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2017

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Articles 10351 - 10380 of 11102

Full-Text Articles in Physical Sciences and Mathematics

Dynamical Systems Modeling To Identify A Cohort Of Problem Drinkers With Similar Mechanisms Of Behavior Change, Kidist Maxwell, Rebecca Everett, Sijing Shao, Alexis Kuerbis, Lyric Stephenson, H. T. Banks, Jon Morgenstern Jan 2017

Dynamical Systems Modeling To Identify A Cohort Of Problem Drinkers With Similar Mechanisms Of Behavior Change, Kidist Maxwell, Rebecca Everett, Sijing Shao, Alexis Kuerbis, Lyric Stephenson, H. T. Banks, Jon Morgenstern

Publications and Research

One challenge to understanding mechanisms of behavior change (MOBC) completely among individuals with alcohol use disorder is that processes of change are theorized to be complex, dynamic (time varying), and at times non-linear, and they interact with each other to influence alcohol consumption. We used dynamical systems modeling to better understand MOBC within a cohort of problem drinkers undergoing treatment. We fit a mathematical model to ecological momentary assessment data from individual patients who successfully reduced their drinking by the end of the treatment. The model solutions agreed with the trend of the data reasonably well, suggesting the cohort patients …


A Measurement Of The Parity Violating Asymmetry In The Neutron Capture On 3He At Sns, Md Latiful Kabir Jan 2017

A Measurement Of The Parity Violating Asymmetry In The Neutron Capture On 3He At Sns, Md Latiful Kabir

Theses and Dissertations--Physics and Astronomy

Weak nucleon nucleon couplings are largely unknown because of the involved theoretical and experimental challenges. Theoretically the topic is difficult due to the non-perturbative nature of the strong interaction, which makes calculations of the couplings challenging. Experimentally, the topic is difficult given that 1) the observables are determined by ratios between strong couplings and weak couplings which differ in size by seven orders of magnitude, and 2) theoretically clean and predictable measurements are almost always restricted to simple systems that do not allow for effects that enhance the size of the asymmetry. However parity violation (PV) can be used to …


Developing Conceptual Understanding And Procedural Fluency In Algebra For High School Students With Intellectual Disability, Andrew J. Wojcik Jan 2017

Developing Conceptual Understanding And Procedural Fluency In Algebra For High School Students With Intellectual Disability, Andrew J. Wojcik

Theses and Dissertations

Teaching students with Intellectual Disability (ID) is a relatively new endeavor. Beginning in 2001 with the passage of the No Child Left Behind Act, the general education curriculum integrated algebra across the K-12 curriculum (Kendall, 2011; National Governors Association Center for Best Practices & Council of Chief State School Officers, 2010), and expansion of the curriculum included five intertwined skills (productive disposition, procedural fluency, strategic competence, adaptive reasoning, and conceptual understanding) (Kilpatrick, Swafford, & Findell, 2001). Researchers are just beginning to explore the potential of students with ID with algebra (Browder, Spooner, Ahlgrim-Delzell, Harris & Wakeman, 2008; Creech-Galloway, Collins, Knight, …


Mathematical Models Of The Inflammatory Response In The Lungs, Sarah B. Minucci Jan 2017

Mathematical Models Of The Inflammatory Response In The Lungs, Sarah B. Minucci

Theses and Dissertations

Inflammation in the lungs can occur for many reasons, from bacterial infections to stretch by mechanical ventilation. In this work we compare and contrast various mathematical models for lung injuries in the categories of acute infection, latent versus active infection, and particulate inhalation. We focus on systems of ordinary differential equations (ODEs), agent-based models (ABMs), and Boolean networks. Each type of model provides different insight into the immune response to damage in the lungs. This knowledge includes a better understanding of the complex dynamics of immune cells, proteins, and cytokines, recommendations for treatment with antibiotics, and a foundation for more …


Big Data Visualization Platform For Mixed Reality, Aliakbar Panahi Jan 2017

Big Data Visualization Platform For Mixed Reality, Aliakbar Panahi

Theses and Dissertations

The visualization of data helps to provide faster and deeper insight into the data. In this work, a system for visualizing and analyzing big data in an interactive mixed reality environment is proposed. Such a system can be used for representing different types of data such as temporal, geospatial, network graph, and high dimensional. Also, an implementation of this system for four different data types are created. The data types include network data, volumetric data, high dimensional, and spectral data for different mixed reality devices such as Microsoft HoloLens, Oculus Rift, Samsung Gear VR, and Android ARCore were created. It …


