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2021

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More Alike Than Different: Student Perceptions Of Academic Librarians By Genders And Subject Areas, Elizabeth Price, Jody C. Fagan Dec 2021

More Alike Than Different: Student Perceptions Of Academic Librarians By Genders And Subject Areas, Elizabeth Price, Jody C. Fagan

Libraries

This study explored differences in how undergraduate students of different genders and academic disciplines perceived academic librarians at a U.S. public university. No evidence indicated differences between students identifying as male or female, and few statistically significant differences were found among four Subject Areas (Arts, Humanities + Social Sciences, Business, Health + Education, and STEM). Our results have implications for local practice though they are not generalizable to other institutions. Despite a lack of significant findings, librarians should continue to explore ways to measure how students of different disciplines perceive academic libraries and/or librarians as valuable to their academic success.


2021 Grand River Water Quality, Allison Romanski, Madeleine Lang Dec 2021

2021 Grand River Water Quality, Allison Romanski, Madeleine Lang

Student Summer Scholars Manuscripts

2021 Grand River Water Quality Sampling

The goals of this research project were to collect repeat samples at designated reaches and under different flow conditions along the Grand River, sample the entire Grand River over a short period of time, collaborate with wastewater treatment plant labs and technicians to analyze water samples, and to calculate a Water Quality Index (WQI) for samples collected.

Seven different reaches were sampled and over 120 samples were collected between May 7th and August 12th of 2021. Water samples were collected and analyzed for nitrate, total phosphate, ammonium, chloride, dissolved oxygen, biological oxygen demand , …


Teaching Computer Science Csc 222, Harrison Dekker Dec 2021

Teaching Computer Science Csc 222, Harrison Dekker

Library Impact Statements

No abstract provided.


The North Dakota Dual Aurora Camera (Noddac), A Student-Led Citizen Science Project: One-Year Retrospective, Future Developments, And Scientific Potential, Vincent Ledvina, Elizabeth Macdonald, Steven Collins, Michael Mccormack, Timothy Young, Wayne Barkhouse Dec 2021

The North Dakota Dual Aurora Camera (Noddac), A Student-Led Citizen Science Project: One-Year Retrospective, Future Developments, And Scientific Potential, Vincent Ledvina, Elizabeth Macdonald, Steven Collins, Michael Mccormack, Timothy Young, Wayne Barkhouse

Arts & Sciences Undergraduate Showcase

The North Dakota Dual Aurora Camera (NoDDAC) is a student-led project operated in conjunction with the University of North Dakota (UND), the LiveAuroraNetwork, and Aurorasaurus citizen science. Aurora cameras are valuable tools for aurora chasers, and scientists, providing ground-truth visual data to gauge auroral activity, yet at midlatitudes, these facilities are few in number. Deploying aurora cameras in these areas provides a valuable resource for aurora-chasing communities, but also demonstrates scientific merit as the analysis of rare phenomena, such as STEVEs, benefit from multiple geographic observations. What makes this project unique is the student initiative being based at a university …


Mansouramycins E–G, Cytotoxic Isoquinolinequinones From Marine Streptomycetes, Mohamed Shaaban, Khaled A. Shaaban, Gerhard Kelter, Heinz Herbert Fiebig, Hartmut Laatsch Dec 2021

Mansouramycins E–G, Cytotoxic Isoquinolinequinones From Marine Streptomycetes, Mohamed Shaaban, Khaled A. Shaaban, Gerhard Kelter, Heinz Herbert Fiebig, Hartmut Laatsch

Center for Pharmaceutical Research and Innovation Faculty Publications

Chemical investigation of the ethyl acetate extract from the marine-derived Streptomyces sp. isolate B1848 resulted in three new isoquinolinequinone derivatives, the mansouramycins E–G (1a–3a), in addition to the previously reported mansouramycins A (5) and D (6). Their structures were elucidated by computer-assisted interpretation of 1D and 2D NMR spectra, high-resolution mass spectrometry, and by comparison with related compounds. Cytotoxicity profiling of the mansouramycins in a panel of up to 36 tumor cell lines indicated a significant cytotoxicity and good tumor selectivity for mansouramycin F (2a), while the activity profile of E ( …


Laser Forming Of Compliant Mechanisms And Flat-Foldable Furniture, Daniel Calvin Ames Dec 2021

