HW-TSC's Participation in the WAT 2020 Indic Languages Multilingual
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The What and Why of Whole Number Arithmetic: Foundational Ideas from History, Language and Societal Changes
Portland State University PDXScholar Mathematics and Statistics Faculty Fariborz Maseeh Department of Mathematics Publications and Presentations and Statistics 3-2018 The What and Why of Whole Number Arithmetic: Foundational Ideas from History, Language and Societal Changes Xu Hu Sun University of Macau Christine Chambris Université de Cergy-Pontoise Judy Sayers Stockholm University Man Keung Siu University of Hong Kong Jason Cooper Weizmann Institute of Science SeeFollow next this page and for additional additional works authors at: https:/ /pdxscholar.library.pdx.edu/mth_fac Part of the Science and Mathematics Education Commons Let us know how access to this document benefits ou.y Citation Details Sun X.H. et al. (2018) The What and Why of Whole Number Arithmetic: Foundational Ideas from History, Language and Societal Changes. In: Bartolini Bussi M., Sun X. (eds) Building the Foundation: Whole Numbers in the Primary Grades. New ICMI Study Series. Springer, Cham This Book Chapter is brought to you for free and open access. It has been accepted for inclusion in Mathematics and Statistics Faculty Publications and Presentations by an authorized administrator of PDXScholar. Please contact us if we can make this document more accessible: [email protected]. Authors Xu Hu Sun, Christine Chambris, Judy Sayers, Man Keung Siu, Jason Cooper, Jean-Luc Dorier, Sarah Inés González de Lora Sued, Eva Thanheiser, Nadia Azrou, Lynn McGarvey, Catherine Houdement, and Lisser Rye Ejersbo This book chapter is available at PDXScholar: https://pdxscholar.library.pdx.edu/mth_fac/253 Chapter 5 The What and Why of Whole Number Arithmetic: Foundational Ideas from History, Language and Societal Changes Xu Hua Sun , Christine Chambris Judy Sayers, Man Keung Siu, Jason Cooper , Jean-Luc Dorier , Sarah Inés González de Lora Sued , Eva Thanheiser , Nadia Azrou , Lynn McGarvey , Catherine Houdement , and Lisser Rye Ejersbo 5.1 Introduction Mathematics learning and teaching are deeply embedded in history, language and culture (e.g. -
Tai Lü / ᦺᦑᦟᦹᧉ Tai Lùe Romanization: KNAB 2012
Institute of the Estonian Language KNAB: Place Names Database 2012-10-11 Tai Lü / ᦺᦑᦟᦹᧉ Tai Lùe romanization: KNAB 2012 I. Consonant characters 1 ᦀ ’a 13 ᦌ sa 25 ᦘ pha 37 ᦤ da A 2 ᦁ a 14 ᦍ ya 26 ᦙ ma 38 ᦥ ba A 3 ᦂ k’a 15 ᦎ t’a 27 ᦚ f’a 39 ᦦ kw’a 4 ᦃ kh’a 16 ᦏ th’a 28 ᦛ v’a 40 ᦧ khw’a 5 ᦄ ng’a 17 ᦐ n’a 29 ᦜ l’a 41 ᦨ kwa 6 ᦅ ka 18 ᦑ ta 30 ᦝ fa 42 ᦩ khwa A 7 ᦆ kha 19 ᦒ tha 31 ᦞ va 43 ᦪ sw’a A A 8 ᦇ nga 20 ᦓ na 32 ᦟ la 44 ᦫ swa 9 ᦈ ts’a 21 ᦔ p’a 33 ᦠ h’a 45 ᧞ lae A 10 ᦉ s’a 22 ᦕ ph’a 34 ᦡ d’a 46 ᧟ laew A 11 ᦊ y’a 23 ᦖ m’a 35 ᦢ b’a 12 ᦋ tsa 24 ᦗ pa 36 ᦣ ha A Syllable-final forms of these characters: ᧅ -k, ᧂ -ng, ᧃ -n, ᧄ -m, ᧁ -u, ᧆ -d, ᧇ -b. See also Note D to Table II. II. Vowel characters (ᦀ stands for any consonant character) C 1 ᦀ a 6 ᦀᦴ u 11 ᦀᦹ ue 16 ᦀᦽ oi A 2 ᦰ ( ) 7 ᦵᦀ e 12 ᦵᦀᦲ oe 17 ᦀᦾ awy 3 ᦀᦱ aa 8 ᦶᦀ ae 13 ᦺᦀ ai 18 ᦀᦿ uei 4 ᦀᦲ i 9 ᦷᦀ o 14 ᦀᦻ aai 19 ᦀᧀ oei B D 5 ᦀᦳ ŭ,u 10 ᦀᦸ aw 15 ᦀᦼ ui A Indicates vowel shortness in the following cases: ᦀᦲᦰ ĭ [i], ᦵᦀᦰ ĕ [e], ᦶᦀᦰ ăe [ ∎ ], ᦷᦀᦰ ŏ [o], ᦀᦸᦰ ăw [ ], ᦀᦹᦰ ŭe [ ɯ ], ᦵᦀᦲᦰ ŏe [ ]. -
