The Alphabet Tree Dren’S Puzzles
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F(P,Q) = Ffeic(R+TQ)
674 MATHEMA TICS: N. H. McCOY PR.OC. N. A. S. ON THE FUNCTION IN QUANTUM MECHANICS WHICH CORRESPONDS TO A GIVEN FUNCTION IN CLASSICAL MECHANICS By NEAL H. MCCoy DEPARTMENT OF MATHEMATICS, SMrTH COLLEGE Communicated October 11, 1932 Let f(p,q) denote a function of the canonical variables p,q of classical mechanics. In making the transition to quantum mechanics, the variables p,q are represented by Hermitian operators P,Q which, satisfy the com- mutation rule PQ- Qp = 'y1 (1) where Y = h/2ri and 1 indicates the unit operator. From group theoretic considerations, Weyll has obtained the following general rule for carrying a function over from classical to quantum mechanics. Express f(p,q) as a Fourier integral, f(p,q) = f feiC(r+TQ) r(,r)d(rdT (2) (or in any other way as a linear combination of the functions eW(ffP+T)). Then the function F(P,Q) in quantum mechanics which corresponds to f(p,q) is given by F(P,Q)- ff ei(0P+7Q) t(cr,r)dodr. (3) It is the purpose of this note to obtain an explicit expression for F(P,Q), and although we confine our statements to the case in which f(p,q) is a polynomial, the results remain formally correct for infinite series. Any polynomial G(P,Q) may, by means of relation (1), be written in a form in which all of the Q-factors occur on the left in each term. This form of the function G(P,Q) will be denoted by GQ(P,Q). -
X|X Is a Letter in the English Alphabet
Example: Let Example: Let U be the set of all senators in Congress. Then U = {x|x is a letter in the English alphabet} = {a, b, c, ..., z} A = {x|x is a vowel} = {a, e, i, o, u} D={x ∈ U| x is a Democrat} R={x ∈ U| x is a Republican} B = {x|x is a letter in the word texas} = { t, e, x, a, s} F={x ∈ U|x is a female} L={x ∈ U|x is a lawyer} Find the following sets and express your answer in a Venn diagram Find the region on the Venn diagram that corresponds to the set of b all senators that are democrats and are female or lawyers. Express this set symbolically. c z d A B y u a e x i t f o w s g v h j r k l m n pq a) What is AB? b) What is Ac B? c) What is A Bc? 1 2 The Number of Elements in a Finite Set Example: A store has 150 clocks in stock. 100 of these clocks have AM or FM radios. 70 clocks had FM circuitry and 90 had AM The number of elements in set A is n(A). circuitry. How many had both AM and FM? How many were AM only? How many were FM only? if A = {x|x is a letter in the English alphabet}, then n(A)=26. Answer: Let If A = ∅ then n(A) = 0. U = {x|x is a clock in stock}, n(U) = A = {x|x is a set that can receive FM}, n(A) = B = {x|x is a set that can receive AM}, n(B) = We are also given that n(A B) = A B y Use the union rule to find the number in AB, x z n(A B) = UNION RULE: Find n(Ac B) = = how many have only AM. -
Jssea 42 (2015-2016) 71
Demotic and Hieratic Scholia in Funerary Papyri and their Implications for the Manufacturing Process1 Foy Scalf Abstract: Many ancient Egyptian papyrus manuscripts inscribed with funerary compositions contain annotations within the text and margins. Some of these annotations relate directly to the production process for illustrating and inscribing the manuscripts by providing instructions for scribes and artists. Two overlooked examples, pKhaemhor (MMA 25.3.212) and pRyerson (OIM E9787), allow for new interpretations of parallel texts previously considered as labels or captions. An analysis of the corpus of scholia and marginalia demonstrates specific manufacturing proclivities for selective groups of texts, while simultaneously revealing a wide variety of possible construction sequences and techniques in others. Résumé: Plusieurs manuscrits anciens de papyrus égyptiens sur lesquels sont inscrites des compositions funéraires contiennent des annotations dans le texte et dans les marges. Certaines de ces annotations sont directement liées au processus de production relatif à l’illustration et à l’inscription des manuscrits en donnant des instructions destinées aux scribes et aux artistes. Deux exemples