack geometry, and finite elements, which ...
Toshio Nagashima, Chenyu Wang
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Excitation of medium by Heaviside step function of electric field
2016 10th European Conference on Antennas and Propagation (EuCAP), 2016An analytical solution in a closed form to the problem of excitation of a medium by Heaviside step function of electric field has been obtained. It allows for studying fields excited by impulse (non-smooth) sources. Numerical results of fields' calculation in a medium are presented.
Denys S. Shumakov, V. I. Naydenko
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On the Hausdorff distance between the Heaviside step function and Verhulst logistic function
Journal of Mathematical Chemistry, 2015In this note we prove more precise estimates for the approximation of the step function by sigmoidal logistic functions. Numerical examples, illustrating our results are given, too.
Svetoslav Markov, Nikolay Kyurkchiev
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Derivative of Heaviside step function vs. delta function in continuum surface force (CSF) models
International Journal of Multiphase Flow, 2018Abstract In Continuum Surface Force (CSF) model for implementing surface tension forces in multiphase flows, singular delta function is used to merge two continuous sets of flow equations. Discretizing the delta function has attracted a great deal of attention and has led to developing many different approaches. It has been shown numerically that two
Seyed Hadi Zandavi, Hanif Montazeri
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2011 Frontiers in Education Conference (FIE), 2011
The need for finding the deflections of shafts, many of which are stepped or varying cross-sectional areas is timeless. Each generation of engineers has used that part of mechanics of materials theory that fit the calculating capability available to them. The method presented here is offered in that vein.
C. J. Egelhoff, Edwin Odom
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The need for finding the deflections of shafts, many of which are stepped or varying cross-sectional areas is timeless. Each generation of engineers has used that part of mechanics of materials theory that fit the calculating capability available to them. The method presented here is offered in that vein.
C. J. Egelhoff, Edwin Odom
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Chemical Physics Letters, 1995
Abstract A new approach to density functional theory is presented. The ground state electronic density and energy of a many-electron system are obtained directly using a polynomial representation of the Heaviside step operator acting on a trial wavefunction.
Youhong Huang +2 more
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Abstract A new approach to density functional theory is presented. The ground state electronic density and energy of a many-electron system are obtained directly using a polynomial representation of the Heaviside step operator acting on a trial wavefunction.
Youhong Huang +2 more
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IEEE Transactions on Neural Networks, 2010
This paper presents a k-winners-take-all (kWTA) neural network with a single state variable and a hard-limiting activation function. First, following several kWTA problem formulations, related existing kWTA networks are reviewed. Then, the kWTA model model with a single state variable and a Heaviside step activation function is described and its global
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This paper presents a k-winners-take-all (kWTA) neural network with a single state variable and a hard-limiting activation function. First, following several kWTA problem formulations, related existing kWTA networks are reviewed. Then, the kWTA model model with a single state variable and a Heaviside step activation function is described and its global
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2011
This paper presents a one-layer recurrent neural network for solving linear programming problems. The proposed neural network is guaranteed to be globally convergent in finite time to the optimal solutions under a mild condition on a derived lower bound of a single gain parameter. The number of neurons in the neural network is the same as the number of
Jun Wang, Qingshan Liu
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This paper presents a one-layer recurrent neural network for solving linear programming problems. The proposed neural network is guaranteed to be globally convergent in finite time to the optimal solutions under a mild condition on a derived lower bound of a single gain parameter. The number of neurons in the neural network is the same as the number of
Jun Wang, Qingshan Liu
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