Laser Forming Of Compliant Mechanisms And Flat-Foldable Furniture, Daniel Calvin Ames

Theses and Dissertations

Compliant mechanisms are useful for improving existing machines and creating new ones that were not previously possible. They also help us to think of new methods and technologies needed to both improve existing systems as well as manufacture systems that have not been done before. The purpose of this thesis is to show novel implementations of compliant mechanisms into folding systems, and to show new methods for fabricating such mechanisms with nontraditional materials and on difficult scales. Folding systems are shown in furniture applications with chairs, stools, and childcare furniture applications as results of research into how such structures could …


Understanding Dyslexia As A Neurological Learning Disability: A Plan For An Instructive Website For Parents And Early Elementary Teachers, Rasma M. Gertners Dec 2021

Understanding Dyslexia As A Neurological Learning Disability: A Plan For An Instructive Website For Parents And Early Elementary Teachers, Rasma M. Gertners

Masters Projects

The learning disability known as “dyslexia” is often misunderstood by parents and educators. Dyslexia is a life-long, neurodevelopmental disorder characterized by a deficit in phonological awareness and processing. Its likely causes are genetic as well as environmental. Other conditions known to co-occur with dyslexia are Speech and Language Disorder, Attention Deficit Hyperactivity Disorder, Autism Spectrum Disorder, memory problems, and others. In order for children with dyslexia to reach their highest reading potential, the disorder must be remediated before age seven or eight using intensive, explicit reading interventions. Teachers and other education professionals, using prescribed screening instruments, can identify phonological awareness …


Cuny York College–Hosted Nasa Stem Outreach Program Graduates Over 30,000 Students – The Legacy Continues Amidst The Covid-19 Pandemic, Nazrul I. Khandaker Dec 2021

Cuny York College–Hosted Nasa Stem Outreach Program Graduates Over 30,000 Students – The Legacy Continues Amidst The Covid-19 Pandemic, Nazrul I. Khandaker

Publications and Research

The NASA MUREP (Minority University Research and Education Project) and SEMAA (Science, Engineering, Mathematics and Aerospace Academy) at York College CUNY (City University of New York), borough of Queens, New York City, recently earned a distinction by graduating over 30,000 underrepresented minority students since 1999 with the culmination of the fall 2021 session! African American students are leading the graduates, followed by Hispanic and Asian students being almost equal in proportion. The primary objective of both MAA (MUREP Aerospace Academy) and SEMAA is getting underrepresented minority students exposure to innovative STEM content and prepare many of them to enter higher …


Functional Characterization Of Arabidopsis Synaptotagmin-4 Protein Through Reverse Genetics Strategy, Zahid Jawed Dec 2021

Functional Characterization Of Arabidopsis Synaptotagmin-4 Protein Through Reverse Genetics Strategy, Zahid Jawed

Theses and Dissertations

Calcium ion plays a significant role in plant signal transduction pathways, including regulation of stress-induced gene expression. Sensor proteins such as proteins with calcium-binding C2 domains can perceive changes in cellular calcium level. Functional analysis of such sensor proteins will give us a better understanding of plant stress signaling. Synaptotagmins are a group of proteins containing C2 domains that are capable of binding calcium ions and regulate gene expression in response to external abiotic stress stimuli. Here, we used a reverse genetic approach to analyze the function of synaptotagmin – 4, which is one of the five identified synaptotagmin proteins …


Teachers’ Perceptions About Mathematics In A Socio-Religious Context: A Case From Pakistan, Munira Amirali, Anjum Halai Dec 2021

Teachers’ Perceptions About Mathematics In A Socio-Religious Context: A Case From Pakistan, Munira Amirali, Anjum Halai

Institute for Educational Development, Karachi

This study investigated mathematics teachers’ beliefs about the nature of mathematics and the contributory factors shaping them. A survey of 200 trained and untrained mathematics teachers from public and private schools was carried out in Karachi Pakistan, a context with a strong influence of religion on the socio-cultural practices of the people. The survey was followed by a focus-group discussion with selected teachers and is the focus of this paper. This is a ground-breaking study in a hitherto under-researched socio-religious context.
Teachers across the system showed a strong similarity in beliefs. A commonly held view was that mathematics is created …


Usage Statistics: Project Counter R5 Tr_J1 Report Fy2021 - Journal Requests (Excluding Oa_Gold) By Title, Andrée Rathemacher Dec 2021

Usage Statistics: Project Counter R5 Tr_J1 Report Fy2021 - Journal Requests (Excluding Oa_Gold) By Title, Andrée Rathemacher

Technical Services Reports and Statistics

Project COUNTER R5 Report TR_J1 for the University of Rhode Island for the period from July 1, 2020 - June 30, 2021. The TR_J1 report is defined as "Journal Requests (Excluding OA_Gold)." This report presents an annual total only and only includes those platforms successfully configured for automated harvesting via SUSHI.

