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Articles 60901 - 60930 of 302639
Full-Text Articles in Physical Sciences and Mathematics
Dietary Inflammatory Index Is Associated With Inflammation In Japanese Men, Ayaka Kotemori, Norie Sawada, Motoki Iwasaki, Taiki Yamaji, Nitin Shivappa Mbbs, Mph, Ph.D., James Hébert Scd, Junko Ishihara, Manami Inoue, Shoichiro Tsugane
Dietary Inflammatory Index Is Associated With Inflammation In Japanese Men, Ayaka Kotemori, Norie Sawada, Motoki Iwasaki, Taiki Yamaji, Nitin Shivappa Mbbs, Mph, Ph.D., James Hébert Scd, Junko Ishihara, Manami Inoue, Shoichiro Tsugane
Faculty Publications
Background: Dietary components are known to affect chronic low-grade inflammation status. The dietary inflammatory index (DII®) was developed to measure the potential impact of a diet on an individual's inflammatory status, and it has been validated mainly in Western countries.
Objective: This study aimed to examine the validity of the energy-adjusted DII (E-DIITM) using high-sensitivity C-reactive protein (hs-CRP) concentration in Japanese men and women.
Methods: In total, 6,474 volunteers from a cancer-screening program (3,825 men and 2,649 women) completed a food frequency questionnaire (FFQ) and their hs-CRP concentrations were evaluated. E-DII scores were calculated on the basis of 30 food …
Ethics Of Ai In Education: Towards A Community-Wide Framework, Wayne Holmes, Kaska Poraysa-Pomsta, Ken Holstein, Emma Sutherland, Toby Baker, Simon Buckingham Shum, Olga C. Santos, Ma. Mercedes T. Rodrigo, Mutlu Cukurova, Ig Ibert Bittencourt, Kenneth R. Koedinger
Ethics Of Ai In Education: Towards A Community-Wide Framework, Wayne Holmes, Kaska Poraysa-Pomsta, Ken Holstein, Emma Sutherland, Toby Baker, Simon Buckingham Shum, Olga C. Santos, Ma. Mercedes T. Rodrigo, Mutlu Cukurova, Ig Ibert Bittencourt, Kenneth R. Koedinger
Department of Information Systems & Computer Science Faculty Publications
While Artificial Intelligence in Education (AIED) research has at its core the desire to support student learning, experience from other AI domains suggest that such ethical intentions are not by themselves sufficient. There is also the need to consider explicitly issues such as fairness, accountability, transparency, bias, autonomy, agency, and inclusion. At a more general level, there is also a need to differentiate between doing ethical things and doing things ethically, to understand and to make pedagogical choices that are ethical, and to account for the ever-present possibility of unintended consequences. However, addressing these and related questions is far …
Is A Common Goal A False Hope In Convergence Research?: Opportunities And Challenges Of International Convergence Research To Address Arctic Change, Jessica G. Ernakovich, N. Eklund, Ruth K. Varner, N. Kirchner, J. Jeuring, Katharine Duderstadt, A. Granebeck, E. Golubeva, Asiaq Participants
Is A Common Goal A False Hope In Convergence Research?: Opportunities And Challenges Of International Convergence Research To Address Arctic Change, Jessica G. Ernakovich, N. Eklund, Ruth K. Varner, N. Kirchner, J. Jeuring, Katharine Duderstadt, A. Granebeck, E. Golubeva, Asiaq Participants
Faculty Publications
The Arctic faces multiple pressures including climate change, shifting demographics, human health risks, social justice imbalances, governance issues, and expanding resource extraction. A convergence of academic disciplines—such as natural and social sciences, engineering and technology, health and medicine—and international perspectives is required to meaningfully contribute to solving the challenges of Arctic peoples and ecosystems. However, successfully carrying out convergent, international research and education remains a challenge. Here, lessons from the planning phase of a convergence research project concerned with the health of Arctic waters developed by the Arctic Science IntegrAtion Quest (ASIAQ) are discussed. We discuss our perspective on the …
Combination Of Time Series Analysis And Sentiment Analysis For Stock Market Forecasting, Hsiao-Chuan Chou
Combination Of Time Series Analysis And Sentiment Analysis For Stock Market Forecasting, Hsiao-Chuan Chou
USF Tampa Graduate Theses and Dissertations
The goal of this research is to build a model to predict trend of financial asset price using sentiment from news headlines and financial indicators of the asset. Objective of the model is to conclude good results but also to minimize the difference between predicted values and actual values. Unlike previous approaches where the sentiments are usually calculated into score, we focus on combination of word embedding of news and financial indicators due to nonavailability of sentiment lexicon.
