Relevant bibliographies by topics / Numeration system

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

Academic literature on the topic 'Numeration system'

Author: Grafiati
Published: 8 June 2024
Last updated: 31 July 2025

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Journal articles on the topic "Numeration system"

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BELL, JASON, EMILIE CHARLIER, AVIEZRI S. FRAENKEL, and MICHEL RIGO. "A DECISION PROBLEM FOR ULTIMATELY PERIODIC SETS IN NONSTANDARD NUMERATION SYSTEMS." International Journal of Algebra and Computation 19, no. 06 (2009): 809–39. http://dx.doi.org/10.1142/s0218196709005330.

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Consider a nonstandard numeration system like the one built over the Fibonacci sequence where nonnegative integers are represented by words over {0,1} without two consecutive 1. Given a set X of integers such that the language of their greedy representations in this system is accepted by a finite automaton, we consider the problem of deciding whether or not X is a finite union of arithmetic progressions. We obtain a decision procedure for this problem, under some hypothesis about the considered numeration system. In a second part, we obtain an analogous decision result for a particular class o
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Uy, Frederick L. "The Chinese Numeration System and Place Value." Teaching Children Mathematics 9, no. 5 (2003): 243–47. http://dx.doi.org/10.5951/tcm.9.5.0243.

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Ichi, ni, san … Otu, abuo, ato… Eins, zwei, drei … Have you heard these words before? What might they mean? In case you are not familiar with these words, they mean “One, two, three…” in Japanese, Igbo, and German, respectively.
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BIAGUI, Noël Bernard. "La numération cardinale en créole casamançais : Emplois morphosyntaxiques et système de comptage de l’argent." ALTRALANG Journal 5, no. 01 (2023): 128–51. http://dx.doi.org/10.52919/altralang.v5i01.266.

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The Cardinal Numeration in Casamance Creole: Morphosyntactic Uses and Money Counting System 
 ABSTRACT: Even if more than 50% of its lexicon comes from Portuguese, the Casamance Creole is now an autonomous linguistic system. This autonomy is also manifested in the field of numeration. Like many African languages, the numeration of Casamance Creole is based on an oral basis due to the absence of writing. The presentation of the numeral system, of which we will make case, will be limited only to the presentation of the cardinal numbers and counting numeration. This study is part of the prob
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Bóka, Dávid, Péter Burcsi, and Orsolya Ignéczi. "Numeration systems defined by addition rules." Annales Universitatis Scientiarum Budapestinensis de Rolando Eötvös Nominatae. Sectio computatorica, no. 54 (2023): 105–24. https://doi.org/10.71352/ac.54.105.

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We investigate the problem of reconstructing polynomial-based ternary number systems when the expansion of certain elements — the pairwise sums of digits — is given. We call these expansions the “addition rules” for the system. We define a randomized process for expanding arbitrary elements based on these addition rules. For some rules, the expansion is not-well defined. We search for addition rules below a certain length that yield well-defined expansion for all elements, which we call the uniqueness property. We also give algorithms for the reconstruction of the base polynomial and the digit
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Sekido, Hiroto, and Masashi Iwasaki. "Integer representations in numeration system with Fibonacci squares." Research in Mathematics 9, no. 1 (2022): 1–5. http://dx.doi.org/10.1080/27684830.2022.2069647.

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Charlier, Émilie, Marion Le Gonidec, and Michel Rigo. "Representing real numbers in a generalized numeration system." Journal of Computer and System Sciences 77, no. 4 (2011): 743–59. http://dx.doi.org/10.1016/j.jcss.2010.07.002.

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Sirvent, Víctor F. "Integer Semigroups Associated with Dumont-Thomas Numeration Systems." ISRN Combinatorics 2014 (January 23, 2014): 1–5. http://dx.doi.org/10.1155/2014/275260.