The Kharoṣṭhī Documents from Niya and Their Contribution to Gāndhārī Studies
The Kharoṣṭhī Documents from Niya and Their Contribution to Gāndhārī Studies Stefan Baums University of Munich [email protected] Niya Document 511 recto 1. viśu͚dha‐cakṣ̄u bhavati tathāgatānaṃ bhavatu prabhasvara hiterṣina viśu͚dha‐gātra sukhumāla jināna pūjā suchavi paramārtha‐darśana 4 ciraṃ ca āyu labhati anālpakaṃ 5. pratyeka‐budha ca karoṃti yo s̄ātravivegam āśṛta ganuktamasya 1 ekābhirāma giri‐kaṃtarālaya 2. na tasya gaṃḍa piṭakā svakartha‐yukta śamathe bhavaṃti gune rata śilipataṃ tatra vicārcikaṃ teṣaṃ pi pūjā bhavatu [v]ā svayaṃbhu[na] 4 1 suci sugaṃdha labhati sa āśraya 6. koḍinya‐gotra prathamana karoṃti yo s̄ātraśrāvaka {?} ganuktamasya 2 teṣaṃ ca yo āsi subha͚dra pac̄ima 3. viśāla‐netra bhavati etasmi abhyaṃdare ye prabhasvara atīta suvarna‐gātra abhirūpa jinorasa te pi bhavaṃtu darśani pujita 4 2 samaṃ ca pādo utarā7. imasmi dāna gana‐rāya prasaṃṭ́hita u͚tama karoṃti yo s̄ātra sthaira c̄a madhya navaka ganuktamasya 3 c̄a bhikṣ̄u m It might be going to far to say that Torwali is the direct lineal descendant of the Niya Prakrit, but there is no doubt that out of all the modern languages it shows the closest resemblance to it. [...] that area around Peshawar, where [...] there is most reason to believe was the original home of Niya Prakrit. That conclusion, which was reached for other reasons, is thus confirmed by the distribution of the modern dialects. (Burrow 1936) Under this name I propose to include those inscriptions of Aśoka which are recorded at Shahbazgaṛhi and Mansehra in the Kharoṣṭhī script, the vehicle for the remains of much of this dialect. To be included also are the following sources: the Buddhist literary text, the Dharmapada found in Khotan, written likewise in Kharoṣṭhī [...]; the Kharoṣṭhī documents on wood, leather, and silk from Caḍ́ota (the Niya site) on the border of the ancient kingdom of Khotan, which represented the official language of the capital Krorayina [...]. -
Devan¯Agar¯I for TEX Version 2.17.1
Devanagar¯ ¯ı for TEX Version 2.17.1 Anshuman Pandey 6 March 2019 Contents 1 Introduction 2 2 Project Information 3 3 Producing Devan¯agar¯ıText with TEX 3 3.1 Macros and Font Definition Files . 3 3.2 Text Delimiters . 4 3.3 Example Input Files . 4 4 Input Encoding 4 4.1 Supplemental Notes . 4 5 The Preprocessor 5 5.1 Preprocessor Directives . 7 5.2 Protecting Text from Conversion . 9 5.3 Embedding Roman Text within Devan¯agar¯ıText . 9 5.4 Breaking Pre-Defined Conjuncts . 9 5.5 Supported LATEX Commands . 9 5.6 Using Custom LATEX Commands . 10 6 Devan¯agar¯ıFonts 10 6.1 Bombay-Style Fonts . 11 6.2 Calcutta-Style Fonts . 11 6.3 Nepali-Style Fonts . 11 6.4 Devan¯agar¯ıPen Fonts . 11 6.5 Default Devan¯agar¯ıFont (LATEX Only) . 12 6.6 PostScript Type 1 . 12 7 Special Topics 12 7.1 Delimiter Scope . 12 7.2 Line Spacing . 13 7.3 Hyphenation . 13 7.4 Captions and Date Formats (LATEX only) . 13 7.5 Customizing the date and captions (LATEX only) . 14 7.6 Using dvnAgrF in Sections and References (LATEX only) . 15 7.7 Devan¯agar¯ıand Arabic Numerals . 15 7.8 Devan¯agar¯ıPage Numbers and Other Counters (LATEX only) . 15 1 7.9 Category Codes . 16 8 Using Devan¯agar¯ıin X E LATEXand luaLATEX 16 8.1 Using Hindi with Polyglossia . 17 9 Using Hindi with babel 18 9.1 Installation . 18 9.2 Usage . 18 9.3 Language attributes . 19 9.3.1 Attribute modernhindi . -
