In mathematics , the Pochhammersymbol introduced by Leo August Pochhammer is the notation math x sub n sub , where math n is a non negative integer . Depending on the context the Pochhammersymbol may represent either the rising factorial or the falling factorial as defined below. Care needs to be taken to check which interpretation is being used in any particular article. Pochhammer himself actually used math x sub n sub with yet another meaning, namely to denote the binomial coefficient math tbinom xn math . ref name Knuth citation first1 Donald E. last1 Knuth author1 link Donald Knuth year 1992 title Two notes on notation journal American Mathematical Monthly volume 99 issue 5 pages 403&ndash 422 doi 10.2307 2325085 jstor 2325085 arxiv math 9205211 . The remark about the Pochhammersymbol is on page 414. ref In this article the Pochhammersymbol math x sub n sub is used to represent the falling factorial sometimes called the descending factorial , ref name Steffensen falling sequential product , lower factorial math x n x x 1 x 2 cdots x n 1 math In this article the symbol math x sup n sup is used for the rising factorial sometimes called the Pochhammer function , Pochhammer polynomial ... function the Pochhammersymbol math x sub n sub is used to represent the rising factorial ... other notations like math sub x sub P sub n sub and P x,n are commonly used. The Pochhammersymbol ... The Pochhammersymbol has a generalized version called the generalized Pochhammersymbol , used in multivariate analysis. There is also a q analog q analogue , the q Pochhammersymbol q Pochhammersymbol ... sup and x sup k &minus 1 sup , respectively. See also Pochhammer k symbol Chu Vandermonde identity Notes ... publisher Cambridge University Press isbn 0 521 55821 2 . DEFAULTSORT PochhammerSymbol Category Gamma and related functions Category Factorial and binomial topics Category Finite differences de PochhammerSymbol es S mbolo de Pochhammer fr Symbole de Pochhammer it Fattoriale crescente pl Pot gi ... more details
Unreferenced date December 2006 In mathematics , the generalized Pochhammersymbol of parameter math alpha 0 math and partition number theory partition math kappa kappa 1, kappa 2, ldots, kappa m math generalizes the classical Pochhammersymbol , named after Leo August Pochhammer , and is defined as math a alpha kappa prod i 1 m prod j 1 kappa i left a frac i 1 alpha j 1 right . math DEFAULTSORT Generalized PochhammerSymbol Category Gamma and related functions Category Factorial and binomial topics numtheory stub ... more details
In the mathematical theory of special functions , the Pochhammer k symbol and the k gamma function , introduced by Rafael D az and Eddy Pariguan ref cite arxiv date 2005 class math.CA eprint math 0405596 first Rafael last D az coauthors Eddy Pariguan title On hypergeometric functions and k Pochhammersymbol ref , are generalizations of the Pochhammersymbol and gamma function . They differ from the Pochhammersymbol and gamma function in that they can be related to a general arithmetic progression in the same manner as those are related to the sequence of consecutive integer s. The Pochhammer k symbol x sub n,k sub is defined as math x n,k x x k x 2k cdots x n 1 k , , math and the k gamma function sub k sub , with k 0, is defined as math Gamma k x lim n to infty frac n k n nk x k 1 x n,k . math When k 1 the standard Pochhammersymbol and gamma function are obtained. D az and Pariguan use these definitions to demonstrate a number of properties of the hypergeometric function . Although D az and Pariguan restrict these symbols to k 0, the Pochhammer k symbol as they define it is well defined for all real k, and for negative k gives the falling factorial , while for k 0 it reduces to the Exponentiation power x sup n sup . The D az and Pariguan paper does not address the many analogies between the Pochhammer k symbol and the power function, such as the fact that the binomial theorem can be extended to Pochhammer k symbols. It is true, however, that many equations involving the power function x sup n sup continue to hold when x sup n sup is replaced by x sub n,k sub . References references Category Gamma and related functions Category Factorial and binomial topics sl Pochhammerjev k simbol ... more details
