THE LANGUAGE of the GURUS an Introductory Course in Gurmukhi
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GEO ROO DIST BUC PRO Prep ATE 111 Cha Dec Expi OTECHNICA OSEVELT ST TRICT CKEYE, ARI OJECT # 15 Pared By
GEOTECHNICAL EXPLORARATION REPORT ROOSEVELT STREET IMPROVEMENT DISTRICT BUCKEYE, ARIZONA PROJECT # 150004 Prepared by: ATEK Engineering Consultants, LLC 111 South Weber Drive, Suite 1 Chandler, Arizona 85226 Exp ires 9/30/2018 December 14, 2015 December 14, 2015 ATEK Project #150004 RITOCH-POWELL & Associates 5727 North 7th Street #120 Phoenix, AZ 85014 Attention: Mr. Keith L. Drunasky, P.E. RE: GEOTECHNICAL EXPLORATION REPORT Roosevelt Street Improvement District Buckeye, Arizona Dear Mr. Drunasky: ATEK Engineering Consultants, LLC is pleased to present the attached Geotechnical Exploration Report for the Roosevelt Street Improvement Disstrict located in Buckeye, Arizona. The purpose of our study was to explore and evaluate the subsurface conditions at the proposed site to develop geotechnical engineering recommendations for project design and construction. Based on our findings, the site is considered suittable for the proposed construction, provided geotechnical recommendations presented in thhe attached report are followed. Specific recommendations regarding the geotechnical aspects of the project design and construction are presented in the attached report. The recommendations contained within this report are depeendent on the provisions provided in the Limitations and Recommended Additional Services sections of this report. We appreciate the opportunity of providing our services for this project. If you have questions regarding this report or if we may be of further assistance, please contact the undersigned. Sincerely, ATEK Engineering Consultants, LLC Expires 9/30/2018 James P Floyd, P.E. Armando Ortega, P.E. Project Manager Principal Geotechnical Engineer Expires 9/30/2017 111 SOUTH WEBER DRIVE, SUITE 1 WWW.ATEKEC.COM P (480) 659-8065 CHANDLER, AZ 85226 F (480) 656-9658 TABLE OF CONTENTS 1. -
Positional Notation Or Trigonometry [2, 13]
The Greatest Mathematical Discovery? David H. Bailey∗ Jonathan M. Borweiny April 24, 2011 1 Introduction Question: What mathematical discovery more than 1500 years ago: • Is one of the greatest, if not the greatest, single discovery in the field of mathematics? • Involved three subtle ideas that eluded the greatest minds of antiquity, even geniuses such as Archimedes? • Was fiercely resisted in Europe for hundreds of years after its discovery? • Even today, in historical treatments of mathematics, is often dismissed with scant mention, or else is ascribed to the wrong source? Answer: Our modern system of positional decimal notation with zero, to- gether with the basic arithmetic computational schemes, which were discov- ered in India prior to 500 CE. ∗Bailey: Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA. Email: [email protected]. This work was supported by the Director, Office of Computational and Technology Research, Division of Mathematical, Information, and Computational Sciences of the U.S. Department of Energy, under contract number DE-AC02-05CH11231. yCentre for Computer Assisted Research Mathematics and its Applications (CARMA), University of Newcastle, Callaghan, NSW 2308, Australia. Email: [email protected]. 1 2 Why? As the 19th century mathematician Pierre-Simon Laplace explained: It is India that gave us the ingenious method of expressing all numbers by means of ten symbols, each symbol receiving a value of position as well as an absolute value; a profound and important idea which appears so simple to us now that we ignore its true merit. But its very sim- plicity and the great ease which it has lent to all computations put our arithmetic in the first rank of useful inventions; and we shall appre- ciate the grandeur of this achievement the more when we remember that it escaped the genius of Archimedes and Apollonius, two of the greatest men produced by antiquity. -
A Practical Sanskrit Introductory
