In mathematics , the greatestcommondivisor gcd , also known as the greatestcommon factor gcf , or highest ... can be extended to polynomials, see greatestcommondivisor of two polynomials . Overview Notation In this article we will denote the greatestcommondivisor of two integers a and b as gcd a , b . Some ..., 6. , math The greatest of these is 6. That is the greatestcommondivisor of 54 and 24. One writes math gcd 54,24 6. , math Reducing fractions The greatestcommondivisor is useful for reducing Fraction ... Two numbers are called relatively prime , or coprime if their greatestcommondivisor equals 1. For example ... squares or 12 by 12 squares. Therefore, 12 is the greatestcommondivisor of 24 and 60. A 24 by 60 rectangular ... example, illustrated by a Venn diagram . Suppose it is desired to find the greatestcommondivisor ... × 3 × 3 × 5 720 Greatestcommondivisor 2 × 2 × 3 12. Using Euclid s algorithm ... methods If a and b are not both zero, the greatestcommondivisor of a and b can be computed by using ... R. title Q Binomials and the GreatestCommonDivisor journal Integers Electronic Journal of Combinatorial ... of the greatestcommondivisor journal Integers Electronic Journal of Combinatorial Number ... of the Euclidean algorithm places the decision problem version of the greatestcommondivisor ... random integers has greatestcommondivisor d is d sup k sup k . ref name chid cite journal first ... The notion of greatestcommondivisor can more generally be defined for elements of an arbitrary commutative ... d , then d is called a greatestcommondivisor of a and b . Note that with this definition, two ... with the set of multiples of some ring element d then this d is a greatestcommondivisor of a and b . But the ideal a , b can be useful even when there is no greatestcommondivisor of a and b ... Binary GCD algorithm Euclidean algorithm Extended Euclidean algorithm Greatestcommondivisor ..., 1997. ISBN 0 201 89684 2. Section 4.5.2 The GreatestCommonDivisor, pp. 333&ndash 356. Thomas ... more details
unreferenced date March 2012 Informally, the greatestcommondivisor GCD of two polynomial s math p x math and math q x math is the largest polynomial that divides both math p x math and math q x math evenly. The definition is modeled on the concept of the greatestcommondivisor of two integer s, the greatest ..., and often so that its leading coefficient equals one i.e., it is Monic polynomial monic . The greatestcommondivisor is also sometimes referred to as the greatestcommon factor or the highest common ... in a field mathematics field math F math . A greatestcommondivisor of math p x math and math q x math is a polynomial math d x math of highest degree such that math d x math is a divisor of math p x math and of math q x math . We may denote the greatestcommondivisor of math p x math ... is a greatestcommondivisor of math p math and math q math if and only if math f math is equal ..., and it is convenient to avoid having alternative equivalent greatestcommon divisors. For this reason it is usual to define the greatestcommondivisor of math p x math and math q x math as the unique ... is a commondivisor of math p x math and math q x math . Thus no greatestcommondivisor exists ... , p n x . math Methods for finding the GCD There are several ways to find the greatestcommondivisor ... difficult than computing the greatestcommondivisor. Moreover, there are fields of coefficient for which ... 1 is always a commondivisor of math p x math and math q x math we may regard it as a monic polynomial ... a field, exists and is unique. If math c x math is any commondivisor of math p x math and math ... of requiring math d x math to be the commondivisor of highest degree. The two definitions are equivalent ..., then selects the set of common factors held by all from within each set of factors. This method ... completely. Then, take the product of all common factors. At this stage, we do not necessarily have ... of the two polynomials as it includes all common divisors and is monic. Example one Find ... more details
The lowest commondivisor is a meaningless term, often mistakenly usen when one actually wishes to refer to either the least common multiple of a set of numbers, or in particular, the lowest common denominator of a set of vulgar fraction s. the greatestcommondivisor , which is the largest integer that divides all the numbers in a set of integers. disambig ... more details