négligés, le pKhaemhor (MMA 25.3.212) et le pRyerson (OIM E9787), permettent de nouvelles interprétations de textes parallèles précédemment considérés comme des étiquettes ou des légendes. Une analyse du corpus des scholia et marginalia démontre des tendances de fabrication spécifiques pour des groupes particuliers de textes, tout en révélant simultanément une grande variété de séquences et de techniques de construction dans d'autres cas. Keywords: Book of the Dead – Funerary Papyri – Scholia – Marginalia – Hieratic – Demotic Mots-clés: Livre des Morts – Papyrus funéraire – Scholia – Marginalia – hiératique – démotique The production of illustrated funerary papyri in ancient Egypt was a complex and expensive process that often involved the efforts of a team of skilled scribes and artisans. -
Roman Numerals
History of Numbers 1c. I can distinguish between an additive and positional system, and convert between Roman and Hindu-Arabic numbers. Roman Numerals The numeric system represented by Roman numerals originated in ancient Rome (753 BC–476 AD) and remained the usual way of writing numbers throughout Europe well into the Late Middle Ages. By the 11th century, the more efJicient Hindu–Arabic numerals had been introduced into Europe by way of Arab traders. Roman numerals, however, remained in commo use well into the 14th and 15th centuries, even in accounting and other business records (where the actual calculations would have been made using an abacus). Roman numerals are still used today, in certain contexts. See: Modern Uses of Roman Numerals Numbers in this system are represented by combinations of letters from the Latin alphabet. Roman numerals, as used today, are based on seven symbols: The numbers 1 to 10 are expressed in Roman numerals as: I, II, III, IV, V, VI, VII, VIII, IX, X. This an additive system. Numbers are formed by combining symbols and adding together their values. For example, III is three (three ones) and XIII is thirteen (a ten plus three ones). Because each symbol (I, V, X ...) has a Jixed value rather than representing multiples of ten, one hundred and so on (according to the numeral's position) there is no need for “place holding” zeros, as in numbers like 207 or 1066. Using Roman numerals, those numbers are written as CCVII (two hundreds, plus a ive and two ones) and MLXVI (a thousand plus a ifty plus a ten, a ive and a one). -
ISO Basic Latin Alphabet
ISO basic Latin alphabet The ISO basic Latin alphabet is a Latin-script alphabet and consists of two sets of 26 letters, codified in[1] various national and international standards and used widely in international communication. The two sets contain the following 26 letters each:[1][2] ISO basic Latin alphabet Uppercase Latin A B C D E F G H I J K L M N O P Q R S T U V W X Y Z alphabet Lowercase Latin a b c d e f g h i j k l m n o p q r s t u v w x y z alphabet Contents History Terminology Name for Unicode block that contains all letters Names for the two subsets Names for the letters Timeline for encoding standards Timeline for widely used computer codes supporting the alphabet Representation Usage Alphabets containing the same set of letters Column numbering See also References History By the 1960s it became apparent to thecomputer and telecommunications industries in the First World that a non-proprietary method of encoding characters was needed. The International Organization for Standardization (ISO) encapsulated the Latin script in their (ISO/IEC 646) 7-bit character-encoding standard. To achieve widespread acceptance, this encapsulation was based on popular usage. The standard was based on the already published American Standard Code for Information Interchange, better known as ASCII, which included in the character set the 26 × 2 letters of the English alphabet. Later standards issued by the ISO, for example ISO/IEC 8859 (8-bit character encoding) and ISO/IEC 10646 (Unicode Latin), have continued to define the 26 × 2 letters of the English alphabet as the basic Latin script with extensions to handle other letters in other languages.[1] Terminology Name for Unicode block that contains all letters The Unicode block that contains the alphabet is called "C0 Controls and Basic Latin". -