One idea is that the sentiment of news headline should have impact on financial asset val- ues. In other words, it would …
Geological, Mineralogical And Geochemical Process Controls On Ni Tenor Variations In The Metasedimentary-Hosted Thompson 1d Orebody At Vale’S Thompson Mine (T3), Northern Manitoba, Canada, Povilas G. Grigutis
Geological, Mineralogical And Geochemical Process Controls On Ni Tenor Variations In The Metasedimentary-Hosted Thompson 1d Orebody At Vale’S Thompson Mine (T3), Northern Manitoba, Canada, Povilas G. Grigutis
Electronic Thesis and Dissertation Repository
The Proterozoic Thompson Nickel Belt (TNB) contains rift-related mafic-ultramafic igneous rocks, in a collisional belt at the NW margin of the Archean Superior province in Northern Manitoba, Canada. The TNB hosts world class Ni-Cu-(PGE) mineralization, that has undergone polyphase deformation (D1 – D4) and upper amphibolite to lower granulite facies metamorphism, up to ~750ºC and 7.5 kbars (Lightfoot et al., 2017). Komatiitic magmas (1880 ± 5 Ma; Hulbert et al., 2005) fertile in Ni & PGE elements intruded Ospwagan Group metasedimentary sequences and through sulfur assimilation and segregation produced primary magmatic sulfides (Lesher and Burnham, 2001).
The …
Lecture 08: Partial Eigen Decomposition Of Large Symmetric Matrices Via Thick-Restart Lanczos With Explicit External Deflation And Its Communication-Avoiding Variant, Zhaojun Bai
Mathematical Sciences Spring Lecture Series
There are continual and compelling needs for computing many eigenpairs of very large Hermitian matrix in physical simulations and data analysis. Though the Lanczos method is effective for computing a few eigenvalues, it can be expensive for computing a large number of eigenvalues. To improve the performance of the Lanczos method, in this talk, we will present a combination of explicit external deflation (EED) with an s-step variant of thick-restart Lanczos (s-step TRLan). The s-step Lanczos method can achieve an order of s reduction in data movement while the EED enables to compute eigenpairs in batches along with a number …
Socastee Interview, Participant #11, April 8, 2021, Jennifer Mokos, Jaime Mccauley
Socastee Interview, Participant #11, April 8, 2021, Jennifer Mokos, Jaime Mccauley
Flood Survivor Interviews
A community member of the Rosewood neighborhood in Socastee is interviewed by a CCU student.
Impact Of Whitetail Deer Overpopulation With Hunting On The Decline, Matthew J. Lamprinos
Impact Of Whitetail Deer Overpopulation With Hunting On The Decline, Matthew J. Lamprinos
English Department: Research for Change - Wicked Problems in Our World
The whitetail deer is a key species for Pennsylvania’s forests, but their ecological balance has been disturbed by unregulated growth and urban sprawl. The deer population in Pennsylvania has exploded since the 1880’s causing a wide range of damage on the ecosystem, and humans. To reduce deer populations to sustainable levels, the Pennsylvania Game Commission relies heavily on hunters to dedicate time in the fall to go out and fill the tags the they issue. Hunter participation all around the world is decreasing for a variety of reasons. Fewer hunters out in the field causes revenue losses for the Game …
Investigating The Use Of Ultraviolet Light Emitting Diodes (Uv-Leds) For The Inactivation Of Bacteria In Powdered Food Ingredients, Laura Nyhan, Milosz Przyjalgowski, Liam O'Faolain, Máire Begley, Michael Callanan
Investigating The Use Of Ultraviolet Light Emitting Diodes (Uv-Leds) For The Inactivation Of Bacteria In Powdered Food Ingredients, Laura Nyhan, Milosz Przyjalgowski, Liam O'Faolain, Máire Begley, Michael Callanan
Cappa Publications
The addition of contaminated powdered spices and seasonings to finished products which do not undergo further processing represents a significant concern for food manufacturers. To reduce the incidence of bacterial contamination, seasoning ingredients should be subjected to a decontamination process. Ultraviolet light emitting diodes (UV-LEDs) have been suggested as an alternative to UV lamps for reducing the microbial load of foods, due to their increasing efficiency, robustness and decreasing cost. In this study, we investigated the efficacy of UV-LED devices for the inactivation of four bacteria (Listeria monocytogenes, Escherichia coli, Bacillus subtilis and Salmonella Typhimurium) on a plastic surface and …
