Sumerian Grammar Bibliography

Total Page:16

File Type:pdf, Size:1020Kb

Sumerian Grammar Bibliography Sumerian Grammar Bibliography compiled by Carsten Peust, 2017 ● Intended to be complete from 1970 on, selective prior to that date. ● Vocabulary studies are not normally included, with some exceptions for highly grammaticalized words. ● I also cite a choice of internet publications. An address is provided only if not easily retrievable by search engines. ● If you miss any items, please email me under [email protected]. My particular thanks goes to Tomoki Kitazumi who contributed numerous additions. C.T. van Aalderen 1982: Some Observations on Ergativity in Sumerian, OLP 13: 25–44 F. d’Agostino 1990: Il sistema verbale sumerico nei testi lessicali di Ebla (StSem NS 7), Roma ––– 1991: The Study of Sumerian Grammar at Ebla I, ASJ 13: 157–180 F. d’Agostino & P. Mander 2007: Appunti di grammatica sumerica. Corso elementare, Roma R. Ahlberg 1991: Sumerian and Japanese, Chiba B. Alster 1982: Emesal in Early Dynastic Sumerian? What is the UD.GAL.NUN-orthography?, ASJ 4: 1– 6 ––– 2002: Relative Clauses and Case Relations in Sumerian, WZKM 92: 7–31 J. Aro 1961: Die akkadischen Infinitivkonstruktionen (StOr 26), Helsinki [p. 323–332: Die sumerischen Entsprechungen und Vorbilder der akkadischen Infinitivkonstruktionen] H. Assadian & A. Hakola 2003: Sumerian and Proto-Duraljan. A Lexical Comparison Concerning the Suduraljan Hypothesis, Kuopio P. Attinger 1985: Les préfixes absolutifs de la première et de la deuxième personne singulier dans les formes marû ergatives, ZA 75: 161–178 ––– 1993: Eléments de linguistique sumérienne: La construction de du11/e/di “dire”, Fribourg [addenda et corrigenda in NABU 1993/14] ––– 1996: /b/ facultatif ou agrammatical?, NABU 1996/110 ––– 1998: /n/ réflexif?, NABU 1998/41 ––– 1999: L’infixe directif /i/, /y/, NABU 1999/94 ––– 2000: L’infixe directif /i/, /y/ (II), NABU 2000/44 ––– 2004: Les préfixes personnels finaux, NABU 2004/75 ––– 2004: Les ‘verbes composés’ en sumerien, NABU 2004/79 ––– 2005: A propos de AK ‘faire’, ZA 95: 46–64 and 208–275 ––– 2007: Remarques à propos de F. Karahashi, The Locative-Terminative Verbal Infix in Sumerian, NABU 2007/55 ––– 2009: Tableau grammatical du sumérien (problèmes choisis), internet publication ––– 2010: La base marû singulier de tuš, NABU 2010/65 ––– 2010: a-ba-a = {aba + e(ergatif)}?, NABU 2010/92 ––– 2011: Remarques à propos des bases pluriel, NABU 2011/05 ––– 2011: /ug/ versus uš2, NABU 2011/06 ––– 2012: Les pronoms personnels indépendants de la 1re et de la 2e singulier en sumérien, ZA 101: 173– 190 ––– 2014: L’enclitique démonstratif de proximité -/(’)e/, NABU 2014/03 ––– 2014: si-a-na «lorsqu’il a occupé», NABU 2014/41 ––– 2015: La variation textuelle dans la littérature sumérienne d’époche paléobabylonienne, OLZ 110: 1– 8 ––– 2015(?): Lexique sumérien-français, internet publication C. Autran 1925: Sumérien et indo-européen. L’aspect morphologique de la question, Paris N. Aydın 2000: Sümerce Dilbilgisi, Antalya F.J. Badiny 1974: The Sumerian Wonder, Buenos Aires T.E. Balke 1994: About Sumerian personal names, ONOMA 32: 71–82 ––– 1999: Kasus im Sumerischen, Sprachtypologie und Universalienforschung 52: 118–129 ––– 2001: Finale Satzkonstruktionen im Sumerischen, in U.H. Waßner (ed.), Lingua et Linguae. Festschrift für Clemens-Peter Herbermann, Aachen, 15–30 ––– 2002: Die sumerischen Dimensionaladjektive nim und sig. Anmerkungen zur Polysemie und Grammatikalisierung dimensionaler Ausdrücke im Sumerischen, in O. Loretz (ed.), Ex Mesopotamia et Syria Lux. Festschrift für Manfred Dietrich (AOAT 281), Münster, 31–53 ––– 2006: Das sumerische Dimensionalkasussystem (AOAT 331), Münster ––– 2008: Index zur Valenz sumerischer Verben, NABU 2008/48 ––– 