lowercase title q Pochhammersymbol In mathematics , in the area of combinatorics , a q Pochhammersymbol , also called a q shifted factorial , is a q analog of the common Pochhammersymbol . It is defined as math a q n prod k 0 n 1 1 aq k 1 a 1 aq 1 aq 2 cdots 1 aq n 1 math with math a q 0 1 math by definition. The q Pochhammersymbol is a major building block in the construction of q analogs for instance, in the theory of basic hypergeometric series , it plays the role that the ordinary Pochhammersymbol plays in the theory of generalized hypergeometric series . Unlike the ordinary Pochhammersymbol, the q Pochhammersymbol can be extended to an infinite product math a q infty prod k 0 infty 1 aq k . math This is an analytic function of q in the interior of the unit disk , and can also be considered as a formal power series in q . The special case math phi q q q infty prod k 1 infty 1 q ... of q , typically depending on q via q Pochhammer symbols. Identities The finite product can be expressed ... n q n prod k 1 n frac 1 1 a q k math and math a q n frac q a n q n n 1 2 q a q n . math The q Pochhammersymbol is the subject of a number of q series identities, particularly the infinite series expansions ... q infty x q infty sum n 0 infty frac a q n q q n x n. math Combinatorial interpretation The q Pochhammersymbol is closely related to the enumerative combinatorics of partitions. The coefficient of math ... flavour. Multiple arguments convention Since identities involving q Pochhammer symbols so frequently involve products of many symbols, the standard convention is to write a product as a single symbol ... of the q factorial function to the real number system. See also Basic hypergeometric series Pochhammersymbol Q derivative Q theta function Elliptic gamma function Theta function Jacobi theta function ... theory Category Q analogs es S mbolo q Pochhammer it Fattoriale crescente di base q ja Q pl Symbol q Pochhammera ... more details
Orphan date April 2012 Expand Polish Conrad Pochhammer date April 2012 Conrad Pochhammer 1873 1932 was a Germany German physician and surgeon. Persondata Metadata see Wikipedia Persondata . NAME Pochhammer, Conrad ALTERNATIVE NAMES SHORT DESCRIPTION DATE OF BIRTH 1873 PLACE OF BIRTH DATE OF DEATH 1932 PLACE OF DEATH DEFAULTSORT Pochhammer, Conrad Category 1873 births Category 1932 deaths Category German physicians Category German surgeons Germany bio stub de Conrad Pochhammer pl Conrad Pochhammer ... more details
File Pochhammer.curve.svg thumb 300px A Pochhammer contour winds clockwise around one point, then clockwise around another point, then counterclockwise around the first point, then counterclockwise around the second. The exact position, curvature, etc. are in this case not essential the sequence of windings around the two special points is. In mathematics, the Pochhammer contour , introduced by harvs txt authorlink Camille Jordan first Camille last Jordan year 1887 and harvs txt authorlink Leo Pochhammer first Leo last Pochhammer year 1890 , is a contour in the complex plane with two points removed, used for contour integration . If A and B are loops around the two points, both starting at some fixed point P , then the Pochhammer contour is the commutator ABA sup &minus 1 sup B sup &minus 1 sup , where the superscript &minus 1 denotes a path taken in the opposite direction. With the two points taken as 0 and 1, the fixed basepoint P being on the real axis between them, an example is the path that starts at P , encircles the point 1 in the counter clockwise direction and returns to P , then encircles 0 counter clockwise and returns to P , after that circling 1 and then 0 clockwise, before coming back to P . The class of the contour is an actual commutator when it is considered in the fundamental group with basepoint P of the complement in the complex plane or Riemann sphere of the two points looped. When it comes to taking contour integrals, moving basepoint from P to another ... to a single point. File Pochhammer.homology2.svg thumb 300px Pochhammer cycle is homologous to zero ... be converted into an integral over the Pochhammer contour C as math displaystyle 1 e 2 pi i alpha 1 ... over two nails in such a way that if either one of the nails is removed, the picture falls. The Pochhammer ... File Pochhammer.Borromeo.svg thumb 300px A Borromean link. The Pochhammer curve together with two suitably ... year 1887 Citation last1 Pochhammer first1 L. title Zur Theorie der Euler schen Integrale publisher ... more details
Leo August Pochhammer 25 August 1841, Stendal &ndash 24 March 1920, Kiel was a Prussia n mathematician, known for his work on special function s. He introduced the Pochhammersymbol , now generally used for expressing hypergeometric function s in a compact notation. See also Pochhammersymbol Generalized Pochhammersymbol q PochhammersymbolPochhammer contour Jordan&ndash Pochhammer differential equation External links http scienceworld.wolfram.com biography Pochhammer.html Eric W. Weisstein s world of science Persondata Metadata see Wikipedia Persondata . NAME Pochhammer, Leon August ALTERNATIVE NAMES SHORT DESCRIPTION DATE OF BIRTH 25 August 1841 PLACE OF BIRTH DATE OF DEATH 24 March 1920 PLACE OF DEATH DEFAULTSORT Pochhammer, Leon August Category 1841 births Category 1920 deaths Category German mathematicians Category People from the Province of Saxony Category People from Stendal Germany mathematician stub de Leo August Pochhammer es Leo August Pochhammer fr Leo Pochhammer ht Leo August Pochhammer nl Leo Pochhammer pt Leo Pochhammer sl Leo August Pochhammer ... more details
