text:
Projective line over a ring

In mathematics, the projective line over a ring is an extension of the concept of projective line over a field. Given a ring A (with 1), the projective line P1(A) over A consists of points identified by projective coordinates. Let A× be the group of units of A; pairs (a, b) and (c, d) from A × A are related when there is a u in A× such that ua = c and ub = d. This relation is an equivalence relation. A typical equivalence class is written U[a, b].

P1(A) = $\{ U[a, b] | aA + bA = A \}$, that is, U[a, b] is in the projective line if the one-sided ideal generated by a and b is all of A.

The projective line P1(A) is equipped with a group of homographies. The homographies are expressed through use of the matrix ring over A and its group of units V as follows: If c is in Z(A×), the center of A×, then the group action of matrix $$\left(\begin{smallmatrix}c & 0 \\ 0 & c \end{smallmatrix}\right)$$ on P1(A) is the same as the action of the identity matrix. Such matrices represent a normal subgroup N of V. The homographies of P1(A) correspond to elements of the quotient group V/N.

P1(A) is considered an extension of the ring A since it contains a copy of A due to the embedding E : a → U[a, 1]. The multiplicative inverse mapping u → 1/u, ordinarily restricted to A×, is expressed by a homography on P1(A):
 * $$U[a,1]\begin{pmatrix}0&1\\1&0\end{pmatrix} = U[1, a] \thicksim U[a^{-1}, 1].$$

Furthermore, for u,v ∈ A×, the mapping a → uav can be extended to a homography:
 * $$\begin{pmatrix}u & 0 \\0 & 1 \end{pmatrix}\begin{pmatrix}0 & 1 \\ 1 & 0 \end{pmatrix}\begin{pmatrix} v & 0 \\ 0 & 1 \end{pmatrix}\begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix} = \begin{pmatrix} u & 0 \\ 0 & v \end{pmatrix}. $$
 * $$U[a,1]\begin{pmatrix}v&0\\0&u\end{pmatrix} = U[av,u] \thicksim U[u^{-1}av,1].$$

Since u is arbitrary, it may be substituted for u−1. Homographies on P1(A) are called linear-fractional transformations since
 * $$U[z,1] \begin{pmatrix}a&c\\b&d\end{pmatrix} = U[za+b,zc+d] \thicksim U[(zc+d)^{-1}(za+b),1].$$

Instances

Rings that are fields are most familiar: The projective line over GF(2) has three elements: U[0, 1], U[1, 0], and U[1, 1]. Its homography group is the permutation group on these three.

The ring Z/3Z, or GF(3), has the elements 1, 0, and −1; its projective line has the four elements U[1, 0], U[1, 1], U[0, 1], U[1, −1] since both 1 and −1 are units. The homography group on this projective line has 12 elements, also described with matrices or as permutations. For a finite field GF(q), the projective line is the Galois geometry PG(1, q). J. W. P. Hirschfeld has described the harmonic tetrads in the projective lines for q = 4, 5, 7, 8, 9.

Over discrete rings
Consider P1(Z/nZ) when n is a composite number. If p and q are distinct primes dividing n, then $\langlep\rangle$ and $\langleq\rangle$ are maximal ideals in Z/nZ and by Bézout's identity there are a and b in Z such that ap + bq = 1, so that U[p, q] is in P1(Z/nZ) but it is not an image of an element under the canonical embedding. The whole of P1(Z/nZ) is filled out by elements U[up, vq], where u ≠ v and u, v ∈ A×, A× being the units of Z/nZ. The instances Z/nZ are given here for n = 6, 10, and 12, where according to modular arithmetic the group of units of the ring is (Z/6Z)× = $\{1, 5\}$, (Z/10Z)× = $\{1, 3, 7, 9\}$, and (Z/12Z)× = $\{1, 5, 7, 11\}$ respectively. Modular arithmetic will confirm that, in each table, a given letter represents multiple points. In these tables a point U[m, n] is labeled by m in the row at the table bottom and n in the column at the left of the table. For instance, the point at infinity A = U[v, 0], where v is a unit of the ring.

The extra points can be associated with Q ⊂ R ⊂ C, the rationals in the extended complex upper-half plane. The group of homographies on P1(Z/nZ) is called a principal congruence subgroup.

For the rational numbers Q, homogeneity of coordinates means that every element of P1(Q) may be represented by an element of P1(Z). Similarly, a homography of P1(Q) corresponds to an element of the modular group, the automorphisms of P1(Z).

