On the Weak Solutions of a Delay Composite Functional Integral Equation of Volterra-Stieltjes Type in Reflexive Banach Space

Differential and integral equations in reflexive Banach spaces have gained great attention and hve been investigated in many studies and monographs. Inspired by those, we study the existence of the solution to a delay functional integral equation of Volterra-Stieltjes type and its corresponding delay-functional integro-differential equation in reflexive Banach space E. Sufficient conditions for the uniqueness of the solutions are given. The continuous dependence of the solutions on the delay function, the initial data, and some others parameters are proved.

Dynamics of Physical Autonomous Robotic Network With Constant And Time-Varying Communication Delays

A Connected Autonomous Vehicle Network (CAVN) is an emerging paradigm that can reduce traffic congestion by allowing vehicles to cooperatively behave according to information out of the line of sight and improve traffic flow by decreasing inter-vehicular gaps on roadways. In this paper, the stability of CAVN with constant and time-varying communication delays is studied. When the time delay depends on time, the semi-discretization method is used to study the plant stability of the flow equilibrium of CAVN and construct approximate stability regions charts over control gain space. To study the influence of time-varying delay, a constant delay is considred as the average value of the time delay function. Then, explicit sufficient conditions are provided for the stability of the flow equilibrium and study the string stability of the CAVN. The proposed controller is validated using simulations and experimentally with a platoon of four autonomous robots under time-varying delays.

An Implicit Hybrid Delay Functional Integral Equation: Existence of Integrable Solutions and Continuous Dependence

In this work, we are discussing the solvability of an implicit hybrid delay nonlinear functional integral equation. We prove the existence of integrable solutions by using the well known technique of measure of noncompactnes. Next, we give the sufficient conditions of the uniqueness of the solution and continuous dependence of the solution on the delay function and on some functions. Finally, we present some examples to illustrate our results.

A Novel Band-Stop Filter with Band-Pass, High-Pass, and Low-Pass Negative Group Delay Characteristics

A band-stop filter with three different negative group delay functions in the passband, namely, band pass, high pass and low pass, is proposed, which has small insertion loss. The capacitance, inductance, and resistance meet different conditions, and the circuit can realize three different negative group delay characteristics. The theoretical calculation and equation derivation are given. A band-stop filter with negative group delay function is fabricated, and the measured results are basically consistent with the simulation results. The correctness of the design is verified.

MP-9S Industrial Manipulator Handling and Scrapping Tasks in Industrial Environments

The main goal of the project was to carry out a handling task using a color sensor and thermal sensor, as well as an industrial robotic unit. The selection by color made it possible to represent the sub-process of the production of a sample, where each color can be matched to the corresponding or rejected product. The function of the thermal sensor is to show the delay function for the pro-cess, which occurs when the product does not reach a point in the process at the wrong tempera-ture and needs cooling between the two workflows. The thermal sensor and color sensor were pro-grammed using the ATmega microprocessor, while the manipulator was controlled with industrial PLC. The completed project will serve educational purposes in training for students.

An efficient convergent method for the delay reaction-diffusion equations

In this manuscript, we consider the delay reaction-diffusion equation and implement an efficient spectral collocation method to approximate the solution of this equation. We first replace the delay function in the delay reaction-diffusion equation and achieve an equivalent system of equations. We then utilize the Legendre-Gauss-Lobatto and two-dimensional interpolating polynomial to approximate the solution of obtained system. Moreover, we prove the convergent of method under some mild conditions. Finally, the capability and efficiency of the method is illustrated by providing several numerical examples and comparing them with others

Toe Initiation Sleeve With Time-Delay Functionality Improves Operational Efficiency of Offshore NCS Wells

A toe initiation sleeve is a tool installed in the toe of a completion liner and is used to establish a flowpath to the reservoir without the use of intervention. Conventional toe initiation sleeves require either intervention or increasing pressure to higher than the liner test pressure to activate. These methods have inherent cost and operational risks. This paper will present the development, qualification, and deployment of a multicycle, time-delay cementable toe initiation sleeve that allows for interventionless activation without exceeding the liner test pressure. This development greatly improves operational efficiency and eliminates risk associated with conventional toe initiation sleeves. A major operator in the North Sea required an ISO V0 rated toe initiation sleeve to be developed and qualified. Design criteria for the tool was identified, and the design was developed based on field-qualified seal technology. Individual component and full-scale validation testing was performed to complete the product qualification, followed by field trials in 2019. With its unique time-delay feature, the newly developed ATS (Advanced Toe Sleeve) allows for an unlimited number of pressure cycles to be performed while also keeping the well V0 barrier in place, and activates at below liner test pressure. This paper will discuss the technology development and implementation project, resulting in ISO 14998 V0-qualified cemented ATS being installed in nearly 40 wells in the same field. This paper will also provide insight into how the ATS provides unique benefits to the operator during various phases of the well's life. Cementing: One moving part and opening sleeve isolated from the inside diameter (ID) allow for pumping darts through the ATS without the risk of opening Setting liner/testing liner: Time-delay features allow for setting liner and testing the liner at higher pressures than ATS opening pressure. Well cleanup/displacing to lower density fluid: Time-delay function allows for opening the ATS at lower pressure than the well has seen during previous operations. Completion: ATS design and qualification grade reduce completion steps and costs for the operator. Stimulation: ATS eliminates the need for intervention, reducing the operational steps and costs for the operator. The advanced toe sleeve with built-in time-delay features maintains the liner integrity throughout the various well operations. The number of available pressure cycles can be predetermined, and the activation of the various cycles can be precisely controlled thereby also controlling when the tool is activated to achieve injectivity. This paper will present the development and field-wide implementation of the ATS technology, which has rapidly gained operator acceptance and resulted in significant time and cost savings.