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Journal articles on the topic 'Numeration system'

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Published: 8 June 2024

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1

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 (September 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 of abstract numeration systems built on an infinite regular language.

2

Uy, Frederick L. "The Chinese Numeration System and Place Value." Teaching Children Mathematics 9, no. 5 (January 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.

3

BIAGUI, Noël Bernard. "La numération cardinale en créole casamançais : Emplois morphosyntaxiques et système de comptage de l’argent." ALTRALANG Journal 5, no. 01 (June 10, 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 problem of numeration and languages with an oral tradition and is concerned with its importance in the achievements of the numeration of languages in contact. RÉSUMÉ : Même si plus de 50% de son lexique proviendrait du portugais, le créole casamançais à aujourd’hui un système linguistique autonome. Cette autonomie se manifeste aussi dans le domaine de la numération. A l’image de bon nombre de langues africaines, la numération du créole casamançais repose sur une base orale due à l’absence de l’écriture. La présentation du système numéral, dont nous ferons cas, se limitera uniquement à la présentation des nombres cardinaux et à la numération comptable. La présente étude s’inscrit dans la problématique de la numération et langues à tradition orale et se préoccupe de son importance dans les acquis de la numération des langues en contact.

4

Sekido, Hiroto, and Masashi Iwasaki. "Integer representations in numeration system with Fibonacci squares." Research in Mathematics 9, no. 1 (May 3, 2022): 1–5. http://dx.doi.org/10.1080/27684830.2022.2069647.

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5

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 (July 2011): 743–59. http://dx.doi.org/10.1016/j.jcss.2010.07.002.

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6

JUSTIN, JACQUES, and GIUSEPPE PIRILLO. "EPISTURMIAN WORDS: SHIFTS, MORPHISMS AND NUMERATION SYSTEMS." International Journal of Foundations of Computer Science 15, no. 02 (April 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 ?

7

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.

8

Walmsley, Angela L. E. "Math Roots: Understanding Aztec and Mayan Numeration Systems." Mathematics Teaching in the Middle School 12, no. 1 (August 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 reveal to students that our current system finds its roots in what has come before.

9

Overbay, Shannon R., and Mary Jean Brod. "Magic with Mayan Math." Mathematics Teaching in the Middle School 12, no. 6 (February 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 transactions (Closs 1986).

10

R. S. Gates, K. D. Casey, H. Xin, E. F. Wheeler, and J. D. Simmons. "FAN ASSESSMENT NUMERATION SYSTEM (FANS) DESIGN AND CALIBRATION SPECIFICATIONS." Transactions of the ASAE 47, no. 5 (2004): 1709–15. http://dx.doi.org/10.13031/2013.17613.

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11

Labbé, Sébastien, and Jana Lepšová. "A Fibonacci analogue of the two’s complement numeration system." RAIRO - Theoretical Informatics and Applications 57 (2023): 12. http://dx.doi.org/10.1051/ita/2023007.

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Using the classic two’s complement notation of signed integers, the fundamental arithmetic operations of addition, subtraction, and multiplication are identical to those for unsigned binary numbers. We introduce a Fibonacci-equivalent of the two’s complement notation and we show that addition in this numeration system can be performed by a deterministic finite-state transducer. The result is based on the Berstel adder, which performs addition of the usual Fibonacci representations of nonnegative integers and for which we provide a new constructive proof. Moreover, we characterize the Fibonacci-equivalent of the two’s complement notation as an increasing bijection between ℤ and a particular language.

12

Thouvenot, Marc. "La numération cardinale en nahuatl, aux XVIe-XVIIe siècles." Faits de Langues 51, no. 2 (April 7, 2021): 63–97. http://dx.doi.org/10.1163/19589514-05102005.

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Abstract The vigesimal Nahuatl numeration has been well known, in language, since the 16th century. But its graphic expression in pictographic writing is less well known. It is this difference that this text seeks to reduce, by presenting, jointly, the writing of the referential numeration and that which is denominative. The sources used - both pictographic and alphabetic – are diverse both spatially and temporally. They come from Mexico-Tenochtitlan as well as from nearby but distinct localities such as Texcoco, Chalco or the Puebla region. Some sources are probably close to the time of the Conquest, while others were written a century later. For the purposes of this presentation everything has been put together. This therefore represents the state of numeration and its writing over a period of a century after the Conquest and over a wide area. It would, of course, be desirable to have a more precise view of the local forms and developments that occurred during this century, because it is inconceivable that the brutality of the shock of conquest and colonization had no effect on the system that the Nahuatl language and its pictographic writing constituted, especially in the field of numeration.

13

BARAT, GUY, and PETER GRABNER. "Combinatorial and probabilistic properties of systems of numeration." Ergodic Theory and Dynamical Systems 36, no. 2 (September 16, 2014): 422–57. http://dx.doi.org/10.1017/etds.2014.69.