Effect Of Charged Species On The Gradient Properties, Kayesh Ashraf Jan 2017

Effect Of Charged Species On The Gradient Properties, Kayesh Ashraf

Theses and Dissertations

Surface chemical gradients are materials that exhibit continuous, gradually varying chemical or physical properties along and across the length of a substrate. As a result, each point on the gradient surface can represent an individual sample. They are broadly classified as chemical and physical gradients depending upon the properties that the gradient exhibits. A physical gradient involves a continuous variation of physical properties such as surface roughness and film porosity on the micrometer scale. Chemical gradients involve a gradual variation of chemical properties such as polarity, acidity and basicity, etc. Such gradients have found various applications in cell adhesion, nanoparticle …


A Novel Synthesis And Subsequent Decyclization Of Iminothiozolidinones: Expansion Of Thiourea Chemistry For Biological Applications, Constance D. Franklin Jan 2017

A Novel Synthesis And Subsequent Decyclization Of Iminothiozolidinones: Expansion Of Thiourea Chemistry For Biological Applications, Constance D. Franklin

Theses and Dissertations

Small molecule synthesis has become a valuable tool in the study of biological systems. Biologically active compounds can be designed based on well-characterized endogenous systems or they can be found through the screening of large libraries of small molecules. This work involves the development of a small library of cyclic thiourea-based small molecules by use of an unreported synthetic pathway. Briefly, parent thioureas were cyclized by reaction with bromoacetyl bromide, and one or two isomeric heterocycles were found to form. Further studies indicated that the reaction could be easily manipulated by temperature or solvent to effectively control the product distribution. …


Application Of Agisoft Photoscan And Sediment Transport Modeling For The Analysis Of Sediment Wave Propagation Succeeding Gravel Augmentation, Oak Grove Fork Of The Clackamas River, Oregon, Mindi Lea Curran Jan 2017

Application Of Agisoft Photoscan And Sediment Transport Modeling For The Analysis Of Sediment Wave Propagation Succeeding Gravel Augmentation, Oak Grove Fork Of The Clackamas River, Oregon, Mindi Lea Curran

Cal Poly Humboldt theses and projects

Application of agisoft photoscan and sediment transport modeling for the analysis of sediment wave propagation succeeding gravel augmentation, oak grove fork of the clackamas river, oregon

Mindi Lea Curran

Physical features in alluvial rivers such as riffles, gravel bars, pools, and side channels provide refugia, nutrients, and spawning and rearing habitat for anadromous fish and other aquatic organisms. The downstream transport of gravels that continuously replenish these features is prevented by dams, and often leads to a coarsened channel bed condition and other geomorphic changes that have negative impacts on aquatic organisms. Geomorphic change in rivers can be challenging to …


Multiscale Habitat Suitability Modeling For Canary Rockfish (Sebastes Pinniger) Along The Northern California Coast, Portia N. Saucedo Jan 2017

Multiscale Habitat Suitability Modeling For Canary Rockfish (Sebastes Pinniger) Along The Northern California Coast, Portia N. Saucedo

Cal Poly Humboldt theses and projects

Detailed spatially-explicit data of the potential habitat of commercially important rockfish species are a critical component for the purposes of marine conservation, evaluation, and planning. Predictive habitat modeling techniques are widely used to identify suitable habitat in un-surveyed regions. This study elucidates the predicted distribution of canary rockfish (Sebastes pinniger) along the largely un-surveyed northern California coast using data from visual underwater surveys and predictive terrain complexity covariates. I used Maximum Entropy (MaxEnt) modelling software to identify regions of suitable habitat for S. pinniger greater than nine cm in total length at two spatial scales. The results of …


Hubble Parameter Measurement Constraints On The Redshift Of The Deceleration-Acceleration Transition, Dynamical Dark Energy, And Space Curvature, Omer Farooq, Foram Ranjeet Madiyar, Sara Crandall, Bharat Ratra Jan 2017

Hubble Parameter Measurement Constraints On The Redshift Of The Deceleration-Acceleration Transition, Dynamical Dark Energy, And Space Curvature, Omer Farooq, Foram Ranjeet Madiyar, Sara Crandall, Bharat Ratra