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Given a primitive substitution, we define different binary operations on infinite subsets of the nonnegative integers. These binary operations are defined with the help of the Dumont-Thomas numeration system; that is, a numeration system associated with the substitution. We give conditions for these semigroups to have an identity element. We show that they are not finitely generated. These semigroups define actions on the set of positive integers. We describe the orbits of these actions. We also estimate the density of these sets as subsets of the positive integers.
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Walmsley, Angela L. E. "Math Roots: Understanding Aztec and Mayan Numeration Systems." Mathematics Teaching in the Middle School 12, no. 1 (2006): 55–62. http://dx.doi.org/10.5951/mtms.12.1.0055.

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Numbers have been recorded in a variety of ways throughout time. For example, the Babylonians used marks pressed in clay; the Egyptians used papyrus and ink brushes to create tally marks; and the Maya introduced a symbol for zero (Billstein, Libeskind, and Lott 2001). All these ancient peoples used numerals, or written symbols, to express what they meant mathematically. They created their own numeration system, which is a collection of uniform symbols and properties to express numbers systematically. The Hindu- Arabic system is one such numeration method; however, understanding others can reve
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Overbay, Shannon R., and Mary Jean Brod. "Magic with Mayan Math." Mathematics Teaching in the Middle School 12, no. 6 (2007): 340–47. http://dx.doi.org/10.5951/mtms.12.6.0340.

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The ancient Mayan system of numeration is quite sophisticated, yet the basics are beautifully simple. It is an appealing system to teach to students of almost any age. Mayan numerals are composed of only three symbols, but with the power of place value and a symbol for zero, large numbers can be concisely written. With their interest in astronomy and the passage of time, the Maya (located in what is now Central America and Southern Mexico) developed accurate calendars using this numeration system. Mayan merchants often used cacao beans in making computations to keep track of their business tra
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JUSTIN, JACQUES, and GIUSEPPE PIRILLO. "EPISTURMIAN WORDS: SHIFTS, MORPHISMS AND NUMERATION SYSTEMS." International Journal of Foundations of Computer Science 15, no. 02 (2004): 329–48. http://dx.doi.org/10.1142/s0129054104002455.

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Episturmian words, which include the Arnoux-Rauzy sequences, are infinite words on a finite alphabet generalizing the Sturmian words and sharing many of their same properties. This was studied in previous papers. Here we gain a deeper insight into these properties. This leads in particular to consider numerations systems similar to the Ostrowski ones and to give a matrix formula for computing the number of representations of an integer in such a system. We also obtain a complete answer to the question: if an episturmian word is morphic, which shifts of it, if any, also are morphic ?
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Dissertations / Theses on the topic "Numeration system"

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Edson, Marcia Ruth Zamboni Luca Quardo. "Around the Fibonacci numeration system." [Denton, Tex.] : University of North Texas, 2007. http://digital.library.unt.edu/permalink/meta-dc-3676.

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Edson, Marcia Ruth. "Around the Fibonacci Numeration System." Thesis, University of North Texas, 2007. https://digital.library.unt.edu/ark:/67531/metadc3676/.

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Let 1, 2, 3, 5, 8, … denote the Fibonacci sequence beginning with 1 and 2, and then setting each subsequent number to the sum of the two previous ones. Every positive integer n can be expressed as a sum of distinct Fibonacci numbers in one or more ways. Setting R(n) to be the number of ways n can be written as a sum of distinct Fibonacci numbers, we exhibit certain regularity properties of R(n), one of which is connected to the Euler φ-function. In addition, using a theorem of Fine and Wilf, we give a formula for R(n) in terms of binomial coefficients modulo two.
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Morello, Gabriela Munhoz. "INFLUENCE OF FAN OPERATION ON FAN ASSESSMENT NUMERATION SYSTEM (FANS) TEST RESULTS." UKnowledge, 2011. http://uknowledge.uky.edu/gradschool_theses/153.