2009: Das sumerische Numeraliasystem: Versuch einer typologischen Einordnung, in G.J. Selz (ed.), Empirical Dimensions in Ancient Near Eastern Studies, Wien, 671–698 ––– 2010: The Sumerian Ternary Numeral System, JCS 62: 45–52 A.S. Bartelmus 2016: Fragmente einer großen Sprache: Sumerisch im Kontext der Schreiberausbildung des kassitenzeitlichen Babylonien, Berlin G.A. Barton 1929: Whence Came the Sumerians?, JAOS 49: 263–268 J. Bauer 1975: Zum /dr/-Phonem des Sumerischen, WdO 8: 1–9 ––– 2001: Zum sumerischen Verbalpräfix ba-, NABU 2001/34 ––– 2005: Gudea-Studien, in Y. Sefati (ed.), An experienced Scribe who Neglects Nothing. Ancient Near Eastern Studies in Honor of Jacob Klein, Bethesda, 19–28 ––– 2005: Zum Gebrauch des Ablativs im Sumerischen, NABU 2005/31 ––– 2010: Kasussuffixe mit eingeschränkter Verwendbarkeit?, in J.C. Fincke (ed.), Festschrift für Gernot Wilhelm, Dresden, 57–69 J.D. Bengtson 1990: Notes on the Sino-Caucasian Affinity of Sumerian (Preliminary Report), in V. Shevoroshkin (ed.), Proto-Languages and Proto-Cultures, Bochum, 56–59 ––– 1997: The Riddle of Sumerian: A Dene-Caucasic Language?, Mother Tongue 3: 63–74 E. Bergmann 1964/5: Untersuchungen zu syllabisch geschriebenen sumerischen Texten, ZA 56: 1–43 and 57: 31–42 M. Bielitz 1970: Melismen und ungewöhnliche Vokal- und Silbenwiederholung, bzw. Alternanz in sumerischen Kulttexten der Seleukidenzeit, Or 39: 152–156 J.A. Black 1984: Sumerian Grammar in Babylonian Theory (StPohl SM 12), Roma ––– 1986: Review of Thomsen, The Sumerian Language, AfO 33: 77–83 ––– 1989: The Babylonian Grammatical Tradition: The First Grammars of Sumerian, Transactions of the Philological Society 87: 75–99 ––– 1990: The Alleged Extra Phonemes of Sumerian, RA 84: 107–118 ––– 1995: Real and Unreal Conditional Sentences in Sumerian, ASJ 17: 15–39 ––– 2000: Some Sumerian Adjectives, ASJ 22: 4–27 ––– 2002: Sumerian Lexical Categories, ZA 92: 60–77 ––– 2003: Sumerian Noises: Ideophones in Context, in W. Sallaberger (ed.), Literatur, Politik und Recht in Mesopotamien. Festschrift für Claus Wilcke, Wiesbaden, 35–52 ––– 2004: Sprachwandel im Sumerischen, in J. Meyer & N. Sommerfeld (eds.), 2000 v.Chr. (CDOG 3), Saarbrücken, 171–183 ––– 2007: Sumerian, in J.N. Postgate (ed.), Languages of Iraq, Ancient and Modern, London, 4–30 J.A. Black & G. Zólyomi 2000: The Study of Diachronic and Synchronic Variation in Sumerian, ASJ 22: 249–272, also as internet publication ––– 2007: Introduction to the Study of Sumerian, in J. Ebeling & G. Cunningham (eds.), Analysing Literary Sumerian. Corpus-based Approaches, London, 1–32 V. Blažek & C. Boisson 1992: The Diffusion of Agricultural Terms from Mesopotamia, ArOr 60: 16–37 L.V. Bobrova 1989: Ženskij dialekt v šumerskih tekstah svjaščennogo braka, in Lingvističeskaja rekonstrukcija i drevnejšaja istorija vostoka III, Moskva, 16–18 L.V. Bobrova & A.Ju. Militarëv 1989: Towards the Reconstruction of Sumerian Phonology, in Lingvističeskaja rekonstrukcija i drevnejšaja istorija vostoka I, Moskva, 96–105 I.M. Bobula 1951: Sumérian affiliations. A plea for reconsideration, Washington ––– 1961: A sumér-magyar rokonság kérdése, Buenos Aires ––– 1982: A sumír-magyar rokonság, Buenos Aires C. Boisson 1989: Contraintes typologiques sur le système phonologique du sumérien, Bulletin de la Société de Linguistique 84: 201–233 ––– 1992: The Sumerian Pronominal System: A Nostratic Perspective, in V. Shevoroshkin (ed.), Nostratic, Dene-Caucasian, Austric and Amerind, Bochum, 433–461 ––– 1997: The Phonotactics of Sumerian, in I. Hegeds et al. (eds.), Indo-European, Nostratic, and Beyond, Washington, 30–50 A.R. Bomhard 1997: On the Origin of Sumerian, Mother Tongue 3: 75–92 L.J. Bord 2003: Petite grammaire du sumérien à l’usage des débutants, 2nd ed., Paris