Publications

We compile an updated list of 38 measurements of the Hubble parameter H(z) between redshifts 0.07 ≤ z ≤ 2.36 and use them to place constraints on model parameters of constant and time-varying dark energy cosmological models, both spatially flat and curved. We use five models to measure the redshift of the cosmological deceleration-acceleration transition, zda, from these H(z) data. Within the error bars, the measured zda are insensitive to the model used, depending only on the value assumed for the Hubble constant H0. The weighted mean of our measurements is zda = 0.72±0.05 (0.84±0.03) for H0 = 68 ± …


Exploring Myths In Digital Forensics: Separating Science From Ritual, Gary C. Kessler, Gregory H. Carlton Jan 2017

Exploring Myths In Digital Forensics: Separating Science From Ritual, Gary C. Kessler, Gregory H. Carlton

Publications

Digital forensic methodology deviates significantly relative to the methods of other forensic sciences for numerous practical reasons, and it has been largely influenced by factors derived from the inception and evolution of this relatively new and rapidly changing field. Digital forensics methodology was developed more by practitioners in its early days rather than by computer scientists. This led to accepted best practices in the field that may not represent the best or, at least, tested, science. This paper explores some of these differences in the practice and evolution between digital and other forensic sciences, and recommends scientific approaches to apply …


Assessing The Efficiency Of Different Sustainable Farming Practices In Reducing The Environmental Impacts Caused By Aquaculture, Rajee Olaganathan, Alicia Tang Kar Mun Jan 2017

Assessing The Efficiency Of Different Sustainable Farming Practices In Reducing The Environmental Impacts Caused By Aquaculture, Rajee Olaganathan, Alicia Tang Kar Mun

Publications

Sustainability of aquaculture is achieved when aquaculture farming systems are capable of preserving the natural resource base and involves an institutional change to the environment by the attainment and continued satisfaction for present and future generations. Sustainable farming practices produce sufficient aquaculture output to satisfy the seafood demand while not burdening the environment more. The potentiality and efficiency of different sustainable aqua farming practices in reducing anthropogenic impacts to the environment by aquaculture are assessed in this paper. Polyculture is mostly adopted by small-scale rural farmers as it requires low entry barrier and help in income diversification. The input of …


Technological Modernization And Its Impact On Agriculture, Fisheries And Fossil Fuel Utilization In The Asia Pacific Countries With Emphasis On Sustainability Perspective, Rajee Olaganathan, Kathleen Quigley Jan 2017

Technological Modernization And Its Impact On Agriculture, Fisheries And Fossil Fuel Utilization In The Asia Pacific Countries With Emphasis On Sustainability Perspective, Rajee Olaganathan, Kathleen Quigley

Publications

Modernization is a process that moves towards efficiency. This affects most of the fields such as agriculture, fisheries, forestry, urban planning, policy, fossil fuel usage, manufacturing, technology, economic growth etc. This process plays a major role in moving forward making things faster, better and basically more efficient. The effects of modernization on all these fields bring about the major changes to aspects such as social, economic and the environment. The level of operation has increased from a domestic level; small family scale business to large commercial levels. As the level of operation increased, the utilization of natural resources increased gradually …


The Basic Physics Of The Binary Black Hole Merger Gw150914, B. P. Abbott, K. Gill, B. Hughey, J. Pratt, M. J. Szczepańczyk, M. Zanolin, Et Al. Jan 2017

The Basic Physics Of The Binary Black Hole Merger Gw150914, B. P. Abbott, K. Gill, B. Hughey, J. Pratt, M. J. Szczepańczyk, M. Zanolin, Et Al.

Publications

The first direct gravitational-wave detection was made by the Advanced Laser Interferometer Gravitational Wave Observatory on September 14, 2015. The GW150914 signal was strong enough to be apparent, without using any waveform model, in the filtered detector strain data. Here, features of the signal visible in the data are analyzed using concepts from Newtonian physics and general relativity, accessible to anyone with a general physics background. The simple analysis presented here is consistent with the fully general-relativistic analyses published elsewhere, in showing that the signal was produced by the inspiral and subsequent merger of two black holes. The black holes …


The Remote Observatories Of The Southeastern Association For Research In Astronomy (Sara), William C. Keel, Terry D. Oswalt, Peter Mack, Gary Henson, Todd Hillwig, Et Al. Jan 2017

The Remote Observatories Of The Southeastern Association For Research In Astronomy (Sara), William C. Keel, Terry D. Oswalt, Peter Mack, Gary Henson, Todd Hillwig, Et Al.