Over continuous rings
The projective line over a division ring results in a single auxiliary point ∞ = U[1, 0]. Examples include the real projective line, the complex projective line, and the projective line over quaternions. These examples of topological rings have the projective line as their one-point compactifications. The case of the complex number field C has the Möbius group as its homography group.

The projective line over the dual numbers was described by Josef Grünwald in 1906. This ring includes a nonzero nilpotent n satisfying nn = 0. The plane $\{ z = x + yn | x, y ∈ R \}$ of dual numbers has a projective line including a line of points U[1, xn], x ∈ R. Isaak Yaglom has described it as an "inversive Galilean plane" that has the topology of a cylinder when the supplementary line is included. Similarly, if A is a local ring, then P1(A) is formed by adjoining points corresponding to the elements of the maximal ideal of A.

The projective line over the ring M of split-complex numbers introduces auxiliary lines $\{ U[1, x(1 + j)] | x ∈ R \}$ and $\{ U[1, x(1 − j)] | x ∈ R \}$ Using stereographic projection the plane of split-complex numbers is closed up with these lines to a hyperboloid of one sheet. The projective line over M may be called the Minkowski plane when characterized by behaviour of hyperbolas under homographic mapping.

Modules
The projective line P1(A) over a ring A can also be identified as the space of projective modules in the module A ⊕ A. An element of P1(A) is then a direct summand of A ⊕ A. This more abstract approach follows the view of projective geometry as the geometry of subspaces of a vector space, sometimes associated with the lattice theory of Garrett Birkhoff or the book Linear Algebra and Projective Geometry by Reinhold Baer. In the case of the ring of rational integers Z, the module summand definition of P1(Z) narrows attention to the U[m, n], m coprime to n, and sheds the embeddings that are a principal feature of P1(A) when A is topological. The 1981 article by W. Benz, Hans-Joachim Samaga, & Helmut Scheaffer mentions the direct summand definition.

In an article "Projective representations: projective lines over rings" the group of units of a matrix ring M2(R) and the concepts of module and bimodule are used to define a projective line over a ring. The group of units is denoted by GL(2, R), adopting notation from the general linear group, where R is usually taken to be a field.

The projective line is the set of orbits under GL(2, R) of the free cyclic submodule R(1, 0) of R × R. Extending the commutative theory of Benz, the existence of a right or left multiplicative inverse of a ring element is related to P1(R) and GL(2, R). The Dedekind-finite property is characterized. Most significantly, representation of P1(R) in a projective space over a division ring K is accomplished with a (K, R)-bimodule U that is a left K-vector space and a right R-module. The points of P1(R) are subspaces of P1(K, U × U) isomorphic to their complements.

Cross-ratio
A homography h that takes three particular ring elements a, b, c to the projective line points U[0, 1], U[1, 1], U[1, 0] is called the cross-ratio homography. Sometimes the cross-ratio is taken as the value of h on a fourth point x : (x, a, b, c) = h(x).

To build h from a, b, c the generator homographies
 * $$\begin{pmatrix}0 & 1\\1 & 0 \end{pmatrix}, \begin{pmatrix}1 & 0\\t & 1 \end{pmatrix}, \begin{pmatrix}u & 0\\0 & 1 \end{pmatrix}$$

are used, with attention to fixed points: +1 and −1 are fixed under inversion, U[1, 0] is fixed under translation, and the "rotation" with u leaves U[0, 1] and U[1, 0] fixed. The instructions are to place c first, then bring a to U[0, 1] with translation, and finally to use rotation to move b to U[1, 1].

Lemma: If A is a commutative ring and b − a, c − b, c − a are all units, then (b − c)−1 + (c − a)−1 is a unit.

Proof: Evidently $$\frac{b-a}{(b-c)(c-a)} = \frac{(b-c)+(c-a)}{(b-c)(c-a)}$$ is a unit, as required.

Theorem: If (b − c)−1 + (c − a)−1 is a unit, then there is a homography h in G(A) such that
 * h(a) = U[0, 1], h(b) = U[1, 1], and h(c) = U[1, 0].

Proof: The point p = (b − c)−1 + (c − a)−1 is the image of b after a was put to 0 and then inverted to U[1, 0], and the image of c is brought to U[0, 1]. As p is a unit, its inverse used in a rotation will move p to U[1, 1], resulting in a, b, c being all properly placed. The lemma refers to sufficient conditions for the existence of h.

One application of cross ratio defines the projective harmonic conjugate of a triple a, b, c, as the element x satisfying (x, a, b, c) = −1. Such a quadruple is a harmonic tetrad. Harmonic tetrads on the projective line over a finite field GF(q) were used in 1954 to delimit the projective linear groups PGL(2, q) for q = 5, 7, and 9, and demonstrate accidental isomorphisms.