A Practical Sanskrit Intro ductory This print le is available from ftpftpnacaczawiknersktintropsjan Preface This course of fteen lessons is intended to lift the Englishsp eaking studentwho knows nothing of Sanskrit to the level where he can intelligently apply Monier DhatuPat ha Williams dictionary and the to the study of the scriptures The rst ve lessons cover the pronunciation of the basic Sanskrit alphab et Devanagar together with its written form in b oth and transliterated Roman ash cards are included as an aid The notes on pronunciation are largely descriptive based on mouth p osition and eort with similar English Received Pronunciation sounds oered where p ossible The next four lessons describ e vowel emb ellishments to the consonants the principles of conjunct consonants Devanagar and additions to and variations in the alphab et Lessons ten and sandhi eleven present in grid form and explain their principles in sound The next three lessons p enetrate MonierWilliams dictionary through its four levels of alphab etical order and suggest strategies for nding dicult words The artha DhatuPat ha last lesson shows the extraction of the from the and the application of this and the dictionary to the study of the scriptures In addition to the primary course the rst eleven lessons include a B section whichintro duces the student to the principles of sentence structure in this fully inected language Six declension paradigms and class conjugation in the present tense are used with a minimal vo cabulary of nineteen words In the B part of -
Devanagari in Luatex
Devanagari in LuaTeX Using OpenType features Ivo Geradts Kai Eigner 1. About us 2. Foreign scripts in TeX, past and present 3. OpenType features 4. OpenType rendering engines 5. ConTeXt engine 6. Example 1: Latin with mark and mkmk 7. Example 2: Arabic 8. Example 3: Devanagari 1. About us TAT Zetwerk offers academic typesetting services Specialties: - critical editions - foreign scripts PlainTeX, for two reasons: - our exotic needs - well documented 2. Foreign scripts in TeX, past and present Past: 8-bit PostScript fonts; e.g. approach for classical greek: - encoding: α = a, β = b, γ = g - ligature table: σ = s, ς = /s, ἄ = a)' - multitude of font-related files: tfm, vf, pfb, enc Present: new TeX-engines XeTeX and LuaTeX can handle OpenType fonts containing Unicode glyph table: - ἄ is unicode position 1F04 3. OpenType features OpenType fonts contain more information than traditional fonts - tfm: bounding boxes, kerning, ligaturen, etc. - OpenType additions: GPOS, GSUB, marks Introduction of XeTeX and LuaTeX removes old limitations: - vocalized Hebrew, Arabic - CJK - Devanagari 4. OpenType rendering engines OpenType fonts require rendering engine, such as: - Uniscribe (Windows) - AAT (OS X); XeTeX on OS X - Graphite (Windows and Linux); XeTeX on all platforms - ConTeXt engine: collection of Lua-scripts attached to various callbacks related to font calls and processing of node list 5. ConTeXt engine - independent of operating system - readable and modifiable - work in progress 6. Example 1: Latin script with mark and mkmk 7. Example 2: Arabic 8. Example 3: Devanagari - Introduction: what is Devanagari? - Devanagari and OpenType - Examples Devanagari Script - Sanskrit (old Indic) - Hindi - Nepali Abugida (consonant–vowel sequences are written as a unit) क = “ka” ◌ क् = “k” क + ् (halant) ◌ क = “ku” क + ु (matra) Mahabharata Syllable structure - Consonants: e.g. -
Kharosthi Manuscripts: a Window on Gandharan Buddhism*