R. Borger 1977: Zur Bezeichnung der sumerischen und akkadischen Lautwerte, ZA 67: 20–41 ––– 2004: Mesopotamisches Zeichenlexikon (AOAT 305), Münster J. Braun 2001: Sumerian and Tibeto-Burman, Warszawa N. Brisch 2007: Tradition and the Poetics of Innovation. Sumerian Court Literature of the Larsa Dynasty (c. 2003–1763 BCE) (AOAT 339), Münster [p. 91–113: “Larsa Sumerian”] B. Brogyanyi 2008: Die ungarische alternative Sprachforschung und ihr ideologischer Hintergrund – Versuch einer Diagnose, Sprache & Sprachen 38: 3–15 K. Cathcart 2011: The earliest contribution to the decipherment of Sumerian and Akkadian, Cuneiform Digital Library Journal 2011/1 A. Cavigneaux 1976: Die sumerisch-akkadischen Zeichenlisten: Überlieferungsprobleme, Paris ––– 1987: Le pluriel du cohortative, ASJ 9: 47–48 ––– 1998: É.AN.NA et le genitiv sumérien, NABU 1998/75 D. Charpin 1994: Le sumérien, langue morte parlée, NABU 1994/6 V. Christian 1931: Die sprachliche Stellung des Sumerischen, Babyloniaca 12: 97–222 ––– 1957: Beiträge zur sumerischen Grammatik (Sitzungsberichte der Österreichischen Akademie der Wissenschaften, Phil.-hist. Klasse 231/2), Wien ––– 1961: Die Herkunft der Sumerer (Sitzungsberichte der Österreichischen Akademie der Wissenschaften, Phil.-hist. Klasse 236/1), Wien M. Civil 1973: From Enki’s Headaches to Phonology, JNES 32: 57–61 ––– 1973: The Sumerian Writing System: Some Problems, Or 42: 21–34 ––– 1984: Bilingualism in logographically written languages: Sumerian in Ebla, in L. Cagni (ed.): Il bilinguismo a Ebla, Napoli, 75–97 ––– 1990: Il sumerico, in G.C. Lepschy (ed.), Storia della Linguistica I, 69–105 ––– 1997: Sumerian, in Oxford Encyclopaedia of Archaeology in the Ancient Near East, vol. 5, 92–95 ––– 2000: Modal Prefixes, ASJ 22: 29–42 ––– 2002: The Forerunners of Marû and Hamṭu in Old Babylonian, in T. Abusch (ed.), Riches Hidden in a Secret Place (Studies Jakobsen), Winona Lake, 63–72 ––– 2007: Early Semitic Loanwords in Sumerian, in M.T. Roth et al. (eds.), Studies Presented to Robert D. Biggs, Chicago, 11–33 ––– 2008: A Sumerian Connective Particle and its Possible Semitic Counterparts, AulOr 26: 7–15 ––– 2010:
Recommended publications
  • A Ternary Arithmetic and Logic
    Proceedings of the World Congress on Engineering 2010 Vol I WCE 2010, June 30 - July 2, 2010, London, U.K. A Ternary Arithmetic and Logic Ion Profeanu which supports radical ontological dualism between the two Abstract—This paper is only a chapter, not very detailed, of eternal principles, Good and Evil, which oppose each other a larger work aimed at developing a theoretical tool to in the course of history, in an endless confrontation. A key investigate first electromagnetic fields but not only that, (an element of Manichean doctrine is the non-omnipotence of imaginative researcher might use the same tool in very unusual the power of God, denying the infinite perfection of divinity areas of research) with the stated aim of providing a new perspective in understanding older or recent research in "free that has they say a dual nature, consisting of two equal but energy". I read somewhere that devices which generate "free opposite sides (Good-Bad). I confess that this kind of energy" works by laws and principles that can not be explained dualism, which I think is harmful, made me to seek another within the framework of classical physics, and that is why they numeral system and another logic by means of which I will are kept far away from public eye. So in the absence of an praise and bring honor owed to God's name; and because adequate theory to explain these phenomena, these devices can God is One Being in three personal dimensions (the Father, not reach the design tables of some plants in order to produce them in greater number.
