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Articles 61 - 90 of 223
Full-Text Articles in Systems and Communications
Estimation Of Atmospheric Conditions Over A Long Horizontal Path Using Multi-Frame Blind Deconvolution (Mfbd) Techniques In Comparison With Delayed Tilt Anisoplanatism (Delta) Software, Hannah Stoll
Dissertations, Master's Theses and Master's Reports
The potential to track and view objects in space from the ground with greater near real time knowledge of the intervening turbulence would be a revolutionary capability. The objective of this thesis is to cross-validate two separate methods used to estimate the Fried parameter. This verification is a step toward a commercial grade product that would make real-time estimates of the turbulence strength along an optical path from a ground-based observatory to a satellite in orbit around the Earth. Michigan Technological University has developed a multi-frame blind deconvolution (MFBD) algorithm used to estimate r0 and it was tested against MZA’s …
Communication Debugging Platform, Husam Beitello
Communication Debugging Platform, Husam Beitello
Honors Theses
More and more products are becoming “connected” devices, integrating multiple communications subsystems into their design. These subsystems increase the complexity of a design, and require extensive testing and debugging before they reach an end user. The purpose of the project was to create a prototype for a peripheral device that enables bidirectional communication between a typical smartphone and another target device communicating using the infrared, Bluetooth, and/or CAN communication protocols. Such a device could then be used to debug the behavior of a product relying on these forms of communication, by running test procedures referred to as scripts from the …
A State-Of-The-Art Survey On Deep Learning Theory And Architectures, Md Zahangir Alom, Tarek M. Taha, Christopher Yakopcic, Stefan Westberg, Paheding Sidike, Mst Shamima Nasrin, Mahmudul Hasan, Brian C. Van Essen, Abdul A. S. Awwal, Vijayan K. Asari
A State-Of-The-Art Survey On Deep Learning Theory And Architectures, Md Zahangir Alom, Tarek M. Taha, Christopher Yakopcic, Stefan Westberg, Paheding Sidike, Mst Shamima Nasrin, Mahmudul Hasan, Brian C. Van Essen, Abdul A. S. Awwal, Vijayan K. Asari
Electrical and Computer Engineering Faculty Publications
In recent years, deep learning has garnered tremendous success in a variety of application domains. This new field of machine learning has been growing rapidly and has been applied to most traditional application domains, as well as some new areas that present more opportunities. Different methods have been proposed based on different categories of learning, including supervised, semi-supervised, and un-supervised learning. Experimental results show state-of-the-art performance using deep learning when compared to traditional machine learning approaches in the fields of image processing, computer vision, speech recognition, machine translation, art, medical imaging, medical information processing, robotics and control, bioinformatics, natural language …
Development Of A Myoelectric Detection Circuit Platform For Computer Interface Applications, Nickolas Andrew Butler
Development Of A Myoelectric Detection Circuit Platform For Computer Interface Applications, Nickolas Andrew Butler
Master's Theses
Personal computers and portable electronics continue to rapidly advance and integrate into our lives as tools that facilitate efficient communication and interaction with the outside world. Now with a multitude of different devices available, personal computers are accessible to a wider audience than ever before. To continue to expand and reach new users, novel user interface technologies have been developed, such as touch input and gyroscopic motion, in which enhanced control fidelity can be achieved. For users with limited-to-no use of their hands, or for those who seek additional means to intuitively use and command a computer, novel sensory systems …
Active Recall Networks For Multiperspectivity Learning Through Shared Latent Space Optimization, Theus Aspiras, Ruixu Liu, Vijayan K. Asari
Active Recall Networks For Multiperspectivity Learning Through Shared Latent Space Optimization, Theus Aspiras, Ruixu Liu, Vijayan K. Asari
Electrical and Computer Engineering Faculty Publications
Given that there are numerous amounts of unlabeled data available for usage in training neural networks, it is desirable to implement a neural network architecture and training paradigm to maximize the ability of the latent space representation. Through multiple perspectives of the latent space using adversarial learning and autoencoding, data requirements can be reduced, which improves learning ability across domains. The entire goal of the proposed work is not to train exhaustively, but to train with multiperspectivity. We propose a new neural network architecture called Active Recall Network (ARN) for learning with less labels by optimizing the latent space. This …