orphan date November 2009 In abstract algebra , particularly ring theory , maximal common divisors are an abstraction of the number theory concept of greatestcommondivisor GCD . This definition is slightly more general than GCDs, and may exist in rings in which GCDs do not. Halter Koch 1998 provides the following definition. ref name Ideal Systems cite book title Ideal systems publisher Marcel Dekker first Franz last Halter Koch year 1998 isbn 0824701860 ref d H is a maximal commondivisor of a subset, B H , if the following criteria are met d b for all b B Suppose c H d c and c b for all b a . Then math c simeq d math . References Reflist algebra stub Category Abstract algebra ... more details
Divisor may refer to DivisorDivisor algebraic geometry Divisor ring theory disambig Short pages monitor This long comment was added to the page to prevent it from being listed on Special Shortpages. It and the accompanying monitoring template were generated via Template Long comment. Please do not remove the monitor template without removing the comment as well. ... more details
In mathematics , a natural number a is a unitary divisor of a number b if a is a divisor of b and if a and math frac b a math are coprime , having no common factor other than 1. Thus, 5 is a unitary divisor of 60, because 5 and math frac 60 5 12 math have only 1 as a common factor, while 6 is a divisor but not a unitary divisor of 60, as 6 and math frac 60 6 10 math have a common factor other than 1, namely 2. 1 is a unitary divisor of every natural number. Equivalently, a given divisor a of b is a unitary divisor iff every prime factor of a has the same multiplicity mathematics multiplicity in a as it has in b . The sum of unitary divisors function is denoted by the lowercase Greek letter sigma thus n . The sum of the k th powers of the unitary divisors is denoted by sub k sub n math sigma k n sum d mid n, gcd d,n d 1 d k. math If the proper unitary divisors of a given number add up to that number, then that number is called a unitary perfect number . Properties The number of unitary divisors of a number n is 2 sup k sup , where k is the number of distinct prime factor s of n . The sum of the unitary divisors of n is odd if n is a power of 2 including 1 , and even otherwise. Both the count and the sum of the unitary divisors of n are multiplicative function s of n that are not completely multiplicative. The Dirichlet series Dirichlet generating function is math frac zeta s zeta s k zeta 2s k sum n ge 1 frac sigma k n n s . math Odd unitary divisors The sum of the k th powers of the odd unitary divisors is math sigma k o n sum d mid n, d equiv 1 pmod 2, gcd d,n d 1 d k. math It is also multiplicative, with Dirichlet generating function math frac zeta s zeta s k 1 2 k s zeta 2s k 1 2 k 2s sum n ge 1 frac sigma k o n n s . math References cite book author Richard K. Guy ... csolve try.pdf year 2004 External links MathWorld urlname UnitaryDivisor title Unitary Divisor ... n . OEIS2C A192066 is sup o sup sub 1 sub n . Divisor classes navbox Category Number theory numtheory ... more details
The Dow Jones Industrial Average DJIA is a price weighted index that is calculated by dividing the sum of the prices of the 30 component stocks Dow Jones Industrial Average components by a number called the DJIA Divisor or Dow Divisor . The index divisor is updated periodically and adjusted to offset the effect of stock split s, bonus issues, dividend payouts or any change in the component stocks included in the DJIA. This is done in order to keep the index value consistent. The current value of the Dow Divisor is 0.132129493 . Every 1 change in price in a stock within the average, results in a 7.57 1 0.132129493 change in the DJIA. The present divisor, after many adjustments, is less than one meaning the index is actually larger than the sum of the prices of the components . That is math text DJIA sum p over d math where p are the prices of the component stocks and d is the Dow Divisor . Events like stock splits or changes in the list of the companies composing the index alter the sum of the component prices. In these cases, in order to avoid discontinuity in the index, the Dow Divisor is updated so that the quotations right before and after the event coincide math text DJIA sum p text old over d text old sum p text new over d text new . math The value is published regularly in The Wall Street Journal and is available on line at the http www.djindexes.com Dow Jones Indexes web site. External links http online.barrons.com mdc public page 9 3022 djiahourly.html?mod mdc h usshl Barrons Data Center Table http www.cmegroup.com trading equity index files djia history divisor.pdf Dow Jones Industrial Average Historical Divisor Changes from CME Group Category Dow Jones Industrial Average ... more details