    [Show full text]
  • Fibonacci P-Codes and Codes of the “Golden” P-Proportions: New Informational and Arithmetical Foundations of Computer Scienc
    British Journal of Mathematics & Computer Science 17(1): 1-49, 2016, Article no.BJMCS.25969 ISSN: 2231-0851 SCIENCEDOMAIN international www.sciencedomain.org Fibonacci p-codes and Codes of the “Golden” p-proportions: New Informational and Arithmetical Foundations of Computer Science and Digital Metrology for Mission-Critical Applications Alexey Stakhov1* 1International Club of the Golden Section, Canada. Author’s contribution The sole author designed, analyzed and interpreted and prepared the manuscript. Article Information DOI: 10.9734/BJMCS/2016/25969 Editor(s): (1) Wei-Shih Du, Department of Mathematics, National Kaohsiung Normal University, Taiwan. Reviewers: (1) Santiago Tello-Mijares, Instituto Tecnológico Superior de Lerdo, Mexico. (2) Danyal Soybas, Erciyes University, Turkey. (3) Manuel Alberto M. Ferreira, ISCTE-IUL, Portugal. Complete Peer review History: http://sciencedomain.org/review-history/14921 Received: 28th March 2016 Accepted: 2nd June 2016 Original Research Article Published: 7th June 2016 _______________________________________________________________________________ Abstract In the 70s and 80s years of the past century, the new positional numeral systems, called Fibonaссi p-codes and codes of the golden p-proportions, as new informational and arithmetical foundations of computer science and digital metrology, was considered as one of the most important directions of Soviet computer science and digital metrology for mission-critical applications. The main advantage of this direction was to improve the information reliability of computer and measuring systems. This direction has been patented abroad widely (more than 60 patents of US, Japan, England, France, Germany, Canada and other countries). Theoretical basis of this direction have been described in author’s books "Introduction into the Algorithmic Measurement Theory" (1977), and "Codes of the Golden Proportion" (1984).
    [Show full text]
  • Math Book from Wikipedia
    Math book From Wikipedia PDF generated using the open source mwlib toolkit. See http://code.pediapress.com/ for more information. PDF generated at: Mon, 25 Jul 2011 10:39:12 UTC Contents Articles 0.999... 1 1 (number) 20 Portal:Mathematics 24 Signed zero 29 Integer 32 Real number 36 References Article Sources and Contributors 44 Image Sources, Licenses and Contributors 46 Article Licenses License 48 0.999... 1 0.999... In mathematics, the repeating decimal 0.999... (which may also be written as 0.9, , 0.(9), or as 0. followed by any number of 9s in the repeating decimal) denotes a real number that can be shown to be the number one. In other words, the symbols 0.999... and 1 represent the same number. Proofs of this equality have been formulated with varying degrees of mathematical rigour, taking into account preferred development of the real numbers, background assumptions, historical context, and target audience. That certain real numbers can be represented by more than one digit string is not limited to the decimal system. The same phenomenon occurs in all integer bases, and mathematicians have also quantified the ways of writing 1 in non-integer bases. Nor is this phenomenon unique to 1: every nonzero, terminating decimal has a twin with trailing 9s, such as 8.32 and 8.31999... The terminating decimal is simpler and is almost always the preferred representation, contributing to a misconception that it is the only representation. The non-terminating form is more convenient for understanding the decimal expansions of certain fractions and, in base three, for the structure of the ternary Cantor set, a simple fractal.