Numeration Systems Reminder : If a and M Are Whole Numbers Then Exponential Expression Amor a to the Mth Power Is M = ⋅⋅⋅⋅⋅ Defined by A Aaa
MA 118 – Section 3.1: Numeration Systems Reminder : If a and m are whole numbers then exponential expression amor a to the mth power is m = ⋅⋅⋅⋅⋅ defined by a aaa... aa . m times Number a is the base ; m is the exponent or power . Example : 53 = Definition: A number is an abstract idea that indicates “how many”. A numeral is a symbol used to represent a number. A System of Numeration consists of a set of basic numerals and rules for combining them to represent numbers. 1 Section 3.1: Numeration Systems The timeline indicates recorded writing about 10,000 years ago between 4,000–3,000 B.C. The Ishango Bone provides the first evidence of human counting, dated 20,000 years ago. I. Tally Numeration System Example: Write the first 12 counting numbers with tally marks. In a tally system, there is a one-to-one correspondence between marks and items being counted. What are the advantages and drawbacks of a Tally Numeration System? 2 Section 3.1: Numeration Systems (continued) II. Egyptian Numeration System Staff Yoke Scroll Lotus Pointing Fish Amazed (Heel Blossom Finger (Polywog) (Astonished) Bone) Person Example : Page 159 1 b, 2b Example : Write 3248 as an Egyptian numeral. What are the advantages and drawbacks of the Egyptian System? 3 Section 3.1: Numeration Systems (continued) III. Roman Numeral System Roman Numerals I V X L C D M Indo-Arabic 1 5 10 50 100 500 1000 If a symbol for a lesser number is written to the left of a symbol for a greater number, then the lesser number is subtracted. -
Course: M.A. Sanskrit Total Seats: 509 Seats Distribution
Course: M.A. Sanskrit Total Seats: 509 Seats Distribution Exam Type General SC ST OBC EWS Total Entrance 116 38 19 69 13 255 Merit 117 38 19 68 12 254 Eligibility in Entrance Category Category Course Requirements Marks Requirements Id 1 B.A. (Hons.) Sanskrit from recognized Minimum 45% marks for General Category and 40.5% for OBC University. and admission of SC/ST/PwD category candidates will be done as per University rules or equivalent grade 2 B.A. (Pass)/B.A. (Programme) or BA (Hons.) 50% marks in aggregate for General category and 45% for OBC in Hindi of the University of Delhi or any & admission of SC/ST/PwD category candidates will be done as recognized university with at least two papers per University rules or equivalent grade of Sanskrit 3 Acharya/Shastri (Sanskrit) examination of 50% in aggregate for General Category and 45% for OBC and recognized University/Deemed University admission of SC/ST/PwD category candidates will be done as and Rashtriya Sanskrit Sansthan. per University rules or equivalent grade 5 B.A. (H) Examination in any subject of the Minimum 50% for General Category and 45% for OBC in Delhi University of an examination Hons. And minimum 60% for general 54% for OBC in Sanskrit recognized as equivalent there to with Subsidiary/Concurrent Subject & admission of SC/ST/PwD Sanskrit as subsidiary/concurrent subject. category candidates will be done as University rules or equivalent grade 6 M.A. examination in any arts and Humanities Minimum 50% for General & 45% for OBC marks in aggregate (except Sanskrit) from University of Delhi. -