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Let $G=(G_{n})_{n}$ be a strictly increasing sequence of positive integers with $G_{0}=1$. We study the system of numeration defined by this sequence by looking at the corresponding compactification ${\mathcal{K}}_{G}$ of $\mathbb{N}$ and the extension of the addition-by-one map ${\it\tau}$ on ${\mathcal{K}}_{G}$ (the ‘odometer’). We give sufficient conditions for the existence and uniqueness of ${\it\tau}$-invariant measures on ${\mathcal{K}}_{G}$ in terms of combinatorial properties of $G$.

14

Lubis, Siti Masyitoh Azzahra, and Dian Permatasari. "Level of critical thinking ability in solving numeration problems in the minimum competency assessment." Desimal: Jurnal Matematika 6, no. 1 (April 30, 2023): 63–72. http://dx.doi.org/10.24042/djm.v6i1.14611.

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Minimum Competency Assessment (MCA) is a form of evaluation of the education system launched by the government in order to measure the achievement of students' cognitive learning outcomes in literacy and numeracy abilities. MCA numeration is related to critical thinking skills. This study aims to describe the level of students' critical thinking skills in solving the MCA numeration questions. This type of research is descriptive-qualitative research. Data collection techniques in the form of written tests and interviews with test instruments are MCA numeration questions with four questions. The data analysis technique was carried out by giving tests, then interviewing the selected subjects to find out more about critical thinking skills, and then describing the results. The results showed that the level of critical thinking ability of class VIII students in solving MCA numeration questions in the number domain met the same criteria, namely the criteria of focus, reason, and situation. Domain algebra found that students have various levels of critical thinking skills with criteria that meet the criteria of focus and reason. In the geometry domain, it was found that students had a low ability to solve geometric problems, and in the uncertainty data domain, students only reached conclusions without giving reasons.

15

CORTEZ, MARÍA ISABEL, and JUAN RIVERA-LETELIER. "Topological orbit equivalence classes and numeration scales of logistic maps." Ergodic Theory and Dynamical Systems 32, no. 5 (November 1, 2011): 1501–26. http://dx.doi.org/10.1017/s0143385711000435.

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16

Hajnal, Péter. "Binary Numeration System with Alternating Signed Digits and Its Graph Theoretical Relationship." Algorithms 17, no. 2 (January 25, 2024): 55. http://dx.doi.org/10.3390/a17020055.

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The binary number system is the basic number representation in computing. We can encode natural numbers with finite 0-1 sequences. The representation of natural numbers is based on this system. However, this poses problems and is technically not perfect. Several attempts have been made to handle integers (signed numbers). We mention only two: the balanced triple number system and the number system with base −2. Our paper introduces new possibilities. We also shed light on the graph theoretical background of the new number systems.

17

MASUI, KENICHI, FUMIAKI SUGISAKI, and MASAMICHI YOSHIDA. "Denjoy systems and dimension groups." Ergodic Theory and Dynamical Systems 28, no. 3 (June 2008): 877–913. http://dx.doi.org/10.1017/s0143385707000582.

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AbstractWe construct an adic model for the Denjoy system (X,T) of finite double orbit number. It is based on the dual Ostrowski numeration system. By using this construction, we can determine the K-theory of $C(X)\rtimes _T \mathbb {Z}$ associated with (X,T) in an effective way.

18

Ambrož, Petr, Daniel Dombek, Zuzana Masáková, and Edita Pelantová. "Numbers with integer expansion in the numeration system with negative base." Functiones et Approximatio Commentarii Mathematici 47, no. 2 (December 2012): 241–66. http://dx.doi.org/10.7169/facm/2012.47.2.8.

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19

Davlet′yarova, E. P., A. A. Zhukova, and A. V. Shutov. "Geometrization of the Fibonacci numeration system, with applications to number theory." St. Petersburg Mathematical Journal 25, no. 6 (September 8, 2014): 893–907. http://dx.doi.org/10.1090/s1061-0022-2014-01321-0.

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20

Shiokawa, I., and Y. Tachiya. "Linear relations between pattern sequences in a 〈q,r〉-numeration system." Acta Mathematica Hungarica 132, no. 1-2 (March 2, 2011): 190–206. http://dx.doi.org/10.1007/s10474-011-0082-6.

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21

Hoppan, Jean-Michel, and Sylviane Schwer. "De la protraction en maya?" Faits de Langues 51, no. 2 (April 7, 2021): 39–62. http://dx.doi.org/10.1163/19589514-05102004.