    [Show full text]
  • Dirac's Principle of Mathematical Beauty, Mathematics of Harmony
    1 Dirac’s Principle of Mathematical Beauty, Mathematics of Harmony and “Golden” Scientific Revolution Alexey Stakhov The International Club of the Golden Section 6 McCreary Trail, Bolton, ON, L7E 2C8, Canada [email protected] • www.goldenmuseum.com Abstract. In this study we develop the Mathematics of Harmony as a new interdisciplinary direction of modern science. The newest discoveries in different fields of modern science based on the Mathematics of Harmony, namely, mathematics (a general theory of hyperbolic functions and a solution to Hilbert’s Fourth Problem, algorithmic measurement theory and “golden” number theory), computer science (the “golden information technology), crystallography (quasi-crystals), chemistry (fullerenes), theoretical physics and cosmology (Fibonacci-Lorentz transformations, the “golden” interpretation of special theory of relativity and “golden” interpretation of the Universe evolution), botany (new geometric theory of phyllotaxis), genetics (“golden” genomatrices) and so on, are creating a general picture of the “Golden” Scientific Revolution, which can influence fundamentally on the development of modern science and education. Contents Preface 1. Introduction: Dirac’s Principle of Mathematical Beauty and “beautiful” mathematical objects 2. A new approach to the mathematics origins 3. The Mathematics of Harmony as a “beautiful” mathematical theory 4. The “Golden” Fibonacci goniometry: a revolution in the theory of hyperbolic functions 5. The “Golden” Fibonacci goniometry and Hilbert’s Fourth Problem: revolution in hyperbolic geometry 6. Fibonacci and “golden” matrices: a unique class of square matrices 7. New scientific principles based on the Golden Section 8. The Mathematics of Harmony: a renaissance of the oldest mathematical theories 9. The “Golden” information technology: a revolution in computer science 10.
    [Show full text]
  • The Sumerian Ternary System and the Concept of Number António José Gonçalves De Freitas Centro De Estudos Humanísticos Universidade Do Minho Portugal
    Paper delivered at 1st CLE Colloquium for Philosophy and Formal Sciences Campinas, 21-23 March 2013 Accepted for publication in the Proceedings of the Conference DRAFT &1 The Sumerian ternary system and the concept of number António José Gonçalves de Freitas Centro de Estudos Humanísticos Universidade do Minho Portugal Abstract It is well known that Sumerians and Babylonians used a numeration system of base 12 and 60. We still have influence of that system in our nowadays counting of the hours of a day, twelve plus twelve, each hour has 60 minute and each minute 60 seconds. Also the circle has 360 degrees. What is not so well known is that the Sumerians in an earlier period used a ternary system of numeration; the first notice about that system is in Thureau- Dangin (1928). Later Diakonoff (1983) described it in good details and recently, Balke (2010) studied the system and described it with more precision. Still the use of this system and the concept of number involved are open questions. I will answer to those problems making a formalization of the system and showing how it could be related to a cosmogonic design. DRAFT &2 1. Numeral systems. DRAFT &3 ��� 1 11 21 31 41 51 � �� ��� �� �� � ��� 2 12 22 32 41 52 � �� ��� �� �� � � �� ��� � 3 13 23 33 42 53 � �� � � � � � �� ��� � 4 14 24 34 43 54 � �� � � � � � �� ��� � 5 15 25 35 44 55 � �� � � � � � �� ��� � 6 16 26 36 45 56 � �� �DRAFT� � � � �� ��� � 7 17 27 37 46 57 � �� � � � � &4 � �� � 8 18 28 38 47 58 � �� �� � � � � �� � � 9 19 29 39 48 59 � �� � � � � 10 20 30 ��� 40 50 � �� � � The main Babylonian and Sumerian counting system was a sexagesimal system.
