Relevant bibliographies by topics / Perfect numbers

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Perfect numbers'

Author: Grafiati
Published: 4 June 2021
Last updated: 25 July 2025

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Journal articles on the topic "Perfect numbers"

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Ausubel, Ramona. "Perfect Numbers." Ploughshares 50, no. 2 (2024): 32–46. http://dx.doi.org/10.1353/plo.2024.a932313.

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Abstract: The Summer 2024 Issue. Ploughshares is an award-winning journal of new writing. Since 1971, Ploughshares has discovered and cultivated the freshest voices in contemporary American literature, and now provides readers with thoughtful and entertaining literature in a variety of formats. Find out why the New York Times named Ploughshares “the Triton among minnows.” The Summer 2024 Issue, guest-edited by Rebecca Makkai, features prose by Dur e Aziz Amna, Ramona Ausubel, Peter Mountford, Khaddafina Mbabazi, DK Nnuro, and more.
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Hassler, Uwe. "Perfect Numbers." Euleriana 3, no. 2 (2023): 176–85. http://dx.doi.org/10.56031/2693-9908.1052.

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Holdener, Judy, and Emily Rachfal. "Perfect and Deficient Perfect Numbers." American Mathematical Monthly 126, no. 6 (2019): 541–46. http://dx.doi.org/10.1080/00029890.2019.1584515.

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Fu, Ruiqin, Hai Yang, and Jing Wu. "The Perfect Numbers of Pell Number." Journal of Physics: Conference Series 1237 (June 2019): 022041. http://dx.doi.org/10.1088/1742-6596/1237/2/022041.

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Pollack, Paul, and Vladimir Shevelev. "On perfect and near-perfect numbers." Journal of Number Theory 132, no. 12 (2012): 3037–46. http://dx.doi.org/10.1016/j.jnt.2012.06.008.

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Panda, G. K., and Ravi Kumar Davala. "Perfect Balancing Numbers." Fibonacci Quarterly 53, no. 3 (2015): 261–64. http://dx.doi.org/10.1080/00150517.2015.12428268.

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Heath-Brown, D. R. "Odd perfect numbers." Mathematical Proceedings of the Cambridge Philosophical Society 115, no. 2 (1994): 191–96. http://dx.doi.org/10.1017/s0305004100072030.

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It is not known whether or not odd perfect numbers can exist. However it is known that there is no such number below 10300 (see Brent[1]). Moreover it has been proved by Hagis[4]and Chein[2] independently that an odd perfect number must have at least 8 prime factors. In fact results of this latter type can in priniciple be obtained solely by calculation, in view of the result of Pomerance[6] who showed that if N is an odd perfect number with at most k prime factors, thenPomerance's work was preceded by a theorem of Dickson[3]showing that there can be only a finite number of such N. Clearly how
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Klurman, Oleksiy. "Radical of perfect numbers and perfect numbers among polynomial values." International Journal of Number Theory 12, no. 03 (2016): 585–91. http://dx.doi.org/10.1142/s1793042116500378.

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It is conjectured that [Formula: see text] for any perfect number [Formula: see text]. We prove that [Formula: see text] improving the previous bound of Luca and Pomerance as well as Acquaah and Konyagin. As a consequence, we prove that assuming the [Formula: see text]-conjecture, any integer polynomial of degree [Formula: see text] without repeated factors can take only finitely many perfect values. We also show that the latter holds unconditionally for even perfect numbers.
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Tang, Min, Xiao-Zhi Ren, and Meng Li. "On near-perfect and deficient-perfect numbers." Colloquium Mathematicum 133, no. 2 (2013): 221–26. http://dx.doi.org/10.4064/cm133-2-8.

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J. J., Segura, and Ortega S. "All KnownPerfect Numbers other than 6 Satisfy N=4+6n." international journal of mathematics and computer research 12, no. 03 (2024): 4103–6. http://dx.doi.org/10.47191/ijmcr/v12i3.04.

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For all 51 known perfect numbers ranging from (p=2 to p= 82589933) and with the only exception of N=6, all perfect numbers belong to the group of natural numbers formed by N=4+6n. If this observation can be proven valid for all existing even perfect numbers, that would automatically exclude 2/3 of all even numbers out of the possibility of being perfect. If this can be proven a necessary condition for all perfect numbers, then it would rule out the possibility of having any odd perfect numbers.
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Dissertations / Theses on the topic "Perfect numbers"

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Yamada, Tomohiro. "Unitary super perfect numbers." 京都大学 (Kyoto University), 2009. http://hdl.handle.net/2433/124385.