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Abstract Overcounting is a neologism which was proposed in the late XXth century to define « the operation that designates a number by its orientation towards a boundary ». With a few examples taken from Asiatic languages, Mayan numerations from Central America are generally given as representative of this uncommon type of linguistic operation to build words for numbers. However, our analysis of the operative pattern in this kind of Mayan numeration (which has cohabited for many centuries with a more simply additive type of number construction) as well as the analysis of the data from pre-hispanic times and the colonial period brought us to question this definition, at least for Mayan languages. Our study indeed shows that the so-called “overcounting” system in Mayan numerations, if it was definitely present there a long time before the Europeans, was strongly associated to an aspect of the comput that sets to work an “encapsulation” of the vigesimal scores and where a number is actually not designated for its orientation towards the higher boundary but where the aim is to process in a non-linear way following an “encapsulation of the numerical knots” and looking for a retrograde anteriority.

22

Parteki, Prajakta P. "A Review Paper on Automatic Coin Sorter for Temples using IOT." International Journal for Research in Applied Science and Engineering Technology 9, no. VI (July 15, 2021): 597–99. http://dx.doi.org/10.22214/ijraset.2021.36289.

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At non-secular places like temples, gurdwaras, and lots of others, devotees gift cash within the donation box. It's a giant deal to sight the truth of the given cash. Similarly, cash numeration has been a giant task because it is allotted manually. Mistakes on numeration happen most of the time because of several reasons like eyes temporary state, losing focus, etc. typically fiddle of cash happens at the time of numeration money. To prevail over these issues Automatic Coin Sorter for Temples using IOT is meant. During this system, the truth of the coin is detected employing a dimension standardization method. Then the coins when some delay area unit sorted and area unit inserted into the various assigned box with the assistance of the motor. All the data regarding the coin is distributed to the Associate in Nursing digital display wherever the worth, reality, and count of the coin area unit are displayed. The overall count of the noon and full-day is distributed to the various head person through the applying. The advantage of this review paper for the reader is to achieve information about numerous technologies used for creating this method.

23

Guo, Yanfeng, Chunxiao Guo, and Donglong Li. "Existence and Approximation of Manifolds for the Swift-Hohenberg Equation with a Parameter." Discrete Dynamics in Nature and Society 2018 (July 12, 2018): 1–6. http://dx.doi.org/10.1155/2018/1423170.

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The existence and approximation of manifolds for the Swift-Hohenberg equation with a proper parameter have mainly been studied. Using the backward-forward systems from Swift-Hohenberg equation, the existence and specific representation forms of manifolds for Swift-Hohenberg equation with a parameter have been obtained. Meanwhile, we make use of technique of deposition of lower and higher frequency spaces of solutions and assume the reduced system to obtain the main numeration approximation system of approximation solution for the original system Swift-Hohenberg equation with a proper parameter.

24

Moldavan, Carla C. "Culture in the Curriculum: Enriching Numeration and Number Operations." Teaching Children Mathematics 8, no. 4 (December 2001): 238–43. http://dx.doi.org/10.5951/tcm.8.4.0238.

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Students hear, “Pretend that you live on an island. You have no contact with others. You do not know words or written symbols for numbers. Your task is to develop a numeration system—a method that would allow you to count coconuts or shells, for example.” This task was the first one given to fourth graders in an attempt to embed multiculturalism in their mathematics curriculum. This article describes the content of the project and the students' reactions.

25

Liu, Shu Qing, and Xing Song Wang. "Dynamic Modeling and Numeration of Flexible Multi-Body System with Closed Loop." Applied Mechanics and Materials 44-47 (December 2010): 1519–24. http://dx.doi.org/10.4028/www.scientific.net/amm.44-47.1519.

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The dynamic model of flexible multi-body system with closed loop is described with natural coordinates. The method is formulaic and especially appropriate to the modeling of system with repetitive substructures, but Lagrange multipliers as unknown variables are contained in the model. The dynamic model is reduced to a system with minimum dimensions by means of null-space orthogonal basis of constraint Jacobin. The result is correspondence with the dynamic model of rigid multi- body system while the rigid and flexible coupling is considered. The numerical method and the simulation steps are given in detail. Numerical example dealing with a flexible parallel four-bar linkage widely used in engineering illustrates the performance of the proposed method. The dynamic response of the angle between flexible linkage and horizontal axis are presented. The results indicate that there are clearly fluctuation in the angular velocity and acceleration of crank. The motion of connecting linkage contains not only translation but also narrow range rotation especially in the start instant.

26

Cortina, José Luis. "Supporting indigenous students’ understanding of the numeration system of their first language." Mathematics Education Research Journal 25, no. 1 (August 15, 2012): 23–42. http://dx.doi.org/10.1007/s13394-012-0043-6.

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27

Zaslavsky, Claudia. "The Influence of Ancient Egypt on Greek and Other Numeration Systems." Mathematics Teaching in the Middle School 9, no. 3 (November 2003): 174–78. http://dx.doi.org/10.5951/mtms.9.3.0174.