of a zero divisor in the ring of 2 by 2 matrix mathematics matrices is the matrix math begin pmatrix ... with an element that is a zero divisor on one side only. Let S be the set of all sequences of integers ... zero, so L is a left zero divisor and R is a right zero divisor in the ring of additive maps from S to S . However, L is not a right zero divisor and R is not a left zero divisor the composite LR ..., note that while RL is a left zero divisor RL T R LT is 0 because LT is , LR is not a zero divisor on either side because it is the identity. Concretely, we can interpret additive maps from ... LR is the identity. In particular, as matrices A is a left zero divisor but not a right zero divisor ... a 1 is a zero divisor, since a sup 2 sup a implies a a &minus 1 a &minus 1 a 0. Nonzero nilpotent ... associated prime ideals of the ring. See also Integral domain Zero product property Divisor ring theory ... 0 MathWorld title Zero Divisor urlname ZeroDivisor DEFAULTSORT Zero Divisor Category Abstract algebra Category Ring theory Category Zero ca Divisor de zero cs D litel nuly de Nullteiler et Nullitegur el es Divisor de cero fr Diviseur de z ro ko he hu Z rusoszt nl Nuldeler pl Dzielnik zera pt Divisor de zero ru sk Delite nuly sl Delitelj ni a sv Nolldelare ... more details
In mathematics , specifically algebraic geometry , an exceptional divisor for a regular map algebraic geometry regular map math f X rightarrow Y math of varieties is a kind of large subvariety of math X math which is crushed by math f math , in a certain definite sense. More strictly, f has an associated exceptional locus which describes how it identifies nearby points in codimension one, and the exceptional divisor is an appropriate algebraic construction whose support is the exceptional locus. The same ideas can be found in the theory of holomorphic mappings of complex manifold s. More precisely, suppose that math f X rightarrow Y math is a regular map of varieties which is birational that is, it is an isomorphism between open subsets of math X math and math Y math . A codimension 1 subvariety math Z subset X math is said to be exceptional if math f Z math has codimension at least 2 as a subvariety of math Y math . One may then define the exceptional divisor of math f math to be math sum i Z i in Div X , math where the sum is over all exceptional subvarieties of math f math , and is an element of the group of Divisor algebraic geometry Weil divisors on math X math . Consideration of exceptional divisors is crucial in birational geometry an elementary result see for instance Shafarevich, II.4.4 shows that any birational regular map that is not an isomorphism has an exceptional divisor. A particularly important example is the Blowing up blowup math sigma tilde X rightarrow X math of a subvariety math W subset X math in this case the exceptional divisor is exactly the preimage of math W math . References cite book author Shafarevich, Igor title Basic Algebraic Geometry, Vol. 1 publisher Springer Verlag year 1994 id ISBN 3 540 54812 2 Category Algebraic geometry Category Birational geometry ... more details
In mathematics , the theta divisor is the divisor algebraic geometry divisor in the sense of algebraic geometry defined on an abelian variety A over the complex numbers and principally polarized by the zero locus of the associated Riemann theta function . It is therefore an algebraic subvariety of A of dimension dim A &minus 1. Classical theory Classical results of Bernhard Riemann describe in another way, in the case that A is the Jacobian variety J of an algebraic curve compact Riemann surface C . There is, for a choice of base point P on C , a standard mapping of C to J , by means of the interpretation of J as the linear equivalence classes of divisors on C of degree 0. That is, Q on C maps to the class of Q &minus P . Then since J is an algebraic group , C may be added to itself k times on J , giving rise to subvarieties W sub k sub . If g is the genus mathematics genus of C , Riemann proved that is a translate on J of W sub g &minus 1 sub . He also described which points on W sub g &minus 1 sub are non singular they correspond to the effective divisors D of degree g &minus 1 with no associated meromorphic functions other than constants. In more classical language, these D do not move in a linear system of divisors on C , in the sense that they do not dominate the polar divisor of a non constant function. Riemann further proved the Riemann singularity theorem , identifying the multiplicity of a point p class D on W sub g &minus 1 sub as the number of independent meromorphic functions with pole divisor dominated by D, or equivalently as h sup 0 sup O D , the number of independent global section s of the holomorphic line bundle associated to D as Cartier divisor on C . Later work The Riemann singularity theorem was extended by George Kempf in 1973, ref cite journal author G. Kempf title On the geometry of a theorem of Riemann journal Ann. Of Math. volume 98 year 1973 pages 178 185 doi 10.2307 1970910 jstor 1970910 issue 1 ref building on work of David Mumford ... more details