    [Show full text]
  • Numbers and Calculators ARCHI 2019 Summit 2,397,824 Cores 2,801,664 GB Mem 200,795 Tflop/S
    Numbers and Calculators ARCHI 2019 Summit 2,397,824 Cores 2,801,664 GB mem 200,795 TFlop/s 13,000,000 W 200,000,000 $ Summit MareNostrum P9 CTE 2,397,824 Cores 19,440 Cores 2,801,664 GB mem 27,648 GB mem 200,795 TFlop/s 1,018 TFlop/s 13,000,000 W 85,000 W 200,000,000 $ 34,000,000 € Summit MareNostrum P9 CTE 2,397,824 Cores 19,440 Cores 2,801,664 GB mem 27,648 GB mem Version N°3 200,795 TFlop/s 1,018 TFlop/s 38 PFlop/s 13,000,000 W 85,000 W 20 Watts 200,000,000 $ 34,000,000 € 30,000 € Summit MareNostrum P9 CTE 2,397,824 Cores 19,440 Cores 2,801,664 GB mem 27,648 GB mem Version N°3 200,795 TFlop/s 1,018 TFlop/s 38 PFlop/s 13,000,000 W 85,000 W 20 Watts 200,000,000 $ 34,000,000 € 30,000 € Outline 1.Analogic computation 2.Computer’s Zoo 3.A few words about gate 4.How to use transistors 5.Number’s representation Outline 1.Analogic computation 2.Computer’s Zoo 3.A few words about gate 4.How to use transistors 5.Number’s representation Numbers in continuous space: Analog computer • Uses continuous property of physical phenomena (electrical, mechanical, hydraulic) • Resilient to quantization noise But subject to physical noise (electronic, °C, …) • Can be more powerful than digital computer • Dominant in HPC until the 70s • Example: • Used for the Apollo 11 mission • Tide-Prediction machine (William & James Thomson) Alternatives to numerical computer • Human Brain • 38 PetaFlops, 20 Watts • Analog computer • Not program by algorithm no need to store, fetch, decode instructions and operand • Hybrid digital / analog computer • Complement their digital counterparts in solving equations relevant in: Biology, fluid dynamics, weather prediction, quantum chemistry, plasma physics, … Toward an hybrid analog co-processor Telefunken RA770 • System configured by the equations similar to the targeted system and allow variables in the analog computer to evolve with time • Analog computer to provide a quick approximation • Digital computer for programming, storage and precision • Example 2 diff.
    [Show full text]
  • Download Book // Positional Numeral Systems: Hexadecimal, Octal
    QUB7RMIDHRDN » eBook » Positional numeral systems: Hexadecimal, Octal, Duodecimal, Senary, Ternary numeral system, Decimal mark,... Download eBook Online POSITIONAL NUMERAL SYSTEMS: HEXADECIMAL, OCTAL, DUODECIMAL, SENARY, TERNARY NUMERAL SYSTEM, DECIMAL MARK, SEXAGESIMAL, BINARY NUMERAL SYSTEM To save Positional numeral systems: Hexadecimal, Octal, Duodecimal, Senary, Ternary numeral system, Decimal mark, Sexagesimal, Binary numeral system eBook, remember to click the link beneath and download the ebook or have accessibility to other information that are highly relevant to POSITIONAL NUMERAL SYSTEMS: HEXADECIMAL, OCTAL, DUODECIMAL, SENARY, TERNARY NUMERAL SYSTEM, DECIMAL MARK, SEXAGESIMAL, BINARY NUMERAL SYSTEM book. Download PDF Positional numeral systems: Hexadecimal, Octal, Duodecimal, Senary, Ternary numeral system, Decimal mark, Sexagesimal, Binary numeral system Authored by Source: Wikipedia Released at 2016 Filesize: 7.7 MB Reviews It in just one of my personal favorite pdf. I could comprehended every thing out of this written e book. Its been written in an remarkably basic way and is particularly just following i finished reading through this book by which actually transformed me, affect the way i think. -- Jace Johns These types of pdf is the best ebook accessible. Sure, it is actually enjoy, nonetheless an interesting and amazing literature. I am pleased to inform you that this is basically the very best pdf i actually have read through in my own daily life and may be he finest ebook for ever. -- Prince Haag A top quality ebook and the typeface used was interesting to learn. This can be for all who statte that there had not been a well worth reading through. I am just pleased to tell you that this is basically the very best ebook i actually have go through in my individual life and can be he finest book for at any time.