Publications

We describe the remote facilities operated by the Southeastern Association for Research in Astronomy (SARA) , a consortium of colleges and universities in the US partnered with Lowell Observatory, the Chilean National Telescope Allocation Committee, and the Instituto de Astrofísica de Canarias. SARA observatories comprise a 0.96 m telescope at Kitt Peak, Arizona; one of 0.6 m aperture on Cerro Tololo, Chile; and the 1 m Jacobus Kapteyn Telescope at the Roque de los Muchachos, La Palma, Spain. All are operated using standard VNC or Radmin protocols communicating with on-site PCs. Remote operation offers considerable flexibility in scheduling, allowing long-term …


Using Journals To Assess Non-Stem Student Learning In Stem Courses: A Case Study In Cybersecurity Education, Gary Kessler, Glenn S. Dardick, Douglas L. Holton Jan 2017

Using Journals To Assess Non-Stem Student Learning In Stem Courses: A Case Study In Cybersecurity Education, Gary Kessler, Glenn S. Dardick, Douglas L. Holton

Publications

Embry-Riddle Aeronautical University offers a minor course of study in cybersecurity as an option in our undergraduate Homeland Security program. Since the students are, by and large, social scientists, the focus of the program is to build hyper-awareness of how cybersecurity integrates within their professional aspirations rather than to provide cybersecurity career-level proficiency. Assessing student learning of the technical aspects cannot be performed using traditional tests, as they would not properly measure what the students are learning in a practical sense. Instead, we employ journals and self-reflection to ask the students to express and demonstrate their learning. Although somewhat harder …


Utilizing The O-C Method To Determine Third-Body Existence In Eclipsing Binary Systems, Patrice Majewski, Tomomi Otani, Terry D. Oswalt Jan 2017

Utilizing The O-C Method To Determine Third-Body Existence In Eclipsing Binary Systems, Patrice Majewski, Tomomi Otani, Terry D. Oswalt

Publications

Previous studies on the subject of eclipsing binaries (EBs) within the Kepler field have been adequately determined the period, distance, and other stellar parameters of these systems (Borkovits, et al. 2015). Additionally, with the use of Observed-minus-Calculated (O-C) plots, variation in the timing of timing of eclipses can be easily detected. The eclipse timing shifts may be caused by dynamical effects or by light-travel time effects (LTTE) caused by the existence of a third body. The following research was conducted on ten binaries within the Kepler “K2” Campaign 5 field whose light curves (LCs) showed evidence of eclipses with periods …


Gyrochronology Of Wide Binaries In The Kepler K2 Fields, Alexander Stone-Martinez, Gustavo Villarroel, Patrice Majewski, Tomomi Otani, Terry Oswalt, Andrew Mcnaughton Jan 2017

Gyrochronology Of Wide Binaries In The Kepler K2 Fields, Alexander Stone-Martinez, Gustavo Villarroel, Patrice Majewski, Tomomi Otani, Terry Oswalt, Andrew Mcnaughton

Publications

Gyrochronology is the method of determining a stars age based on its rotation period and mass. A cool main sequence star loses it's angular momentum as it ages, so the rotation rate slows down. Gyrochronology has been tested on star clusters in previous studies and now we are applying the theory to binary stars. Components of a binary should be the same age, so Gyrochronology should return the same age for both stars in binary systems. We examined the rotation periods for 290 wide binary main sequence stars in the Kepler K2 fields. These observations are part of a continuing …


O-C Analysis Of The Pulsating Subdwarf B Star Pg 1219 + 534, Tomomi Otani, Terry Oswalt, Alexander Stone-Martinez, Dana Singh, Kenneth Sampson, Aliyah Khan, Austin Seepersad, Caila Deabreu, Adam Moss, Claudia Morello Jan 2017

O-C Analysis Of The Pulsating Subdwarf B Star Pg 1219 + 534, Tomomi Otani, Terry Oswalt, Alexander Stone-Martinez, Dana Singh, Kenneth Sampson, Aliyah Khan, Austin Seepersad, Caila Deabreu, Adam Moss, Claudia Morello