In mathematics, more specifically general topology , the divisor topology is an example of a topology given to the set X of positive integer s that are greater than or equal to two, i.e., nowrap 1 X 2, 3, 4, 5, &hellip . The divisor topology is the poset topology for the partial order relation of divisibility on the positive integers. To give the set X a topology means to say which subset s of X are open , and to do so in a way that the following axiom s are met ref name CEIT Citation first L. A. last Steen first2 J. A. last2 Seebach title Counterexamples in Topology publisher Dover year 1995 ISBN 048668735X ref The union mathematics union of open sets is an open set. The finite intersection mathematics intersection of open sets is an open set. The set X and the empty set are open sets. Construction The set X and the empty set are required to be open sets, and so we define X and to be open sets in this topology. Denote by Z sup sup the set of positive integer s, i.e., the set of positive whole number greater than or equal to one. Read the notation x n as x divides n , and consider the sets math S n x in bold Z x n math Then the set S sub n sub is the set of divisor s of n . For different values of n , the sets S sub n sub are used as a basis topology basis for the divisor topology. ref name CEIT The open sets in this topology are the lower set s for the partial order defined by nowrap 1 x y if x &thinsp &thinsp y . Properties The set of prime number s is dense topology dense in X . In fact, every dense open set must include every prime, and therefore X is a Baire space . ref name CEIT X is a Kolmogorov space that is not T1 space T1 . In particular, it is Hausdorff space non Hausdorff . X is second countable space second countable . X is connected space connected and locally connected . X is not compact space compact , since the basic open sets S sub n sub comprise an infinite ... are the complements of prime ideal s. References Reflist DEFAULTSORT Divisor topology Category General ... more details
Image Divisor.svg thumb right Divisor function sub 0 sub n up to n 250 Image Sigma function.svg thumb right Sigma function sub 1 sub n up to n 250 Image Divisor square.svg thumb right Sum of the squares of divisors, sub 2 sub n , up to n 250 Image Divisor cube.svg ... in number theory , a divisor function is an arithmetical function related to the divisor s of an integer . When referred to as the divisor function, it counts the number of divisors of an integer ... zeta function and the Eisenstein series of modular form s. Divisor functions were studied by Ramanujan ... . A related function is the divisor summatory function , which, as the name implies, is a sum over the divisor function. Definition The sum of positive divisors function sub x sub n , for a real or complex number x , is defined as the sum of the x th Exponentiation powers of the positive divisor ... A013955 ... Properties For a non square integer every divisor d of n is paired with divisor n d of n and math sigma 0 n math is then even for a square integer one divisor namely math sqrt n math is not paired with a distinct divisor and math sigma 0 n math is then odd. For a prime number p , math ... proper divisor formed. Clearly, 1 d n n and n n for all n 2. The divisor function is multiplicative function multiplicative , but not Completely ... Two Dirichlet series involving the divisor function are math sum n 1 infty frac sigma a n n s zeta ... zeta s a b zeta 2s a b . math A Lambert series involving the divisor function is math sum n 1 infty ... o notation little o notation , the divisor function satisfies the inequality see page 296 of Apostol ... order of an arithmetic function average order of the divisor function satisfies the following ... Euler s constant . Improving the bound math O sqrt x math in this formula is known as Divisor summatory function Dirichlet s divisor problem Dirichlet s divisor problem anchor Robin s theorem Robin s inequality ... more details