File for download is Excel spreadsheet generated by Alma Analytics.

Results:

  • Total Item Requests - 696,705
  • Unique Item Requests - 513,492


2012 August University Of Memphis Commencement Program Dec 2021

2012 August University Of Memphis Commencement Program

Commencements

Program for the Summer convocation of the 100th commencement of the University of Memphis at Memphis, Tennessee, held at the FedEx Forum on August 12, 2012.


Blue Red Hackenbush Spiders, Ravi Cho Dec 2021

Blue Red Hackenbush Spiders, Ravi Cho

Master's Theses

One of the goals of Combinatorial Game Theory is to find provable winning strategiesfor certain games. In this paper, we give winning strategies for certain spider positions played using the rules of Blue Red Hackenbush and a variant. Blue Red Hackenbush and its variants are played on a graph of a bLue and Red edges that are connected to a vertex called the ground. We will represent the ground as a horizontal black line. In this paper, we study spider graphs played under two different variants: Blue Red Hackenbush and Reverse Blue Red Hackenbush. Both variants are played by two …


Linear Inverse Problems And Neural Networks, Jasjeet Dhaliwal Dec 2021

Linear Inverse Problems And Neural Networks, Jasjeet Dhaliwal

Master's Theses

We investigate two ideas in this thesis. First, we analyze the results of adaptingrecovery algorithms from linear inverse problems to defend neural networks against adversarial attacks. Second, we analyze the results of substituting sparsity priors with neural network priors in linear inverse problems. For the former, we are able to extend the framework introduced in [1] to defend neural networks against ℓ0, ℓ2,and ℓ∞ norm attacks, and for the latter, we find that our method yields an improvement over reconstruction results of [2].


Sparse Coding For Data Augmentation Of Hyperspectral Medical Images, Rojin Zandi Dec 2021

Sparse Coding For Data Augmentation Of Hyperspectral Medical Images, Rojin Zandi

Master's Theses

Hyperspectral imaging presents detailed information about the electromagneticspectrum of an object in three dimensions. The significant point about the hyperspectral images is that it contains tens or hundreds of spectral layers, which provide precise data about the composition of the studied material. Therefore, hyperspectral images have been popular in many fields of study, such as medical diagnostic imaging. Speed and precision are key points to save human life in disease diagnosis, and applying machine learning techniques to medical hyperspectral images helps answer this need. Convolutional neural networka are one of the most popular machine learning methods for classifying medical images. …


Development And Characterization Of An Underwater Acoustics Laboratory Via In Situ Impedance Boundary Measurements, Cameron Taylor Vongsawad Dec 2021

Development And Characterization Of An Underwater Acoustics Laboratory Via In Situ Impedance Boundary Measurements, Cameron Taylor Vongsawad

Theses and Dissertations

Modeling underwater acoustic propagation comes with a variety of challenges due to the need for proper characterization of the environmental conditions. These conditions include ever changing and complex water properties as well as boundary conditions. The BYU underwater acoustics open-air tank test-bed and measurement chain were developed to study underwater acoustic propagation within a controlled environment. It was also developed to provide ways to test and validate ocean models without the high cost associated with obtaining open ocean measurements. However, tank measurements require additional characterization of boundary conditions associated with the walls of the tank which would not be present …


Investigating Hypersonic Plasma Sheath And Heat Ablation Effects On Rf Transmission Using Dsmc Method, Andrew J. Derubertis, Ramesh K. Agarwal Dec 2021

Investigating Hypersonic Plasma Sheath And Heat Ablation Effects On Rf Transmission Using Dsmc Method, Andrew J. Derubertis, Ramesh K. Agarwal