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Abu-Arish, Hiba Ibrahim. "Perfect Numbers and Perfect Polynomials: Motivating Concepts From Kindergarten to College." The Ohio State University, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=osu1461154144.

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Kolenick, Joseph F. "On exponentially perfect numbers relatively prime to 15 /." Connect to resource online, 2007. http://rave.ohiolink.edu/etdc/view?acc_num=ysu1196698780.

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Kolenick, Joseph F. Jr. "On Exponentially Perfect Numbers Relatively Prime to 15." Youngstown State University / OhioLINK, 2007. http://rave.ohiolink.edu/etdc/view?acc_num=ysu1196698780.

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Sutharzan, Sreeskandarajan. "A GENOME-WIDE ANALYSIS OF PERFECT INVERTED REPEATS IN ARABIDOPSIS THALIANA." Miami University / OhioLINK, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=miami1386848607.

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Janse, Sarah A. "INFERENCE USING BHATTACHARYYA DISTANCE TO MODEL INTERACTION EFFECTS WHEN THE NUMBER OF PREDICTORS FAR EXCEEDS THE SAMPLE SIZE." UKnowledge, 2017. https://uknowledge.uky.edu/statistics_etds/30.

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In recent years, statistical analyses, algorithms, and modeling of big data have been constrained due to computational complexity. Further, the added complexity of relationships among response and explanatory variables, such as higher-order interaction effects, make identifying predictors using standard statistical techniques difficult. These difficulties are only exacerbated in the case of small sample sizes in some studies. Recent analyses have targeted the identification of interaction effects in big data, but the development of methods to identify higher-order interaction effects has been
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Benchetrit, Yohann. "Propriétés géométriques du nombre chromatique : polyèdres, structures et algorithmes." Thesis, Université Grenoble Alpes (ComUE), 2015. http://www.theses.fr/2015GREAM049/document.

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Le calcul du nombre chromatique et la détermination d'une colo- ration optimale des sommets d'un graphe sont des problèmes NP- difficiles en général. Ils peuvent cependant être résolus en temps po- lynomial dans les graphes parfaits. Par ailleurs, la perfection d'un graphe peut être décidée efficacement. Les graphes parfaits sont caractérisés par la structure de leur poly- tope des stables : les facettes non-triviales sont définies exclusivement par des inégalités de cliques. Réciproquement, une structure similaire des facettes du polytope des stables détermine-t-elle des propriétés combinatoi
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Spa, Carvajal Carlos. "Time-domain numerical methods in room acoustics simulations." Doctoral thesis, Universitat Pompeu Fabra, 2009. http://hdl.handle.net/10803/7565.

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L'acústica de sales s'encarrega de l'estudi del comportament de les ones sonores en espais tancats.La informació acústica de qualsevol entorn, coneguda com la resposta impulsional, pot ser expressada en termes del camp acústic com una funció de l'espai i el temps. En general, és impossible obtenir solucions analítiques de funcions resposta en habitacions reals. Per tant, en aquests últims anys, l'ús d'ordinadors per resoldre aquest tipus de problemes ha emergit com una solució adecuada per calcular respostes impulsionals.<br/>En aquesta Tesi hem centrat el nostre anàlisis en els mètodes basat
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"Algorithms in the study of multiperfect and odd perfect numbers." Thesis, University of Technology, Sydney. Department of Mathematical Sciences, 2003. http://hdl.handle.net/10453/20034.

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University of Technology, Sydney. Department of Mathematical Sciences.<br>A long standing unanswered question in number theory concerns the existence (or not) of odd perfect numbers. Over time many properties of an odd perfect number have been established and refined. The initial goal of this research was to improve the lower bound on the number of distinct prime factors of an odd perfect number, if one exists, to at least 9. Previous approaches to this problem involved the analysis of a carefully chosen set of special cases with each then being eliminated by a contradiction. This thesis a
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"Algorithms in the Study of Multiperfect and Odd Perfect Numbers." University of Technology, Sydney. Department of Mathematical Sciences, 2003. http://hdl.handle.net/2100/275.