Publications

PG 1219 + 534 (KY Uma) is a subdwarf B pulsating star with multiple periodicities between 120 – 175 s. PG 1219 + 534 was monitored for 90 hours during 2010-1 and 2016 using the 0.9 m SARA-KP telescope at Kitt Peak National Observatory (KPNO) in Arizona and the 0.8m Ortega telescope at Florida Institute of Technology in Melbourne, Florida. So far, the most promising theory for the origin of subdwarf B (sdB) stars is that they result from binary mass transfer near the Helium Flash stage of evolution. The observations of PG 1219 + 534 reported here are part …


Gyrochronology Of Wide Binaries In The Kepler K2 Campaign 5 Field, Terry D. Oswalt, Derek Buzasi, Tomomi Otani Jan 2017

Gyrochronology Of Wide Binaries In The Kepler K2 Campaign 5 Field, Terry D. Oswalt, Derek Buzasi, Tomomi Otani

Publications

We are determining rotation periods for an ensemble of over 100 wide non-interacting binary stars in the K2 Campaign 5 field that contain two main sequence dwarfs, as well as a smaller sample containing at least one white dwarf component. Observations of such coeval pairs provide the basis for our new investigation of rotation-based age determinations. Such “gyrochronology” ages can achieve a precision that exceeds most other current method of stellar age determination. Here we present a status report on our analysis of the light curves extracted from the K2 Campaign 5 field.


Search For Binaries In The Kepler K2 Fields Using Pulsation Timing Method, Tomomi Otani, Terry Oswalt Jan 2017

Search For Binaries In The Kepler K2 Fields Using Pulsation Timing Method, Tomomi Otani, Terry Oswalt

Publications

Finding orbital solutions of binaries which have small mass ratios (50 days) is challenging using traditional techniques. The radial velocity method is a good way to detect such binary stars, however it requires large telescopes. Therefore, the search for binaries in those regions is still incomplete. For binaries in this regime with at least one component that pulsates, pulsation timing is a better approach. Orbital solutions for such systems can be obtained from the periodic change in pulse arrival times as the star’s reflex motion is manifested by the changing distance along the line of sight. We present a search …


Testing The Stellar Rotation Vs. Age Paradigm Using Wide Binaries In The Kepler & K2 Fields, T. D. Oswalt, T. Otani, A. Stone-Martinez, P. Majewski, D. Buzasi Jan 2017

Testing The Stellar Rotation Vs. Age Paradigm Using Wide Binaries In The Kepler & K2 Fields, T. D. Oswalt, T. Otani, A. Stone-Martinez, P. Majewski, D. Buzasi

Publications

Essential to understanding the history of the Galaxy’s stellar populations, ages are among the most difficult to measure properties of stars. Accurate stellar ages would provide key leverage on problems ranging from the habitability of exoplanets to the Galaxy’s chemical evolution and age. Gyrochronology, the empirical relation between rotation and age, is believed to be among the best current methods of stellar age determination. Using several hundred wide non-interacting binaries identified in the Kepler mission “K2” extended mission fields we are testing this paradigm. Such wide pairs afford a unique opportunity to unravel and calibrate the effects of mass, rotation, …


First Performance Results Of A New Field-Widened Spatial Heterodyne Spectrometer For Geocoronal Hα Research, D. D. Gardner, E. J. Mierkiewicz, F. L. Roesler, J. M. Harlander, K. P. Jaehnig, S. M. Nossal, L. M. Haffner Jan 2017

First Performance Results Of A New Field-Widened Spatial Heterodyne Spectrometer For Geocoronal Hα Research, D. D. Gardner, E. J. Mierkiewicz, F. L. Roesler, J. M. Harlander, K. P. Jaehnig, S. M. Nossal, L. M. Haffner

Publications

A new, high-resolution field-widened spatial heterodyne spectrometer (FW-SHS) designed to observe geocoronal Balmer α (Hα, 6563 Å) emission was installed at Pine Bluff Observatory (PBO) near Madison, Wisconsin. FW-SHS observations were compared with an already well-characterized dual-etalon Fabry-Perot Interferometer (PBO FPI) optimized for Hα, also at PBO. The FW-SHS is a robust Fourier transform instrument that combines a large throughput advantage with high spectral resolution and a relatively long spectral baseline (~10 times that of the PBO FPI) in a compact, versatile instrument with no moving parts.Coincident Hα observations by FW-SHS and PBO FPI were obtained over similar integration times, …


Success Stories In Knowledge Management Systems, Leila Halawi, Richard Mccarthy, Janine Aronson Jan 2017