An Introduction to Indic Scripts
An Introduction to Indic Scripts Richard Ishida W3C [email protected] HTML version: http://www.w3.org/2002/Talks/09-ri-indic/indic-paper.html PDF version: http://www.w3.org/2002/Talks/09-ri-indic/indic-paper.pdf Introduction This paper provides an introduction to the major Indic scripts used on the Indian mainland. Those addressed in this paper include specifically Bengali, Devanagari, Gujarati, Gurmukhi, Kannada, Malayalam, Oriya, Tamil, and Telugu. I have used XHTML encoded in UTF-8 for the base version of this paper. Most of the XHTML file can be viewed if you are running Windows XP with all associated Indic font and rendering support, and the Arial Unicode MS font. For examples that require complex rendering in scripts not yet supported by this configuration, such as Bengali, Oriya, and Malayalam, I have used non- Unicode fonts supplied with Gamma's Unitype. To view all fonts as intended without the above you can view the PDF file whose URL is given above. Although the Indic scripts are often described as similar, there is a large amount of variation at the detailed implementation level. To provide a detailed account of how each Indic script implements particular features on a letter by letter basis would require too much time and space for the task at hand. Nevertheless, despite the detail variations, the basic mechanisms are to a large extent the same, and at the general level there is a great deal of similarity between these scripts. It is certainly possible to structure a discussion of the relevant features along the same lines for each of the scripts in the set. -
Origin of the Numerals Al-Biruni's Testimony
Origin of the numerals Al-Biruni’s testimony Ahmed Boucenna Laboratoire DAC, Department of Physics, Faculty of Sciences, Ferhat Abbas University 19000 Stif, Algeria [email protected] [email protected] Abstract The origin of the numerals that we inherited from the arabo-Islamic civilization remained one enigma. The hypothesis of the Indian origin remained, with controversies, without serious rival. It was the dominant hypothesis since more of one century. Its partisans found to it and constructed a lot of arguments. The testimonies of the medieval authors have been interpreted to its advantage. The opposite opinions have been dismissed and ignored. An amalgam between the history of our modern numerals and the Indian mathematics history is made. Rational contradictions often passed under silence. A meticulous observation of the numerals permits to affirm that our numerals are in fact more or less modified Arabic letters. The "Ghubari" shape of the numerals shows that the symbol of a numeral corresponds to the Arabic letter whose numerical value is equal to this numeral. The numerals don't have a simple resemblance with some Arabic letters, but every number looks like the Arabic letter whose numerical value is equal to this numeral. The elements of the ''Abjadi'' calculation gives us a theoretical support, independent of the letters and numerals, witch explains our observation. Besides a re-lecture of the testimonies of the medieval authors, particularly the testimony of Al-Biruni, that is probably at the origin of all others testimonies speaking of the Indian origin of the numerals, is in agreement with the fact that our numerals are Arabic letters. -