About the graphic symbol used to denote prohibition the Japanese kana No kana Image ProhibitionSign2.svg thumb 150px right The ISO 3864 ISO 3864 1 prohibition sign File Do Not Enter sign.svg thumb 150px right Do Not Enter sign, made to the specifications of the 2004 edition of Standard Highway Signs ref http mutcd.fhwa.dot.gov SHSm regulatory.pdf 2004 edition of Standard Highway Signs ref Regulatory sign sign R5 1 . The no symbol also prohibition sign , circle backslash symbol , or universal no is a circle ... a pictogram used to indicate something is not permitted. The no symbol is usually colored red. The Unicode Architecture and terminology Unicode code point for the prohibition sign also called the no symbol ... within the outer edge of the no symbol must be the symbol itself. Additionally, for printed signs under the UK rules, the width of a no symbol is set at 80 the height of the area it is printed to. Uses The prohibition symbol is used on traffic signs, so that drivers can interpret traffic laws ... sign.svg 50px No U turn Image No Parking symbol sign.svg 50px No parking By analogy, the sign is used ... symbol is useful when the item must be handled by people who understand different languages as it is transported ..., e.g. an insect deterrent spray brand symbol showing the prohibition sign over a mosquito. The Ghostbusters ... left or right or varied in hue is considered acceptable and recognized by the general public as a symbol ... of the no symbol comes from the International Organization for Standardization . In 2002, ISO ... symbol or no symbol is defined as a prohibition surround shape red circular band with a red slash going from the upper left to the lower right over the top of a black graphical symbol. Since ... through it may be used as a Yes symbol , or the anti prohibition sign , indicating that the activity ... on a building site, or the fact that a pathway is for pedestrians and cyclists. The no symbol does not always ... www.freesignage.com prohibited signs.php Printable US signage using the no symbol Category Infographics ... more details
Wiktionarypar symbol NOTOC Symbol s are objects, characters, or other representations of ideas, concepts, objects, or abstractions. Symbol may also refer to Computer science Symbol data , the smallest amount of data transmitted at a time in digital communications Symbol rate , the number of symbols transmitted per second Debug symbol , debugging information used to troubleshoot computer programs, analyze memory dumps Symbol programming , a primitive data type in many programming languages used to name variables and functions Logic Symbol formal , a string, used in formal languages and formal systems Symbol grounding , the problem of how symbols acquire meaning Music Symbol Records , a record label Symbols album Symbols album , 1997 album from the industrial rock band KMFDM Symbol album Symbol album , 2005 album by Japanese electronica musician Susumu Yokota Symbols band , a Brazilian heavy metal band Symbol choir , the name of a choir in Romania Theology Symbol of Nicea or Nicene Creed Symbol liturgical theology , in contrast to a sign, and relevant to liturgy Mathematics Symbol of a differential operator Other uses Symbol Technologies , an AIDC company based in Holtsville, New York, United States Symbol typeface , a font designed by Aldo Novarese 1982 , one of the four standard PostScript fonts Casablanca Conference 1943 , codenamed SYMBOL Simbolul , a Romanian literary magazine Symbol film Symbol film , a movie by Hitoshi Matsumoto See also Symbolic disambiguation Symbolism disambiguation Cymbal , round metal plates used as percussion instruments Semeiotic , the study of signs and sign processes variant spelling Semiotics , the study of signs and sign processes Punctuation , symbols that indicate the structure and organization of written language disambig fr Symbole ro Simbol dezambiguizare ... more details
The symbol of medicine may refer to Emblems of the International Red Cross and Red Crescent Movement Star of Life Caduceus as a symbol of medicine Caduceus See also Rod of Asclepius dab ... more details
