refimprove date October 2010 In computability theory a cylindricnumbering is a special kind of numbering computability theory numbering first introduced by Yuri L. Ershov in 1973. If a numberings math nu math is reducibility numbering reducible to math mu math then there exists a computable function math f math with math nu mu circ f math . Usually math f math is not injective but if math mu math is a cylindricnumbering we can always find an injective math f math . Definition A numbering math nu math is called cylindric if math nu equiv 1 c nu . math That is if it is one equivalent numbering one equivalent to its cylindrification A set math S math is called cylindric if its indicator function math 1 S mathbb N to 0,1 math is a cylindricnumbering. Examples every G del numbering is cylindric Properties cylindric numberings are idempotent , math nu circ nu nu math References Yu. L. Ershov, Theorie der Numerierungen I. Zeitschrift f r mathematische Logik und Grundlagen der Mathematik 19 , 289 388 1973 . Category Theory of computation ... more details
The notion of cylindric algebra , invented by Alfred Tarski , arises naturally in the Algebraic logic algebraization of first order logic with First order logic Equality and its axioms equality . This is comparable to the role Boolean algebra structure Boolean algebra s play for propositional logic . Indeed, cylindric algebras are Boolean algebras equipped with additional cylindrification operations that model quantification and equality. They differ from polyadic algebra s in that the latter do not model equality. Definition of a cylindric algebra A cylindric algebra of dimension math alpha math , where math alpha math is any ordinal number ordinal is an algebraic structure math A, , cdot, ,0,1,c kappa,d kappa lambda kappa, lambda alpha math such that math A, , cdot, ,0,1 math is a Boolean algebra structure Boolean algebra , math c kappa math a unary operator on math A math for every math kappa math , and math d kappa lambda math a distinguished element of math A math for every math kappa math and math lambda math , such that the following hold C1 math c kappa 0 0 math C2 math x leq c kappa x math C3 math c kappa x cdot c kappa y c kappa x cdot c kappa y math C4 math c kappa c lambda x c lambda c kappa x math C5 math d kappa kappa 1 math C6 If math kappa neq lambda mu math , then math d lambda mu c kappa d lambda kappa cdot d kappa mu math C7 If math kappa neq lambda math , then math c kappa d kappa lambda cdot x cdot c kappa d kappa lambda cdot x 0 math Assuming a presentation ... wedge neg x bot math Generalizations Recently, cylindric algebras have been generalized to the Many ... categorical formulation of cylindric algebras First order logic Relation algebra s RA Polyadic algebra References Leon Henkin , Monk, J.D., and Alfred Tarski 1971 Cylindric Algebras, Part I . North Holland. ISBN 978 0 7204 2043 2. 1985 Cylindric Algebras, Part II . North Holland. Caleiro, C., and Gon alves ... Cylindric algebras.pdf Jipsen s algebra page. Category Algebraic logic zh ... more details
Wiktionary numbering There are many different numbering schemes for assigning nominal number s to entities. These generally require an agreed set of rules, or a central coordinator. The schemes can be considered ... table definitions require a database design . TOCright Numbering schemes include Chemistry CAS registry ... numbering plan for telephone numbers, including Country calling code s North American Numbering Plan Telephone numbering plan Numbering plans by country Argentina Argentine telephone numbering plan Australia Australian telephone numbering plan China China telephone numbering plan France French telephone numbering plan Hong Kong Hong Kong telephone numbering plan Japan Japanese telephone numbering plan Singapore Singapore telephone numbering plan United Kingdom UK telephone numbering plan The IP ... www.itu.int Locations Postal code s ZIP code s Global Location Number s by GS1 Road numbering scheme s Arlington County, Virginia, street naming system Great Britain road numbering scheme European route ... layout Montreal Street grid system Montreal Highways in Australia Route numbering systems FIPS place code s House numbering schemes Floor numbering Room number line number See also country code , address geography . Products The GS1 numbering scheme, including GTIN for products, which includes the Universal ... Decimal Classification for books West American Digest System legal topic numbering scheme Transportation Vehicle registration plate s British Carriage and Wagon Numbering and Classification British Rail locomotive and multiple unit numbering and classification UIC classification of goods wagons Others general API well numbers for numbering Natural gas oil and gas Oil well wells in the United ... products National Pok dex The NSAP allocation scheme Post office box Numbering of boxes Post office box Production code number Stamp numbering system Use of ordinals by monarchs Princes of Reuss List of popes Notes on numbering of popes Popes Help Wiki markup Lists Wikipedia markup syntax for numbered ... more details