Mechanical Engineering and Materials Science Independent Study

The transmission and degradation of RF signals through the plasma sheath surrounding hypersonic vehicles is investigated using a DSMC flow solver method. Starfish software, made publicly available by its creator, Lubos Brieda, a professor at USC, is adapted and used to run the hypersonic flow simulations. Additionally, heat ablation materials are briefly investigated for their effect on RF transmission. The study of RF signal degradation and the viability of communications for hypersonic vehicles is of supreme importance for the future of aerospace as hypersonic travel and warfare is becoming technologically possible. Integrating over the flow solver’s resulting electron number density …


Finding Neverland? Artificial Intelligence And The Jurisprudence Of Legal Certainty, Omar Zaky Dec 2021

Finding Neverland? Artificial Intelligence And The Jurisprudence Of Legal Certainty, Omar Zaky

Theses and Dissertations

The development of artificial intelligence (AI) models that are capable of predicting the decisions of prominent courts – most notably the European Court of Human Rights and United States Supreme Court – provides us with an opportunity to revisit important jurisprudential debates regarding the quest for legal certainty. Through providing clear distinctions within formalistic jurisprudence, and its, subsequent, realist critique; this thesis seeks to analyze legal decision-making and its relationship with artificial intelligence. I argue that, AI’s deterministic nature and its support for the law being an “entirely self-contained process” does lend some credence to certain jurisprudential arguments. However, this …


Crucial File Selection Strategy (Cfss) For Enhanced Download Response Time In Cloud Replication Environments, M.A. Fazlina, Rohaya Latip, Azizol Abdullah, Hamidah Ibrahim, Mohamed A. Alrshah Dec 2021

Crucial File Selection Strategy (Cfss) For Enhanced Download Response Time In Cloud Replication Environments, M.A. Fazlina, Rohaya Latip, Azizol Abdullah, Hamidah Ibrahim, Mohamed A. Alrshah

Baghdad Science Journal

Cloud Computing is a mass platform to serve high volume data from multi-devices and numerous technologies. Cloud tenants have a high demand to access their data faster without any disruptions. Therefore, cloud providers are struggling to ensure every individual data is secured and always accessible. Hence, an appropriate replication strategy capable of selecting essential data is required in cloud replication environments as the solution. This paper proposed a Crucial File Selection Strategy (CFSS) to address poor response time in a cloud replication environment. A cloud simulator called CloudSim is used to conduct the necessary experiments, and results are presented to …


Deep Learning For Human Microrna Precursor Prediction: A Systematic Literature Review, Martina Ojonah Dec 2021

Deep Learning For Human Microrna Precursor Prediction: A Systematic Literature Review, Martina Ojonah

Master of Science in Information Technology Theses

The discovery of MicroRNA (miRNA) sparked medical breakthroughs, leading to the development of drugs/vaccines and biomarkers for some terminal diseases such as cancer. Due to the relatively short length of microRNAs, research has shown that discovering them on their own is a difficult task; thus, the focus has shifted to predicting precursor miRNAs, which are longer than miRNAs. Computational techniques evolve because of flaws discovered in existing designs, discoveries, and the desire to make the process as seamless as possible. Most researchers in recent studies indicated that the use of few input features and a lack of domain understanding of …


Acute Pediatric Chagas Disease In Antioquia, Colombia: A Geographic Location Of Suspected Oral Transmission, Lídia Gual-Gonzalez, Catalina Aango-Ferreira, Laura Camila Lopera-Restrepo, Omar Cantillo-Barraza, Daniela Velásquez Marín, Natalia Restrepo Bustamante, Omar Triana-Chavez, Melissa Nolan Ph.D., Mph Dec 2021

Acute Pediatric Chagas Disease In Antioquia, Colombia: A Geographic Location Of Suspected Oral Transmission, Lídia Gual-Gonzalez, Catalina Aango-Ferreira, Laura Camila Lopera-Restrepo, Omar Cantillo-Barraza, Daniela Velásquez Marín, Natalia Restrepo Bustamante, Omar Triana-Chavez, Melissa Nolan Ph.D., Mph