Deep Temporal Convolutional Networks For Short-Term Traffic Flow Forecasting, Wentian Zhao, Yanyun Gao, Tingxiang Ji, Xili Wan, Feng Ye, Guangwei Bai
Deep Temporal Convolutional Networks For Short-Term Traffic Flow Forecasting, Wentian Zhao, Yanyun Gao, Tingxiang Ji, Xili Wan, Feng Ye, Guangwei Bai
Electrical and Computer Engineering Faculty Publications
To reduce the increasingly congestion in cities, it is essential for intelligent transportation system (ITS) to accurately forecast the short-term traffic flow to identify the potential congestion sites. In recent years, the emerging deep learning method has been introduced to design traffic flow predictors, such as recurrent neural network (RNN) and long short-term memory (LSTM), which has demonstrated its promising results. In this paper, different from existing work, we study the temporal convolutional network (TCN) and propose a deep learning framework based on TCN model for short-term city-wide traffic forecast to accurately capture the temporal and spatial evolution of traffic …
Recurrent Residual U-Net For Medical Image Segmentation, Md Zahangir Alom, Christopher Yakopcic, Mahmudul Hasan, Tarek M. Taha, Vijayan K. Asari
Recurrent Residual U-Net For Medical Image Segmentation, Md Zahangir Alom, Christopher Yakopcic, Mahmudul Hasan, Tarek M. Taha, Vijayan K. Asari
Electrical and Computer Engineering Faculty Publications
Deep learning (DL)-based semantic segmentation methods have been providing state-of-the-art performance in the past few years. More specifically, these techniques have been successfully applied in medical image classification, segmentation, and detection tasks. One DL technique, U-Net, has become one of the most popular for these applications. We propose a recurrent U-Net model and a recurrent residual U-Net model, which are named RU-Net and R2U-Net, respectively. The proposed models utilize the power of U-Net, residual networks, and recurrent convolutional neural networks. There are several advantages to using these proposed architectures for segmentation tasks. First, a residual unit helps when training deep …
A Survey Of Techniques For Mobile Service Encrypted Traffic Classification Using Deep Learning, Pan Wang, Xuejiao Chen, Feng Ye, Zhixin Sun
A Survey Of Techniques For Mobile Service Encrypted Traffic Classification Using Deep Learning, Pan Wang, Xuejiao Chen, Feng Ye, Zhixin Sun
Electrical and Computer Engineering Faculty Publications
The rapid adoption of mobile devices has dramatically changed the access to various net- working services and led to the explosion of mobile service traffic. Mobile service traffic classification has been a crucial task that attracts strong interest in mobile network management and security as well as machine learning communities for past decades. However, with more and more adoptions of encryption over mobile services, it brings a lot of challenges about mobile traffic classification. Although classical machine learning approaches can solve many issues that port and payload-based methods cannot solve, it still has some limitations, such as time-consuming, costly handcrafted …
On The Distortion Of Uwb Circularly Polarized Time-Domain Pulses In Presence Of Rotation, Adam Narbudowicz, Janusz Przewocki, Max Ammann
On The Distortion Of Uwb Circularly Polarized Time-Domain Pulses In Presence Of Rotation, Adam Narbudowicz, Janusz Przewocki, Max Ammann
Conference Papers
The paper provides a first theoretical study on the effect of rotational Doppler on circularly polarized pulsed communication. Despite the circularly polarized communication being considered immune to signal fading due to rotary misalignment, such misalignment will cause a frequency-invariant phase-shift. This phase shift will significantly distort the shape of the time-domain pulse. The property can be used for integration of orientation sensing into well establish pulse-based localization. However, it has also the potential to distort communication for some pulse-modulated UWB systems.
Smart Garage Opener, Jacob Wasson
Smart Garage Opener, Jacob Wasson
Williams Honors College, Honors Research Projects
The purpose of this research project was to design an anti-theft device that interfaces with a standard garage door opener to allow packages to easily be delivered into a garage in a safe and secure manner. Primary functionality of the device is to use a package’s tracking number and corresponding barcode to open and close a garage door to a preset height so that a package can be delivered inside the garage before it closes. My contribution to the project revolved around the programming and board design of the microcontroller circuit that controls the input and output signals of the …
Ict-Enabled Control And Energy Management Of Community Microgrids For Resilient Smart Grid Operation, Mahmoud Saleh
Ict-Enabled Control And Energy Management Of Community Microgrids For Resilient Smart Grid Operation, Mahmoud Saleh
Dissertations and Theses
Our research has focused on developing novel controllers and algorithms to enhance the resilience of the power grid and increase its readiness level against major disturbances.