In computability theory complete numberings are generalizations of G del numbering first introduced by A.I. Mal tsev in 1963. They are studied because several important results like the Kleene s recursion theorem and Rice s theorem , which were originally proven for the G del numbered set of computable function s, still hold for arbitrary sets with complete numberings. Definition A numbering computability theory numbering math nu math of a set math A math is called complete with respect to an element math a in A math if for every partial computable function math f math there exists a total computable function math h math so that math nu circ h i left begin matrix nu circ f i & mbox if i in mathrm dom f , a & mbox otherwise . end matrix right. math The numbering math nu math is called precomplete if math nu circ f i nu circ h i qquad i in mathrm dom f . , math Examples any numbering of a singleton set is complete the identity function on the natural numbers is not complete a g del numbering is precomplete References A.I. Mal tsev, Sets with complete numberings . Algebra i Logika , 1963, vol. 2, no. 2, 4 29 Russian Category Computability theory ... more details
File Batesmachinedetailfull.png right thumb 200px Bates Automatic Numbering Machine, circa 1906, with a number printed by the machine. Bates numbering also known as Bates stamping , Bates branding , Bates coding or Bates labeling is used in the legal, medical, and business fields to place identifying numbers and or date time marks on images and documents as they are scanned or processed for example, during the discovery stage of preparations for trial or identifying business receipts . Bates stamping can be used to mark and identify images with copyrights by putting a company name, logo and or legal copyright on them. This process provides identification, protection, and auto increment numbering of the images. History The first Bates Stamping machine was invented in 1892 by the Bates Manufacturing Company in NJ. It was advertised as the first automatic Bates numbering machine ever to be created ... Numbering. ref cite web url http www.parmispdf.com pdf bates numbering.php publisher Infordesk s ParmisPDF title Bates Numbering Legal Documents date March 11, 2010 ref Usage Bates numbering is commonly ... in electronic bates numbering mostly in PDF format , rather than printed, material. During the Discovery ... of unique identifiers for each page of each document for reference and retrieval. Bates numbering named for the Bates automatic numbering machine assigns an arbitrary unique identifier to each page. Such numbering may be solely numeric or may contain a combination of letters and numbers alphanumeric . There is no standard method for numbering documents. Manual Bates stamping uses a self inking ... by superimposing numbers onto them. The Bates Automatic Numbering Machine has been steadily replaced ... to produce. The Bates Automatic Numbering Machine was patented in 1891 93 by the Bates ... standard for Font and Font Size attributed to Bates numbering. References Reflist DEFAULTSORT Bates Numbering Category Legal documents Category Universal identifiers de Paginierstempel tool ... more details
In computing , bit numbering or sometimes bit endianness is the convention used to identify the bit positions in a Binary numeral system binary number or a container for such a value. The bit number starts with zero and is incremented by one for each subsequent bit position. LSB 0 bit numbering Image Lsb0.svg thumb 300px right LSB 0 A container for 8 bit binary number with the highlighted least significant bit assigned the bit number 0 When the bit numbering starts at zero for the least significant bit the numbering scheme is called LSB 0 . ref cite book author Langdon, Glen G. title Computer Design publisher Computeach Press Inc year 1982 isbn 0 9607864 0 6 page 52 ref This bit numbering method has the advantage that for any Integral data type Common integral data types unsigned integral data type the value of the number can be calculated by using Positional notation Exponentiation exponentiation with the bit number and a Radix base of 2. MSB 0 bit numbering Image Msb0.svg thumb 300px ... number 0 Similarly, when the bit numbering starts at zero for the most significant bit the numbering scheme is called MSB 0 . Other ALGOL 68 s elem operator is effectively MSB 1 bit numbering as the bits ... the most significant bit . Usage endianness Little endian CPUs usually employ LSB 0 bit numbering, however both bit numbering conventions can be seen in endianness big endian machines. Some architectures like SPARC and Motorola 68000 use LSB 0 bit numbering, while S 390 , PowerPC and PA RISC use ... to the MSB ref The recommended style for Request for Comments documents is MSB 0 bit numbering. ref ... byte order, with each word horizontal on the page and bit numbering at the top ref Bit numbering ... titan XCSB DOC bit numbers.html Bit Numbers Bit numbering for different CPUs http developer.apple.com ... Numbering sections http publib.boulder.ibm.com infocenter systems scope syssw index.jsp?topic eiccj tutorial cbet 1byteorder.html IBM Cell Broadband Processors Byte ordering and bit numbering Category ... more details
date August 2011 ref Door numbering is also beneficial for new students to find their classrooms on time. Door numbering is also useful for telling drivers which exit to pick someone up at, directing deliveries coming to the school, as well as assisting in other administrative functions. Door numbering ... more details