Unreferenced date February 2011 Image Venus symbol.svg 100px thumb right Venus symbol Image Woman power emblem.svg 100px thumb right Symbol of feminism based on Venus symbol The Venus symbol is a depiction of a circle with a small Cross symbol cross below it. The symbol is historically associated with the Roman goddess Venus mythology Venus or the Greek goddess Aphrodite . It has a Unicode designation of U 2640, and is used in various media to represent things associated in some way with the mythological character, including The female sex The planet Venus The chemical element copper Feminism in philosophy and sociology The female connector in a pair of mating connectors or fasteners It is also believed by some to represent a hand mirror , with the top half of the symbol representing the actual mirror, and the bottom half representing the handle of the mirror. See also Classical planets in Western alchemy Mars symbol Gender symbol The ankh , an Egyptian hieroglyph resembling the Venus symbol DEFAULTSORT Venus Symbol Category Roman mythology Category Symbols Category Alchemy cs de Venussymbol fa fr ko it nl ja no oc pl pt ru sk Venu a symbol fi Venus symboli sv Venussymbol tr Ven s sembol zh ... more details
Punctuation marks caption Tee A tee , top in TeX is a symbol used to represent Top element in lattice theory . A logical constant denoting a tautology logic tautology in logic . In Unicode the symbol is encoded unichar 22a4 Down tack html . See also Turnstile symbol Turnstile Up tack Falsum Table of mathematical symbols Table of logic symbols Category Logic symbols ... more details
A symbol in computer programming is a primitive datatype whose instance s have a unique human readable ... class wikitable sortable language type name s example literal s Clojure symbol, ref http clojure.org ... ref tt symbol tt , tt keyword tt ANSI Common Lisp symbol, keyword tt symbol tt , tt keyword tt Scheme programming language R6RS Scheme symbol tt sym tt Ruby programming language Ruby Symbol tt sym tt or tt sym tt Scala programming language Scala scala.Symbol tt symbol tt Smalltalk Symbol tt sym tt or tt sym tt PICAXE Basic symbol tt symbol let name variable tt Ericsson Erlang programming language Erlang atom tt sym tt Objective C SEL tt selector sym tt SML NJ Atom.atom Lisp A symbol in Lisp ... reads data that contains textual represented symbols, existing symbols are referenced. If a symbol is unknown, the Lisp reader creates a new symbol. In Common Lisp symbols have the following attributes ... HyperSpec Body t symbol.htm Common Lisp HyperSpec, system class Symbol ref In Common Lisp symbols may use any characters, including whitespace, such as spaces and newlines. If a symbol contains a whitespace character it needs to be written as this is a symbol . Symbols can be used as identifiers ... Lisp symbol source lang lisp this is a symbol source Symbols can contain whitespace and all other characters source lang lisp This is a symbol with whitespace source In Common Lisp symbols with a leading ... in the keyword package. source lang lisp keyword symbol source A printed representation of a symbol may include a package name. Two colons are written between the name of the package and the name of the symbol. source lang lisp package name symbol name source Packages can export symbols. Then only one colon is written between the name of the package and the name of the symbol. source lang lisp package exported symbol source Ruby In Ruby programming language Ruby , symbols can be created ... at a Ruby Symbol url http www.randomhacks.net articles 2007 01 20 13 ways of looking at a ruby symbol ... more details
Null symbol may refer to Null character , U 0000 , U 2400 symbol for null , a single character glyph NUL Null sign for the empty set Null SQL in database theory , , or , for the empty string See also Null disambiguation dab ... more details
Unreferenced date February 2011 Image Mars symbol.svg 100px thumb right Mars symbol The Mars symbol is a depiction of a circle with an arrow emerging from it, pointing at at angle to the upper right. In old manuscripts, it is usually interpreted as the shield and spear from the war god Mars god Mars Ares . The symbol has the Unicode entry U 2642. It is used in many fields as a representation of things historically associated with the mythological figure. These include In science The male gender The planet Mars The chemical element iron In mythology The Roman god Mars god Mars or the Greek god Ares In vehicles Part of the logo for Volvo automobiles In other uses The male connector in a pair of mating connectors or fasteners The men s bathroom See also Venus symbol Gender symbol DEFAULTSORT Mars Symbol Category Roman mythology Category Symbols Category Alchemy ar ca Llan a de Mart cs de Marssymbol fa fr ko it ms Simbol Marikh nl ja no pl pt sk Mars symbol fi Mars symboli sv J rnsymbolen tr zh ... more details