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You may have learned how the ancient Egyptians wrote numbers. For example, for the number 600, you would write a symbol for a scroll six times. Actually, ancient Egypt had two main systems of writing: hieroglyphic and hieratic. Hieroglyphics, dating back over 5,000 years, were used mainly for inscriptions on stone walls and monuments. Hieratic writing was a cursive script suitable for writing on papyrus, the Egyptian form of paper. Much of our knowledge of ancient Egyptian mathematics comes from a papyrus written by the scribe Ahmose around 1650 B.C.E. Although he wrote in hieratic script, recent historians transcribed this document and others into hieroglyphics, giving readers the impression that all Egyptian writing was in hieroglyphics, the system that you may have learned.

28

Bender, Andrea, and Sieghard Beller. "The Power of 2: How an Apparently Irregular Numeration System Facilitates Mental Arithmetic." Cognitive Science 41, no. 1 (February 24, 2016): 158–87. http://dx.doi.org/10.1111/cogs.12337.

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29

Tamura, Hideyuki, Ken-ichiro Matsuzaki, and Tadashi Okabe. "Exact Solutions and Numeration Program for Free Oscillation in Duffing Hard Spring System." Transactions of the Japan Society of Mechanical Engineers Series C 59, no. 567 (1993): 3267–74. http://dx.doi.org/10.1299/kikaic.59.3267.

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Tamura, Hideyuki, Ken-Ichiro Matsuzaki, and Tadashi Okabe. "Exact Solutions and Numeration Program for Free Oscillation in Duffing Soft Spring System." Transactions of the Japan Society of Mechanical Engineers Series C 60, no. 579 (1994): 3719–26. http://dx.doi.org/10.1299/kikaic.60.3719.

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31

Zaslavsky, Claudia, and Bianka Crespo. "The Inka Quipu: Positional Notation on a Knotted Cord." Mathematics Teaching in the Middle School 6, no. 3 (November 2000): 164–84. http://dx.doi.org/10.5951/mtms.6.3.0164.

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WE INHERITED A MARVELOUS SYSTEM of numeration from India by way of the Arab world. The Indo-Arabic (also called Hindu-Arabic, or, simply, Arabic) system of number notation is considered one of the most important inventions in the history of humankind. The amazingly efficient system encompasses the following features: (1) distinct symbols for the numbers from 1 to 9, (2) a symbol for 0, (3) place value for successive powers of base ten, and (4) the ability to write any numeral with just ten symbols.

32

Hopkins, Martha H. "Number Facts—or Fantasy?" Arithmetic Teacher 34, no. 7 (March 1987): 38–42. http://dx.doi.org/10.5951/at.34.7.0038.

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Articles in the Arithmetic Teacher have stressed the use of the history of mathematics to enhance motivation in the elementary classroom (Cowie 1970; Jackson 1964; Kreitz and Flournoy 1960; Krulik 1980; Willerding 1954). The increased emphasis on other numeration systems in the “new math” produced several articles that encouraged teachers to include historical information about the development of the decimal system in their programs of study (Baker 1963; Delaney 1963; Fisher et al. 1963; Schaaf 1961; Young 1964). The rationale for including these topics was that they would help students appreciate the development of our number system and would stimulate interest, enthusiasm, and a better understanding of our civilization.

33

CARPI, ARTURO. "ON REPRESENTATION SYSTEMS." International Journal of Algebra and Computation 04, no. 04 (December 1994): 657–90. http://dx.doi.org/10.1142/s0218196794000191.

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We introduce the notion of a representation system: it can be viewed as a generalization of a numeration system in an integer base by means of which certain words on a finite alphabet can be represented. We show that under suitable hypotheses, concatenation of words is represented by a right-synchronized rational relation. We study languages which are represented by rational sets (this is the case, e. g., of the languages of binary overlap-free words, of partially abelian square-free words on three letters, and of a large class of PD0L languages). Several results on these languages are obtained, concerning density, prolongability, pattern-freeness.

34

Tang, Wei Dong, Bi Wen Li, Wen Fu Tan, and Jun Zhou. "Research of Virtual Prototype System on Aiming Device of Setting Screws in Acetabulum Anterior Column." Advanced Materials Research 805-806 (September 2013): 1852–55. http://dx.doi.org/10.4028/www.scientific.net/amr.805-806.1852.

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With medical image three-dimensional reconstruction software reconstruct three-dimensional model of the pelvic, Not only the principle of aiming device design is introduced, but also deduces the relationship between the measurements of pre-operative pictures and the angles of drilling ringers of the aiming device, and also compiles applied software for numeration, By the virtual prototype on aiming device of setting screws in acetabulum anterior column, the doctors can simulate the operative environment before operation, The study provides a dependable approach to advance the accuracy rate during operation of acetabulum anterior column setting screws deeply.