The U.S. power grid currently encounters two main challenges: (1) the massive and extended blackouts caused by natural disasters, such as hurricane Sandy. These blackouts have raised a national call to explore innovative approaches for enhanced grid resiliency. Scrutinizing how previous blackouts initiated and propagated throughout the power grid, the major reasons are lack of situational awareness, lack of real-time monitoring and control, underdeveloped controllers at both the transmission and distribution levels, and lack …
Demand Response Management In Smart Grid Networks: A Two-Stage Game-Theoretic Learning-Based Approach, Pavlos Athanasios Apostolopoulos
Demand Response Management In Smart Grid Networks: A Two-Stage Game-Theoretic Learning-Based Approach, Pavlos Athanasios Apostolopoulos
Shared Knowledge Conference
In this paper, the combined problem of power company selection and demand response management (DRM) in a smart grid network consisting of multiple power companies and multiple customers is studied via adopting a reinforcement learning and game-theoretic technique. Each power company is characterized by its reputation and competitiveness. The customers, acting as learning automata select the most appropriate power company to be served, in terms of price and electricity needs’ fulfillment, via a reinforcement learning based mechanism. Given customers’ power company selection, the DRM problem is formulated as a two-stage game theoretic optimization framework. At the first stage the optimal …
Effect Of Wireless Communication Delay On Dc Microgrids Performance, Mahmoud Saleh, Yusef Esa, Ahmed Mohamed
Effect Of Wireless Communication Delay On Dc Microgrids Performance, Mahmoud Saleh, Yusef Esa, Ahmed Mohamed
Publications and Research
This paper investigates the effect of wireless communication technologies latency on the converters and the bus voltage of centrally communication based controlled DC microgrids (MGs) during islanding. A DC microgrid with its communication based control scheme was modeled to show the impact of latency. Simulation results show that the impact may be severe depending on the design, and the operational condition of the microgrid before latency occurs.
Impact Of Communication Latency On The Bus Voltage Of Centrally Controlled Dc Microgrid During Islanding, Mahmoud Saleh, Yusef Esa, Ahmed Mohamed
Impact Of Communication Latency On The Bus Voltage Of Centrally Controlled Dc Microgrid During Islanding, Mahmoud Saleh, Yusef Esa, Ahmed Mohamed
Publications and Research
Maintaining a sustainable and reliable source of energy to supply critical loads within a renewable energy based microgrid (MG) during blackouts is directly related to its bus voltage variations. For example, voltage variation might trigger protection devices and disconnect DERs within the MG. Centrally controlled MGs (CCMGs) type is dependent on communication. Therefore, it is very important to analyze the impact of communication networks performance degradation, such as latency, on the bus voltage of CCMGs. This paper investigates the effect of wireless communication technologies latency on the bus voltage and performance of centralized DC MGs. Two mathematical models were developed …
Cmos Radioactive Isotope Identification With Multichannel Analyzer And Embedded Neural Network, Samuel Murray
Cmos Radioactive Isotope Identification With Multichannel Analyzer And Embedded Neural Network, Samuel Murray
Department of Electrical and Computer Engineering: Dissertations, Theses, and Student Research
A radiation detection and identification system is designed and implemented to perform gamma ray spectroscopy on radioactive sources and identify which isotopes are present in the sources. A multichannel analyzer is implemented on an ASIC to process the signal produced from gamma rays detected by a scintillator and photomultiplier tube and to quantize the gamma ray energies to build a histogram. A fast, low memory embedded neural network is implemented on a microcontroller ASIC to identify the isotopes present in the gamma ray histogram produced by the multichannel analyzer in real time.