    [Show full text]
  • Arxiv:1706.00480V2 [Math.CO] 4 Oct 2017 Where N Ekyicesn Euneof Sequence Increasing Weakly Any Ihvrie in Vertices with Sas Atc Oyoe Ntecs F∆ of Case the in Polytope
    SIMPLICES FOR NUMERAL SYSTEMS LIAM SOLUS Abstract. The family of lattice simplices in Rn formed by the convex hull of the standard basis vectors together with a weakly decreasing vector of negative integers include simplices that play a central role in problems in enumerative algebraic geometry and mirror symmetry. From this perspective, it is use- ful to have formulae for their discrete volumes via Ehrhart h∗-polynomials. Here we show, via an association with numeral systems, that such simplices yield h∗-polynomials with properties that are also desirable from a combinato- rial perspective. First, we identify n-simplices in this family that associate via their normalized volume to the nth place value of a positional numeral system. We then observe that their h∗-polynomials admit combinatorial formula via descent-like statistics on the numeral strings encoding the nonnegative integers within the system. With these methods, we recover ubiquitous h∗-polynomials including the Eulerian polynomials and the binomial coefficients arising from the factoradic and binary numeral systems, respectively. We generalize the bi- nary case to base-r numeral systems for all r ≥ 2, and prove that the associated h∗-polynomials are real-rooted and unimodal for r ≥ 2 and n ≥ 1. 1. Introduction We consider the family of simplices defined by the convex hull Rn ∆(1,q) := conv(e1,...,en, −q) ⊂ , n where e1,...,en denote the standard basis vectors in R , and q = (q1, q2,...,qn) is any weakly increasing sequence of n positive integers. A convex polytope P ⊂ Rn with vertices in Zn (i.e. a lattice polytope) is called reflexive if its polar body P ◦ := {y ∈ Rn : yT x ≤ 1 for all x ∈ P }⊂ Rn is also a lattice polytope.
    [Show full text]
  • Numeral Systems with Irrational Bases for Mission-Critical Applications
    16 СЕКЦІЯ 2. Методи та засоби захисту інформації Numeral Systems with Irrational Bases for Mission-Critical Applications. The Basic Concepts and Scientific Results Oleksiy Stakhov Computer Firm FibTech (Fibonacci Technology), Ontario, Canada [email protected] Системи числення з іраціональними основами для критично важливих застосувань. Головні концепції та наукові результати Олексій Стахов Компютерна фірма FibTech (Fibonacci Technology), Онтаріо, Канада [email protected] Abstract— This speech is of an overview nature. Its main INTRODUCTION goal is to substantiate the basic concepts and scientific results of a new direction in the theory of coding-the numeral system In 2017 the International Publishing House ―World with irrational bases, and their application in mission-critical Scientific‖ has published new book of the author systems. This scientific direction began to develop in the ―Numeral Systems with Irrational Bases for Mission- Taganrog Radiotechnical Institute after the defense of the Critical Applications‖. doctoral dissertation of the author of this speech (1972), and then successfully continued to develop in the Vinnytsya Polytechnic Institute at the Department of Computer Technology. Nowadays this scientific direction is developing in Canada (computer firm FibTech (Fibonacci Technology)) and at Sumy University. Анотація—Ця доповідь має оглядовий характер. Її основна мета – обгрунтувати головні концепції та наукові результати нового напрямку в теорії кодування – системи числення з ірраціональними основами, та їх застосування в критично-важливих системах. Цей науковий напрямок почав розвиаатися в Таганрогському . радіотехнічному інституті після захисту докторської дисертації автора цієї доповіді (1972), потім успішно Advertising information on the book is posted at the продовжив розвиватися в Вінницькому політехнічному site of "World Scientific" інституті на кафедрі обчислювальної техніки.