two different generalizations are in common use, Cartier divisors and Weil divisors named for Pierre ... of the free abelian group of points on the surface. Equivalently, a divisor is a finite linear combination of points of the surface with integer coefficients. The degree of a divisor is the sum of its coefficients. We define the divisor of a meromorphic function f as math f sum z nu in R f s nu z nu ... math A divisor that is the divisor of a meromorphic function is called principal . It follows from ... divisor is 0. Since the divisor of a product is the sum of the divisors, the set of principal divisors is a subgroup of the group of divisors. Two divisors that differ by a principal divisor are called linearly equivalent . We define the divisor of a meromorphic 1 form similarly. Since the space of meromorphic ... is called the canonical divisor usually denoted K . The Riemann Roch theorem is an important relation between the divisors of a Riemann surface and its topology. Weil divisor Riemann Roch theorem links here A Weil divisor is a locally finite linear combination with integer integral coefficients of irreducible ... subvarieties of dimension n &minus 1 . For example, a divisor on an algebraic curve is a formal sum of its closed points. An effective Weil divisor is then one in which all the coefficients of the formal sum are non negative. Cartier divisor A Cartier divisor can be represented by an open cover by affine ... divisor is said to be effective if these math f i math can be chosen to be regular function s, and in this case the Cartier divisor defines an associated subvariety of codimension 1 by forming the ideal ... divisors. A Cartier divisor is a global section of the quotient sheaf K sub X sub sup sup O sub X ... to Gamma X, O X to Gamma X, K X to Gamma X, K X mathcal O X to H 1 X, mathcal O X math . A Cartier divisor ... is a divisor of 0, so that the total quotient sheaves are zero, so that the sheaf contains no non trivial Cartier divisor. From Cartier divisors to Weil divisor There is a natural homomorphism ... more details
Lowest common factor may refer to the following mathematical terms Greatestcommondivisor , also known as the greatestcommon factor Least common multiple Lowest common denominator disambiguation ... more details
In mathematics , an element z of a Banach algebra A is called a topological divisor of zero if there exists a sequence x sub 1 sub , x sub 2 sub , x sub 3 sub , ... of elements of A such that The sequence zx sub n sub converges to the zero element, but The sequence x sub n sub does not converge to the zero element. If such a sequence exists, then one may assume that x sub n sub 1 for all n . If A is not commutativity commutative , then z is called a left topological divisor of zero, and one may define right topological divisors of zero similarly. Examples If A has a unit element, then the invertible elements of A form an open set open subset of A , while the non invertible elements are the complementary closed set closed subset . Any point on the boundary topology boundary between these two sets is both a left and right topological divisor of zero. In particular, any quasinilpotent element is a topological divisor of zero e.g. the Volterra operator . An operator on a Banach space math X math , which is injective , not surjective , but whose image is dense in math X math , is a left topological divisor of zero. Generalization The notion of a topological divisor of zero may be generalized to any topological algebra . If the algebra in question is not first countable space first countable , one must substitute net mathematics nets for the sequences used in the definition. Unreferenced date January 2011 DEFAULTSORT Topological Divisor Of Zero Category Topological algebra algebra stub de Topologischer Nullteiler ... more details
About harmonic divisor numbers meanings of harmonic number harmonic number disambiguation In mathematics , a harmonic divisor number , or Ore number named after ystein Ore who defined it in 1948 , is a positive integer whose divisors have a harmonic mean that is an integer . The first few harmonic divisor numbers are 1 number 1 , 6 number 6 , 28 number 28 , 140 number 140 , 270 number 270 , 496 number 496 , 672, 1638, 2970, 6200, 8128 number 8128 , 8190 OEIS id A001599 . For example, the harmonic divisor number 6 has the four divisors 1, 2, 3, and 6. Their harmonic mean is an integer math frac 4 frac 1 1 frac 1 2 frac 1 3 frac 1 6 2. math The number 140 has divisors 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, and 140. Their harmonic mean is math frac 12 frac 1 1 frac 1 2 frac 1 4 frac 1 5 frac 1 7 frac 1 10 frac 1 14 frac 1 20 frac 1 28 frac 1 35 frac 1 70 frac 1 140 5 math 5 is an integer, making 140 a harmonic divisor number. Harmonic divisor numbers and perfect numbers For any integer M , as Ore observed, the