Advisors: Sina Balkir and Michael W. Hoffman
Communication Based Control For Dc Microgrids, Mahmoud S. Saleh, Yusef Esa, Ahmed Mohamed
Communication Based Control For Dc Microgrids, Mahmoud S. Saleh, Yusef Esa, Ahmed Mohamed
Publications and Research
Centralized communication-based control is one of the main methods that can be implemented to achieve autonomous advanced energy management capabilities in DC microgrids. However, its major limitation is the fact that communication bandwidth and computation resources are limited in practical applications. This can be often improved by avoiding redundant communications and complex computations. In this paper, an autonomous communication-based hybrid state/event driven control scheme is proposed. This control scheme is hierarchical and heuristic, such that on the primary control level, it encompasses state-driven local controllers, and on the secondary control level, an event-driven MG centralized controller (MGCC) is used. This …
Datanet: Deep Learning Based Encrypted Network Traffic Classification In Sdn Home Gateway, Pan Wang, Feng Ye, Xuejiao Chen, And Yi Qian
Datanet: Deep Learning Based Encrypted Network Traffic Classification In Sdn Home Gateway, Pan Wang, Feng Ye, Xuejiao Chen, And Yi Qian
Electrical and Computer Engineering Faculty Publications
A smart home network will support various smart devices and applications, e.g., home automation devices, E-health devices, regular computing devices, and so on. Most devices in a smart home access the Internet through a home gateway (HGW). In this paper, we propose a software-defined- network (SDN)-HGW framework to better manage distributed smart home networks and support the SDN controller of the core network. The SDN controller enables efficient network quality-of-service management based on real-time traffic monitoring and resource allocation of the core network. However, it cannot provide network management in distributed smart homes. Our proposed SDN-HGW extends the control to …
Anomaly Inference Based On Heterogeneous Data Sources In An Electrical Distribution System, Yachen Tang
Anomaly Inference Based On Heterogeneous Data Sources In An Electrical Distribution System, Yachen Tang
Dissertations, Master's Theses and Master's Reports
Harnessing the heterogeneous data sets would improve system observability. While the current metering infrastructure in distribution network has been utilized for the operational purpose to tackle abnormal events, such as weather-related disturbance, the new normal we face today can be at a greater magnitude. Strengthening the inter-dependencies as well as incorporating new crowd-sourced information can enhance operational aspects such as system reconfigurability under extreme conditions. Such resilience is crucial to the recovery of any catastrophic events. In this dissertation, it is focused on the anomaly of potential foul play within an electrical distribution system, both primary and secondary networks as …
Handwritten Bangla Character Recognition Using The State-Of-The-Art Deep Convolutional Neural Networks, Md Zahangir Alom, Paheding Sidike, Mahmudul Hasan, Tarek M. Taha, Vijayan K. Asari
Handwritten Bangla Character Recognition Using The State-Of-The-Art Deep Convolutional Neural Networks, Md Zahangir Alom, Paheding Sidike, Mahmudul Hasan, Tarek M. Taha, Vijayan K. Asari
Electrical and Computer Engineering Faculty Publications
In spite of advances in object recognition technology, handwritten Bangla character recognition (HBCR) remains largely unsolved due to the presence of many ambiguous handwritten characters and excessively cursive Bangla handwritings. Even many advanced existing methods do not lead to satisfactory performance in practice that related to HBCR. In this paper, a set of the state-of-the-art deep convolutional neural networks (DCNNs) is discussed and their performance on the application of HBCR is systematically evaluated. The main advantage of DCNN approaches is that they can extract discriminative features from raw data and represent them with a high degree of invariance to object …
Fundamentals Of Neutrosophic Logic And Sets And Their Role In Artificial Intelligence (Fundamentos De La Lógica Y Los Conjuntos Neutrosóficos Y Su Papel En La Inteligencia Artificial ), Florentin Smarandache, Maykel Leyva-Vazquez
Fundamentals Of Neutrosophic Logic And Sets And Their Role In Artificial Intelligence (Fundamentos De La Lógica Y Los Conjuntos Neutrosóficos Y Su Papel En La Inteligencia Artificial ), Florentin Smarandache, Maykel Leyva-Vazquez
Branch Mathematics and Statistics Faculty and Staff Publications
Neutrosophy is a new branch of philosophy which studies the origin, nature and scope of neutralities. This has formed the basis for a series of mathematical theories that generalize the classical and fuzzy theories such as the neutrosophic sets and the neutrosophic logic. In the paper, the fundamental concepts related to neutrosophy and its antecedents are presented. Additionally, fundamental concepts of artificial intelligence will be defined and how neutrosophy has come to strengthen this discipline.