35

Popovic, Dragan, and Snezana Mijailovic. "Evaluation of post-dynamic quasi-stationary states during the islands operation of power system parts." Facta universitatis - series: Electronics and Energetics 18, no. 1 (2005): 71–86. http://dx.doi.org/10.2298/fuee0501071p.

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This paper presents the development and practical examples of an efficient method for the simultaneous solution of post-dynamic quasi-stationary states in each of the islands, using a unique numerical procedure, retaining the same node numeration which existed in the power system before its disintegration. At the same time, the developed method enables a simple incorporation of the effects of primary frequency and voltage control emergency control devices and a series of possible dispatch actions, both during the monitoring of the disintegration process and during power system restoration with island synchronization, if the necessary conditions are met.

36

Mahieu, Marc-Antoine. "Numération et repérage temporel en inuktitut du Nunavik." Faits de Langues 51, no. 2 (April 7, 2021): 99–119. http://dx.doi.org/10.1163/19589514-05102006.

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Abstract Although the Inuit numeration system has no structural limits, its actual use is limited to concrete situations where the quantities involved are small. In Inuktitut (Inuit dialects of the Canadian Eastern Arctic), this system has traditionally had very little use in measuring the passage of time. As a result of contact with Westerners, the situation has partially changed, as shown by the expression of the days of the week and the time of the day. This article presents the essential data relevant to the dialect of Nunavik (Arctic Quebec).

37

Tesfay, Dr Abreha. "Analysis on The Origin, Development and Contribution of Ge’ez Numerals to The Modern Mathematics Education in Ethiopia: Status, Challenges and Future Opportunities." International Journal of Social Sciences and Humanities Invention 10, no. 11 (November 9, 2023): 8049–59. http://dx.doi.org/10.18535/ijsshi/v10i11.01.

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From the Ethiopian ancient history, it is believed that among the first peoples to inhabit was the Ge’ez speaking agrarians who settled in the Tigrayan highlands (Northern Ethiopia) around 2000BC. The inland Axum Kingdom was founded by Menilik I, a descendent of King Solomon and the Queen of Sheba, after the fall of the Da’amat Kingdom. Associated with the letters in the Ethiopian alphabet starting from ancient times, there are the Ge’ez numerals also called Ethiopic numerals. This study, therefore, purely used qualitative data obtained from interviewees and document analysis. The data obtained are narrated and organized. Patterns are identified and categorized. Finally, interpretations and implications of findings are included in the analysis. Findings indicated that there is a need for modification of the Ge’ez numbers by removing the bars above and below the original skeleton of the numbers so that doing mathematics with them becomes easier. Beyond this modification, evidence indicated that the Ge’ez numbers cannot be used for doing mathematical operations without the introduction of Ge’ez zero. Without the Ge’ez zero, it is impossible to deal with place value, decimal, and fractions, as well as with the common operations (addition, subtraction, multiplication, and division) and higher mathematics in general. Finally, it is the recommendation of this study to work towards awareness creation and consensus building about the common understanding and misunderstanding of Ge’ez numeration system at all levels as well as introducing this numeration system in to the school system.

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HIERONYMI, PHILIPP. "EXPANSIONS OF THE ORDERED ADDITIVE GROUP OF REAL NUMBERS BY TWO DISCRETE SUBGROUPS." Journal of Symbolic Logic 81, no. 3 (May 10, 2016): 1007–27. http://dx.doi.org/10.1017/jsl.2015.34.

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AbstractThe theory of (ℝ, <, +, ℤ, ℤa) is decidable if a is quadratic. If a is the golden ratio, (ℝ, <, +, ℤ, ℤa) defines multiplication by a. The results are established by using the Ostrowski numeration system based on the continued fraction expansion of a to define the above structures in monadic second order logic of one successor. The converse that (ℝ, <, +, ℤ, ℤa) defines monadic second order logic of one successor, will also be established.

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FROUGNY, CHRISTIANE, and JACQUES SAKAROVITCH. "TWO GROUPS ASSOCIATED WITH QUADRATIC PISOT UNITS." International Journal of Algebra and Computation 12, no. 06 (December 2002): 825–47. http://dx.doi.org/10.1142/s0218196702001188.