For numberings of the set of computable functions Numbering computability theory In mathematical logic , a G del numbering is a function mathematics function that assigns to each symbol and well formed formula of some formal language a unique natural number , called its G del number . The concept was famously used by Kurt G del for the proof of his G del s incompleteness theorems incompleteness theorems . harvnb G del 1931 A G del numbering can be interpreted as an Semantics encoding encoding in which a number is assigned to each symbol of a mathematical notation , after which a sequence of natural .... Since G del s paper was published in 1931, the term G del numbering or G del code has been ... concise ways to construct a G del numbering for sequences . Example In the specific G del numbering ... sup 6 sup 243,000,000. Lack of uniqueness A G del numbering is not unique, in that for any proof using ..., supposing there are K basic symbols, an alternative G del numbering could be constructed by invertibly ... own G del number. Application to formal arithmetic Once a G del numbering for a formal theory is established ... g sub r sub of natural numbers such that math g r f A ,f B f C . math This is true for the numbering G del used, and for any other numbering where the encoded formula can be arithmetically recovered ... statements about numbers and their arithmetical relationships to each other, one can use a G del numbering ... theory , the term G del numbering is used in settings more general than the one described ... of the mathematical object. Also, the term G del numbering is sometimes used when the assigned numbers ... G del numbering relating to numbering computability theory numberings of the class of computable function ... and summary of the proof, with a large section dedicated to G del s numbering. reflist Further reading ... defines and uses an alternative G del numbering. I Am a Strange Loop by Douglas Hofstadter . This is a newer book by Hofstadter that includes the history of G del s numbering. DEFAULTSORT Godel ... more details
COI date August 2010 Personal numbering is the name for virtual telephone number services in a number of countries including the Telephone numbers in the United Kingdom Non geographic numbering UK and Telephone numbers in Spain Personal Numbering Spain . Typically the E.164 Number structure for geographic area national destination code used for this service is 0 70 service. This service has historically been poorly defined by Oftel and also Ofcom . ref http www.ofcom.org.uk telecoms ioi numbers num 070 guide ref More recently Ofcom has made an in depth study into the service and is now proposing ... numbering plan context of 070 numbers see Telephone numbers in the United Kingdom ... 20History 20of 20the 20Global 20Personal 20Number 20Market 700 Personal Numbering Trials in the USA ... 11, 1992 ref of follow me numbers, on area code 700 in the United States USA North American Numbering Plan Numbering plan . Early Days After protracted lobbying of Oftel throughout 1992, Stanford White of Numbering Viewed Worldwide Ltd and Will Goodall of Goodall Personal Numbering Ltd, renamed ... telecommunications services. The UK s first commercial Personal Numbering service was launched by FleXtel ... for Personal Numbering, imitating the United States USA Area code 700 and ensuring adequate number ... from the Personal Numbering Market. ref http www.serviceview.bt.com list Public current Exch Lines ... numbering pers0501.htm Oftel Restoring trust in Personal Numbering ref on the introduction of Personal Numbering guidelines ref http www.ofcom.org.uk static archive oftel ind info numbering 070guide.htm Oftel Personal Numbering Guidance on the acceptable use of 070 Numbers ref and banning ... Numbering delivers a valuable service to specialist applications, ref http www.ofcom.org.uk consult condocs 070options 070options.pdf Ofcom Review of the 070 personal numbering range Consultation published ... Personal Telecommunications DEFAULTSORT Personal Numbering Category Telephone numbers Category ... more details
File Page number.jpg thumb 250 px Page number in a book Page numbering is the process of applying a sequence of numbers although, sometimes the pages are identified not by numbers but by other symbols, like letters a, b, c, , z, aa, ab, ac, , zz to the pages of a book or other document. The number itself, which may appear in various places on the page, can be referred to as a page number or as a folio . Citation needed date July 2011 Like other numbering schemes such as Chapter books chapter numbering, page numbers allow the citation of a particular page of the numbered document and facilitates to the reader to find specific parts of the document and to know the size of the complete text by checking the number of the last page . Numbering conventions Even numbers usually appear on Recto and verso verso pages, while odd numbers appear on Recto and verso recto pages. In the printing industry, in cases where odd numbers appear on verso pages and even numbers on recto pages, this is referred to as non traditional folios in the past, it had been referred to as Chinese folios , however this non politically correct term has fallen out of favor in recent years . In books, some pages Citation needed date July 2008 of the front matter and back matter are numbered, but the numbers are not always printed on the pages. Publishers are not consistent about how they number the pages of their books. Some publishers stick with the default numbering of the tool they are using, which is typically to number the first page of the front matter as one and all pages after that in a consecutive order. When publishers wish to distinguish between the front matter and the story, the initial title pages are not numbered, the front matter is numbered using small Roman numerals i, ii, iii, etc. and the first ... may be included in the numbering but not shown of the page. The first page of Chapter One would then be numbered ... in the same numbering as the text. Page numbers do not appear on part titles. Electronic documents ... more details
