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Relevant bibliographies by topics / Numeral notation systems

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Academic literature on the topic 'Numeral notation systems'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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Journal articles on the topic "Numeral notation systems"

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Chrisomalis, Stephen. "Constraint, cognition, and written numeration." Pragmatics and Cognition 21, no. 3 (2013): 552–72. http://dx.doi.org/10.1075/pc.21.3.08chr.

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The world’s diverse written numeral systems are affected by human cognition; in turn, written numeral systems affect mathematical cognition in social environments. The present study investigates the constraints on graphic numerical notation, treating it neither as a byproduct of lexical numeration, nor a mere adjunct to writing, but as a specific written modality with its own cognitive properties. Constraints do not refute the notion of infinite cultural variability; rather, they recognize the infinity of variability within defined limits, thus transcending the universalist/particularist dicho

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Cantlon, Jessica F., Melissa E. Libertus, Philippe Pinel, Stanislas Dehaene, Elizabeth M. Brannon, and Kevin A. Pelphrey. "The Neural Development of an Abstract Concept of Number." Journal of Cognitive Neuroscience 21, no. 11 (2009): 2217–29. http://dx.doi.org/10.1162/jocn.2008.21159.

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As literate adults, we appreciate numerical values as abstract entities that can be represented by a numeral, a word, a number of lines on a scorecard, or a sequence of chimes from a clock. This abstract, notation-independent appreciation of numbers develops gradually over the first several years of life. Here, using functional magnetic resonance imaging, we examine the brain mechanisms that 6- and 7-year-old children and adults recruit to solve numerical comparisons across different notation systems. The data reveal that when young children compare numerical values in symbolic and nonsymbolic

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Kittler, Friedrich. "Number and Numeral." Theory, Culture & Society 23, no. 7-8 (2006): 51–61. http://dx.doi.org/10.1177/0263276406069882.

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In his essay Thinking Colours and/or Machines Kittler hints at a key point in the emergence of modern European culture: the point at which ‘letters and numbers no longer coincide’. In this essay - first published in 2003 as Zahl und Ziffer - Kittler traces the split between numerals and numbers in sweeping historical detail. This is part of a much larger project, the aim of which is to think about technology, history and culture anew by considering the ways in which ‘letters, numbers, images and tones’ have been differentiated and re-integrated by developing notation systems and media technolo

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Olson, David R. "The written representation of negation." Pragmatics and Cognition 5, no. 2 (1997): 235–52. http://dx.doi.org/10.1075/pc.5.2.03ols.

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While negatives are fundamental to the functioning of human languages and while they are acquired extremely early by children, there is some evidence that an aware-ness of the logical and representational functions of negation is late to develop and may depend in part on the invention of notational means for representing it. This hypothesis is explored by reference to the presence or absence of notations for negation in the world's writing systems, the acquisition of notational devices for representing negation by young children, and the invention of numerical notation for representing nothing

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Mora-Marín, David F. "IZAPAN WRITING: CLASSIFICATION AND PRELIMINARY OBSERVATIONS." Ancient Mesoamerica 29, no. 1 (2018): 93–112. http://dx.doi.org/10.1017/s0956536117000190.

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AbstractThis paper reviews the limited evidence for the classification of the script attested at the site of Izapa. Sufficient data for assessing the nature of key formal traits exists, thanks to the more recent documentation of the sculptural corpus (Clark and Moreno 2007). After a review of the archaeological and historical linguistic context, the paper examines the history of research on the classification of the writing systems of Mesoamerica (Justeson 1986; Justeson and Mathews 1990; Justeson et al. 1985; Prem 1973), focusing on the Southeastern Tradition. Three diagnostic traits allow fo

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Chrisomalis, Stephen. "A Cognitive Typology for Numerical Notation." Cambridge Archaeological Journal 14, no. 1 (2004): 37–52. http://dx.doi.org/10.1017/s0959774304000034.

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The numerical notation associated with texts and other representational media used in ancient societies is an important means by which past cognitive processes may be reconstructed. No satisfactory typology exists, however, to help understand the relationship between numerical symbols and cognitive processes. As a result, theories concerning the development of numeration remain mired in a unilinear and ethnocentric framework in which our own (Hindu-Arabic or Western) numerals are seen as the ultimate stage of evolution. It is suggested herein that there are two separate dimensions that need to

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Widom, Theodore Reed, and Dirk Schlimm. "Methodological Reflections on Typologies for Numerical Notations." Science in Context 25, no. 2 (2012): 155–95. http://dx.doi.org/10.1017/s0269889712000038.