Faculty Publications

Chagas disease, Trypanosoma cruzi infection, is an insidious cause of heart failure in Latin America. Early diagnosis and treatment are critical to prevent irreversible myocardial damage that progressively accumulates over decades. Several structural barriers account for the less than 1% of cases in Colombia being treated, including poor physician knowledge, especially considering that some regions are considered non-endemic. The two cases reported here represent an emerging epidemiologic scenario associated with pediatric Chagas disease. Both cases are suspected oral transmitted parasitic infection in a geographic region of Colombia (Andean region of Antioquia) where no previous oral transmission of Chagas disease had …


Stability And Mechanical Properties Of W1-X Mox B4.2 (X=0.0-1.0) From First Principles, Weiguang Gong, Rui Xu, Xuecheng Shao, Quan Li, Changfeng Chen Dec 2021

Stability And Mechanical Properties Of W1-X Mox B4.2 (X=0.0-1.0) From First Principles, Weiguang Gong, Rui Xu, Xuecheng Shao, Quan Li, Changfeng Chen

Physics & Astronomy Faculty Research

Heavy transition-metal tetraborides (e.g., tungsten tetraboride, molybdenum tetraboride, and molybdenum-doped tungsten tetraboride) exhibit superior mechanical properties, but solving their complex crystal structures has been a long-standing challenge. Recent experimental x-ray and neutron diffraction measurements combined with first-principles structural searches have identified a complex structure model for tungsten tetraboride that contains a boron trimer as an unusual structural unit with a stoichiometry of 1:4.2. In this paper, we expand the study to binary MoB4.2 and ternary W1-xMoxB4.2 (x=0.0-1.0) compounds to assess their thermodynamic stability and mechanical properties using a tailor-designed crystal structure search method in conjunction with first-principles energetic calculations. Our …


Bayesian, Frequentist, And Information Geometry Approaches To Parametric Uncertainty Quantification Of Classical Empirical Interatomic Potentials, Yonatan Kurniawan Dec 2021

Bayesian, Frequentist, And Information Geometry Approaches To Parametric Uncertainty Quantification Of Classical Empirical Interatomic Potentials, Yonatan Kurniawan

Theses and Dissertations

Uncertainty quantification (UQ) is an increasingly important part of materials modeling. In this paper, we consider the problem of quantifying parametric uncertainty in classical empirical interatomic potentials (IPs). Previous work based on local sensitivity analysis using the Fisher Information has shown that IPs are sloppy, i.e., are insensitive to coordinated changes of many parameter combinations. We confirm these results and further explore the non-local statistics in the context of sloppy model analysis using both Bayesian (MCMC) and Frequentist (profile likelihood) methods. We interface these tools with the Knowledgebase of Interatomic Models (OpenKIM) and study three models based on the Lennard-Jones, …


Effects Of Extra-Curricular Project-Based Learning Experiences On Self-Efficacy And Interest In Stem Fields In High School, Taihao Kevin Wan Dec 2021

Effects Of Extra-Curricular Project-Based Learning Experiences On Self-Efficacy And Interest In Stem Fields In High School, Taihao Kevin Wan

Dissertations

As our society and systems become more technologically advanced, increasing opportunities exist for students interested to pursue careers in Science, Technology, Engineering, and Mathematics (STEM) fields. However, pervasive inequities have led to differences in the extent to which women and underrepresented racial/ethnic groups choose to pursue study and career pathways in STEM. Project-Based Learning (PBL) is among the most widely researched strategies suggested to support student learning and motivation and has more recently been applied to school-based efforts to increase student interest in STEM related fields. Rooted in Social Cognitive Career Theory, this study examined changes in students’ self-reported general …


New Understanding On Scientific Research, Peng Du, Hua Shen, Feng Zhang Dec 2021

New Understanding On Scientific Research, Peng Du, Hua Shen, Feng Zhang

Bulletin of Chinese Academy of Sciences (Chinese Version)

With the continuous deepening of the nested influence of scientific research and economic society, scientific research has received unprecedented attention. At the same time, it faces bottlenecks in its own development. The scientific research itself, the scientific establishment, and the scientific policy are in a state of change. It is necessary to understand the new laws of scientific knowledge production, and re-understand the interactive relationship between science, technology, and engineering to expand the boundaries of scientific research. This article analyzes the reasons for re-understanding scientific research, expounds the new connotation of scientific research from aspects of object, function and method, …


Optimization Of Funding Policies Of Science Foundation Of China For High-Quality Development Of Basic Research, Shouyang Wang, Rui Tao, Jue Wang Dec 2021