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The use of velocity traverses to measure in-situ air flow rate of ventilation fans can be subject to significant errors. The Fan Assessment Numeration System (FANS) was developed by the USD-ARS Southern Poultry Research Laboratory and refined at the University of Kentucky to measure air flow of fans in-situ. The procedures for using the FANS unit to test fans in-situ are not completely standardized. This study evaluated the effect of operating fan positions relative to the FANS unit for ten 1.22 m diameter fans in two types of poultry barns, with fans placed immediately next to each other and
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Lopes, Igor Moreira. "EVALUATION OF TRANSITIONS FOR TESTING AGRICULTURAL VENTILATION FANS WITH THE FAN ASSESSMENT NUMERATION SYSTEM (FANS)." UKnowledge, 2012. http://uknowledge.uky.edu/bae_etds/8.

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The Fan Assessment Numeration System (FANS) is an improved air velocity traverse method for measuring in situ fan performance. The FANS has been widely used, but variations of its test procedure are commonly employed to accommodate physical or operational barriers encountered in the field. This laboratory study evaluated the use of transitions to connect a 1.37m FANS unit to two smaller fans (1.22m and 0.91m diameter) and one 1.37m diameter fan. Tests were conducted with the FANS unit positioned on both intake and discharge sides of the fans. Three different transition angles (30o, 45o and 60o
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范世鳴 and Sai-ming Fan. "On m-arrays and M-arrays." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1986. http://hub.hku.hk/bib/B31207248.

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Montalvo, Luis Anibal. "Systèmes de numération pour la conception de diviseurs rapides." Grenoble INPG, 1995. http://www.theses.fr/1995INPG0045.

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Le but de cette these est de developper un algorithme de division en virgule fixe, efficace, oriente implantation materielle, pour operer sur des mantisses normalisees d'apres la norme des operations arithmetiques en virgule flottante ieee-754. L'efficacite de cet algorithme est due a l'utilisation d'une addition/soustraction hybride et d'une fonction de choix du quotient tres simple. L'addition/soustraction hybride s'effectue sans propagation de retenue et donc elle est rapide. Le choix du chiffre du quotient est realise en deux pas. Dans le premier pas, sous certaines conditions, les deux ch
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Nguema, Ndong Florent. "Étude de la dynamique symbolique des développements en base négative, système de Lyndon." Thesis, Poitiers, 2013. http://www.theses.fr/2013POIT2276/document.

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Ce travail est consacré à l'étude de systèmes de Lyndon (pour la relation d'ordre alterné) et àla dynamique symbolique des développements des nombres en base négative. Pour un réel ß > 1fixé, nous construisons un code préfixe récurrent positif permettant non seulement de montrerl'intrinsèque ergodicité du —ß-shift mais aussi de déterminer la fonction zêta qui lui est associée.Nous étudions les conditions pour lesquelles le —ß-shift possède la spécification.En outre, lorsque ß est strictement plus petit que le nombre d'or, le langage du —ß-shift admet desmots intransitifs. Cet état de fait e
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Hollander, Michael Israel. "Linear numeration systems, finite beta expansions, and discrete spectrum of substitution dynamical systems /." Thesis, Connect to this title online; UW restricted, 1996. http://hdl.handle.net/1773/5747.

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Eraso, Natalia. "Gramática tanimuka, una lengua de la Amazonía colombiana." Thesis, Lyon 2, 2015. http://www.theses.fr/2015LYO20076/document.

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Cette grammaire du tanimuka, langue tucano d’Amazonie colombienne, s’organise en quatre parties. La première partie, ‘le tanimuka : la langue et ses locuteurs’, est divisée en trois chapitres (1 à 3), qui établissent le profil sociolinguistique de la langue, et décrivent les conditions d’enquête de terrain. La deuxième partie, divisée en deux chapitres (5 et 6), présente une description de la phonologie et morphophonologie de la langue, avec une description du phénomène d’épenthèse syllabique dans le verbe. La troisième partie (chapitres 7 et 8) présente d’abord une étude générale de la gramma
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Fasteen, Jodi I. "An Investigation of the Role of Alternate Numeration Systems in Preservice Teacher Mathematics Content Courses." PDXScholar, 2015. https://pdxscholar.library.pdx.edu/open_access_etds/2314.

