scholarly journals Analog Realization of a Fractional Recursive Variable-Type and Order Operator for a Particular Switching Strategy

Electronics ◽  
2020 ◽  
Vol 9 (5) ◽  
pp. 855
Author(s):  
Dominik Sierociuk ◽  
Michal Macias ◽  
Wiktor Malesza ◽  
Michał Sławomir Wiraszka
Keyword(s):  
Experimental Validation ◽  
Hardware Implementation ◽  
Difference Operator ◽  
Variable Order ◽  
Practical Realization ◽  
Analog Model ◽  
Order Difference ◽  
Variable Type ◽  
Proposed Model ◽  
Type Variable

In this paper, we propose a method of practical realization and an actual, physical hardware implementation of a fractional variable-type and order difference operator that switches between two (i.e., B - and D -type) variable-order definitions. After the theoretical model of such a switch, we report the experimental validation on an analog model to prove its adequacy. The tests prove with great certainty that the proposed model and the realization behave correctly. They also let the authors assume that the proposed method is the only one suitable for this case, based on the counterexamples presented.

scholarly journals Spectrum of discrete 2n-th order difference operator with periodic boundary conditions and its applications

2021 ◽  
Vol 41 (4) ◽  
pp. 489-507
Author(s):  
Abdelrachid El Amrouss ◽  
Omar Hammouti
Keyword(s):  
Boundary Conditions ◽  
Variational Methods ◽  
Critical Point Theory ◽  
Periodic Boundary ◽  
Eigenvalue Problems ◽  
Difference Operator ◽  
Periodic Boundary Conditions ◽  
Point Theory ◽  
Existence Of A Solution ◽  
Order Difference

Let \(n\in\mathbb{N}^{*}\), and \(N\geq n\) be an integer. We study the spectrum of discrete linear \(2n\)-th order eigenvalue problems \[\begin{cases}\sum_{k=0}^{n}(-1)^{k}\Delta^{2k}u(t-k) = \lambda u(t) ,\quad & t\in[1, N]_{\mathbb{Z}}, \\ \Delta^{i}u(-(n-1))=\Delta^{i}u(N-(n-1)),\quad & i\in[0, 2n-1]_{\mathbb{Z}},\end{cases}\] where \(\lambda\) is a parameter. As an application of this spectrum result, we show the existence of a solution of discrete nonlinear \(2n\)-th order problems by applying the variational methods and critical point theory.

scholarly journals Design of a Wearable Eye-Movement Detection System Based on Electrooculography Signals and Its Experimental Validation

Biosensors ◽  
2021 ◽  
Vol 11 (9) ◽  
pp. 343
Author(s):  
Chin-Teng Lin ◽  
Wei-Ling Jiang ◽  
Sheng-Fu Chen ◽  
Kuan-Chih Huang ◽  
Lun-De Liao
Keyword(s):  
Eye Movement ◽  
Experimental Validation ◽  
Hardware Implementation ◽  
Detection System ◽  
Real Life ◽  
People With Disabilities ◽  
Research Area ◽  
General Purpose ◽  
Classification Algorithm ◽  
Human Computer Interface

In the assistive research area, human–computer interface (HCI) technology is used to help people with disabilities by conveying their intentions and thoughts to the outside world. Many HCI systems based on eye movement have been proposed to assist people with disabilities. However, due to the complexity of the necessary algorithms and the difficulty of hardware implementation, there are few general-purpose designs that consider practicality and stability in real life. Therefore, to solve these limitations and problems, an HCI system based on electrooculography (EOG) is proposed in this study. The proposed classification algorithm provides eye-state detection, including the fixation, saccade, and blinking states. Moreover, this algorithm can distinguish among ten kinds of saccade movements (i.e., up, down, left, right, farther left, farther right, up-left, down-left, up-right, and down-right). In addition, we developed an HCI system based on an eye-movement classification algorithm. This system provides an eye-dialing interface that can be used to improve the lives of people with disabilities. The results illustrate the good performance of the proposed classification algorithm. Moreover, the EOG-based system, which can detect ten different eye-movement features, can be utilized in real-life applications.

scholarly journals Oscillation Results for a Class of Nonlinear Fractional Order Difference Equations with Damping Term

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
A. George Maria Selvam ◽  
Jehad Alzabut ◽  
Mary Jacintha ◽  
Abdullah Özbekler
Keyword(s):  
Fractional Order ◽  
Difference Equations ◽  
Difference Operator ◽  
Fractional Operators ◽  
Damping Term ◽  
Fractional Difference ◽  
Riccati Technique ◽  
Order Difference ◽  
Numerical Examples ◽  
Positive Integers

The paper studies the oscillation of a class of nonlinear fractional order difference equations with damping term of the form Δψλzηλ+pλzηλ+qλF∑s=λ0λ−1+μ λ−s−1−μys=0, where zλ=aλ+bλΔμyλ, Δμ stands for the fractional difference operator in Riemann-Liouville settings and of order μ, 0<μ≤1, and η≥1 is a quotient of odd positive integers and λ∈ℕλ0+1−μ. New oscillation results are established by the help of certain inequalities, features of fractional operators, and the generalized Riccati technique. We verify the theoretical outcomes by presenting two numerical examples.

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