Covid-19 And Preparing Planetary Health For Future Ecological Crises: Hopes From Glycomics For Vaccine Innovation, Xueqing Wang, Zhaohua Zhong, Wei Wang
Covid-19 And Preparing Planetary Health For Future Ecological Crises: Hopes From Glycomics For Vaccine Innovation, Xueqing Wang, Zhaohua Zhong, Wei Wang
Research outputs 2014 to 2021
A key lesson emerging from COVID-19 is that pandemic proofing planetary health against future ecological crises calls for systems science and preventive medicine innovations. With greater proximity of the human and animal natural habitats in the 21st century, it is also noteworthy that zoonotic infections such as COVID-19 that jump from animals to humans are increasingly plausible in the coming decades. In this context, glycomics technologies and the third alphabet of life, the sugar code, offer veritable prospects to move omics systems science from discovery to diverse applications of relevance to global public health and preventive medicine. In this expert …
Utilizing Headspace Solid-Phase Microextraction For The Characterization Of Volatile Organic Compounds Released From Contraband And Its Implications For Detector Dog Training, Kelvin Joseph Frank Jr
Utilizing Headspace Solid-Phase Microextraction For The Characterization Of Volatile Organic Compounds Released From Contraband And Its Implications For Detector Dog Training, Kelvin Joseph Frank Jr
FIU Electronic Theses and Dissertations
Improving the accuracy and reliability of odor detection dogs is of utmost importance particularly for legal reasons. Field testing in conjunction with headspace analysis of volatile organic compounds (VOCs) has in recent times allowed for these improvements, by providing scientifically based recommendations for optimum training protocols. The current project leveraged on these established capabilities to enhance three areas of odor detection: illicit drugs, explosives and mass storage devices.
With hemp being legalized under the 2018 Farm Bill, legal questions have been raised regarding a dog’s ability to ignore hemp if trained to detect marijuana, as both are types of Cannabis …
Teaching Social-Emotional Skills Through Storytelling: Development Of A Mobile App For Children, Sally Devitry
Teaching Social-Emotional Skills Through Storytelling: Development Of A Mobile App For Children, Sally Devitry
Student Research Symposium
Children today are born into a world where technology is deeply integrated into daily life. A study completed in 2016 found that 85% of children ages 5-10 participate in some form of screen time (e.g., television, tablet, or smart phone) daily. More than 75% of these children do so for more than two hours a day on average. The increasing use of technology, specifically tablet and smartphone use, will fundamentally redefine childhood experiences. In a child’s formative years, learning social-emotional skills such as empathy, communication, resilience, etc. is vital. Obviously, human interaction cannot be replaced in teaching these social-emotional skills, …
Nitrogen Use Efficiency And Soil Bioavailable Nitrogen In Corn Silage Production In A Semi-Arid Environment, Phearen Miller
Nitrogen Use Efficiency And Soil Bioavailable Nitrogen In Corn Silage Production In A Semi-Arid Environment, Phearen Miller
Student Research Symposium
As agriculture intensifies, the world faces a dual challenge of increasing food production while reducing impacts of excess reactive nitrogen (N) in the environment. A field study examining different N sources in corn silage under semi-arid conditions was conducted at the Greenville farm in northern Utah (41°45’ N, 1111°48’52 W) since 2012. The experimental design is a randomized complete block design with four blocks and four treatments: control (no nitrogen), low ammonium sulfate (AS 112 kg N/ha), high ammonium sulfate (AS 224 kg N/ha), and steer manure compost (224 kg total N/ha). We examined yield, nitrogen use efficiency (NUE), and …