Assessment of Options for Handling Full Unicode Character Encodings in MARC21 a Study for the Library of Congress
1 Assessment of Options for Handling Full Unicode Character Encodings in MARC21 A Study for the Library of Congress Part 1: New Scripts Jack Cain Senior Consultant Trylus Computing, Toronto 1 Purpose This assessment intends to study the issues and make recommendations on the possible expansion of the character set repertoire for bibliographic records in MARC21 format. 1.1 “Encoding Scheme” vs. “Repertoire” An encoding scheme contains codes by which characters are represented in computer memory. These codes are organized according to a certain methodology called an encoding scheme. The list of all characters so encoded is referred to as the “repertoire” of characters in the given encoding schemes. For example, ASCII is one encoding scheme, perhaps the one best known to the average non-technical person in North America. “A”, “B”, & “C” are three characters in the repertoire of this encoding scheme. These three characters are assigned encodings 41, 42 & 43 in ASCII (expressed here in hexadecimal). 1.2 MARC8 "MARC8" is the term commonly used to refer both to the encoding scheme and its repertoire as used in MARC records up to 1998. The ‘8’ refers to the fact that, unlike Unicode which is a multi-byte per character code set, the MARC8 encoding scheme is principally made up of multiple one byte tables in which each character is encoded using a single 8 bit byte. (It also includes the EACC set which actually uses fixed length 3 bytes per character.) (For details on MARC8 and its specifications see: http://www.loc.gov/marc/.) MARC8 was introduced around 1968 and was initially limited to essentially Latin script only. -
Early-Alphabets-3.Pdf
Early Alphabets Alphabetic characteristics 1 Cretan Pictographs 11 Hieroglyphics 16 The Phoenician Alphabet 24 The Greek Alphabet 31 The Latin Alphabet 39 Summary 53 GDT-101 / HISTORY OF GRAPHIC DESIGN / EARLY ALPHABETS 1 / 53 Alphabetic characteristics 3,000 BCE Basic building blocks of written language GDT-101 / HISTORY OF GRAPHIC DESIGN / EARLY ALPHABETS / Alphabetic Characteristics 2 / 53 Early visual language systems were disparate and decentralized 3,000 BCE Protowriting, Cuneiform, Heiroglyphs and far Eastern writing all functioned differently Rebuses, ideographs, logograms, and syllabaries · GDT-101 / HISTORY OF GRAPHIC DESIGN / EARLY ALPHABETS / Alphabetic Characteristics 3 / 53 HIEROGLYPHICS REPRESENTING THE REBUS PRINCIPAL · BEE & LEAF · SEA & SUN · BELIEF AND SEASON GDT-101 / HISTORY OF GRAPHIC DESIGN / EARLY ALPHABETS / Alphabetic Characteristics 4 / 53 PETROGLYPHIC PICTOGRAMS AND IDEOGRAPHS · CIRCA 200 BCE · UTAH, UNITED STATES GDT-101 / HISTORY OF GRAPHIC DESIGN / EARLY ALPHABETS / Alphabetic Characteristics 5 / 53 LUWIAN LOGOGRAMS · CIRCA 1400 AND 1200 BCE · TURKEY GDT-101 / HISTORY OF GRAPHIC DESIGN / EARLY ALPHABETS / Alphabetic Characteristics 6 / 53 OLD PERSIAN SYLLABARY · 600 BCE GDT-101 / HISTORY OF GRAPHIC DESIGN / EARLY ALPHABETS / Alphabetic Characteristics 7 / 53 Alphabetic structure marked an enormous societal leap 3,000 BCE Power was reserved for those who could read and write · GDT-101 / HISTORY OF GRAPHIC DESIGN / EARLY ALPHABETS / Alphabetic Characteristics 8 / 53 What is an alphabet? Definition An alphabet is a set of visual symbols or characters used to represent the elementary sounds of a spoken language. –PM · GDT-101 / HISTORY OF GRAPHIC DESIGN / EARLY ALPHABETS / Alphabetic Characteristics 9 / 53 What is an alphabet? Definition They can be connected and combined to make visual configurations signifying sounds, syllables, and words uttered by the human mouth. -
The Origins of the Alphabet but Their Numbers Tally Into of Greeks and Later Through Their Manuscripts