Punctuation marks The trademark symbol , unichar 2122 trade mark sign html ref http www.unicode.org charts PDF U2100.pdf ref ref http www.w3.org TR REC html40 sgml entities.html ref , is a symbol used to provide notice that the preceding mark is a trademark . Use of this symbol does not mean that the trademark has been registered. Registered trademarks are indicated using the registered trademark symbol . Anyone can use the symbol. ref http lahserpatent.com tm symbol ref Entering the symbol On Microsoft Windows Windows systems, a superscript trademark symbol may be entered by means of Alt codes , by holding the Alt key while typing the numbers 0153 on the numeric keypad . In the X Window System , it may be entered with compose key Multi key T M . On GNOME systems, is may be entered by pressing key press Ctrl key press Shift key press u key press 2 key press 1 key press 2 key press 2 . On Macintosh systems, it may be entered with keypress Option key Opt 2 . In LaTeX , code textsuperscript texttrademark code is used in text or math mode. Apple s iOS keyboards iPad, iPhone, iPod Touch support the symbol in iOS 5 and above. The service mark symbol , , has a similar function and denotation. See also Australian trade mark law Canadian trade mark law Trademark law United Kingdom trade mark law United States trademark law References references Category United States trademark law Category Typographical symbols typ stub ko he ... more details
Unreferenced stub auto yes date December 2009 Symbol group is a mainly United Kingdom British term for a form of Franchising franchise in the retail sector. They do not own or operate stores, but act as suppliers to independent grocers and small supermarkets and produce stores which then trade under a common banner. Unlike other forms of franchise, they have expanded primarily by selling their services to existing stores, rather than by actively developing new outlets. SPAR is a well known symbol group with stores in many countries. There are several smaller symbol groups in the United Kingdom , such as Londis , Costcutter , Premier Stores and Nisa Today s . In 2009, IDG reported that the symbol group market is worth 10.4bn, with a 35.9 share of the UK convenience market and a 7.3 share of the total UK grocery market. IDG report http www.igd.com index.asp?id 1&fid 1&sid 7&tid 26&cid 108 DEFAULTSORT Symbol Group Category Distribution, retailing, and wholesaling Category Business models Category Franchises Category Purchasing consortia Org stub ... more details
A gender symbol is a symbol used to denote the sex of a organism life form or to characterize an agent by gender . The two standard gender symbols denoting male and female are derived from astrological symbols , denoting the classical planets Mars and Venus , respectively. These symbols have been in use since the Renaissance ref continuing medieval 11th century symbols known from Byzantine manuscripts, possibly with precedents in horoscopic papyri of Late Antiquity late 4th century . ref also denoting elements in Classical planets in Western alchemy alchemy , specifically the metals iron and copper . They were first used to denote the effective gender of plants i.e. sex of individual in a given .... 11, No. 4 May, 1962 , pp. 109 113 ref class wikitable Image Mars symbol.svg & x2642 50px Mars symbol U 2642 unicode . The symbol for a male organism or man . Image Venus symbol.svg & x2640 50px Venus symbol U 2640 unicode . The symbol for a female organism or woman . LGBT Culture Refimprove date October ... & x263F 60px From the symbol of Mercury planet Mercury U 263F unicode . This symbol is used to indicate ... & x26A7 50px Another transgender symbol, a combination of the male and female sign with a third ... female homosexual symbol big unicode big U 26A3 Double male sign, sometimes used as a LGBT symbols Gender symbols male homosexual symbol big unicode big U 26A4 Interlocked male and female sign, occasionally used as a heterosexuality heterosexual symbol also bisexual big unicode big U 26A6 Male with stroke sign, used as a symbol for transgendered. also transgendered big unicode big U 26A8 Vertical ... big U 26AA Medium white circle base, used as a symbol for asexuality , sexless or genderless big unicode big U 26B2 Neuter. This is in fact the shape of the original medieval Venus symbol depicting ... 1&lang 2 Decode Unicode, showing all Unicode symbols DEFAULTSORT Gender Symbol Category Gender Category Symbols bg ca S mbol de g nere cs Genderov symbol de Gender Symbol nl Seksesymbool ... more details