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A long standing unanswered question in number theory concerns the existence (or not) of odd perfect numbers. Over time many properties of an odd perfect number have been established and refined. The initial goal of this research was to improve the lower bound on the number of distinct prime factors of an odd perfect number, if one exists, to at least 9. Previous approaches to this problem involved the analysis of a carefully chosen set of special cases with each then being eliminated by a contradiction. This thesis applies an algorithmic, factor chain approach to the problem. The implementatio
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Books on the topic "Perfect numbers"

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R, Jorge Emilio Molina. La tetraléctica de los números perfectos. Producciones CIMA, 1999.

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Rivero, Jorge Emilio Molina. La tetraléctica de los números perfectos. Producciones CIMA, 1999.

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Julia, Line, ed. The book of love numbers: Use your love number to discover your perfect partner. Aquarian Press, 1986.

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Coppa, Max. Does your love life add up?: How to use numbers to find your perfect relationship. Jeremy P. Tarcher/Penguin, 2009.

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Moraes, Augusto C. M. Compressible laminar boundary layers for perfect and real gases in equilibrium at Mach numbers to 30. American Institute of Aeronautics and Astronautics, 1992.

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Perfect, Amicable and Sociable Numbers: A Computational Approach. World Scientific Publishing Co Pte Ltd, 1996.

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Perfect, amicable, and sociable numbers: A computational approach. World Scientific, 1996.

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Perfect, Amicable and Sociable Numbers: A Computational Approach. World Scientific Publishing Co Pte Ltd, 1996.

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Deza, Elena. Perfect and Amicable Numbers. World Scientific Publishing Co Pte Ltd, 2022.

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Cai, Tianxin. Perfect Numbers and Fibonacci Sequences. World Scientific Publishing Co Pte Ltd, 2022.

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Book chapters on the topic "Perfect numbers"

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Hunacek, Mark. "Perfect Numbers." In Introduction to Number Theory. Chapman and Hall/CRC, 2023. http://dx.doi.org/10.1201/9781003318712-5.

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Anglin, W. S., and J. Lambek. "Perfect Numbers." In The Heritage of Thales. Springer New York, 1995. http://dx.doi.org/10.1007/978-1-4612-0803-7_9.

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Rassias, Michael Th. "Perfect numbers, Fermat numbers." In Problem-Solving and Selected Topics in Number Theory. Springer New York, 2010. http://dx.doi.org/10.1007/978-1-4419-0495-9_3.

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Gupta, Shyam Sunder. "Perfect, Multiply Perfect, and Sociable Numbers." In Springer Praxis Books. Springer Nature Singapore, 2025. https://doi.org/10.1007/978-981-97-2465-9_6.

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Bressoud, David M. "Primes and Perfect Numbers." In Factorization and Primality Testing. Springer New York, 1989. http://dx.doi.org/10.1007/978-1-4612-4544-5_2.

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Solov’eva, Faina I. "Switchings and Perfect Codes." In Numbers, Information and Complexity. Springer US, 2000. http://dx.doi.org/10.1007/978-1-4757-6048-4_25.

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Cook, R. "Bounds for odd perfect numbers." In CRM Proceedings and Lecture Notes. American Mathematical Society, 1999. http://dx.doi.org/10.1090/crmp/019/07.

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Jeba S, Flora, Anirban Roy, and Manjil P. Saikia. "On k-Facile Perfect Numbers." In Springer Proceedings in Mathematics & Statistics. Springer Nature Singapore, 2025. https://doi.org/10.1007/978-981-97-6798-4_9.

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Allen, G. Donald. "Primes, Perfect Numbers and Magic Numbers (Just for Fun)." In Pedagogy and Content in Middle and High School Mathematics. SensePublishers, 2017. http://dx.doi.org/10.1007/978-94-6351-137-7_7.

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Sándor, J., and B. Crstici. "Perfect numbers: Old and new issues; perspectives." In Handbook of Number Theory II. Springer Netherlands, 2004. http://dx.doi.org/10.1007/1-4020-2547-5_1.

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Conference papers on the topic "Perfect numbers"

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Boancă, Sara. "Pseudorandom Number Generators, Perfect Learning and Model Visualization with Neural Networks: Expanding on LFSRs and Geffe." In 10th International Conference on Internet of Things, Big Data and Security. SCITEPRESS - Science and Technology Publications, 2025. https://doi.org/10.5220/0013298500003944.

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Eisenhauer, Nicci. "Industrial Marketing & Sales in a Digital Age." In SSPC 2012 Greencoat. SSPC, 2012. https://doi.org/10.5006/s2012-00012.