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Alternate numeration systems are common in preservice teacher (PST) mathematics curricula, but there is limited research on how to leverage alternate systems to promote the development of mathematical knowledge for teaching. I analyzed the role of alternate numeration systems in three ways. I conducted a thematic analysis of current PST textbooks to consider the role of alternate numeration systems in written curricula. I conducted a teaching experiment to analyze PSTs' mathematical activity as they engaged with a base five task sequence to reinvent an algorithm for multiplication. And I intro
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Books on the topic "Numeration system"

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Borchardt, Nadine. The numeral system of Ikaan, a Benue-Congo language of Nigeria. Harrassowitz Verlag, 2011.

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2

ill, Browne Rob, ed. Hands on base ten blocks: Problem-solving activities. Wright Group/McGraw-Hill, 1986.

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3

Lóńgẹ́, Olú. The Yorùbá ancient, traditional number system and a Yorùbá New decimal number system: Ancient éwá ogún ibga egbewa egbaáwá òké, New-Decimal ewa-alagbára / Olu Longe. Origination Concepts, 2016.

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Goodnow, Judy. Cooperative problem solving with base ten blocks. Creative Publications, 1991.

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Rigo, Michel. Formal Languages, Automata and Numeration Systems 1. John Wiley & Sons, Inc., 2014. http://dx.doi.org/10.1002/9781119008200.

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Rigo, Michel. Formal Languages, Automata and Numeration Systems 2. John Wiley & Sons, Inc., 2014. http://dx.doi.org/10.1002/9781119042853.

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Seiler, Hansjakob. A dimensional view on numeral systems. Institut für Sprachwissenschaft, Universität zu Köln, 1989.

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Mimica, Jadran. Intimations of infinity: The mythopoeia of the Iqwaye counting system and number. Berg, 1988.

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Association of Records Managers and Administrators., ed. ARMA International guideline for records and information management. ARMA International, 1989.

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Mendelson, Elliott. Number systems and the foundations of analysis. R.E. Krieger Pub. Co., 1985.

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Book chapters on the topic "Numeration system"

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Weik, Martin H. "numeration system." In Computer Science and Communications Dictionary. Springer US, 2000. http://dx.doi.org/10.1007/1-4020-0613-6_12613.

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Weik, Martin H. "hexadecimal numeration system." In Computer Science and Communications Dictionary. Springer US, 2000. http://dx.doi.org/10.1007/1-4020-0613-6_8337.

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Weik, Martin H. "octal numeration system." In Computer Science and Communications Dictionary. Springer US, 2000. http://dx.doi.org/10.1007/1-4020-0613-6_12695.

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Weik, Martin H. "positional numeration system." In Computer Science and Communications Dictionary. Springer US, 2000. http://dx.doi.org/10.1007/1-4020-0613-6_14323.

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Weik, Martin H. "radix numeration system." In Computer Science and Communications Dictionary. Springer US, 2000. http://dx.doi.org/10.1007/1-4020-0613-6_15431.

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Weik, Martin H. "binary numeration system." In Computer Science and Communications Dictionary. Springer US, 2000. http://dx.doi.org/10.1007/1-4020-0613-6_1549.

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Weik, Martin H. "decimal numeration system." In Computer Science and Communications Dictionary. Springer US, 2000. http://dx.doi.org/10.1007/1-4020-0613-6_4500.

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Weik, Martin H. "straight binary numeration system." In Computer Science and Communications Dictionary. Springer US, 2000. http://dx.doi.org/10.1007/1-4020-0613-6_18365.

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Weik, Martin H. "fixed-radix numeration system." In Computer Science and Communications Dictionary. Springer US, 2000. http://dx.doi.org/10.1007/1-4020-0613-6_7261.

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Weik, Martin H. "mixed-base numeration system." In Computer Science and Communications Dictionary. Springer US, 2000. http://dx.doi.org/10.1007/1-4020-0613-6_11606.