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ArgumentPast and present societies world-wide have employed well over 100 distinct notational systems for representing natural numbers, some of which continue to play a crucial role in intellectual and cultural development today. The diversity of these notations has prompted the need for classificatory schemes, or typologies, to provide a systematic starting point for their discussion and appraisal. The present paper provides a general framework for assessing the efficacy of these typologies relative to certain desiderata, and it uses this framework to discuss the two influential typologies of

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LEPORATI, ALBERTO, CLAUDIO ZANDRON, and MIGUEL A. GUTIÉRREZ-NARANJO. "P SYSTEMS WITH INPUT IN BINARY FORM." International Journal of Foundations of Computer Science 17, no. 01 (2006): 127–46. http://dx.doi.org/10.1142/s0129054106003735.

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Current P systems which solve NP–complete numerical problems represent the instances of the problems in unary notation. However, in classical complexity theory, based upon Turing machines, switching from binary to unary encoded instances generally corresponds to simplify the problem. In this paper we show that, when working with P systems, we can assume without loss of generality that instances are expressed in binary notation. More precisely, we propose a simple method to encode binary numbers using multisets, and a family of P systems which transforms such multisets into the usual unary nota

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Gawrysiak, Piotr. "RACHUNKI I LICZBY STAROŻYTNYCH GREKÓW I RZYMIAN." Zeszyty Prawnicze 6, no. 1 (2017): 65. http://dx.doi.org/10.21697/zp.2006.6.1.05.

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Ancient Greek and Roman Numerical Notation and Counting AidsSummary The abilities to count and write down numbers are usually regarded as trivial, while in fact these skills are early technologies that significantly influenced the development of science, trade, culture and law. The lack of understanding of the way in which numerical information was conveyed among people and the ways in which daily computations - such as taxes, livestock accounts, prices etc. - were carried out, might lead to improper reasoning about the culture itself. It is, therefore, useful to know the basics of „daily” mat

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Hsieh, Jung-Fa. "NUMERICAL ANALYSIS OF DISPLACEMENTS IN SPATIAL MECHANISMS WITH SPHERICAL JOINTS UTILIZING AN EXTENDED D-H NOTATION." Transactions of the Canadian Society for Mechanical Engineering 34, no. 3-4 (2010): 417–31. http://dx.doi.org/10.1139/tcsme-2010-0025.

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Spherical joints consist of a pair of concave and convex spherical surfaces engaged in such a way as to prevent translational motion of the ball and socket whilst simultaneously allowing three degrees of rotational freedom. The kinematics of spatial mechanisms comprising links and joints are commonly analyzed using the Denavit-Hartenberg (D-H) notation. However, whilst this method allows the kinematics of mechanisms containing prismatic, revolute, helical and cylindrical joints to be explicitly defined, it cannot be directly applied to mechanical systems containing spherical pairs. Accordingly

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Dissertations / Theses on the topic "Numeral notation systems"

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Carnes, Tara Barker. "Hartley Wood Day: Inventor of Numeral Notation and Adversary of Lowell Mason." Thesis, University of North Texas, 1991. https://digital.library.unt.edu/ark:/67531/metadc500655/.

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Ignorance of the basic principles of music reading was one of the primary obstacles to the improvement of congregational singing in nineteenth-century America. Six separate numeral notation systems arose to provide a simple way for the common man to learn the basic principles of music. Hartley Day developed his own numeral notation system and published six tune-books that enjoyed modest success in the New England area. This thesis examines Day's numeral notation system as it appeared in the Boston Numeral Harmony (1845), and the One-Line Psalmist (1849). It also studies Day's periodical, The M

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Agranionih, Neila Tonin. "Escritas numéricas de milhares e valor posicional : concepções iniciais de alunos de 2ª série." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2008. http://hdl.handle.net/10183/13485.