Application Of Real Field Connected Vehicle Data For Aggressive Driving Identification On Horizontal Curves, Arash Jahangiri, Vincent Berardi, Sahar Ghanipoor Machiani
Application Of Real Field Connected Vehicle Data For Aggressive Driving Identification On Horizontal Curves, Arash Jahangiri, Vincent Berardi, Sahar Ghanipoor Machiani
Psychology Faculty Articles and Research
The emerging technology of connected vehicles generates a vast amount of data that could be used to enhance roadway safety. In this paper, we focused on safety applications of a real field connected vehicle data on a horizontal curve. The database contains connected vehicle data that were collected on public roads in Ann Arbor, Michigan with instrumented vehicles. Horizontal curve negotiations are associated with a great number of accidents, which are mainly attributed to driving errors. Aggressive/risky driving is a contributing factor to the high rate of crashes on horizontal curves. Using basic safety message data in connected vehicle data …
Design And Simulation Of An 8-Bit Successive Approximation Register Charge-Redistribution Analog-To-Digital Converter, Sumit K. Verma
Design And Simulation Of An 8-Bit Successive Approximation Register Charge-Redistribution Analog-To-Digital Converter, Sumit K. Verma
Electrical Engineering Theses
The thesis initially investigates the history of the monolithic ADCs. The next chapter explores the different types of ADCs available in the market today. Next, the operation of a 4-bit SAR ADC has been studied. Based on this analysis, an 8-bit charge-redistribution SAR ADC has been designed and simulated with Multisim (National Instruments, Austin, TX). The design is divided into different blocks which are individually implemented and tested. Level-1 SPICE MOSFET models representative of 5μm devices were used wherever individual MOSFETs were used in the design. Finally, the power dissipation during the conversion period was also estimated. The supply voltage …
Hardware Based Testing Of Communication Based Control For Dc Microgrid, Mahmoud Saleh, Yusef Esa, Ahmed Mohamed
Hardware Based Testing Of Communication Based Control For Dc Microgrid, Mahmoud Saleh, Yusef Esa, Ahmed Mohamed
Publications and Research
This paper further describes our work presented in Industry Application Society 2016 Conference, with more details related to the control and operation of the microgrid. The DC microgrid facility was custom designed and implemented at CCNY with minimal off-the-shelf components to enable flexibility and reconfiguration capability. The design steps, requirements, and experimental results of the developed testbed were discussed. As a case study, a central controller for energy management algorithm was developed and tested under several operational scenarios. The experimental results verify the applicability of the developed testbed for validating DC microgrid controllers.
University Of Maine High Altitude Ballooning Eclipse Experience, Kent Seneres, Derek Haas, William Bessette, Richard Eason
University Of Maine High Altitude Ballooning Eclipse Experience, Kent Seneres, Derek Haas, William Bessette, Richard Eason
2017 Academic High Altitude Conference
The University of Maine High Altitude Ballooning (UMHAB) team launched two balloons during the August 21, 2017 total solar eclipse, producing a consistent online video stream of the eclipse to an altitude of 110,000 feet. This paper discusses the key factors that lead to a successful launch and recovery, such as thorough testing procedures, redesign of components, choice of launch site, and a touch of luck. In preparation for the event, the team tested the equipment and code over eleven balloon launches. Airplane based testing and land testing were conducted for the tracking and video stream components. The payloads and …
Quantitative Analysis Of Regenerative Energy In Electric Rail Traction Systems, Mahmoud Saleh, Oindrilla Dutta, Yusef Esa, Ahmed Mohamed
Quantitative Analysis Of Regenerative Energy In Electric Rail Traction Systems, Mahmoud Saleh, Oindrilla Dutta, Yusef Esa, Ahmed Mohamed
Publications and Research
This paper aims at determining the influential factors affecting regenerative braking energy in DC rail transit systems. This has been achieved by quantitatively evaluating the dependence of regenerative energy on various parameters, such as vehicle dynamics, train scheduling, ground inclination and efficiency of the electrical devices. The recuperated power and energy have been presented by a mathematical model, comprising of a set of empirical forms, which allows for thorough analysis. A detailed simulation model of a typical DC-traction system has been developed to validate the developed empirical forms. The results verified the validity of the proposed mathematical model, and demonstrated …