Europe an house number. House numbering is the system of giving a unique number to each building ... building. The house number is often part of a Address geography postal address . House numbering ... city to introduce house numbering, on the Pont Notre Dame in 1512. ref New York Times, July 16, 1898 ... slogin ref In Europe the most common house numbering scheme is to number each plot on one side of the road ... upon, there may be considerable gaps in the numbering scheme. If a lot of buildings are later ... thumb Clockwise scheme Before the early mid nineteenth century, it was common in England for numbering ... way to boustrephedon writing . Subsequent changes to local numbering can present pitfalls to researchers using historic Kelly s directory street directories , for instance. This approach numbering all ... which surround squares are usually numbered consecutively clockwise. Consecutive numbering is also used ... 13 for house numbering, because that number is considered unlucky. ref Bowlby, Chris. http news.bbc.co.uk ... above. gallery File stanbul kap numaras .jpg An example of new house numbering system in stanbul ... 2.jpg Different aged house numbers in Venyov , Russia gallery Double numbering In some Czech Republic Czech and Slovakia Slovak cities and settlements, two numbering systems are used concurrently ... is preferred instead of roman numerals. The first descriptive numbering was ordered by Maria Theresa ... come in 1805 1815. In 1857, the Austrian emperor allowed a new system of numbering by streets. This new ... of buildings. The new orientation numbers stay to be used concurrently. The double numbering ... number is white black, the orientation number red white. File Czech and Slovak house numbering .... File 21 Batuv mrakodrap.jpg In the city of Zl n , only one numbering is used. This is a number 21 ... hosting large scientific or military research centers in Soviet time, the numbering might be different ... 14 Leo Tolstoy Street, plot 14, building b . On very long roads in suburban areas kilometer numbering ... more details
refimprove date February 2010 In computability theory a numbering is the assignment of natural number s to a Set mathematics set of objects like rational number s, Graph mathematics graph s or words in some language . A numbering can be used to transfer the idea of computability and related concepts, which are strictly defined on the natural numbers using computable function s, to different objects. Important numberings are the G del numbering of the terms in first order predicate calculus and numberings of the set of computable functions which can be used to apply results of computability theory on the set of computable functions itself. Definition A numbering of a set math S math is a partial function partial surjective function math nu subseteq mathbb N to S. math The value of math nu math at math i math if defined is often written math nu i math instead of the usual math nu i math . math nu math is called a total numbering if math nu math is a total function . If math S math is a set of natural numbers, then math nu math is required to be a partial recursive function . If math S math is a set of subsets of the natural numbers, then the set math langle i,j rangle j in nu i math using the Cantor pairing function is required to be recursively enumerable . Examples Given a G del numbering math varphi i math we can define a numbering of the recursively enumerable set s by math W i mathrm domain varphi i math Properties It is often more convenient to work with a total numbering than with a partial one. If the domain function domain of a partial numbering is recursively enumerable then there always exists an equivalent total numbering. Comparison of numberings Using computable function we can define a partial ordering on the set of all numberings. Given two numberings math nu 1 subseteq mathbb N to S 1 math and math nu 2 subseteq mathbb N to S 2 math we say math nu 1 math ... math . See also G del numbering complete numbering cylindrification References V.A. Uspenski , A.L. ... more details