1 ORIGINS OF THE ALPHABET gchgchgchgchgchgchgchgcggchgchgchgchgchgchggchch disadvantages to this system: not the development of the alphabet, letters developed as a natural result of only were the symbols complex, for it was through the auspices the use of the fl exible reed pen for writing The origins of the alphabet but their numbers tally into of Greeks and later through their manuscripts. Lowercase letters for the begin within the shadowy realms of the tens of thousands, making cultural admirers, the Romans, most part require fewer strokes for their prehistory. At some time within that learning diffi cult and writing slow. that the alphabet was to fi nally formation, allowing the scribes to fi t more shadowed prehistory, humankind An early culture that take on a distinct resemblance letters in a line of type. The combination began to communicate visually. inspired to innovate a simpler, to the modern Western alphabet. of speed and space conservation was Motivated by the need to communicate more effi cient writing system was important to monks writing lengthy facts about the environment around the Phoenicians. The Phoenicians manuscripts on expensive parchment, them, humans made simple drawings v were a wide-fl ung trading people When the Romans adopted and the use of lowercase letters was widely of everyday objects such as people, of great vitality, with complex the Greek alphabet, along with adopted in animals, weapons and so forth. These business transactions that other aspects of Greek culture, a relatively object drawings are called pictographs. required accurate record keeping. they continued the development short time It was through their need for and usage of the alphabet. -
Concretismo and the Mimesis of Chinese Graphemes
Signmaking, Chino-Latino Style: Concretismo and the Mimesis of Chinese Graphemes _______________________________________________ DAVID A. COLÓN TEXAS CHRISTIAN UNIVERSITY Concrete poetry—the aesthetic instigated by the vanguard Noigandres group of São Paulo, in the 1950s—is a hybrid form, as its elements derive from opposite ends of visual comprehension’s spectrum of complexity: literature and design. Using Dick Higgins’s terminology, Claus Clüver concludes that “concrete poetry has taken the same path toward ‘intermedia’ as all the other arts, responding to and simultaneously shaping a contemporary sensibility that has come to thrive on the interplay of various sign systems” (Clüver 42). Clüver is considering concrete poetry in an expanded field, in which the “intertext” poems of the 1970s and 80s include photos, found images, and other non-verbal ephemera in the Concretist gestalt, but even in limiting Clüver’s statement to early concrete poetry of the 1950s and 60s, the idea of “the interplay of various sign systems” is still completely appropriate. In the Concretist aesthetic, the predominant interplay of systems is between literature and design, or, put another way, between words and images. Richard Kostelanetz, in the introduction to his anthology Imaged Words & Worded Images (1970), argues that concrete poetry is a term that intends “to identify artifacts that are neither word nor image alone but somewhere or something in between” (n/p). Kostelanetz’s point is that the hybridity of concrete poetry is deep, if not unmitigated. Wendy Steiner has put it a different way, claiming that concrete poetry “is the purest manifestation of the ut pictura poesis program that I know” (Steiner 531). -
THE ZEROS of QUASI-ANALYTIC FUNCTIONS1 (3) H(V) = — F U-2 Log
THE ZEROS OF QUASI-ANALYTICFUNCTIONS1 ARTHUR O. GARDER, JR. 1. Statement of the theorem. Definition 1. C(Mn, k) is the class of functions f(x) ior which there exist positive constants A and k and a sequence (Af„)"_0 such that (1) |/(n)(x)| ^AknM„, - oo < x< oo,» = 0,l,2, • • • . Definition 2. C(Mn, k) is a quasi-analytic class if 0 is the only element / of C(Mn, k) ior which there exists a point x0 at which /<">(*„)=0 for « = 0, 1, 2, ••• . We introduce the functions (2) T(u) = max u"(M„)_l, 0 ^ m < oo, and (3) H(v) = — f u-2 log T(u)du. T J l The following property of H(v) characterizes quasi-analytic classes. Theorem 3 [5, 78 ].2 Let lim,,.,*, M„/n= °o.A necessary and sufficient condition that C(Mn, k) be a quasi-analytic class is that (4) lim H(v) = oo, where H(v) is defined by (2) and (3). Definition 4. Let v(x) be a function satisfying (i) v(x) is continuously differentiable for 0^x< oo, (ii) v(0) = l, v'(x)^0, 0^x<oo, (iii) xv'(x)/v(x)=0 (log x)-1, x—>oo. We shall say that/(x)GC* if and only if f(x)EC(Ml, k), where M* = n\[v(n)]n and v(n) satisfies the above conditions. Definition 5. Let Z(u) be a real-valued function which is less Received by the editors November 29, 1954 and, in revised form, February 24, 1955. 