History-dependent fractional hemivariational inequality with time-delay system for a class of new frictionless quasistatic contact problems

2021 ◽  
pp. 108128652110541
Author(s):  
Jianwei Hao ◽  
JinRong Wang ◽  
Jiangfeng Han
Keyword(s):  
Time Delay ◽  
Mild Solutions ◽  
Contact Problems ◽  
Delay System ◽  
Hemivariational Inequalities ◽  
Generalized Gradient ◽  
Time Delay System ◽  
Contact Conditions ◽  
Rothe Method ◽  
Clarke Generalized Gradient

We study a new frictionless quasistatic contact problem for viscoelastic materials, in which contact conditions are described by the fractional Clarke generalized gradient of nonconvex and nonsmooth functions and a time-delay system. In addition, our constitutive relation is modeled using the fractional Kelvin–Voigt law with long memory. The existence of mild solutions for new history-dependent fractional differential hemivariational inequalities with a time-delay system are obtained by the Rothe method, properties of the Clarke generalized gradient, and a fixed-point theorem.

The Use of Response Prompting and Frames for Teaching Sentence Writing to Students With Moderate Intellectual Disability

2016 ◽  
Vol 33 (3) ◽  
pp. 142-149 ◽  
Author(s):  
Robert Pennington ◽  
Allison Flick ◽  
Kendra Smith-Wehr
Keyword(s):  
Intellectual Disability ◽  
Time Delay ◽  
Delay System ◽  
Constant Time Delay ◽  
Intervention Package ◽  
Time Delay System ◽  
Moderate Intellectual Disability ◽  
System Of Least Prompts ◽  
Response Prompting ◽  
Multiple Probe

In the current study, we examined the effects of response prompting strategies (i.e., constant time delay, system of least prompts) and frames on sentence writing for three participants, ages 7 to 12, with moderate intellectual disability. We used a concurrent multiple probe across behaviors design to evaluate the efficacy of the intervention package and posttest probes to assess generalized responding to untrained stimulation. During intervention, the teacher taught two students to construct sentences using selection-based software and another to generate handwritten responses across three different writing frames (i.e., I want _________, I see _____, The _____ is ______). Our findings suggest that the package was effective and produced variable levels of maintenance and generalized responding for all three participants.

Stabilizing Gain Regions of PID Controller for Time Delay Systems

2013 ◽  
Vol 313-314 ◽  
pp. 432-437
Author(s):  
Fu Min Peng ◽  
Bin Fang
Keyword(s):  
Stability Analysis ◽  
Time Delay ◽  
Pid Controller ◽  
Delay System ◽  
Nyquist Plot ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Frequency Range ◽  
Time Delay System ◽  
Key Points

Based on the inverse Nyquist plot, this paper proposes a method to determine stabilizing gain regions of PID controller for time delay systems. According to the frequency characteristic of the inverse Nyquist plot, it is confirmed that the frequency range is used for stability analysis, and the abscissas of two kind key points are obtained in this range. PID gain is divided into several regions by abscissas of key points. Using an inference and two theorems presented in the paper, the stabilizing PID gain regions are determined by the number of intersections of the inverse Nyquist plot and the vertical line in the frequency range. This method is simple and convenient. It can solve the problem of getting the stabilizing gain regions of PID controller for time delay system.

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