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As escritas numéricas e o valor posicional do número são o tema desta pesquisa que tem como objetivos: investigar concepções construídas na interação criança-escrita numérica que contribuem para a construção do valor posicional característico do sistema de numeração decimal; identificar contribuições das notações de números multidígitos à conceituação do valor posicional do número, e verificar as formas cognitivas por meio das quais estas contribuições se efetivam. Consiste num estudo de análise qualitativa.Fundamenta-se na concepção epistemológica construtivista, e volta-se para as microapren

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Savas, Berkant. "Algorithms in data mining using matrix and tensor methods." Doctoral thesis, Linköpings universitet, Beräkningsvetenskap, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-11597.

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In many fields of science, engineering, and economics large amounts of data are stored and there is a need to analyze these data in order to extract information for various purposes. Data mining is a general concept involving different tools for performing this kind of analysis. The development of mathematical models and efficient algorithms is of key importance. In this thesis we discuss algorithms for the reduced rank regression problem and algorithms for the computation of the best multilinear rank approximation of tensors. The first two papers deal with the reduced rank regression problem,

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Books on the topic "Numeral notation systems"

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name, No. Recommended practice: The CFD general notation system--standard interface data structures. American Institute of Aeronautics and Astronautics, 2003.

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Book chapters on the topic "Numeral notation systems"

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"NOTATIONS AND SYMBOLS." In Numerical Methods for Linear Control Systems. Elsevier, 2004. http://dx.doi.org/10.1016/b978-012203590-6/50004-5.

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Overmann, Karenleigh A. "Materiality and the Prehistory of Number." In Squeezing Minds From Stones. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780190854614.003.0021.

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Modern humans produce number systems with striking cross-cultural similarities. Understanding prehistoric numerical cognition, however, addressed in this chapter, requires looking at when cognitive prerequisites emerged—morphological factors like parietal encephalization; abilities like quantity perception, language, concept formation and manipulation, categorization, and ordinality; and demographic factors suggesting societal motivations for numerical development. These establish the “probably not before” timeline for numerical emergence. The question is then approached from the earliest emergence of unambiguous numbers in Mesopotamia, clay tokens used in the late fourth millennium, and subsequent numerical notations. With tokens and notations, the archaeological and textual evidence of precursor technologies such as tallies and fingers forms a sequence capable of elaborating the innate perceptual experience of quantity into simple counting sequences and complex mathematics. Along with the cognitive prerequisites, the sequence of material forms also provides insight into potential archaeological evidence (material forms and demographic factors) that might indicate numerical emergence in prehistoric times.

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Mazur, Joseph. "Refuting Origins." In Enlightening Symbols. Princeton University Press, 2016. http://dx.doi.org/10.23943/princeton/9780691173375.003.0008.

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This chapter discusses the debate among experts over the origins of the Hindu-Arabic numerals. One such expert was the French mathematician and historian Michel Chasles, who argued that by the fifth century, France already had a decimal place-value system for computations documented in Boethius's Arithmetic, which seemed to use a multiplication table with Arabic numbers. For much of the nineteenth century, the Indian origin of positional decimal notation had been challenged. The chapter also considers the claim made by George Rusby Kaye in 1907 that the numerals and the decimal system could not have been Indian in origin and that the history of Hindu-Arabic number representation was complicated by the existence of so many forgeries of the time. Whatever the truth, it is quite likely that sometime in the fifth century, Indian numbers had come to Alexandria via a trade route through Syria before moving westward.

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Smullyan, Raymond M. "Prerequisites." In Recursion Theory for Metamathematics. Oxford University Press, 1993. http://dx.doi.org/10.1093/oso/9780195082326.003.0004.