Optimization Of Funding Policies Of Science Foundation Of China For High-Quality Development Of Basic Research, Shouyang Wang, Rui Tao, Jue Wang

Bulletin of Chinese Academy of Sciences (Chinese Version)

Nowadays, with the vigorous rise of a new round of scientific and technological revolution around the world, emerging disciplines continue to spring up, science and technology develop rapidly and show the characteristics of intersection and fusion. Meanwhile, complex models appear in the field of scientific research, and talents play an increasingly prominent role in the process of scientific and technological innovation. In this context, National Natural Science Foundation of China (NSFC) is facing a new development opportunity and challenge. It is increasingly significant for how to optimize funding policies, strengthen basic research, enhance talent support for basic research, and build …


Development Experience Of International Open Source And Its Enlightenment To Construction Of Open Source Innovation System In China, Yuntao Long, Xiaoming Wang, Rong Gu, Yungang Bao Dec 2021

Development Experience Of International Open Source And Its Enlightenment To Construction Of Open Source Innovation System In China, Yuntao Long, Xiaoming Wang, Rong Gu, Yungang Bao

Bulletin of Chinese Academy of Sciences (Chinese Version)

Open source has become an essential innovation model for global technological progress and the construction of an open source innovation system is an important path for China to achieve self-reliance and self-improvement in science and technology. As an indispensable part of the global software value chain and high-tech industry chain, China needs to improve its open source innovation ecosystem. The paper, based on a systematic review of the related development policies and successful experiences on the open source work in US and Europe, puts forward a series of policy suggestions to solve the practical problems faced by the construction of …


Experiment And Simulation Platform For Oasis-Desert Symbiotic Relationship (Odp), Yan Li, Xinjun Zheng, Yuguang Wang, Guiqing Xu, Ran Liu Dec 2021

Experiment And Simulation Platform For Oasis-Desert Symbiotic Relationship (Odp), Yan Li, Xinjun Zheng, Yuguang Wang, Guiqing Xu, Ran Liu

Bulletin of Chinese Academy of Sciences (Chinese Version)

Junggar Basin is a typical arid inland region in the northern temperate zone of the Earth. The surrounding high mountains form runoff, which flows into the basin and develops oasis. Oasis and desert are interdependent. Oasis needs to leach out its naturally accumulated salts through drainage. This drainage provides water and nutrients to desert vegetation. Desert vegetation, in turn, provides an ecological protection for oasis. Hence, oasis and desert have a symbiotic relationship. With excessive exploitation of land and water resources with water-saving technologies, salts cannot be leached out of the oasis region anymore. As a result, the groundwater level …


Recurrent Stroke Prediction Using Machine Learning Algorithms With Clinical Public Datasets: An Empirical Performance Evaluation, Fadratul Hafinaz Hassan, Mohd Adib Omar Dec 2021

Recurrent Stroke Prediction Using Machine Learning Algorithms With Clinical Public Datasets: An Empirical Performance Evaluation, Fadratul Hafinaz Hassan, Mohd Adib Omar

Baghdad Science Journal

Recurrent strokes can be devastating, often resulting in severe disability or death. However, nearly 90% of the causes of recurrent stroke are modifiable, which means recurrent strokes can be averted by controlling risk factors, which are mainly behavioral and metabolic in nature. Thus, it shows that from the previous works that recurrent stroke prediction model could help in minimizing the possibility of getting recurrent stroke. Previous works have shown promising results in predicting first-time stroke cases with machine learning approaches. However, there are limited works on recurrent stroke prediction using machine learning methods. Hence, this work is proposed to perform …


Numerical Analysis Of Least-Squares Group Finite Element Method For Coupled Burgers' Problem, Najat Jalil Noon Dec 2021

Numerical Analysis Of Least-Squares Group Finite Element Method For Coupled Burgers' Problem, Najat Jalil Noon

Baghdad Science Journal

In this paper, a least squares group finite element method for solving coupled Burgers' problem in 2-D is presented. A fully discrete formulation of least squares finite element method is analyzed, the backward-Euler scheme for the time variable is considered, the discretization with respect to space variable is applied as biquadratic quadrangular elements with nine nodes for each element. The continuity, ellipticity, stability condition and error estimate of least squares group finite element method are proved. The theoretical results show that the error estimate of this method is . The numerical results are compared with the exact solution and other …