In computer science , a symbol table is a data structure used by a language translator such as a compiler or interpreter computing interpreter , where each identifier in a program s source code is associated with information relating to its declaration or appearance in the source, such as its data type type , scope programming scope level and sometimes its Memory address location . Implementation A common implementation technique is to use a hash table implementation. A compiler may use one large symbol table for all symbols or use separated, hierarchical symbol tables for different Scope programming scopes . Uses An object file will contain a symbol table of the identifiers it contains that are externally visible. During the linking of different object files, a Linker computing linker will use these symbol tables to resolve any unresolved references. A symbol table may only exist during the translation process, or it may be embedded in the output of that process for later exploitation ... an executable, many tools refer to the symbol table to check what addresses have been assigned to global variables and known functions. If the symbol table has been strip Unix stripped or cleaned out ..., a compiler should perform many works and as such the extended stack model requires the symbol table . Elucidate date June 2011 Example The symbol table of a small program is listed below. The table ... data symbol, noted by the D type , and many functions self defined as well as from the standard library . The first column is where the symbol is located in the memory, the second is http sourceware.org binutils docs 2.17 binutils nm.html nm The symbol type and the third is the name of the symbol. By passing suitable parameters, the symbol table was made to sort on basis of address. class wikitable ... Debug symbol Category Compiler construction Category Data structures Category Executable file formats ... nl Symbol table ja pt Tabela de s mbolos ... more details
Image WPint.svg right thumb The integral symbol. distinguish Long s Esh letter The Unicode symbol math int math is used to denote the integral in mathematics . The notation was introduced by the Germany German mathematician Gottfried Wilhelm von Leibniz towards the end of the 17th century. The symbol was based on the Unicode long s character, and was chosen because Leibniz thought of the integral as an infinite summation sum of infinitesimal summands. See long s for more details on the history of Unicode . The Unicode symbol is U 222B in Unicode and code int code in LaTeX . In HTML , it is written as code & x222b code hexadecimal , code & 8747 code decimal and code & int code named entity . The original IBM PC code page 437 character set included a couple of characters Unicode & x2320 and Unicode & x2321 codes 244 and 245, respectively to build the integral symbol. These were deprecated in subsequent MS DOS code page s, but they still remain in Unicode U 2320 and U 2321, respectively for compatibility. The Unicode symbol is very similar to, but not to be confused with, the IPA symbol called esh letter esh . Related symbols are Unicode double integral , U 222C , Unicode triple integral , U 222D , Unicode contour integral , U 222E , Unicode closed manifold closed surface integral , U 222F , and Unicode closed volume integral , U 2230 . Typography in other languages File Integral Uprightness.svg thumb Regional variations English, German, Russian of the integral symbol. In other languages, the shape of the integral symbol differs slightly from the shape commonly seen in English language textbooks. While the English language English integral symbol leans to the right, the German language German symbol used throughout Central Europe is upright, and the Russian language ... symbol math int 0 T f t dt math By contrast, in German and Russian texts, limits of integration limits for definite integral s are placed above and below the integral symbol and as a result the notation ... more details
Unreferenced date December 2009 Orphan date December 2009 In knowledge based systems, agents choose actions based on the principle of rationality to move closer to a desired goal. The agent is able to make decisions based on knowledge it has about the world see knowledge level . But for the agent to actually change its state, it must use whatever means it has available. This level of description for the agent s behavior is the symbol level . For example, in a computer program, the knowledge level consists of the information contained in its data structures that it uses to perform certain actions. The symbol level consists of the program s algorithms, the data structures themselves, and so on. See also Knowledge level modeling DEFAULTSORT Symbol Level Category Artificial intelligence ... more details
File Takamatsu symbol tower04s3200 2.jpg thumb Symbol Tower The Nihongo Symbol Tower Takamatsu Shimboru Taw is a skyscraper located in Takamatsu, Kagawa Takamatsu , Kagawa Prefecture , Japan . Construction of the 151 metre, 30 storey skyscraper was finished in 2001. External links Official website http www.symboltower.com l ja icon coord 34 21 08.5 N 134 02 48.5 E type landmark scale 4000 display title Category Buildings and structures completed in 2001 Category Takamatsu, Kagawa Category Skyscrapers in Japan Category Buildings and structures in Kagawa Prefecture Category Skyscrapers between 150 and 199 meters Japan struct stub ja ... more details