Lollipop sequence numbering is a numbering scheme used in routing protocols . In this numbering scheme, sequence numbers start at a negative value, increase until they reach zero, then cycles through a finite set of positive numbers indefinitely. When a system is rebooted, the sequence is restarted from a negative number again. This allows recently rebooted systems to be distinguished from systems which have simply looped around their numbering space. This path can be visualized as a line with a circle at the end hence a lollipop . Lollipop sequence numbering was originally believed to resolve the ambiguity problem in cyclic sequence numbering schemes, and was used in OSPF version 1 for this reason. Later work showed that this was not the case, and OSPF version 2 no longer uses it, instead replacing it with a linear numbering space, with special rules for what happens when the sequence numbers reach the end of the numbering space. References R. Perlman. Fault Tolerant Broadcasting of Routing Information. Computer Networks , Vol. 7, December 1983, pp. 395 405. External links http www.it.iitb.ac.in it605 dep slides 08 ospf.ppt Powerpoint presentation on routing protocols http www.ciscopress.com articles article.asp?p 24090&seqNum 4 Cisco press article on routing protocols, contains discussion of lollipop numbering, and its failure to resolve ambiguity http archives.neohapsis.com archives microsoft various ospf 2001 q3 0353.html Mailing list post on vulnerabilities of lollipop approach Category Identifiers Category Routing protocols ... more details
The Canadian Numbering Administration Consortium is the corporation responsible for administering Canada s telecommunication numbering resources. The CNA is regulated by the Canadian Radio television and Telecommunications Commission CRTC . ref name CNAC Website cite web url http www.cnac.ca cnac cna consortium.htm title CNA Consortium accessdate 2007 01 24 ref The CNAC selects and funds a neutral administrator known as the Canadian Numbering Administrator who performs the actual administrative duties. The CNAC is also responsible for paying the Canadian portion of the North American Numbering Plan Administration NANPA costs, which are funded by Canadian telecommunication service providers TSP . ref name CNAC Website cite web url http www.cnac.ca cnac cna consortium.htm title CNA Consortium accessdate 2007 01 24 ref See also List of NANP area codes External links http www.cnac.ca CNAC website http www.nanpa.com North American Numbering Plan Administration NANPA References references Category Telecommunications in Canada fr Consortium d administration du plan de num rotation canadien ... more details
In the interest in forming a trans Europe Telephone numbering plan numbering plan as an option or then future movement for anyone needing multi national European telephone presence, the International Telecommunication Union ITU allocated country calling code 388 as a subdivided, catch all container for such services. This was designated the European Telephony Numbering Space or ETNS . Although some ETNS numbers were assigned, few phone companies supported connecting calls to ETNS. ref http www.voip info.org wiki view 3883 http www.voip info.org wiki view 3883 ref Because of limited support, and the belief that the need for ETNS was superseded by Uniform Resource Identifier URI s, ETNS was suspended in 2005 and abolished in 2008. All ETS numbers were cancelled by the beginning of 2010. The 388 code is scheduled to be reclaimed by the ITU at the end of 2010. ref http www.ero.dk etns http www.ero.dk etns ref See also list of country calling codes . Allocation area Geographically the 388 country code was an overlay on top of all the pre existing, state bounded country codes of the countries in Europe. Among special country codes, 388 was unique in that it was both supranational yet geographically bounded other special codes, such as Global mobile satellite system 881 and freephone UIFN 800 , are completely international . Instead of being subdivided geographically as in a typical numbering plan, the ETNS was intended to be subdivided by type of service or customer. It would therefore ... overlay numbering plan. The only country group that comprised the ETNS was given an identification ... application 3883 3 Corporate networks 3883 5 Personal numbering 3883 7 See also Telephone numbers in Europe ...?q cache sV7stXseGSEJ docbox.etsi.org UserGroup Open Archive Numbering etns presentation.PDF 22european ... description http wtng.info wtng reg.html Europewide World Telephone Numbering Guide s information about European regional numbering Telecommunications Category Telephone numbers de Europ ischer Telefonnummerierungsraum ... more details
or postage due stamps. Catalog numbering systems Numbering of stamps cannot be a purely ... , Yvert et Tellier Yvert and Michel catalog s use different arrangements for numbering regular and special ... Catalogue claim copyright on their numbering systems, and grant only limited licences for their use ... to establish an alternative have not yet been successful. Official numbering systems In general ... most of its stamps with a unique numbering system since 1949. In 2002, as part of efforts to control allegedly illegal stamps , the Universal Postal Union introduced the WADP Numbering System WNS ... Alphabet soup Scott catalog prefixes and suffixes DEFAULTSORT Stamp Numbering System ... more details