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In a previous work, we have investigated an automata-theoretic property of numeration systems associated with quadratic Pisot units that yields, for every such number θ, a certain group Gθ. In this paper, we characterize a cross-section of a congruence γθ of ℤ4 that had arisen when constructing Gθ. This allows us to completely describe the quotient Hθ of ℤ4 by γθ, that becomes then a second group associated with θ. Moreover, the cross-section thus described is very similar to the symbolic dynamical system associated, by a theorem of Parry, with the two numeration systems attached to θ. The proof is combinatorial, and based upon rewriting techniques. Résumé: Dans un article précédent, nous avions associé à chaque nombre de Pisot quadratique unitaire θ un certain groupe Gθ par le biais de la construction d'un automate qui réalise le passage entre les représentations des entiers dans deux systèmes de numération naturellement attachés à θ. Dans cet article, nous donnons une caractérisation d'un ensemble de représentants pour une congruence γθ de ℤ4 qui avait été utilisée pour la définition de Gθ. Cette caractérisation permet la description complète du quotient Hθ de ℤ4 par γθ, autre groupe associé à θ. Elle est d'autre part remarquablement similaire à la description, donnée par un théorème de Parry, du système dynamique symbolique associé aux deux systèmes de numération attachés à θ. La preuve est combinatoire et utilise les techniques des systèmes de réécriture.

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Fischer, Florence E. "A Part-Part-Whole Curriculum for Teaching Number in the Kindergarten." Journal for Research in Mathematics Education 21, no. 3 (May 1990): 207–15. http://dx.doi.org/10.5951/jresematheduc.21.3.0207.

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The set-subset relationship is an important mathematical construct that underlies many mathematical concepts developed by young children. Forty-two kindergarten children who received number concept instruction using a part-part-whole curriculum that stressed set-subset relationships developed a more mature concept of number, were more successful in solving addition and subtraction word problems, and developed greater understanding of place value in the base-10 numeration system than a comparable group of 44 kindergarten children who received standard instruction on number concepts.

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Moyon, Marc. "Binary Numeration: From Ancient Egypt to a 19th Century French Mathematical Recreation." REMATEC 19, no. 47 (March 3, 2024): e2024005. http://dx.doi.org/10.37084/rematec.1980-3141.2024.n47.e2024005.id607.

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This article focuses on the use of base 2 in two historical contexts: ancient Egypt during the Middle Kingdom and 19th-century France. In ancient Egypt, base 2 was central to the “duplation” algorithm to multiply two numbers. In 19th-century France, it featured in mathematical recreations by Charles-Ange Laisant and Édouard Lucas. Duplation in ancient Egypt involved doubling a number successively, leveraging the binary nature of the numbering system for rapid calculations. In France, Laisant and Lucas contributed to mathematical recreations rooted in base 2, popularizing mathematics and engaging the public. The article aims to present these historical resources, highlighting their educational potential. It suggests integrating these examples into mandatory education from age 9 onwards, offering students a practical understanding of mathematics and its history. However, specific teaching methods are left to the reader’s discretion.

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Sukestiyarno, Sukestiyarno, Kartono Kartono, Sugeng Priyanto, Agung Setiawan, and Dani Kusuma. "Diffusion of Digital Learning: Increasing Numeration Literacy and Strengthening Pancasila Learners." Jurnal Abdimas 27, no. 2 (November 28, 2023): 106–17. http://dx.doi.org/10.15294/abdimas.v27i2.48529.

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Teachers in Semarang City especially those who join in Group Teacher Work (KKG) complained low ability Study independent participant educate. This thing impact on achievement literacy numeracy is also decreasing. Required earnest effort _ For help the participants educate with introduce approach innovative learning. Project devotion public designed with objective For invite teachers to do so become an internal model utilization technology , in particular through use approach learning digital based . Approach This aim For increase literacy numeracy participant educate and strengthen profile Pancasila students . Learning process started with guide about method designing device learning use Learning Management System (LMS). Digital learning This called “e-sigma” with covers complete material _ including explanation detail , summary , test formative , as well key answer with focus on solving problem. Teachers take advantage module This For give tasks Study independent to participant educate . At face face in class , the teacher plays a role as helpful facilitator _ participant educate collaborate , investigate concept , and finally find conclusion draft in a way independent . Purpose of service public This teacher can : 1) design device learning , incl module learning ; 2) carry out learning simulation with use tool help e-sigma; and 3) utilizing module media For increase literacy numeracy and strengthening profile Pancasila students . Training methods carried out Steps 1 ) identify teacher needs in matter learning ; 2) establish standard achievements in training ; 3) give training simulation with e-sigma; 4) evaluate achievement teacher's abilities in training ; and 5) do reflection over the training process that . Data obtained analyzed with use statistics descriptive . The result of devotion public This show that device resulting learning _ from training with the e-sigma LMS is valid, and its implementation in form simulation is effective and impactful potential increase achievement participant educate.

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Shkol’nyi, O. V. "Random variables determined by the distributions of their digits in a numeration system with complex base." Ukrainian Mathematical Journal 50, no. 12 (December 1998): 1956–62. http://dx.doi.org/10.1007/bf02514213.