product of the harmonic mean and arithmetic mean of its divisors equals M itself ... number M is exactly 2M therefore, the average of the divisors is M 2 M , where M denotes the Divisor ... , for otherwise each divisor d of M can be paired with a different divisor M d . But, no perfect number ... fraction 2 M thus, M is a harmonic divisor number. Ore conjectured that no odd harmonic divisor numbers exist other than 1. If the conjecture is true, this would imply the nonexistence of perfect ... see Muskat showed that any odd harmonic divisor number above 1 must have a prime power factor ... prime factors. Cohen and Sorli 2010 showed that there are no odd harmonic divisor numbers smaller ... listing all small harmonic divisor numbers. From these results, lists are known of all harmonic divisor numbers up to 2 10 sup 9 sup , and all harmonic divisor numbers for which the harmonic mean ... Harmonic Divisor Number urlname HarmonicDivisorNumber Divisor classes navbox Category Divisor function ... more details
Greatest is a title, similar to Greatest hits Greatest Hits , used by several musical artists Greatest , a 1959 album by Johnny Cash Bee Gees Greatest , a 1979 album Greatest The Go Go s album , a 1990 album Greatest Duran Duran album , a 1998 album See also Greatness , a concept of superiority Ultimate sport Greatest , a technique in ultimate frisbee. The Greatest disambiguation page . disambig it Greatest ... more details
The Greatest may refer to Muhammad Ali , former American heavyweight boxing champion The Greatest Ian Brown album The Greatest Ian Brown album , a 2005 compilation album by Ian Brown The Greatest Cat Power album The Greatest Cat Power album , a 2006 album by Cat Power The Greatest song The Greatest , a 2008 song by Michelle Williams. The Greatest 1977 film The Greatest 1977 film , a 1977 film about Muhammad Ali The Greatest 2009 film The Greatest 2009 film , a 2009 film featuring Pierce Brosnan and Susan Sarandon The Greatest TV series The Greatest TV series , a VH1 series of countdowns disambig it The Greatest ... more details
Image Divisor summatory.svg thumb right The summatory function, with leading terms removed, for math x 10 4 math Image Divisor summatory big.svg thumb right The summatory function, with leading terms removed, for math x 10 7 math Image Divisor distribution.jpeg thumb right The summatory function, with leading terms removed, for math x 10 7 math , graphed as a distribution or histogram. The vertical scale is not constant left to right click on image for a detailed description. In number theory , the Divisor summatory function is a function that is a sum over the divisor function . It frequently occurs in the study of the asymptotic behaviour of the Riemann zeta function . The various studies of the behaviour of the divisor function are sometimes called divisor problems . Definition The divisor summatory function is defined as math D x sum n le x d n sum j,k atop jk le x 1 math where math d n sigma 0 n sum j,k atop jk n 1 math is the divisor function . The divisor function counts the number of ways that the integer n can be written as a product of two integers. More generally, one defines math D k x sum n le x d k n sum mn le x d k 1 n math where d sub k sub n counts the number of ways that n can be written as a product of k numbers. This quantity can be visualized as the count of the number of lattice points fenced off by a hyperbolic surface in k dimensions. Thus, for k 2, D x D ... function is known as the Gauss circle problem . Dirichlet s divisor problem Finding a closed ... mathcal O math denotes Big O notation . The Dirichlet divisor problem , precisely stated, is to find .... authorlink Henryk Iwaniec coauthors C. J. Mozzochi year 1988 title On the divisor and circle problems ... deviation of 1 for x up to at least 10 sup 16 sup . Generalized divisor problem In the generalized ... Press, Oxford. See chapter 12 for a discussion of the generalized divisor problem Apostol IANT Provides an introductory statement of the Dirichlet divisor problem. H. E. Rose. A Course in Number ... more details