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Conference papers on the topic "Numeration system"

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Döring, Frederik. "A New Perspective on Coupling Numerator Models." In Vertical Flight Society 80th Annual Forum & Technology Display. The Vertical Flight Society, 2024. http://dx.doi.org/10.4050/f-0080-2024-1292.

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Coupling numerator models are a well-established tool for predicting the closed-loop dynamics of multiple-input multiple-output systems. They describe the input-output dynamics of the open-loop path in a partially controlled system given tight controls and thus may serve as an approximation of the actual dynamics "seen" by the single-axis controller in a controlled multiple-input multiple-output plant. Such models can therefore be employed for a decentralized initial design of multivariable controllers. This paper presents a new, unifying approach for the computation of such constrained input-
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Michael P Sama, Richard S Gates, Will C Adams, George B Day, and Carl L King. "Fan Assessment Numeration System (FANS) Scaling and Upgrades." In 2008 Providence, Rhode Island, June 29 - July 2, 2008. American Society of Agricultural and Biological Engineers, 2008. http://dx.doi.org/10.13031/2013.24990.

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R. S. Gates, J. D. Simmons, K. D. Casey, et al. "Fan Assessment Numeration System (FANS) Design and Calibration Specifications." In 2002 Chicago, IL July 28-31, 2002. American Society of Agricultural and Biological Engineers, 2002. http://dx.doi.org/10.13031/2013.9383.

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Michael P Sama, Gabriela M Morello, Igor M Lopes, George B Day, and Douglas G Overhults. "Visualizing Airflow Using the Fan Assessment Numeration System (FANS)." In 2012 Dallas, Texas, July 29 - August 1, 2012. American Society of Agricultural and Biological Engineers, 2012. http://dx.doi.org/10.13031/2013.41843.

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William S Sympson and Michael P Sama. "Cost Reduction of the Fan Assessment Numeration System through Data Analysis." In 2013 Kansas City, Missouri, July 21 - July 24, 2013. American Society of Agricultural and Biological Engineers, 2013. http://dx.doi.org/10.13031/aim.20131618881.

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Gabriela M Morello, Douglas G Overhults, Igor M Lopes, et al. "Influence of Fan Operations on FANS (Fan Assessment Numeration System) Test Results." In 2010 Pittsburgh, Pennsylvania, June 20 - June 23, 2010. American Society of Agricultural and Biological Engineers, 2010. http://dx.doi.org/10.13031/2013.32048.

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Alapati, Madhu sravya, Raghunandan Swain, and Asisa Kumar Panigrahy. "Hardware Implementation of Posit Numeration System using FPGA for Signal Processing Applications." In 2023 7th International Conference on Trends in Electronics and Informatics (ICOEI). IEEE, 2023. http://dx.doi.org/10.1109/icoei56765.2023.10125920.

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Michael P Sama, Laura Pepple, George B Day V., et al. "Calibration Drift Assessment and Upgrades to the Fan Assessment Numeration System (FANS)." In 2012 Dallas, Texas, July 29 - August 1, 2012. American Society of Agricultural and Biological Engineers, 2012. http://dx.doi.org/10.13031/2013.42165.

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Anisimov, Anatoly V., and Igor O. Zavadskyi. "Forward error correcting codes by means of the two-base (2,3)-numeration system." In 2014 IEEE International Black Sea Conference on Communications and Networking (BlackSeaCom). IEEE, 2014. http://dx.doi.org/10.1109/blackseacom.2014.6849015.

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Xiong, Jishi, Wu Chongjian, Xu Zhiyun, and Gewei Zeng. "Near-field sound radiation numeration in wave superposition method based on the spatially digital space." In 2010 International Conference on Computer Application and System Modeling (ICCASM 2010). IEEE, 2010. http://dx.doi.org/10.1109/iccasm.2010.5620608.

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Reports on the topic "Numeration system"

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Fasteen, Jodi. An Investigation of the Role of Alternate Numeration Systems in Preservice Teacher Mathematics Content Courses. Portland State University Library, 2000. http://dx.doi.org/10.15760/etd.2311.

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