Success Stories In Knowledge Management Systems, Leila Halawi, Richard Mccarthy, Janine Aronson

Publications

Historically, information systems have focused on capturing, storing, managing, and reporting explicit knowledge. Organizations today recognize the need to integrate both explicit and tacit knowledge in formal information systems. Knowledge management continues to be a critical strategy for an organization to achieve a sustainable competitive advantage, and consequently succeed in today's knowledge-based economy. Knowledge management systems (KMS) are a class of information systems that manage, store and distribute knowledge. Knowledge management systems have proliferated in practice. In turn, theoretical research on knowledge management and knowledge management systems has proliferated. Knowledge management systems have emerged as powerful sources of competitive advantage. …


Fact Sheet, Yale University Office Of Institutional Research Jan 2017

Fact Sheet, Yale University Office Of Institutional Research

Fact Sheets

No abstract provided.


Investigation On Security Issues And Features In Social Media Sites (Face Book, Twitter, & Google+), Puneet Kumar Goud Kandikanti Jan 2017

Investigation On Security Issues And Features In Social Media Sites (Face Book, Twitter, & Google+), Puneet Kumar Goud Kandikanti

All Student Theses and Dissertations

Social media sites allow users to communicate and share their information which are a matter of privacy for users, so users should be aware about its limitations and disad-vantages to use social media sites. Likewise, there are many social media sites with its dif-ferent features and it typically works with the latest technology that is provided by the ex-perts to get connected and go along with the flow. The online privacy issues have been a re-al time problem and these however is the main aim for the experts to reduce the problems while sharing the kind of content that is …


Fitting A Linear Regression Model And Forecasting In R In The Presence Of Heteroskedascity With Particular Reference To Advanced Regression Technique Dataset On Kaggle.Com., Samuel Mbah Nde Jan 2017

Fitting A Linear Regression Model And Forecasting In R In The Presence Of Heteroskedascity With Particular Reference To Advanced Regression Technique Dataset On Kaggle.Com., Samuel Mbah Nde

All Student Theses and Dissertations

Since ancient times, men have built and sold houses. But just how much is a house worth? The challenge is to be able to use information about a house such as its location, and the area on which it is built to predict its price. Such predicted prices can be of great importance to any participant in the real estate business be it an agent, a buyer, seller or a bank to make intelligent decisions and the profit that come with such decisions. Since every company’s success depends on its ability to accurately predict financial outcomes, its profitability will depend …


Developments Of 5g Technology, Ankit Nilesh Ganatra Jan 2017

Developments Of 5g Technology, Ankit Nilesh Ganatra

All Student Theses and Dissertations

This technology is the future of current LTE technology which would be a boost to the future of wireless and computer networks, as the speeds would be way higher than the current LTE networks, which will push the technology to a new level. This technology will make the radio channels to support data access speeds up to 10 Gb/s which will turn the bandwidth radio channels as WiFi. Comparing it with other LTE technology's it has high speed and capacity, support interactive multimedia, voice, internet and its data rate is 1 Gbps which makes it faster than other LTE’s . …


Strategies For Overcoming Math Anxiety In Developmental Math Students At Community Colleges, Nika Alex Jan 2017

Strategies For Overcoming Math Anxiety In Developmental Math Students At Community Colleges, Nika Alex

All Student Theses and Dissertations

Math anxiety is a significant problem among both traditional and adult students attending community colleges. The purpose of this study is to examine effective strategies for overcoming math anxiety in community colleges. The research question for this study was: What tools are community colleges using to help developmental math students overcome math anxiety? A qualitative systematic review of literature was used to answer the research question. The research determined various factors contributed to the development of math anxiety, which is a condition capable of persisting throughout an individual’s life. Various instruments such as the Mathematical Anxiety Ratings Scale (MARS), the …


An Introduction To The Lebesgue Integral, Ikhlas Adi Jan 2017

An Introduction To The Lebesgue Integral, Ikhlas Adi

All Student Theses and Dissertations

The Riemann integral is the simplest integral to define, and it allows one to integrate every continuous function. It is really important to have a definition of the integral that allows a wider class of functions to be integrated. However, there are many other types of integrals, the most important of which is the Lebesgue integral. The Lebesgue integral allows one to integrate unbounded or discontinuous functions whose Riemann integral does not exist, and it has mathematical properties that the Riemann integral does not. The definition of the Lebesgue integral requires the use of measure theory since picking out a …