KHAROSTHI MANUSCRIPTS: A WINDOW ON GANDHARAN BUDDHISM* Andrew GLASS INTRODUCTION In the present article I offer a sketch of Gandharan Buddhism in the centuries around the turn of the common era by looking at various kinds of evidence which speak to us across the centuries. In doing so I hope to shed a little light on an important stage in the transmission of Buddhism as it spread from India, through Gandhara and Central Asia to China, Korea, and ultimately Japan. In particular, I will focus on the several collections of Kharo~thi manuscripts most of which are quite new to scholarship, the vast majority of these having been discovered only in the past ten years. I will also take a detailed look at the contents of one of these manuscripts in order to illustrate connections with other text collections in Pali and Chinese. Gandharan Buddhism is itself a large topic, which cannot be adequately described within the scope of the present article. I will therefore confine my observations to the period in which the Kharo~thi script was used as a literary medium, that is, from the time of Asoka in the middle of the third century B.C. until about the third century A.D., which I refer to as the Kharo~thi Period. In addition to looking at the new manuscript materials, other forms of evidence such as inscriptions, art and architecture will be touched upon, as they provide many complementary insights into the Buddhist culture of Gandhara. The travel accounts of the Chinese pilgrims * This article is based on a paper presented at Nagoya University on April 22nd 2004. -
Neural Substrates of Hanja (Logogram) and Hangul (Phonogram) Character Readings by Functional Magnetic Resonance Imaging
ORIGINAL ARTICLE Neuroscience http://dx.doi.org/10.3346/jkms.2014.29.10.1416 • J Korean Med Sci 2014; 29: 1416-1424 Neural Substrates of Hanja (Logogram) and Hangul (Phonogram) Character Readings by Functional Magnetic Resonance Imaging Zang-Hee Cho,1 Nambeom Kim,1 The two basic scripts of the Korean writing system, Hanja (the logography of the traditional Sungbong Bae,2 Je-Geun Chi,1 Korean character) and Hangul (the more newer Korean alphabet), have been used together Chan-Woong Park,1 Seiji Ogawa,1,3 since the 14th century. While Hanja character has its own morphemic base, Hangul being and Young-Bo Kim1 purely phonemic without morphemic base. These two, therefore, have substantially different outcomes as a language as well as different neural responses. Based on these 1Neuroscience Research Institute, Gachon University, Incheon, Korea; 2Department of linguistic differences between Hanja and Hangul, we have launched two studies; first was Psychology, Yeungnam University, Kyongsan, Korea; to find differences in cortical activation when it is stimulated by Hanja and Hangul reading 3Kansei Fukushi Research Institute, Tohoku Fukushi to support the much discussed dual-route hypothesis of logographic and phonological University, Sendai, Japan routes in the brain by fMRI (Experiment 1). The second objective was to evaluate how Received: 14 February 2014 Hanja and Hangul affect comprehension, therefore, recognition memory, specifically the Accepted: 5 July 2014 effects of semantic transparency and morphemic clarity on memory consolidation and then related cortical activations, using functional magnetic resonance imaging (fMRI) Address for Correspondence: (Experiment 2). The first fMRI experiment indicated relatively large areas of the brain are Young-Bo Kim, MD Department of Neuroscience and Neurosurgery, Gachon activated by Hanja reading compared to Hangul reading. -
OSU WPL # 27 (1983) 140- 164. the Elimination of Ergative Patterns Of
OSU WPL # 27 (1983) 140- 164. The Elimination of Ergative Patterns of Case-Marking and Verbal Agreement in Modern Indic Languages Gregory T. Stump Introduction. As is well known, many of the modern Indic languages are partially ergative, showing accusative patterns of case- marking and verbal agreement in nonpast tenses, but ergative patterns in some or all past tenses. This partial ergativity is not at all stable in these languages, however; what I wish to show in the present paper, in fact, is that a large array of factors is contributing to the elimination of partial ergativity in the modern Indic languages. The forces leading to the decay of ergativity are diverse in nature; and any one of these may exert a profound influence on the syntactic development of one language but remain ineffectual in another. Before discussing this erosion of partial ergativity in