    [Show full text]
  • Number Guessing
    NUMBER GUESSING FATIN SEZGIN 1 1Bilkent University, Ankara, TURKEY email: [email protected] Abstract. It is instructive and interesting to find numbers hold by using a positional numeration system on base b = 4. Here we present four cards having integers 1-64 written in different colors. Given the information on the cards, one can guess the secret number hold by the player. Key words: base-4, isomorphism, number guessing, positional number system, qua- ternary numeral system, radix 1Theframework It looks very natural for us to use positional number system based on radix 10, because human beings used their fingers for counting. But mathematically it is completely valid to use any other base b ≥ 2. For example binary, octal, and hexadecimal arithmetic is used in computing and programming. Our time and angle measurements rely on sexagesimal (base-60) system. Although quaternary (base-4) numbers are not very common, there are some areas appropriate for their usage: It is possible to represent directions by base-4 system. Base-4 also can be used in genetic coding of DNA. The four nucleotides are abbreviated as A, C, G, and T. Therefore nucleotide sequences can be represented numerically by coding these letters as A =0, C =1,G =2,andT = 3. Proposed first by Adleman (1994), DNA or molecular computation emerged as a new research area. Within the last decade hundreds of research papers appeared describing biomolecular computation techniques for various challenging problems which require extremely large parallelism and memory in conventional electronic-based computers (Garzon et al (2004), and Jonosca (2004)). It may be surprising to convey and get information by using different radixes.
    [Show full text]
  • Design and Implementation of Ternary Logic Circuits for VLSI Applications
    International Journal of Innovative Technology and Exploring Engineering (IJITEE) ISSN: 2278-3075, Volume-9 Issue-4, February 2020 Design and Implementation of Ternary Logic Circuits for VLSI Applications G. Thrishala, K.Ragini Abstract: This paper mainly concentrates on the design and For instance, more data can be transmitted over an implementation of ternary logic circuits. The ternary numeral arrangement of lines in a given length, diminishing in the system has its base as 3. Ternary logic will use three symbols, complexity of interconnections is observed, decrease in chip which are, 0,1 and 2. The ternary logic has significant merits area can be accomplished, and more significantly the error over binary logic in designing digital circuits. In this paper, it is detection and error correction of codes can be accomplished. proposed to implement a half adder circuit using ternary 3 to 1 multiplexer. The main objective of the work is, to design and The ternary logic system has some significant implement ternary logic circuits and to analyse the function of merits over the binary logic system [2,3]. To implement the the ternary combinational circuits using mentor graphics tool in different logic functions, the decrease in the number of 90nm technology. This paper also compares the ternary half interconnections in a circuit is observed, in this way, the adder design using k-map method with the proposed ternary half chip area has been reduced, and importantly more data can adder using multiplexer in terms of power dissipation, be transmitted and lesser memory is required. Apart from propagation delay and transistor count.
    [Show full text]
  • The Mathematics of the Unknown Bringing to the Present the Knowledge of the Future
    The Mathematics of the Unknown Bringing to the present the knowledge of the future R. A. García Leiva (This book is 69% complete) Copyright c 2020 R. A. García Leiva www.mathematicsunknonw.com PUBLISHED BY THE AUTHOR This book is dedicated to my wife Justi, my son Daniel, and my two daughters Teresa and Lucía. Contents 1 Introduction .................................................. 19 1.1 Entities 20 1.2 Representations 21 1.3 Descriptions 22 1.4 Miscoding 24 1.5 Inaccuracy 25 1.6 Surfeit 27 1.7 Nescience 28 1.8 Evolution of Nescience 31 1.9 Other Metrics 32 1.10 Interesting Research Questions 34 1.11 New Research Entities 36 1.12 References and Further Reading 37 I Part 1: Background 2 Logic ........................................................ 41 2.1 Propositional Logic 41 2.2 Predicate Logic 43 3 Discrete Mathematics ......................................... 45 3.1 Sets, Relations and Functions 46 3.2 Strings 47 3.3 Matrices 48 3.4 Graphs 49 3.5 Probability 51 4 Set Theory .................................................... 55 5 Computability ................................................ 57 5.1 Turing Machines 58 5.2 Universal Turing Machines 61 5.3 Non-Computable Problems 62 5.4 Computable Functions and Sets 63 5.5 Oracle Turing Machine 64 5.6 Computational Complexity 64 6 Coding ...................................................... 67 6.1 Coding 68 6.2 Kraft Inequality 70 6.3 Entropy 72 6.4 Optimal Codes 75 6.5 Huffman Algorithm 76 7 Complexity .................................................. 81 7.1 Strings Complexity 82 7.2 Properties of Complexity 84 7.3 Conditional Kolmogorov complexity 85 7.4 Information Distance 86 7.5 Incompressibility and Randomness 87 8 Learning ....................................................
    [Show full text]