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As we remarked in the preface, although this volume is a sequel to our earlier volume G.I.T. (Gödel’s Incompleteness Theorems), it can be read independently by those readers familiar with at least one proof of Gödel’s first incompleteness theorem. In this chapter we give the notation, terminology and main results of G.I.T. that are needed for this volume. Readers familiar with G.I.T. can skip this chapter or perhaps glance through it briefly as a refresher. §0. Preliminaries. we assume the reader to be familiar with the basic notions of first-order logic—the logical connectives, quantifiers, terms, formulas, free and bound occurrences of variables, the notion of interpretations (or models), truth under an interpretation, logical validity (truth under all interpretations), provability (in some complete system of first-order logic with identity) and its equivalence to logical validity (Gödel’s completeness theorem). we let S be a system (theory) couched in the language of first-order logic with identity and with predicate and/or function symbols and with names for the natural numbers. A system S is usually presented by taking some standard axiomatization of first-order logic with identity and adding other axioms called the non-logical axioms of S.we associate with each natural number n an expression n̅ of S called the numeral designating n (or the name of n).we could, for example, take 0̅,1̅,2̅, . . . ,to be the expressions 0,0', 0",..., as we did in G.I.T. we have our individual variables arranged in some fixed infinite sequence v1, v2,..., vn , . . . . By F(v1, ..., vn) we mean any formula whose free variables are all among v1,... ,vn, and for any (natural) numbers k1,...,kn by F(к̅1 ,... к̅n), we mean the result of substituting the numerals к̅1 ,... к̅n, for all free occurrences of v1,... ,vn in F respectively.

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"Young Children’s Developing Ability to Produce Notations in Different Domains — Drawing, Writing, and Numerical." In Representational Systems and Practices as Learning Tools. Brill | Sense, 2009. http://dx.doi.org/10.1163/9789087905286_004.

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Conference papers on the topic "Numeral notation systems"

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Rykkje, Thorstein R., Daniel Leinebø, Erlend Sande Bergaas, Andreas Skjelde, and Thomas J. Impelluso. "Inspiring Learning: Assessment of Friction in a Real-World Model Using the Moving Frame Method in Dynamics." In ASME 2018 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/imece2018-86189.

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This project conducts research in energy dissipation. It also demonstrates the power of the new Moving Frame Method (MFM) in dynamics to inspire undergraduate students to embark on research in engineering. The MFM is founded on Lie Group Theory to model rotations of objects, Cartan’s moving frames to model the change of a frame in terms of the frame, and a new notation from the discipline of geometrical physics. The MFM presents a consistent notation for single bodies, linked systems and robotics. This work demonstrates that this new method is accessible by undergraduate students. The MFM stru

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Nyland, Joakim, Håkon Teigland, and Thomas J. Impelluso. "Use of the Moving Frame Method in Dynamics to Model Gyroscopic Control of Small Crafts at Sea: Theory — Part 1." In ASME 2017 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/imece2017-70108.

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This paper presents new method in dynamics — the Moving Frame Method (MFM) — and uses it to address a challenge faceing Norwegian shipping. Large offshore renewable energy investments require the use of maintenance boats to keep them in operable conditions. Unfortunately, due to rough seas in some project locations, the transferring of crew members from vessel to turbine or platform is fraught with safety concerns. These concerns can be alleviated by controlling the motion of the transfer vessel. This research studies an add-on stability system for marine vessels to ease the process of offshor

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Jardim, Paulo Alexander Jacobsen, Jan Tore Rein, Øystein Haveland, and Thomas J. Impelluso. "Modeling Crane Induced Ship Motion Using the Moving Frame Method." In ASME 2018 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/imece2018-86190.

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A decline in oil-related revenues challenges Norway to focus on new types of offshore installations and their maintenance. Often, ship-mounted crane systems transfer cargo or crew onto marine structures such as floating windmills. This project analyzes the motion of a ship induced by an onboard crane in operation. It analyzes the motion of a crane mounted on a ship using The Moving Frame Method (MFM). The MFM draws upon Lie group theory and Cartan’s Moving Frames. This, together with a compact notation from geometrical physics, makes it possible to extract the equations of motion, expeditiousl

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Zhang, Wei, and Jialing Hao. "Human Impacts on the Hydrology in Pearl River Delta, China." In ASME 2008 27th International Conference on Offshore Mechanics and Arctic Engineering. ASMEDC, 2008. http://dx.doi.org/10.1115/omae2008-57122.

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The Pearl River Delta (PRD) lies in the south of GuangDong province in China. It is the river networks area of the lower reaches of MaKou of West River, Sanshui of North River and ShiLong of Dongjiang River. Over the last 20 years, in order to keep sustainable development of economy, many regulations engineering to improve grade of channel from river networks to estuary was implemented in 1990’s. At the same time, artificial sand excavation reached the peak level. These human activities impacted the hydrodynamic greatly than natural evolution. As a result, the morphology and hydrology of the P

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