In digital communications , symbol rate also known as baud or modulation rate is the number of symbol ... modulation modulated signal or a line code . The Symbol rate is measured in baud Bd or symbols second. In the case of a line code, the symbol rate is the pulse rate in pulses second. Each symbol can represent or convey one or several bit s of data. The symbol rate is related to, but should not be confused with, the gross bitrate expressed in bit second. Symbols A symbol can be described as either ... an integer number of bits. A theoretical definition of a symbol is a waveform, a state or a significant ... period of time. A sending device places symbols on the channel at a fixed and known symbol rate, and the receiving ... data. There may be a direct correspondence between a symbol and a small unit of data for example, each symbol may Encoding encode needs disambiguation one or several binary digits or bits .... The symbol duration time , also known as Unit interval data transmission unit interval , can be directly ... . The symbol duration time T sub s sub can be calculated as math T s 1 over f s , math where f sub s sub is the symbol rate. A simple example A baud rate of 1 kBd 1,000 Bd is synonymous to a symbol ... of a line code, this corresponds to 1,000 pulses per second. The symbol duration time is 1 ... digital communication links using only one bit per symbol, such that binary 0 is represented by one symbol, and binary 1 by another symbol. In more advanced modems and data transmission techniques, a symbol may have more than two states, so it may represent more than one binary digit a binary digit ... of my COM port is 9,600 if we mean that the bit rate is 9,600 bit s, since there is one bit per symbol ... rate baud is one symbol per second. The flag can be held in one of eight distinct positions Straight ... , 135 right, 90 right, and 45 right. Each signal symbol carries three bits of information. It takes ... per symbol, and the gross bit rate is R , inclusive of channel coding overhead, the symbol rate ... more details
Unreferenced auto yes date December 2009 Orphan date December 2009 In computing , a weak symbol is a symbol definition in an object file or dynamic library that may be overridden by other symbol definitions. Its value will be zero if no definition is found by the loader. Weak symbols are not mentioned by C or C language standards as such, inserting them into code is not portable. Some compilers can create a weak symbol with a special Directive programming pragma , code pragma weak code . However, the GNU Compiler Collection also supports a code attribute weak code syntax as in the example below. Example Example written for the GNU Compiler Collection Source of libfoo.so source lang c extern void foo void attribute weak void fun void if foo foo source weak test.c source lang c include stdio.h void fun void void foo void printf Hello n int main fun return 0 source Compile with gcc weak test.c o weak test lfoo External References http gcc.gnu.org ml gcc 1999 02n msg01219.html See also Link editor Program loader Dynamic linking Weak reference DEFAULTSORT Weak Symbol Compsci stub Category Data types Category Debugging ... more details
about the symbol in number theory Kronecker delta In number theory , the Kronecker symbol , written as math left frac an right math or a n , is a generalization of the Jacobi symbol to all integer s n . It was introduced by Leopold Kronecker . Definition Let n be a non zero integer, with prime factorization math u cdot p 1 e 1 cdots p k e k , math where u is a unit ring theory unit i.e., u is 1 or 1 , and the p sub i sub are prime s. Let a be an integer. The Kronecker symbol a n is defined by math left frac a n right left frac a u right prod i 1 k left frac a p i right e i . math For odd number odd p sub i sub , the number a p sub i sub is simply the usual Legendre symbol . This leaves the case when p sub i sub 2. We define a 2 by math left frac a 2 right begin cases 0 & mbox if a mbox is even, 1 & mbox if a equiv pm1 pmod 8 , 1 & mbox if a equiv pm3 pmod 8 . end cases math Since it extends the Jacobi symbol, the quantity a u is simply 1 when u 1. When u 1, we define it by math left frac a 1 right begin cases 1 & mbox if a 0, 1 & mbox if a ge 0. end cases math Finally, we put math left frac a0 right begin cases 1& text if a pm1, 0& text otherwise. end cases math These extensions suffice to define the Kronecker symbol for all integer values n . Unlike the Jacobi symbol, the Kronecker symbol math tfrac a n math is not a Dirichlet character to the modulus n , because math a equiv b pmod n math does not imply math tfrac a n tfrac b n math when n is even. PlanetMath attribution id 6108 title Kronecker symbol Category Modular arithmetic de Kronecker Symbol es S mbolo de Kronecker nl Kronecker symbool ru uk zh ... more details
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