Chains
The real line in the complex plane gets permuted with circles and other real lines under Möbius transformations, which actually permute the canonical embedding of the real projective line in the complex projective line. Suppose A is an algebra over a field F, generalizing the case where F is the real number field and A is the field of complex numbers. The canonical embedding of P1(F) into P1(A) is
 * $$U_F[x, 1] \mapsto U_A[x, 1], \quad U_F[1, 0] \mapsto U_A[1, 0].$$

A chain is the image of P1(F) under a homography on P1(A). Four points lie on a chain if and only if their cross-ratio is in F. Karl von Staudt exploited this property in his theory of "real strokes" [reeler Zug].

Point-parallelism
Two points of P1(A) are parallel if there is no chain connecting them. The convention has been adopted that points are parallel to themselves. This relation is invariant under the action of a homography on the projective line. Given three pair-wise non-parallel points, there is a unique chain that connects the three.

History
August Ferdinand Möbius investigated the Möbius transformations between his book Barycentric Calculus (1827) and his 1855 paper "Theorie der Kreisverwandtschaft in rein geometrischer Darstellung". Karl Wilhelm Feuerbach and Julius Plücker are also credited with originating the use of homogeneous coordinates. Eduard Study in 1898, and Élie Cartan in 1908, wrote articles on hypercomplex numbers for German and French Encyclopedias of Mathematics, respectively, where they use these arithmetics with linear fractional transformations in imitation of those of Möbius. In 1902 Theodore Vahlen contributed a short but well-referenced paper exploring some linear fractional transformations of a Clifford algebra. The ring of dual numbers D gave Josef Grünwald opportunity to exhibit P1(D) in 1906. Corrado Segre (1912) continued the development with that ring.

Arthur Conway, one of the early adopters of relativity via biquaternion transformations, considered the quaternion-multiplicative-inverse transformation in his 1911 relativity study. In 1947 some elements of inversive quaternion geometry were described by P.G. Gormley in Ireland. In 1968 Isaak Yaglom's Complex Numbers in Geometry appeared in English, translated from Russian. There he uses P1(D) to describe line geometry in the Euclidean plane and P1(M) to describe it for Lobachevski's plane. Yaglom's text A Simple Non-Euclidean Geometry appeared in English in 1979. There in pages 174 to 200 he develops Minkowskian geometry and describes P1(M) as the "inversive Minkowski plane". The Russian original of Yaglom's text was published in 1969. Between the two editions, Walter Benz (1973) published his book, which included the homogeneous coordinates taken from M.

title: Projective line over a ring


text:
List of peers 1100–1109

Peerage of England

 * Earl of Cornwall (1068)||William Fitz-Robert, 2nd Earl of Cornwall||1095||1106||Forfeit
 * Earl of Chester (1071)||Hugh d'Avranches, 1st Earl of Chester||1071||1101||Died
 * ||Richard d'Avranches, 2nd Earl of Chester||1101||1120||
 * Earl of Shrewsbury (1074)||Robert of Bellême, 3rd Earl of Shrewsbury||1098||1102||Forfeit
 * Earl of Northampton (1080)||Simon I de Senlis, Earl of Huntingdon-Northampton||1080||1109||Died
 * ||Simon II de Senlis, Earl of Huntingdon-Northampton||1109||1153||
 * Earl of Albemarle (1081)||Stephen de Blois, 2nd Earl of Albemarle||1090||1127||
 * Earl of Surrey (1088)||William de Warenne, 2nd Earl of Surrey||1099||1138||
 * Earl of Warwick (1088)||Henry de Beaumont, 1st Earl of Warwick||1088||1119||
 * Earl of Buckingham (1097)||Walter Giffard, 1st Earl of Buckingham||1097||1102||Died
 * ||Walter Giffard, 2nd Earl of Buckingham||1102||1164||
 * Earl of Leicester (1107)||Robert de Beaumont, 1st Earl of Leicester||1107||1118||New creation
 * Earl of Albemarle (1081)||Stephen de Blois, 2nd Earl of Albemarle||1090||1127||
 * Earl of Surrey (1088)||William de Warenne, 2nd Earl of Surrey||1099||1138||
 * Earl of Warwick (1088)||Henry de Beaumont, 1st Earl of Warwick||1088||1119||
 * Earl of Buckingham (1097)||Walter Giffard, 1st Earl of Buckingham||1097||1102||Died
 * ||Walter Giffard, 2nd Earl of Buckingham||1102||1164||
 * Earl of Leicester (1107)||Robert de Beaumont, 1st Earl of Leicester||1107||1118||New creation
 * Earl of Buckingham (1097)||Walter Giffard, 1st Earl of Buckingham||1097||1102||Died
 * ||Walter Giffard, 2nd Earl of Buckingham||1102||1164||
 * Earl of Leicester (1107)||Robert de Beaumont, 1st Earl of Leicester||1107||1118||New creation
 * Earl of Leicester (1107)||Robert de Beaumont, 1st Earl of Leicester||1107||1118||New creation
 * Earl of Leicester (1107)||Robert de Beaumont, 1st Earl of Leicester||1107||1118||New creation