Transliteration of <Script Name>
Transliteration of Bengali, Assamese & Manipuri 1/5 BENGALI, ASSAMESE & MANIPURI Script: Bengali* ISO 15919 UN ALA-LC 2001(1.0) 1977(2.0) 1997(3.0) Vowels অ ◌ a a a আ ◌া ā ā ā ই ি◌ i i i ঈ ◌ী ī ī ī উ ◌ু u u u ঊ ◌ূ ū ū ū ঋ ◌ৃ r̥ ṛ r̥ ৠ ◌ৄ r̥̄ — r̥̄ ঌ ◌ৢ l̥ — l̥ ৡ ◌ৣ A l̥ ̄ — — এ ে◌ e(1.1) e e ঐ ৈ◌ ai ai ai ও ে◌া o(1.1) o o ঔ ে◌ৗ au au au অ�া a:yā — — Nasalizations ◌ং anunāsika ṁ(1.2) ṁ ṃ ◌ঁ candrabindu m̐ (1.2) m̐ n̐, m̐ (3.1) Miscellaneous ◌ঃ bisarga ḥ ḥ ḥ ◌্ hasanta vowelless vowelless vowelless (1.3) ঽ abagraha Ⓑ :’ — ’ ৺ isshara — — — Consonants ক ka ka ka খ kha kha kha গ ga ga ga ঘ gha gha gha ঙ ṅa ṅa ṅa চ ca cha ca ছ cha chha cha জ ja ja ja ঝ jha jha jha ঞ ña ña ña ট ṭa ṭa ṭa ঠ ṭha ṭha ṭha ড ḍa ḍa ḍa ঢ ḍha ḍha ḍha ণ ṇa ṇa ṇa ত ta ta ta Thomas T. Pedersen – transliteration.eki.ee Rev. 2, 2005-07-21 Transliteration of Bengali, Assamese & Manipuri 2/5 ISO 15919 UN ALA-LC 2001(1.0) 1977(2.0) 1997(3.0) থ tha tha tha দ da da da ধ dha dha dha ন na na na প pa pa pa ফ pha pha pha ব ba ba ba(3.2) ভ bha bha bha ম ma ma ma য ya ja̱ ya র ⒷⓂ ra ra ra ৰ Ⓐ ra ra ra ল la la la ৱ ⒶⓂ va va wa শ śa sha śa ষ ṣa ṣha sha স sa sa sa হ ha ha ha ড় ṛa ṙa ṛa ঢ় ṛha ṙha ṛha য় ẏa ya ẏa জ় za — — ব় wa — — ক় Ⓑ qa — — খ় Ⓑ k̲h̲a — — গ় Ⓑ ġa — — ফ় Ⓑ fa — — Adscript consonants ◌� ya-phala -ya(1.4) -ya ẏa ৎ khanda-ta -t -t ṯa ◌� repha r- r- r- ◌� baphala -b -b -b ◌� raphala -r -r -r Vowel ligatures (conjuncts)C � gu � ru � rū � Ⓐ ru � rū � śu � hr̥ � hu � tru � trū � ntu � lgu Thomas T. -
Brahminet-ITRANS Transliteration Scheme
BrahmiNet-ITRANS Transliteration Scheme Anoop Kunchukuttan August 2020 The BrahmiNet-ITRANS notation (Kunchukuttan et al., 2015) provides a scheme for transcription of major Indian scripts in Roman, using ASCII characters. It extends the ITRANS1 transliteration scheme to cover characters not covered in the original scheme. Tables 1a shows the ITRANS mappings for vowels and diacritics (matras). Table 1b shows the ITRANS mappings for consonants. These tables also show the Unicode offset for each character. By Unicode offset, we mean the offset of the character in the Unicode range assigned to the script. For Indic scripts, logically equivalent characters are assigned the same offset in their respective Unicode codepoint ranges. For illustration, we also show the Devanagari characters corresponding to the transliteration. ka kha ga gha ∼Na, N^a ITRANS Unicode Offset Devanagari 15 16 17 18 19 a 05 अ क ख ग घ ङ aa, A 06, 3E आ, ◌ा cha Cha ja jha ∼na, JNa i 07, 3F इ, ि◌ 1A 1B 1C 1D 1E ii, I 08, 40 ई, ◌ी च छ ज झ ञ u 09, 41 उ, ◌ु Ta Tha Da Dha Na uu, U 0A, 42 ऊ, ◌ू 1F 20 21 22 23 RRi, R^i 0B, 43 ऋ, ◌ृ ट ठ ड ढ ण RRI, R^I 60, 44 ॠ, ◌ॄ ta tha da dha na LLi, L^i 0C, 62 ऌ, ◌ॢ 24 25 26 27 28 LLI, L^I 61, 63 ॡ, ◌ॣ त थ द ध न pa pha ba bha ma .e 0E, 46 ऎ, ◌ॆ 2A 2B 2C 2D 2E e 0F, 47 ए, ◌े प फ ब भ म ai 10,48 ऐ, ◌ै ya ra la va, wa .o 12, 4A ऒ, ◌ॊ 2F 30 32 35 o 13, 4B ओ, ◌ो य र ल व au 14, 4C औ, ◌ौ sha Sha sa ha aM 05 02, 02 अं 36 37 38 39 aH 05 03, 03 अः श ष स ह .m 02 ◌ं Ra lda, La zha .h 03 ◌ः 31 33 34 (a) Vowels ऱ ळ ऴ (b) Consonants Version: v1.0 (9 August 2020) NOTES: 1. -
Prof. P. Bhaskar Reddy Sri Venkateswara University, Tirupati