as is required today . Therefore in many numbering systems these three players were numbered to reflect ... of the SFU Scottish Rugby Union nrut Scotland first adopted a numbering system in 1928 for the match ..., to 15 for the lock now known as the number 8 . Rugby league still uses this reverse numbering system ... and online in this order though the numbering system has changed, the order in which the positions are listed ... in the numbering are the interchange of 6 and 7 particularly in South Africa and Argentina or of 11 ... 12 shirt. Modern numbering There is nothing in the Laws of Rugby Union that determine if or how ... numbering has been standardized by the IRB for international matches 1 15, with 1 being loosehead ... sides have also adopted this standard numbering system to better aid the understanding of spectators ... custom ref name rugbyfootballhistory.com Standard modern numbering Without the number 13 Letters ... DEFAULTSORT Rugby Union Numbering Schemes Category Rugby union Numbering Category History of rugby ... more details
numbering systems have been widely adopted for presenting family tree s and pedigree chart s in text format. Among the most popular numbering systems are Ahnentafel Sosa Stradonitz Method , and the Register ... July 2009 . Ascending numbering systems Ahnentafel Main Ahnentafel Ahnentafel , also known as the Eytzinger Method , Sosa Method , and Sosa Stradonitz Method , allows for the numbering of ancestors ... or Binary Ahnentafel method uses the same numbering of nodes in the binary ancestors tree as Ahnentafel ... and atree numbering is straightforward, but for male in the root the first digit is 1 i.e. M anyway ... path as a path from the root and binary numbering system is natural for the binary tree. The first 15 ... studied in each generation. ref name Curran Curran, Joan Ferris. Numbering Your Genealogy Sound and Simple Systems. Arlington, Virginia National Genealogical Society, 1992. ref Descending numbering ... . Register Style , of which the numbering system is part, is one of two major styles used in the U.S. ... Curran, Joan Ferris, Madilyn Coen Crane, and John H. Wray. Numbering Your Genealogy Basic Systems ... and the Register Systems is in the method of numbering for children who are not carried forward into future ... numbering method developed by Jacques d Aboville in 1940 that is very similar to the Henry System ... Les syst mes de num rotation Numbering Systems ref It can be organized either by generation ... in numbering are needed for families with more than nine children. ref http www.eogen.com dAbovilleNumbers ... numbering method used for single surname studies and hereditary nobility line studies developed ... ref The numbering system usually appears on or in conjunction with a pedigree chart. Example I Progenitor ... Numbering Systems In Genealogy de Villiers Pama by Richard A. Pence ref and is one of the progenitor ... About.com http genealogy.about.com cs research a numbering.htm Numbering Your Family Tree http www.saintclair.org numbers Numbering Systems in Genealogy by Richard A. Pence refend External links http ... more details
Unreferenced date December 2009 Roads in the People s Republic of China are numbered G , S or X , and four different categories not including expressways and express routes exist Non expressways and non express routes File Yichang Hubei S334 7km 4827.jpg thumb A typical kilometer marker on a provincial road Hubei s S334 distance is measured from Yichang center city G routes stand for Guodao , or China National Highway s . These roads often exist to liaise between different centres. S routes stand for Shengdao , or provincial roads . X routes stand for Xiandao , or county level roads . A rank below them are the xiangdao , or township level roads . G, S, and X roads often become city roads as of the delimitation of the city. At the city border, control of the road switches from the gonglu side public road administration to the shizheng side city government . Expressways and express routes Expressways and express routes are not given any specific numbering at the moment. One possibility, however, has been to label them 0 series G routes e.g. G020 would be the Jingjintang Expressway . Express routes are numbered in a similar manner. See also China National Highways Transportation in the People s Republic of China DEFAULTSORT China Road Numbering Category Transport in the People s Republic of China zh ... more details
Global value numbering GVN is a compiler optimization based on the SSA compilers SSA intermediate representation. It sometimes helps eliminate redundant code that common subexpression elimination CSE does not. At the same time, however, CSE may eliminate code that GVN does not, so both are often found in modern compilers. Global value numbering is distinct from local value numbering in that the value number mappings hold across basic block boundaries as well, and different algorithms are used to compute the mappings. Global value numbering works by assigning a value number to variables and expressions. To those variables and expressions which are provably equivalent, the same value number is assigned. For instance, in the following code w 3 x 3 y x 4 z w 4 a good GVN routine would assign the same value number to code w code and code x code , and the same value number to code y code and code z code . For instance, the map math w mapsto 1, x mapsto 1, y mapsto 2, z mapsto 2 math would constitute an optimal value number mapping for this block. Using this information, the previous code fragment may be safely transformed into w 3 x w y w 4 z y Depending on the code following this fragment, copy propagation may be able to remove the assignments to code x code and to code z code The reason that GVN is sometimes more powerful than CSE comes from the fact that CSE matches lexically identical expressions whereas the GVN tries to determine an underlying equivalence. For instance, in the code a c d e c f e d CSE would not eliminate the recomputation assigned to code f code , but even a poor GVN algorithm should discover and eliminate this redundancy. SSA form is required to perform GVN Citation needed date June 2011 so that false variable name value name mappings are not created. References Alpern, Bowen, Wegman, Mark N., and Zadeck, F. Kenneth. Detecting Equality of Variables in Programs. , Conference Record of the Fifteenth Annual ACM Symposium on Principles of Programming Languages ... more details