Optimal Microgrids Placement In Electric Distribution Systems Using Complex Network Framework, Mahmoud Saleh, Yusef Esa, Nwabueze Onuorah, Ahmed Mohamed
Optimal Microgrids Placement In Electric Distribution Systems Using Complex Network Framework, Mahmoud Saleh, Yusef Esa, Nwabueze Onuorah, Ahmed Mohamed
Publications and Research
This paper provides a new approach to find the optimal location for Microgrids (MGs) in electric distribution systems using complex network analysis. An optimal location in this paper refers to a location that would result in increased grid resilience, reduced power losses, less line loading, higher voltage stability and secured supply to critical loads during power outage. The criteria used to find the optimal placement of MGs were based on the centrality analysis adopted from complex network theory, the center of mass concept used in physics, and the controlled delivery grid (CDG) concept. An IEEE 30-bus system was used as …
Energy Management Algorithm For Resilient Controlled Delivery Grids, Mahmoud Saleh, Yusef Esa, Ahmed Mohamed, Haim Grebel, Roberto Rojas-Cessa
Energy Management Algorithm For Resilient Controlled Delivery Grids, Mahmoud Saleh, Yusef Esa, Ahmed Mohamed, Haim Grebel, Roberto Rojas-Cessa
Publications and Research
Resilience of the power grid is most challenged at power blackouts since the issues that led to it may not be fully resolved by the time the power is back. In this paper, a Real-Time Energy Management Algorithm (RTEMA) has been developed to increase the resilience of power systems based on the controlled delivery grid (CDG) concept. In a CDG, loads communicate with a central controller, periodically sending requests for power. The central controller runs an algorithm, based on which it may decide whether to grant the requested energy fully or partially. Therefore, the CDG limits loads discretionary access to …
On-Chip Training Of Memristor Crossbar Based Multi-Layer Neural Networks, Raqibul Hasan, Tarek M. Taha, Christopher Yakopcic
On-Chip Training Of Memristor Crossbar Based Multi-Layer Neural Networks, Raqibul Hasan, Tarek M. Taha, Christopher Yakopcic
Electrical and Computer Engineering Faculty Publications
Memristor crossbar arrays carry out multiply-add operations in parallel in the analog domain, and so can enable neuromorphic systems with high throughput at low energy and area consumption. On-chip training of these systems have the significant advantage of being able to get around device variability and faults. This paper presents on-chip training circuits for multi-layer neural networks implemented using a single crossbar per layer and two memristors per synapse. Using two memristors per synapse provides double the synaptic weight precision when compared to a design that uses only one memristor per synapse. Proposed on-chip training system utilizes the back propagation …
Application-Aware Cognitive Multi-Hop Wireless Networking Testbed And Experiments, Trenton T. Evans
Application-Aware Cognitive Multi-Hop Wireless Networking Testbed And Experiments, Trenton T. Evans
Department of Electrical and Computer Engineering: Dissertations, Theses, and Student Research
In this thesis, we present a new architecture for application-aware cognitive multihop wireless networks (AC-MWN) with testbed implementations and experiments. Cognitive radio is a technique to adaptively use the spectrum so that the resource can be used more efficiently in a low cost way. Multihop wireless networks can be deployed quickly and flexibly without a fixed infrastructure. In presented new architecture, we study backbone routing schemes with network cognition, routing scheme with network coding and spectrum adaptation. A testbed is implemented to test the schemes for AC-MWN. In addition to basic measurements, we implement a video streaming application based on …
An Exact Analysis For Four-Order Acousto-Optic Bragg Diffraction Which Incorporates Both Incident Light Angle And Sound Frequency Dependencies, Adeyinka Sunday Ademola
An Exact Analysis For Four-Order Acousto-Optic Bragg Diffraction Which Incorporates Both Incident Light Angle And Sound Frequency Dependencies, Adeyinka Sunday Ademola
Electrical Engineering Theses
This thesis extends the prior work which produced an exact solution to the four-order acousto-optic (AO) Bragg cell with assumed fixed center frequency and with exact Bragg angle incident light. The extension predicts the model that incorporates the dependencies of both the input angle of light and the sound frequency. Specifically, a generalized 4th order linear differential equation (DE), is developed from a simultaneous analysis of four coupled AO system of DEs. Through standard methods, the characteristic roots, which requires solving a quartic equation, is produced. Subsequently, a derived system of homogeneous solutions, which absorbs the roots obtained using …