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: List of peers 1100–1109


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User:Jhbadger

Dr. Jonathan Badger The Institute for Genomic Research (TIGR) 9712 Medical Center Drive Rockville, MD 20850

Home page: http://www.ttaxus.com

title: User:Jhbadger


text:
File:Tracy Chapman - Telling Stories.jpg

Cover for album Telling Stories (album) by Tracy Chapman.

Fair use rationale for

 * It is believed that the use of this image on the English-language Wikipedia to illustrate an article on the audio recording in question falls under the "Non-profit educational" clause of the Fair Use doctrine currently upheld by United States law. (17 U.S.C. § 107)
 * The image is irreplaceable; a free analogue is impossible to produce as the original will be covered by copyright for the foreseeable future
 * Owing to the limited web-resolution of the image, only a small portion of a copyrighted work is used
 * For the same reasons, the portion of the copyrighted work used is of inherently lower quality than the original, reducing the risk of competitiveness and therefore the effects of this copy on the market for or value of versions held by the owner of the copyright


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Wikipedia:Articles for deletion/List of people by reported IQ

List of people by reported IQ
List of people by reported IQ was proposed for deletion. This page is an archive of the discussion about the proposed deletion. This page is no longer live. Further comments should be made on the article's talk page rather than here so that this page is preserved as an historic record. The result of the debate was delete.

Isn't this essentially the same as the IQ scores entry that was just nuked? --Calton 05:42, 13 Dec 2004 (UTC)
 * The list that wouldn't die. Delete. --fvw *  06:58, 2004 Dec 13 (UTC)
 * Delete. Consistent with my listing of the other such list. Charles Matthews 09:36, 13 Dec 2004 (UTC)
 * Delete as imbecilic, moronic, or idiotic. [[User:Dpbsmith|Dpbsmith (talk)]] 14:03, 13 Dec 2004 (UTC) For the same reasons given for the other list, namely:
 * An IQ is a specific score on a specific test, administered by a psychologist. An IQ score is meaningless unless the particular test instrument used is specified. This is particularly true in the case of high scores (e.g. 187) since most tests do not go that high and do not claim to be capable of producing valid measurements (of whatever it is they measure) in that range.
 * Since IQ scores are confidential, it is hard to see they can verifiable in most cases. Here, Cite your sources is essential, not just desirable. (And the verification should not be someone else's garbage list!) This list contains only two citations. The one for Bobby Fischer turns out to be a book review in which the reviewer says that the book's author "claims that Bobby Fischer once scored 187 on an IQ test." The second is a Salon article which says "For the record, Mansfield advertised her I.Q. as 163." Even if you accept these as convincing authority, which I do not, that leaves you with a list of... two.
 * As for estimated IQ's of historical individuals who had an IQ test administered to them, you might just as well read their biographies, judge their amorousness, and present those judgement in the form of a list of estimated penis lengths. You can't make such POV nonsense encyclopedic by prefixing it with a disclaimer. [[User:Dpbsmith|Dpbsmith (talk)]] 14:03, 13 Dec 2004 (UTC)
 * Delete: "Reported" IQ is rather like "reported penis length" in the locker room. You can't believe it.  And then there are the usual problems with people who had the grave misfortune of being born before the IQ test was invented.  Geogre 16:42, 13 Dec 2004 (UTC)
 * Delete. Unverifable and unmaintainable. Jayjg 19:39, 13 Dec 2004 (UTC)
 * Heh, heh. This list was found by because I redirected the old IQ scores here. It should survive this VfD just as it survived the last time it was here. The interesting thing about the article is that these people have had their IQs reported (the scores themselves are actually of lesser interest - because it is not really possible to compare). Admittedly this article needs greater sourcing to be really good, but we don't delete articles just because they need work. The votes above seem to be assuming that the we are claiming the IQs themselves are supposed to be of interest. Kind of seems like they haven't the page or the talk page. Pcb21| Pete 22:57, 13 Dec 2004 (UTC)
 * Makes sense to me. I've accordingly removed the dubious, unverifiable, and uninteresting portions of the article while keeping all of the interesting and verifiable information. [[User:Dpbsmith|Dpbsmith (talk)]] 00:44, 14 Dec 2004 (UTC)
 * Which means it's now a short commentary on IQ tests, followed by a couple of lists of random names. -- Cyrius|✎ 06:56, 14 Dec 2004 (UTC)
 * IQ scores, the page which now redirects here but which used to have substantially the same content, was previously deleted however this article pre-dates that page. This article has been edited by a number of contributors during the past year though many of the edits were minor disambiguations.  The current contents of this article are an apparently rank-ordered "list of people by reported IQ" but the IQ scores themselves have been removed as "dubious" which I take to mean unverifiable.  Without the scores, this page is nonsense.  With the scores, I abstain.  Rossami (talk) 02:49, 14 Dec 2004 (UTC)
 * Delete - was unverifiable junk before, with the scores removed there's not much left that's not already in IQ. -- Cyrius|✎ 06:56, 14 Dec 2004 (UTC)
 * Delete useless. EventHorizon 03:55, 15 Dec 2004 (UTC)
 * Delete. The article is now such a good introduction to IQ missusage: IQ was and is meaningless out of therapeutic, pathlogical context. ( I am delighted to read previous comments which make it so plain! ). What is the point of publishing such a list: it is invalid, useless and missleading. Gtabary 10:27, 16 Dec 2004 (UTC)
 * Delete, an IQ score can be a useful diagnostic tool when used in context, but lists like this are no more meaningful or notable than lists of famous people's blood types. Wyss 12:15, 16 Dec 2004 (UTC)
 * Delete: How did such rubbish get onto Wikipedia in the first place? Brianjd 12:22, 2004 Dec 16 (UTC)