A number of different numbering and classification schemes were used for the locomotives owned by the Southern Railway Great Britain Southern Railway SR and its constituent companies. This page explains the principal systems that were used. For information about individual classes and locomotives, see Locomotives of the Southern Railway Numbering Post Grouping Numbering When the SR was created in 1923, it immediately set about finding a solution to the problem that many of its inherited locomotives carried the same numbers. The first solution, was to prefix all locomotive numbers with a letter derived from the first letter of the main locomotive works on each section of the SR. New locomotives were then given a prefixed number in the appropriate series for the area in which they worked. Later, the letter prefix was dropped and numbers were increased by a certain number of thousands, as follows Ex South Eastern and Chatham Railway A for A shford , later 1000 added Ex London, Brighton and South Coast Railway B for B righton , later 2000 added Ex London and South Western Railway E for E astleigh , later reverted to original numbers The LSWR had renumbered its older locomotives into a duplicate list series for locomotives that were no longer in capital stock, but which were not yet life expired by adding 0 to the front of their original number e.g. 0298 . When the prefix letters were dropped by the SR, the surviving locomotives in this list had the 0 replaced with a 3 e.g. 0298 became 3298 . An exception to this general arrangement was the numbering of locomotives on the Isle of Wight. Inherited locomotives and those transferred to the island by the SR were renumbered into a single list commencing at 1 and prefixed by the letter W for W ight . From 1942 , the SR adopted a numbering system for new build locomotives both steam and electric types based on their wheel arrangement ... Correspondence and Travel Society year 1965 ref Bradley1965 British railway rolling stock numbering ... more details
A Linked Numbering Scheme LNS is a telephone numbering plan applied to an area of the country where calling between lines on a number of adjacent exchanges is done without using a dialing code. The largest LNS in the UK is that for the 020 London telephone area formerly known as the Director telephone system London Director area . Here, several million subscribers can call each other by dialing a uniform code. Thus, for example, anyone calling from an 020 number can reach Transport for London travel enquiries by dialing 7222 1234. Smaller schemes apply outside London. Uxbridge , for example, has the subscriber trunk dialing STD code 01895. Uxbridge exchange is the parent for Denham , Harefield , Ruislip and West Drayton anyone connected to any of those exchanges can call any of the others without having to prefix the number with 01895. This is achieved by giving subscriber lines on each exchange different prefix numbers, thus all numbers are six figure Denham numbers start with 83, Harefield with 82, Ruislip with 6 and West Drayton with 4. Uxbridge numbers start with 2 or 81. All calls must have all six digits dialled even if a subscriber is on Denham exchange and is calling another subscriber on Denham exchange, they must still dial 83xxxx. Incoming calls from any other exchange for a subscriber on any of the five exchanges must all be prefixed with the same 01895 code. United States In the United States, from the creation of the Washington, D.C. area code 202 in 1947 until 1991 when the number of telephone lines exceeded the capacity of one area code, all persons in the City of Washington as well as the adjoining communities in the U.S. States of Maryland and Virginia , could call any number in the region by simply dialing the 7 digit local number, even if the number was in a different state. The way this was done was, in the adjoining counties in Maryland and Virginia ... DEFAULTSORT Linked Numbering Scheme Category Telephone numbers ... more details