Extension Of The Two-Step Approach For Informative Dropout In Survival Analysis, Cristina Murray-Krezan
Extension Of The Two-Step Approach For Informative Dropout In Survival Analysis, Cristina Murray-Krezan
Mathematics & Statistics ETDs
Chronic kidney disease (CKD) in children is known to result in poor growth and quality of life, and frequently results in kidney failure. The Chronic Kidney Disease in Children study (CKiD) is a prospective cohort study enrolling children ages 1 to 16 to assess health outcomes in children with CKD including the effects of declining glomerular filtration rate and the resulting consequences of growth failure on morbidity. Quantification of the magnitude of the risk for decreased kidney function and, ultimately, failure has been achieved through a variety of studies, often including cohort studies such as the CKiD study. Longitudinal studies …
Pregnancy And Fertility Amongst Women With The Mthfr C677t Polymorphism: An Anthropological Review, Caroline A. Maclean
Pregnancy And Fertility Amongst Women With The Mthfr C677t Polymorphism: An Anthropological Review, Caroline A. Maclean
USF Tampa Graduate Theses and Dissertations
Effects of the MTHFR C677T allele on reproduction include multiple complications. The frequency of births with neural tube defects, Down Syndrome, or recurrent pregnancy loss of CC, CT, and TT mothers was measured using data collected from existing literature. Total participants n=2605 (n=1111 cases, n=1494 controls). Results show that folic acid supplementation did not prevent the incidence of NTD pregnancy in CT women. Furthermore, CT women are more fecund overall, producing more pregnancies than CC and TT women. While CT case women did have higher incidences of RPL, NTD pregnancy and DS pregnancy, this is due to the overall greater …
Identifying Skeletal Puberty Stages In A Modern Sample From The United States, Jordan T. Wright
Identifying Skeletal Puberty Stages In A Modern Sample From The United States, Jordan T. Wright
USF Tampa Graduate Theses and Dissertations
Investigating the onset and progression of puberty can provide insight and evidence for social changes regarding the transition to adulthood. There are also many social factors that can lead to variation in the timing of the onset and progression of puberty. Methods created by Mary Lewis and Fiona Shapland for assessing changes in skeletal development associated with pubertal timing were applied to computerized tomography scans (n=400) from the New Mexico Decedent Image Database and recorded in an attempt to identify adolescent growth trends in a modern skeletal sample from the United States. This is a novel study using the methods …
Change In Dietary Inflammatory Index Score Is Associated With Control Of Long-Term Rheumatoid Arthritis Disease Activity In A Japanese Cohort: The Tomorrow Study, Yoshinari Matsumoto, Nitin Shivappa Mbbs, Mph, Ph.D., Yuko Sugioka, Masahiro Tada, Tadashi Okano, Kenji Mamoto, Kentaro Inui, Daiki Habu, James R. Hébert Scd, Tatsuya Koike
Change In Dietary Inflammatory Index Score Is Associated With Control Of Long-Term Rheumatoid Arthritis Disease Activity In A Japanese Cohort: The Tomorrow Study, Yoshinari Matsumoto, Nitin Shivappa Mbbs, Mph, Ph.D., Yuko Sugioka, Masahiro Tada, Tadashi Okano, Kenji Mamoto, Kentaro Inui, Daiki Habu, James R. Hébert Scd, Tatsuya Koike
Faculty Publications
Background: The dietary inflammatory index (DII®), a quantitative measure of the inflammatory potential of daily food and nutrient intake, and associations between a variety of health outcomes have been reported. However, the association between DII score and disease activity of rheumatoid arthritis (RA) is unclear. Therefore, this study was designed to test whether higher DII score contributes to disease activity and as a corollary, y, whether reducing DII score helps to achieve or maintain low disease activity or remission in patients with RA.