wiktionary common uncommon Common may refer to COMMON , the largest association of users of mid range IBM computers Common horse , a British Thoroughbred racehorse Common liturgy , a part of certain Christian liturgy Commoner , someone does not hold a title of peerage Common land , land which other people have certain traditional rights graze livestock or collect firewood Lingua franca or common language, shared by speakers of different mother tongues Vernacular , the common but not scientific name of a plant or animal Massachusetts The Common , a nickname of the Commonwealth of Massachusetts COMMON, a Fortran statement a translation of tum ah , a biblical term for ritual impurity, used by some common English translations of the bible Dol Common, a character in The Alchemist play The Alchemist play by Ben Jonson People Common entertainer born 1972 , American hip hop artist, actor and poet Boston Common , a central public park in Boston, Massachusetts. See also lookfrom Common Commons disambiguation Come On disambiguation Common good disambig no Common pt Common desambigua o ... more details
About a computer users group Common disambiguation Common Primary sources date March 2009 infobox Organization name COMMON image CommonLogo.PNG image border size 250px caption The logo of the organization ... to lead Common iSeries user group conference Search 400, September 13, 2006 ref language English ... 11 num volunteers 1,000 budget website http www.common.org www.common.org remarks COMMON is the largest ... experience. Financial problems The Late 2000s recession had a severe effect on COMMON activities. IT professionals ... in COMMON changing from two conferences per year to one. ref Morgan, Timothy Prickett http www.itjungle.com ... 27, 2008 ref Attendance at COMMON s technical events, which increased throughout the 1980s and 1990s ... iseries common board reveals financial situation at meeting of members COMMON board ... Resources COMMON s Annual Meeting and Exposition, the premier IBM System i educational and networking ... Business Technology magazine website Events COMMON s 2008 Annual Meeting and Exposition ref COMMON ... 2008 directions index.html Common.org about COMMON directions 2008 ref COMMON Focus, three days of educational ... Common.org about COMMON focus 2008 ref One day Seminars on leading edge topics, held in partnership with Local User Groups throughout North America. ref http www.common.org seminars Common.org COMMON Seminars ref Web based Education, including Webcast s. ref http www.common.org webcasts Common Webcast info ref and Webinar s. ref http www.common.org webinars index.html Common Webinar info ref Networking and membership directory of all COMMON members. COMMON.CONNECT , the bi monthly professional journal of COMMON. COMMON Connector , the monthly e newsletter from COMMON. IBM Certification discounts. COMMON Online Networking community through iSociety. ref name IBMiSociety COMMON Career Center ... www.itjungle.com tfh tfh042406 story07.html Common User Group Starts Midrange Career Center IT Jungle ... all employees to take advantage of Common s resources. Individual the named individual is entitled ... more details
Infobox Album See Wikipedia WikiProject Albums Name Greatest Type Album Artist Johnny Cash Cover JohnnyCashGreatest.jpg Released Original January 1959 br Re issued May 6, 2003 Recorded July 30, 1955 July 17, 1958 Genre Country music Country Length 25 46 Label Sun Records Sun Producer Sam Phillips , Jack Clement Reviews Last album The Fabulous Johnny Cash br 1959 This album Greatest br 1959 Next album Hymns by Johnny Cash br 1959 Album ratings rev1 Allmusic rev1Score Rating 3 5 ref Allmusic class album id r91918 ref noprose yes Greatest is the fourth album by country music country singer Johnny Cash , released on Sun Records on 12 January 1959 see 1959 in music . It was Cash s third record on the label, which he had left the previous year to join Columbia Records . By the time the album was released, Cash had already recorded The Fabulous Johnny Cash , his first album with Columbia. The tracks on Greatest were recorded between July 1955 and July 1958. Six out of the twelve songs became singles, with Get Rhythm topping the Country charts and becoming the most successful one. The album was rereleased on Var se Sarabande on May 6, 2003 see 2003 in music with four additional tracks, two of them being alternate versions of songs already on the record. Track listing Goodbye Little Darlin Goodbye Gene Autry , Johnny Marvin 2 14 I Just Thought You d Like to Know Charlie Rich 2 23 You Tell Me Roy Orbison 1 48 Just About Time Cash 2 07 I Forgot to Remember to Forget song I Forgot to Remember to Forget Stan Kesler, Charlie Feathers 2 09 Katy Too Cash, Jack Clement 1 57 Thanks a Lot Rich 2 38 Luther Played the Boogie Cash 2 03 You Win Again song You Win Again Hank Williams 2 18 Hey Good ... align left 1 References references Johnny Cash studio DEFAULTSORT Greatest Category 1959 albums ... Category Albums produced by Jack Clement 1950s country album stub de Greatest es Greatest hr Greatest it Greatest pl Greatest pt Greatest ru Greatest fi Greatest ... more details