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Abstract The participation of sales, technical and marketing personnel in the development and implementation of an internet-based communications strategy that represents the company’s expertise in the format of education and information-sharing via various web-based tools will yield brand awareness, brand credibility and brand loyalty, while potentially shortening sales cycles. Using a balanced mix of traditional marketing tactics employed more effectively to drive traffic to informational venues such as blogs, forums and the corporate website for information in the spirit of furthering the in
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Irmak, Nurettin, and Abdullah Açikel. "On perfect numbers close to Tribonacci numbers." In 1ST INTERNATIONAL CONFERENCE ON MATHEMATICAL AND RELATED SCIENCES (ICMRS 2018). Author(s), 2018. http://dx.doi.org/10.1063/1.5047878.

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Savarimuthu, Sabeenian Royappan, Kalaiselvi Cinnu Muthuraji, and Paramasivam Muthan Eswaran. "Square root for perfect square numbers using Vedic mathematics." In 24TH TOPICAL CONFERENCE ON RADIO-FREQUENCY POWER IN PLASMAS. AIP Publishing, 2023. http://dx.doi.org/10.1063/5.0164287.

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Rathore, Tejmal. "Arranging Integer Numbers on a Loop Such That the Sum of any Two Adjacent Numbers Is a Perfect Square." In 2022 IEEE Region 10 Symposium (TENSYMP). IEEE, 2022. http://dx.doi.org/10.1109/tensymp54529.2022.9864484.

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Lohmann, A., W. Stork, and G. Stucke. "Optical Implementation of the Perfect Shuffle." In Optical Computing. Optica Publishing Group, 1985. http://dx.doi.org/10.1364/optcomp.1985.wa3.

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The "perfect shuffle" (PS) is a well-known concept for global interconnection networks in parallel computers. It performs a certain permutation of N = 2k elements. Fig. 1 shows two different graphical representations of the PS-operation. In Fig. 1a the actual pathways of the N elements in one PS-step are drawn. If the addresses (positions) of the elements are represented by binary numbers, ranging from 0 to N-1, it is apparent that the PS can be described as a cyclical rotation (to the left) of the address bits (Fig. 1b).
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aus der Wiesche, Stefan, Felix Reinker, Robert Wagner, Leander Hake, and Max Passmann. "Critical and Choking Mach Numbers for Organic Vapor Flows Through Turbine Cascades." In ASME Turbo Expo 2021: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2021. http://dx.doi.org/10.1115/gt2021-59013.

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Abstract Results are presented of a theoretical and experimental study dealing with critical and choking Mach numbers of organic vapor flows through turbine cascades. A correlation was derived for predicting choking Mach numbers for organic vapor flows using an asymptotic series expansion valid for isentropic exponents close to unity. The theoretical prediction was tested employing a linear turbine cascade and a circular cylinder in a closed-loop organic vapor wind tunnel. The cascade was based on a classical transonic turbine airfoil for which perfect gas literature data were available. The c
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Wan, Lingxiao, Huihui Zhu, Bo Wang, Hui Zhang, Leong Chuan Kwek, and Ai Qun Liu. "A Boson Sampling Chip for Graph Perfect Matching." In CLEO: QELS_Fundamental Science. Optica Publishing Group, 2022. http://dx.doi.org/10.1364/cleo_qels.2022.ff2i.6.

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We map the perfect matching problem in graph theory to a reconfigurable GBS model with the connection of the Hafnian of a matrix. We configure the linear optical circuit and squeeze parameter of the GBS model according to the decomposed unitary matrix and diagonal matrix of the graph’s adjacency matrix. The perfect matching numbers can be directly acquired from the 4-photon coincidence counts with a distribution similarity of 0.9304.
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MORAES, AUGUSTO, JOSEPH FLAHERTY, and HENRY NAGAMATSU. "Compressible laminar boundary layers for perfect and real gases in equilibrium at Mach numbers to 30." In 30th Aerospace Sciences Meeting and Exhibit. American Institute of Aeronautics and Astronautics, 1992. http://dx.doi.org/10.2514/6.1992-757.

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Shade, Gary F., and Bhanu Sood. "The “Perfect Storm” Now Appearing in FA Labs Everywhere." In ISTFA 2011. ASM International, 2011. http://dx.doi.org/10.31399/asm.cp.istfa2011p0446.