Methods: We performed a cross-sectional and longitudinal analysis using 6 years of data (from 2011 to 2017) …
Handwriting Transformers, Ankan Kumar Bhunia, Salman Khan, Hisham Cholakkal, Rao Muhammad Anwer, Fahad Shahbaz Khan, Mubarak A. Shah
Handwriting Transformers, Ankan Kumar Bhunia, Salman Khan, Hisham Cholakkal, Rao Muhammad Anwer, Fahad Shahbaz Khan, Mubarak A. Shah
Computer Vision Faculty Publications
We propose a novel transformer-based styled handwritten text image generation approach, HWT, that strives to learn both style-content entanglement as well as global and local writing style patterns. The proposed HWT captures the long and short range relationships within the style examples through a self-attention mechanism, thereby encoding both global and local style patterns. Further, the proposed transformer-based HWT comprises an encoder-decoder attention that enables style-content entanglement by gathering the style representation of each query character. To the best of our knowledge, we are the first to introduce a transformer-based generative network for styled handwritten text generation. Our proposed HWT …
Broken-Hearted” Carbon Bowl Via Electron Shuttle Reaction: Energetics And Electron Coupling, Gabrielle A. Leith, Allison M. Rice, Brandon J. Yarbrough, Preecha Kittikhunnatham, Abijai Mathur, Nicholas A. Morris, Megan J. Francis, Anna A. Berseneva, Poonam Dhull, Richard D. Adams, M. Victoria Bobo, Aaron A. Vannucci, Mark D. Smith, Sophya Garashchuk, Natalia B. Shustova
Broken-Hearted” Carbon Bowl Via Electron Shuttle Reaction: Energetics And Electron Coupling, Gabrielle A. Leith, Allison M. Rice, Brandon J. Yarbrough, Preecha Kittikhunnatham, Abijai Mathur, Nicholas A. Morris, Megan J. Francis, Anna A. Berseneva, Poonam Dhull, Richard D. Adams, M. Victoria Bobo, Aaron A. Vannucci, Mark D. Smith, Sophya Garashchuk, Natalia B. Shustova
Faculty Publications
Unprecedented one-step CC bond cleavage leading to opening of the buckybowl (π-bowl), that could provide access to carbon-rich structures with previously inaccessible topologies, is reported; highlighting the possibility to implement drastically different synthetic routes to π-bowls in contrast to conventional ones applied for polycyclic aromatic hydrocarbons. Through theoretical modeling, we evaluated the mechanistic pathways feasible for π-bowl planarization and factors that could affect such a transformation including strain and released energies. Through employment of Marcus theory, optical spectroscopy, and crystallographic analysis, we estimated the possibility of charge transfer and electron coupling between “open” corannulene and a strong electron acceptor such …
A Hybrid Method For Auralizing Vibroacoustic Systems And Evaluating Audio Fidelity/Sound Quality Using Machine Learning, Andrew Jared Miller
A Hybrid Method For Auralizing Vibroacoustic Systems And Evaluating Audio Fidelity/Sound Quality Using Machine Learning, Andrew Jared Miller
Theses and Dissertations
Two separate methods are presented to aid in the creation and evaluation of acoustic simulations. The first is a hybrid method that allows separate low and high-frequency acoustic responses to be combined into a single broadband response suitable for auralization. The process consists of four steps: 1) creating separate low-frequency and high-frequency responses of the system of interest, 2) interpolating between the two responses to get a single broadband magnitude response, 3) adding amplitude modulation to the high-frequency portion of the response, and 4) calculating approximate phase information. An experimental setup is used to validate the hybrid method. Listening tests …
Optimal Harvest Time For Medicago Ruthenica Seed, Jiyun Yang, Daowei Zhou
Optimal Harvest Time For Medicago Ruthenica Seed, Jiyun Yang, Daowei Zhou
IGC Proceedings (1993-2023)
No abstract provided.
Evaluation Of Seed And Forage Yield Of Lathyrus Sativus L. In China And Ethiopia, Y. P. Wu, Yanrong Wang, J. Hanson, Z. B. Nan
Evaluation Of Seed And Forage Yield Of Lathyrus Sativus L. In China And Ethiopia, Y. P. Wu, Yanrong Wang, J. Hanson, Z. B. Nan
IGC Proceedings (1993-2023)
No abstract provided.
Getting Over It, Thomas Kade, Kevorc Ibrahimian, Max Simpson
Getting Over It, Thomas Kade, Kevorc Ibrahimian, Max Simpson
Arts & Sciences Student Symposium
The research extended a 2D motion planning system to three dimensional environments. The updated system is now able to plan the motion for robots over 3D terrains modeled by polyhedrons.