The Universal numbering system is a dental notation system for associating information to a specific tooth, ref Cite web title Tooth Numbering Systems work Oral Health Topics A Z publisher American Dental Association url http www.ada.org public topics tooth number.asp accessdate 2010 02 24 Dead link date October 2010 bot H3llBot ref and is commonly used in the USA United States . The designations left and right on the chart correspond to the patient s left and right, respectively. Chart of codes Orientation of the chart is traditionally patient s view , i.e. patient s right corresponds to notation chart right. The designations left and right on the chart correspond to the patient s left and right, respectively. class wikitable Universal numbering system table colspan 16 align center Permanent Teeth colspan 8 align center upper left colspan 8 align center upper right maxillary third molar 16 maxillary second molar 15 maxillary first molar 14 maxillary second premolar 13 maxillary first premolar 12 maxillary canine 11 maxillary lateral incisor 10 maxillary central incisor 9 maxillary central incisor 8 maxillary lateral incisor 7 maxillary canine 6 maxillary first premolar 5 maxillary second premolar 4 maxillary first molar 3 maxillary second molar 2 maxillary third molar 1 mandibular third molar 17 mandibular second molar 18 mandibular first molar 19 mandibular second premolar 20 mandibular first premolar 21 mandibular canine 22 mandibular lateral incisor 23 mandibular central incisor 24 mandibular central incisor 25 mandibular lateral incisor 26 mandibular canine 27 mandibular first premolar 28 mandibular second premolar 29 mandibular first molar 30 mandibular second molar 31 mandibular third molar 32 colspan 8 align center lower left colspan 8 align center lower right colspan 16 align center colspan 16 align center Deciduous teeth baby teeth colspan 8 align center upper ... Federation notation Palmer Notation Method External links http www.drbunn.com faq tooth numbering ... more details
A number of different numbering and classification schemes were used for the locomotives owned by the London, Midland and Scottish Railway LMS and its constituent companies this page explains the principal systems that were used. The following abbreviations for the constituent companies are used on this page Principal Constituents Caledonian Railway CR , Furness Railway FR , Glasgow and South Western Railway GSWR , Highland Railway HR , Lancashire and Yorkshire Railway LYR , London and North Western Railway LNWR , Maryport and Carlisle Railway MCR , Midland Railway MR , North London Railway NLR and North Staffordshire Railway NSR Minor Companies Cleator and Workington Junction Railway C&WJR , Glasgow and Paisley Joint Railway G&PJR , Knott End Railway KER , Stratford Upon Avon & Midland Junction Railway S&MJR , and Wirral Railway WR Later Additions Somerset and Dorset Joint Railway S&DJR absorbed October 1936 For information about individual classes and locomotives, see Locomotives of the London, Midland and Scottish Railway Numbering Constituent Companies London and North Western Railway The LNWR inherited its numbering system from one of its constituents, the Grand Junction Railway . In short, locomotives were numbered in a series commencing at 1. There were no gaps allowed in the series, so a new locomotive would either be numbered at the end of the series or would reuse the number ... ranges set out above. Post Grouping Numbering Shortly after the LMS was formed in 1923, it developed a new numbering scheme for all the locomotives that it had inherited. The scheme dealt with two key ... standard LMS designs were becoming more common, it was decided that modifications should be made to the numbering ... built by British Railways to ex LMS designs after Nationalisation in 1948 continued to use this numbering ... engines see BR locomotive and multiple unit numbering and classification . There were some minor ... of the power range. British railway rolling stock numbering and classification Category London, Midland ... more details
Unreferenced date May 2010 The numbering of Pope John Popes John do not occur in strict numerical order. These discrepancies are due in part to a now discounted belief in another Pope John between John XIV and John XV, and the antipapacy of John XVI. class wikitable John Dates of Papacy N Notes colspan 5 center There is no controversy regarding the numbering of the popes John before XV br Pope John I I Pope John II II Pope John III III Pope John IV IV Pope John V V Pope John VI VI Pope John VII VII Antipope John VIII Anti VIII Pope John VIII VIII Pope John IX IX Pope John X X Pope John XI XI Pope John XII XII Pope John XIII XIII center Pope John XIV 983 984 Pietro Canepanova 14 John Medieval historians misreading the Liber Pontificalis assumed another Pope John between Pope John XIV and the true Pope John XV , mistaking him with the historical character of cardinal deacon John son of Robert, that opposed to Antipope Boniface VII . Pope John XV 985 996 John Sometimes called XVI because of legendary predecessor, born to confusion between the reign of Boniface VII, the four month long imprisonment of John XIV signed as a distinct pontificate in the Liber Pontificalis and the historical cardinal deacon John son of Robert that opposed to Boniface VII after death of John XIV 15 Antipope John XVI 997 998 Johannes Philagathos or Piligato or Filagatto An antipope , according to conventional wisdom, and thus his regnal number XVI should have been reused. This occurred, but some centuries later the sequencing was wrongly corrected by some medieval historians and it has never been corrected again. He was elected in opposition to Pope Gregory V 996 999 . Pope John XVII 1003 Sicco Took the number XVI, but some historians corrected his number in XVII despite Antipope John XVI XVI having been an antipope . br Sometimes called John XVII XVIII due to legend of another John between XIV ... Reflist Portal Christianity Popes Antipopes DEFAULTSORT John Numbering Category Popes Category Antipopes ... more details
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