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Abstract The International Symposium for Testing and Failure Analysis (ISTFA) 2010 event added a focus topic on Counterfeiting in Electronics. This topic was chosen because of the emergence of this concern and the critical role that Failure Analysis plays in this challenge. Failure Analysts will be involved deeply as companies worldwide are attempting to reduce the impact of increasing numbers of counterfeit products in the supply line and in fielded products. This paper will attempt to provide an overview of the topic and support the contributors to ISTFA 2010 while providing additional resou
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Reports on the topic "Perfect numbers"

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Gates, Allison, Michelle Gates, Shannon Sim, Sarah A. Elliott, Jennifer Pillay, and Lisa Hartling. Creating Efficiencies in the Extraction of Data From Randomized Trials: A Prospective Evaluation of a Machine Learning and Text Mining Tool. Agency for Healthcare Research and Quality (AHRQ), 2021. http://dx.doi.org/10.23970/ahrqepcmethodscreatingefficiencies.

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Background. Machine learning tools that semi-automate data extraction may create efficiencies in systematic review production. We prospectively evaluated an online machine learning and text mining tool’s ability to (a) automatically extract data elements from randomized trials, and (b) save time compared with manual extraction and verification. Methods. For 75 randomized trials published in 2017, we manually extracted and verified data for 21 unique data elements. We uploaded the randomized trials to ExaCT, an online machine learning and text mining tool, and quantified performance by evaluati
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Cheng, Peng, James V. Krogmeier, Mark R. Bell, Joshua Li, and Guangwei Yang. Detection and Classification of Concrete Patches by Integrating GPR and Surface Imaging. Purdue University, 2021. http://dx.doi.org/10.5703/1288284317320.

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This research considers the detection, location, and classification of patches in concrete and asphalt-on-concrete pavements using data taken from ground penetrating radar (GPR) and the WayLink 3D Imaging System. In particular, the project seeks to develop a patching table for “inverted-T” patches. A number of deep neural net methods were investigated for patch detection from 3D elevation and image observation, but the success was inconclusive, partly because of a dearth of training data. Later, a method based on thresholding IRI values computed on a 12-foot window was used to localize pavemen
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Cheng, Peng, James V. Krogmeier, Mark R. Bell, Joshua Li, and Guangwei Yang. Detection and Classification of Concrete Patches by Integrating GPR and Surface Imaging. Purdue University, 2021. http://dx.doi.org/10.5703/1288284317320.

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This research considers the detection, location, and classification of patches in concrete and asphalt-on-concrete pavements using data taken from ground penetrating radar (GPR) and the WayLink 3D Imaging System. In particular, the project seeks to develop a patching table for “inverted-T” patches. A number of deep neural net methods were investigated for patch detection from 3D elevation and image observation, but the success was inconclusive, partly because of a dearth of training data. Later, a method based on thresholding IRI values computed on a 12-foot window was used to localize pavemen
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Tang, Jiqin, Gong Zhang, Jinxiao Xing, Ying Yu, and Tao Han. Network Meta-analysis of Heat-clearing and Detoxifying Oral Liquid of Chinese Medicines in Treatment of Children’s Hand-foot-mouth Disease：a protocol for systematic review. INPLASY - International Platform of Registered Systematic Review and Meta-analysis Protocols, 2022. http://dx.doi.org/10.37766/inplasy2022.1.0032.

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Review question / Objective: The type of study was clinical randomized controlled trial (RCT). The object of study is the patients with HFMD. There is no limit to gender and race. In the case of clear diagnosis standard, curative effect judgment standard and consistent baseline treatment, the experimental group was treated with pure oral liquid of traditional Chinese medicine(A: Fuganlin oral liquid, B: huangzhihua oral liquid, C: Lanqin oral liquid, D: antiviral oral liquid, E: Huangqin oral liquid, F: Pudilan oral liquid, G: Shuanghuanglian oral liquid.)and the control group was treated with
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Israel, Alvaro, and John Merrill. Production of Seed Stocks for Sustainable Tank Cultivation of the Red Edible Seaweed Porphyra. United States Department of Agriculture, 2006. http://dx.doi.org/10.32747/2006.7696527.bard.

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Porphyra species (commonly known as ‘nori’ or ‘purple laver’) are edible red seaweeds rich in proteins, vitamins and other highly valued biogenic compounds. For years Porphyra has been cultured using seeded nets extended in the open sea, and its biomass consumed primarily in the Far East. While demands for international markets have increased steadily at an average of 20% per year, supplies are on the verge and not expected to meet future demands. Alternatively, land-based cultivation of seaweed has become attractive in the mariculture industry since (1) important growth parameters can be cont
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