Modern lndic, 1 would like to review the history of what the I ndian grammar- ians call the prayogas ('constructions') of a past tense verb with its subject and direct object arguments; the decay of Indic ergativity is, I believe, best envisioned as the effect of analogical develop- ments on or within the system of prayogas. There are three prayogas in early Modern lndic. The first of these is the kartariprayoga, or ' active construction' of intransitive verbs. In the kartariprayoga, the verb agrees (in number and p,ender) with its subject, which is in the nominative case--thus, in Vernacular HindOstani: (1) kartariprayoga: 'aurat chali. mard chala. woman (nom.) went (fern. sg.) man (nom.) went (masc. -
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 [...]. -
Sanskrit Alphabet
Sounds Sanskrit Alphabet with sounds with other letters: eg's: Vowels: a* aa kaa short and long ◌ к I ii ◌ ◌ к kii u uu ◌ ◌ к kuu r also shows as a small backwards hook ri* rri* on top when it preceeds a letter (rpa) and a ◌ ◌ down/left bar when comes after (kra) lri lree ◌ ◌ к klri e ai ◌ ◌ к ke o au* ◌ ◌ к kau am: ah ◌ं ◌ः कः kah Consonants: к ka х kha ga gha na Ê ca cha ja jha* na ta tha Ú da dha na* ta tha Ú da dha na pa pha º ba bha ma Semivowels: ya ra la* va Sibilants: sa ш sa sa ha ksa** (**Compound Consonant. See next page) *Modern/ Hindi Versions a Other ऋ r ॠ rr La, Laa (retro) औ au aum (stylized) ◌ silences the vowel, eg: к kam झ jha Numero: ण na (retro) १ ५ ॰ la 1 2 3 4 5 6 7 8 9 0 @ Davidya.ca Page 1 Sounds Numero: 0 1 2 3 4 5 6 7 8 910 १॰ ॰ १ २ ३ ४ ६ ७ varient: ५ ८ (shoonya eka- dva- tri- catúr- pancha- sás- saptán- astá- návan- dásan- = empty) works like our Arabic numbers @ Davidya.ca Compound Consanants: When 2 or more consonants are together, they blend into a compound letter. The 12 most common: jna/ tra ttagya dya ddhya ksa kta kra hma hna hva examples: for a whole chart, see: http://www.omniglot.com/writing/devanagari_conjuncts.php that page includes a download link but note the site uses the modern form Page 2 Alphabet Devanagari Alphabet : к х Ê Ú Ú º ш @ Davidya.ca Page 3 Pronounce Vowels T pronounce Consonants pronounce Semivowels pronounce 1 a g Another 17 к ka v Kit 42 ya p Yoga 2 aa g fAther 18 х kha v blocKHead -
KHA in ANCIENT INDIAN MATHEMATICS It Was in Ancient
KHA IN ANCIENT INDIAN MATHEMATICS AMARTYA KUMAR DUTTA It was in ancient India that zero received its first clear acceptance as an integer in its own right. In 628 CE, Brahmagupta describes in detail rules of operations with integers | positive, negative and zero | and thus, in effect, imparts a ring structure on integers with zero as the additive identity. The various Sanskrit names for zero include kha, ´s¯unya, p¯urn. a. There was an awareness about the perils of zero and yet ancient Indian mathematicians not only embraced zero as an integer but allowed it to participate in all four arithmetic operations, including as a divisor in a division. But division by zero is strictly forbidden in the present edifice of mathematics. Consequently, verses from ancient stalwarts like Brahmagupta and Bh¯askar¯ac¯arya referring to numbers with \zero in the denominator" shock the modern reader. Certain examples in the B¯ıjagan. ita (1150 CE) of Bh¯askar¯ac¯arya appear as absurd nonsense. But then there was a time when square roots of negative numbers were considered non- existent and forbidden; even the validity of subtracting a bigger number from a smaller number (i.e., the existence of negative numbers) took a long time to gain universal acceptance. Is it not possible that we too have confined ourselves to a certain safe convention regarding the zero and that there could be other approaches where the ideas of Brahmagupta and Bh¯askar¯ac¯arya, and even the examples of Bh¯askar¯ac¯arya, will appear not only valid but even natural? Enterprising modern mathematicians have created elaborate legal (or technical) machinery to overcome the limitations imposed by the prohibition against use of zero in the denominator.