Infobox protected area name Serra do Divisor National Park alt name iucn category II photo Rio moa.jpg photo alt photo caption Moa River in Serra do Divisor National Park photo width map Brazil map alt map caption Location within Brazil map width location Acre state Acre , Brazil nearest city lat d 8.36 long d 73.33 coords ref ref Cite web url http protectedplanet.net sites Serra Do Divisor National Park title Serra Do Divisor National Park work protectedplanet.net ref region BR AC area Convert 8463 km2 mi2 abbr on established 1989 visitation num visitation year governing body world heritage site url Serra do Divisor National Park is a Convert 8463 km2 mi2 abbr on national park on the westernmost point of Brazil , in the States of Brazil state of Acre state Acre , near Peru vian border. It is also the highest point in that state, reaching 609 meters above sea level. It has been nominated by the Brazilian government as a Tentative World Heritage Site since 1998. References Reflist AcreBR geo stub Brazil protected area stub Protected areas of Brazil Brazilian states highest points Category National parks of Brazil Category Extreme points of Earth Category Acre state Category Highest points of Brazilian states de Sierra del Divisor es Parque nacional de la Sierra del Divisor pt Parque Nacional da Serra do Divisor ... more details
Other uses Common Good disambiguation Refimprove date August 2010 The common good or common weal is a term that can refer to several different concepts. In the popular meaning, the common good describes ... community . This is also how the common good is broadly defined in philosophy , ethics , and political science . However there is no strict definition of the common good for each situation. The good that is common between person A and person B may not be the same as between person A and person C. Thus the common good can often change, although there are some things such as the basic requirements for staying alive food, water, and shelter that are always good for all people. The common good has sometimes been seen as a utilitarianism utilitarian ideal, thus representing the greatest possible good for the greatest possible number of individuals . In the best case scenario, the greatest possible number of individuals would mean all sentience sentient beings. This definition of the common ..., and many would argue impoverished, view of what the common good might encompass. Another definition of the common good, as the quintessential goal of State polity the state , requires an admission ... law . The common good, then, is the sum total of the conditions of social life which enable ... of virtue, but does not prescribe what the common good actually is. Some assert that promoting the common ... of economics . Who date March 2008 Catholic social teaching The common good is a concept ... of the common good requiring regulation state regulation . citation needed Another relevant ... Americans are adopting the language of the common good sometimes referred to as public wealth to describe progressive values. As an ethical and moral imperative, the common good is central to the tenets ... . Aristotle was the first to articulate an ethical understanding of common good, followed by Augustine ... contemporary American politics, the common good language is increasingly identifiable with political ... more details
The Greatest Hits may refer to The Greatest Hits Amii Stewart 2005 The Greatest Hits Amii Stewart 2005 , 2005 The Greatest Hits Boney M. 1993 The Greatest Hits Boney M. 1993 , 1993 The Greatest Hits Boney M. album The Greatest Hits Boney M. album , 2001 The Greatest Hits Cheap Trick album The Greatest Hits Cheap Trick album , 1991 The Greatest Hits Cher album The Greatest Hits Cher album , 1999 The Greatest Hits Five Star album The Greatest Hits Five Star album , 2004 The Greatest Hits Funkoars album The Greatest Hits Funkoars album , 2006 The Greatest Hits GRITS album The Greatest Hits GRITS album , 2007 The Greatest Hits INXS album The Greatest Hits INXS album , 1994 The Greatest Hits Juvenile album The Greatest Hits Juvenile album , 2004 The Greatest Hits Lil Suzy album The Greatest Hits Lil Suzy album , 2003 The Greatest Hits Lulu album The Greatest Hits Lulu album , 2003 The Greatest Hits Newsboys album The Greatest Hits Newsboys album , 2007 The Greatest Hits Sinitta album The Greatest Hits Sinitta album , 2010 The Greatest Hits Texas album The Greatest Hits Texas album , 2000 Whitney The Greatest Hits , a 2000 album by Whitney Houston See also Greatest hits album List of greatest hits albums disambiguation ... more details
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