The School Mathematics Study Group: Lessons In Mathematics Education, Madeline Polhill
The School Mathematics Study Group: Lessons In Mathematics Education, Madeline Polhill
Arts & Sciences Student Symposium
This work argues that the "new math" project called the School Mathematics Study Group offers a valuable case study for mathematics educators seeking to venture into the future better informed about both the successes and failures of previous projects. Understanding this project requires recognizing that the School Mathematics Study Group was wholly a product of the forces—personal, educational, mathematical, and political—that shaped it. Admittedly, some of the SMSG's shortcomings resulted from its members' lack of understanding of the changes needed in mathematics education. Still, the majority of the SMSG's public vilification resulted through no fault of its own, but rather …
The Impact Of Temperature On Seed Germination In Diverse Accessions Of 4 Wild Vigna Species, Yanrong Wang, J. Hanson
The Impact Of Temperature On Seed Germination In Diverse Accessions Of 4 Wild Vigna Species, Yanrong Wang, J. Hanson
IGC Proceedings (1993-2023)
No abstract provided.
Molecular Markers For Classification Of Seed Collections Of Lolium Cultivars, Maragret Wallace, J. Provan, Trevor J. Gilliland
Molecular Markers For Classification Of Seed Collections Of Lolium Cultivars, Maragret Wallace, J. Provan, Trevor J. Gilliland
IGC Proceedings (1993-2023)
No abstract provided.
Lecture 07: Nonlinear Preconditioning Methods And Applications, Xiao-Chuan Cai
Lecture 07: Nonlinear Preconditioning Methods And Applications, Xiao-Chuan Cai
Mathematical Sciences Spring Lecture Series
We consider solving system of nonlinear algebraic equations arising from the discretization of partial differential equations. Inexact Newton is a popular technique for such problems. When the nonlinearities in the system are well-balanced, Newton's method works well, but when a small number of nonlinear functions in the system are much more nonlinear than the others, Newton may converge slowly or even stagnate. In such a situation, we introduce some nonlinear preconditioners to balance the nonlinearities in the system. The preconditioners are often constructed using a combination of some domain decomposition methods and nonlinear elimination methods. For the nonlinearly preconditioned problem, …
Moderate Grazer Density Stabilizes Forage Availability More Than Patch Burning In Low-Stature Grassland, Edward J. Raynor, Devan Allen Mcgranahan, James R. Miller, Diane M. Debinski, Walter H. Schacht, David M. Engle
Moderate Grazer Density Stabilizes Forage Availability More Than Patch Burning In Low-Stature Grassland, Edward J. Raynor, Devan Allen Mcgranahan, James R. Miller, Diane M. Debinski, Walter H. Schacht, David M. Engle
School of Natural Resources: Faculty Publications
Spatially patchy fire creates landscape-level diversity that in turn stabilizes several rangeland ecosystem services, including forage production and habitat availability. To enhance biodiversity and livestock production, efforts are underway to restore fire regimes in rangelands throughout the Great Plains. However, invasive species such as tall fescue Schedonorus arundinaceus syn. Festuca arundinacea, initially introduced for forage production, hamper prescribed fire use. Grazer density, or stocking rate, modulates the effect of patchy fire regimes on ecological patterns in invaded, seminatural rangeland pastures. We compare three diversity–stability responses—temporal variability in aboveground plant biomass, portfolio effects among plant functional groups, and beta diversity in …
Reliable Iterative Method For Solving Volterra -Fredholm Integro Differential Equations, Samaher M. Yassein
Reliable Iterative Method For Solving Volterra -Fredholm Integro Differential Equations, Samaher M. Yassein
Al-Qadisiyah Journal of Pure Science
The aim of this paper, a reliable iterative method is presented for resolving many types of Volterra - Fredholm Integro - Differential Equations of the second kind with initial conditions. The series solutions of the problems under consideration are obtained by means of the iterative method. Four various problems are resolved with high accuracy to make evident the enforcement of the iterative method on such type of integro differential equations. Results were compared with the exact solution which exhibit that this technique has compatible with the right solutions, simple, effective and easy for solving such problems. To evaluate the results …
An Efficient Technique For Solving Bratu Type Equation Via Wavelet Orthonormal Boubakerpolynomials, Eman Hassan Ouda
An Efficient Technique For Solving Bratu Type Equation Via Wavelet Orthonormal Boubakerpolynomials, Eman Hassan Ouda
Al-Qadisiyah Journal of Pure Science
The aim of this research is to show the applicability of new truncated orthonormal Boubaker wavelet polynomials (OBWP's) for solving one dimensional Bratu-type equation with numerically by the aid of iteration technique. Some numerical examples were added to show the ability of this kind of polynomials comparing with exact results using Matlab. Also illustrating graphs were added to verify the efficiency of the method.