Component-I (A) – Personal details: Prof. P. Bhaskar Reddy Sri Venkateswara University, Tirupati. Prof. P. Bhaskar Reddy Sri Venkateswara University, Tirupati. & Dr. K. Muniratnam Director i/c, Epigraphy, ASI, Mysore Dr. Sayantani Pal Dept. of AIHC, University of Calcutta. Prof. P. Bhaskar Reddy Sri Venkateswara University, Tirupati. Component-I (B) – Description of module: Subject Name Indian Culture Paper Name Indian Epigraphy Module Name/Title Kharosthi Script Module Id IC / IEP / 15 Pre requisites Kharosthi Script – Characteristics – Origin – Objectives Different Theories – Distribution and its End Keywords E-text (Quadrant-I) : 1. Introduction Kharosthi was one of the major scripts of the Indian subcontinent in the early period. In the list of 64 scripts occurring in the Lalitavistara (3rd century CE), a text in Buddhist Hybrid Sanskrit, Kharosthi comes second after Brahmi. Thus both of them were considered to be two major scripts of the Indian subcontinent. Both Kharosthi and Brahmi are first encountered in the edicts of Asoka in the 3rd century BCE. 2. Discovery of the script and its Decipherment The script was first discovered on one side of a large number of coins bearing Greek legends on the other side from the north western part of the Indian subcontinent in the first quarter of the 19th century. Later in 1830 to 1834 two full inscriptions of the time of Kanishka bearing the same script were found at Manikiyala in Pakistan. After this discovery James Prinsep named the script as ‘Bactrian Pehelevi’ since it occurred on a number of so called ‘Bactrian’ coins. To James Prinsep the characters first looked similar to Pahlavi (Semitic) characters. -
Simplified Abugidas
Simplified Abugidas Chenchen Ding, Masao Utiyama, and Eiichiro Sumita Advanced Translation Technology Laboratory, Advanced Speech Translation Research and Development Promotion Center, National Institute of Information and Communications Technology 3-5 Hikaridai, Seika-cho, Soraku-gun, Kyoto, 619-0289, Japan fchenchen.ding, mutiyama, [email protected] phonogram segmental abjad Abstract writing alphabet system An abugida is a writing system where the logogram syllabic abugida consonant letters represent syllables with Figure 1: Hierarchy of writing systems. a default vowel and other vowels are de- noted by diacritics. We investigate the fea- ណូ ន ណណន នួន ននន …ជិតណណន… sibility of recovering the original text writ- /noon/ /naen/ /nuən/ /nein/ vowel machine ten in an abugida after omitting subordi- diacritic omission learning ណន នន methods nate diacritics and merging consonant let- consonant character ters with similar phonetic values. This is merging N N … J T N N … crucial for developing more efficient in- (a) ABUGIDA SIMPLIFICATION (b) RECOVERY put methods by reducing the complexity in abugidas. Four abugidas in the south- Figure 2: Overview of the approach in this study. ern Brahmic family, i.e., Thai, Burmese, ters equally. In contrast, abjads (e.g., the Arabic Khmer, and Lao, were studied using a and Hebrew scripts) do not write most vowels ex- newswire 20; 000-sentence dataset. We plicitly. The third type, abugidas, also called al- compared the recovery performance of a phasyllabary, includes features from both segmen- support vector machine and an LSTM- tal and syllabic systems. In abugidas, consonant based recurrent neural network, finding letters represent syllables with a default vowel, that the abugida graphemes could be re- and other vowels are denoted by diacritics.