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Wu, Xian-Ping, Ru-Chun Dai, Peng-Fei Shan, Ling-Qing Yuan, Xing-Zhi Cao, Er-Yuan Liao, and Yebin Jiang. "Establishment of BMD reference curves at different skeletal sites in women, using a Cartesian coordinate numeration system." Osteoporosis International 16, no. 12 (June 15, 2005): 1655–62. http://dx.doi.org/10.1007/s00198-005-1898-0.

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R, Parthiban, Dr J. Sreerambabu, and M. Mohammed Riyaz. "Speed, Direction, Color and Type Identification of NHAI Expansions Using Deep Learning." International Journal for Research in Applied Science and Engineering Technology 10, no. 8 (August 31, 2022): 763–67. http://dx.doi.org/10.22214/ijraset.2022.46281.

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Abstract: Vehicle numeration is associate interaction to appraise the road traffic thickness to judge the traffic conditions for shrewd transportation frameworks. With the broad use of cameras in metropolitan vehicle frameworks, the reconnaissance mission video has become a focal info supply to boot, constant traffic the board framework has become illustrious as lately owing to the accessibility of handheld/versatile cameras and machine learning investigation. In this work, propose video-based vehicle as well as technique in associate superhighway traffic video caught utilizing hand-held cameras. The primary and therefore the necessary step to estimate the vehicle flow; this later helps North American nation to count the vehicles victimization the virtual line Generally, we have a tendency to begin with the background subtraction to isolate moving objects. To facilitate crossing of vehicles with the road, we have a tendency to apply the detection of objects. Our system uses the LBPH (Local Binary Pattern Histogram) algorithmic program as a way to deduct the background, so as to use our numeration algorithmic program. Traffic observance is one space that utilizes Deep Learning for many functions. By exploitation cameras put in in some spots on the roads, several tasks like vehicle investigating, vehicle identification, traffic violation observance, vehicle speed observance, etc. will be completed. Deep Learning may be a common Machine Learning formula that's wide employed in several areas in current way of life. Its strong performance and ready-to-use frameworks and architectures allows many of us to develop varied Deep Learning-based code or systems to support human tasks and activities. During this paper, we tend to discuss a Deep Learning implementation to form a vehicle investigating system while not having to trace the vehicles movements. to reinforce the system performance and to cut back time in deploying Deep Learning design, therefore pre-trained model of YOLOv3 is employed during this analysis because of its sensible performance and moderate process time in object detection. This analysis aims to form a straightforward vehicle investigating system to assist human in classify and investigating the vehicles that cross the road. The investigating relies on four varieties of vehicle, i.e. car, motorcycle, bus, and truck, whereas previous analysis counts the automobile solely. because the result, our planned system capable to count the vehicles crossing the road supported video captured by camera with the very best accuracy of ninety seven.97%.

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Novita, Nanda, Muliani Muliani, and Mellyzar Mellyzar. "PELATIHAN PENGEMBANGAN SOAL MATEMATIKA DAN SAINS BERBASIS NUMERASI PADA GURU UNTUK MENUNJANG ASESMEN NASIONAL." SELAPARANG: Jurnal Pengabdian Masyarakat Berkemajuan 6, no. 1 (March 13, 2022): 486. http://dx.doi.org/10.31764/jpmb.v6i1.7761.