1 Presented to the Graduate School of Washington University in partial fulfill- ment of the requirements for the degree of Doctor of Philosophy. -
Threshold Digraphs
Volume 119 (2014) http://dx.doi.org/10.6028/jres.119.007 Journal of Research of the National Institute of Standards and Technology Threshold Digraphs Brian Cloteaux1, M. Drew LaMar2, Elizabeth Moseman1, and James Shook1 1National Institute of Standards and Technology, Gaithersburg, MD 20899 2The College of William and Mary, Williamsburg, VA 23185 [email protected] [email protected] [email protected] [email protected] A digraph whose degree sequence has a unique vertex labeled realization is called threshold. In this paper we present several characterizations of threshold digraphs and their degree sequences, and show these characterizations to be equivalent. Using this result, we obtain a new, short proof of the Fulkerson-Chen theorem on degree sequences of general digraphs. Key words: digraph realizations; Fulkerson-Chen theorem; threshold digraphs. Accepted: May 6, 2014 Published: May 20, 2014 http://dx.doi.org/10.6028/jres.119.007 1. Introduction Creating models of real-world networks, such as social and biological interactions, is a central task for understanding and measuring the behavior of these networks. A usual first step in this type of model creation is to construct a digraph with a given degree sequence. We examine the extreme case of digraph construction where for a given degree sequence there is exactly one digraph that can be created. What follows is a brief introduction to the notation used in the paper. For notation not otherwise defined, see Diestel [1]. We let G=( VE , ) be a digraph where E is a set of ordered pairs called arcs. If (,vw )∈ E, then we say w is an out-neighbor of v and v is an in-neighbor of w. -
Linguistic Study About the Origins of the Aegean Scripts
Anistoriton Journal, vol. 15 (2016-2017) Essays 1 Cretan Hieroglyphics The Ornamental and Ritual Version of the Cretan Protolinear Script The Cretan Hieroglyphic script is conventionally classified as one of the five Aegean scripts, along with Linear-A, Linear-B and the two Cypriot Syllabaries, namely the Cypro-Minoan and the Cypriot Greek Syllabary, the latter ones being regarded as such because of their pictographic and phonetic similarities to the former ones. Cretan Hieroglyphics are encountered in the Aegean Sea area during the 2nd millennium BC. Their relationship to Linear-A is still in dispute, while the conveyed language (or languages) is still considered unknown. The authors argue herein that the Cretan Hieroglyphic script is simply a decorative version of Linear-A (or, more precisely, of the lost Cretan Protolinear script that is the ancestor of all the Aegean scripts) which was used mainly by the seal-makers or for ritual usage. The conveyed language must be a conservative form of Sumerian, as Cretan Hieroglyphic is strictly associated with the original and mainstream Minoan culture and religion – in contrast to Linear-A which was used for several other languages – while the phonetic values of signs have the same Sumerian origin as in Cretan Protolinear. Introduction The three syllabaries that were used in the Aegean area during the 2nd millennium BC were the Cretan Hieroglyphics, Linear-A and Linear-B. The latter conveys Mycenaean Greek, which is the oldest known written form of Greek, encountered after the 15th century BC. Linear-A is still regarded as a direct descendant of the Cretan Hieroglyphics, conveying the unknown language or languages of the Minoans (Davis 2010).