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ABSTRAKKegiatan PKM yang dilaksanakan untuk guru SMP di kabupaten Aceh Utara ini bertujuan untuk meningkatkan kompetensi pedagogik guru dalam menyusun dan mengembangkan soal matematika dan sains berbasis numerasi, sebagai persiapan guru dalam membimbing siswa menghadapi Asesmen Nasional (AN). AN mulai diterapkan sebagai sistem evaluasi di Indonesia pada tahun 2021 yang bertujuan untuk memperbaiki kualitas pembelajaran. Kegiatan ini didasari oleh permasalahan mitra yaitu:(1) Belum adanya pelatihan khusus untuk penyusunan dan pengembangan soal matematika dan sains berbasis numerasi. (2) Minimnya pemahaman guru dan keterbatasan ide dalam penyusunan soal berbasis numerasi. (3) Guru belum menggunakan soal matematika dan sains berbasis numerasi dalam proses pembelajaran. Kegiatan pelatihan dilakukan dalam tiga tahap, pertama analisis pemahaman awal guru terkait tujuan dan instrumen yang digunakan dalam AN. Tahap kedua pemaparan materi mengenai strategi penyusunan soal matematika dan sains berbasis numerasi serta penerapan di sekolah. Selanjutnya, tahap ketiga penyusunan soal matematika dan sains berbasis numerasi. Soal-soal yang sudah disusun oleh peserta, kemudian dievaluasi dan dianalisis berdasarkan kriteria soal numerasi. Di akhir kegiatan pelatihan, peserta mengisi angket respon untuk mengetahui efektifitas dan keberhasilan kegiatan pelatihan ini. Hasil yang diperoleh yaitu pelaksanaan kegiatan pelatihan ini sangat bermanfaat, dapat meningkatkan motivasi, sesuai dengan kebutuhan guru, pemateri sangat responsive terhadap pertanyaan peserta, dapat meningkatkan pemahaman dan kemampuan peserta dalam menyusun dan mengembangkan soal berbasis numerasi, serta perserta bersedia untuk ikut berpartisipasi jika kegiatan ini diselenggarakan kembali. Kata kunci: pengembangan soal; sains; numerasi;asesmen nasional ABSTRACTThe PKM activity which was carried out for junior high school teachers in Aceh Utara district was aimed at increasing the pedagogic competence of teachers in compiling and developing numeracy-based math and science questions, as a preparation for teachers in guiding students to face the National Assessment (AN). AN will be implemented as an evaluation system in Indonesia in 2021 which aims to improve the quality of learning. This activity is based on partner problems, namely: (1) There is no special training for the preparation and development of numeracy-based math and science questions. (2) The teacher's lack of understanding and limited ideas in the preparation of numeration-based questions. (3) Teachers have not used numeration-based math and science questions in the learning process. The training activities are carried out in three stages, firstly an analysis of the teacher's initial understanding of the objectives and instruments used in the National Assessment. The second stage is the presentation of material on strategies for formulating numeracy-based math and science questions and their application in schools. Next, the third stage is the preparation of numeration-based math and science questions. The questions that have been prepared by the participants are then evaluated and analyzed based on the criteria for numeracy questions. At the end of the training activity, participants filled out a response questionnaire to determine the effectiveness and success of this training activity. The results obtained are that the implementation of this training activity is very useful, can increase motivation, according to the needs of the teacher, the presenters are very responsive to participant questions, can increase the understanding and ability of participants in compiling and developing numeration-based questions, and participants are willing to participate if this activity reorganized. Keywords: question development; science; numeracy; national assessment

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Caalim, Jonathan, and Shiela Demegillo. "BETA CANTOR SERIES EXPANSION AND ADMISSIBLE SEQUENCES." Acta Polytechnica 60, no. 3 (July 1, 2020): 214–24. http://dx.doi.org/10.14311/ap.2020.60.0214.

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We introduce a numeration system, called the <em>beta Cantor series expansion</em>, that generalizes the classical positive and negative beta expansions by allowing non-integer bases in the Q-Cantor series expansion. In particular, we show that for a fix $\gamma \in \mathbb{R}$ and a sequence $B=\{\beta_i\}$ of real number bases, every element of the interval $x \in [\gamma,\gamma+1)$ has a <em>beta Cantor series expansion</em> with respect to B where the digits are integers in some alphabet $\mathcal{A}(B)$. We give a criterion in determining whether an integer sequence is admissible when $B$ satisfies some condition. We provide a description of the reference strings, namely the expansion of $\gamma$ and $\gamma+1$, used in the admissibility criterion.

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León Corredor, Olga Lucía, and Dora Inés Calderón. "Bilingualism of Colombian Deaf Children in the Teaching-Learning of Mathematics in the First Year of Elementary School." Colombian Applied Linguistics Journal 12, no. 2 (April 11, 2011): 9. http://dx.doi.org/10.14483/22487085.80.

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This paper summarizes some results of the first ethnographic research study conducted in Colombia in three different elementary schools for deaf children in which bilingualism (sign-language and written-language) is starting to be emphasized. This study focuses on the teaching of mathematics in classrooms for deaf children using contexts proclaimed as bilingual. The participants in the study were first grade teachers. The analysis presented in this paper illustrates the struggles that teachers experience teaching arithmetic in such a context. The teaching of arithmetic using bilingualism requires three types of semiotic registers: sign-language and written-Spanish, and the Hindu-Arabic numeration system. The analysis indicates some puzzling teaching learning issues interweaving language and mathematics. These issues are of linguistic and communicative, social and cultural, and cognitive and pedagogical nature.

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Tamura, Hideyuki, Ken-Ichiro Matsuzaki, and Tadashi Okabe. "Exact Solutions and Numeration Program for Free Oscillation in Duffing Snap-Through Spring System. 1st Report. Symmetrical Full-Swing Mode." Transactions of the Japan Society of Mechanical Engineers Series C 61, no. 583 (1995): 752–59. http://dx.doi.org/10.1299/kikaic.61.752.

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Tamura, Hideyuki, Tadashi Okabe, and Ken-Ichiro Matsuzaki. "Exact Solutions and Numeration Program for Free Oscillation in Duffing Snap-Through Spring System. 2nd Report. Asymmetrical Half-Swing Mode." Transactions of the Japan Society of Mechanical Engineers Series C 61, no. 583 (1995): 760–67. http://dx.doi.org/10.1299/kikaic.61.760.

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