This page is now preserved as an archive of the debate and, like some other VfD subpages, is no longer 'live'. Subsequent comments on the issue, the deletion or on the decision-making process should be placed on the relevant 'live' pages. Please do not edit this page.


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Talk:Samantha Bee

Untitled
Was Samantha Bee in those "Cash for Life" commercials? (You know, "faaaaaaaantastic!") And if so, should we add that here? Adam Bishop 05:43, 13 Dec 2004 (UTC)

Samantha Bee as Sailor Moon?
From the article: "Bee has also had guest appearances on T.V. shows, including the title role in a live action production of Sailor Moon."

Can anyone confirm this? It doesn't show up in her IMDB info.
 * It was at the CNE. --  user:zanimum
 * I could only find one source with a quote. -- Anonymous

Flashdance
Did she really help write it? How can a 14 year old Canadian girl write for an American movie?

title: Talk:Samantha Bee


text:
2002 Saxony-Anhalt state election

The 2002 Saxony-Anhalt state election was held on 21 April 2002 to elect the members of the 4th Landtag of Saxony-Anhalt. The incumbent Social Democratic Party (SPD) minority government led by Minister-President Reinhard Höppner was defeated. The SPD fell to third place, while the Christian Democratic Union (CDU) moved into first. The CDU subsequently formed a coalition with the Free Democratic Party (FDP), and CDU leader Wolfgang Böhmer was elected Minister-President.

Background
After both the 1994 and 1998 state elections, the SPD formed a minority government with the external support of the Party of Democratic Socialism (PDS). This marked the first time the PDS had been involved in determining government in a German state, and was a unique arrangement, dubbed the "Magdeburg model" after the capital of Saxony-Anhalt. In Germany, governments are typically coalition governments, in which the parties which support the government take part in cabinet and hold a majority of seats between them. However, the SPD/PDS arrangement functioned on a model of "tolerance", in which the PDS remained outside cabinet and abstained from the vote for Minister-President, rather than voting in favour, allowing the SPD to form a minority government. In 1994, this allowed the investment of an SPD–Green minority government; in 1998, after the Greens lost their Landtag representation, the SPD governed alone.

Campaign and issues
At the time, Saxony-Anhalt was the "poorest" state of Germany, and that with the highest unemployment rate. The state election campaign was also influenced by the upcoming federal election.

The German People's Union, which won 12.9% of the vote and 12 seats in 1998, did not run in the election. This came after internal strife and the secession of the Freedom and Democracy People's Party (FDVP), which did run in the election.

Parties
The table below lists parties represented in the 3rd Landtag of Saxony-Anhalt.

Election result
! colspan="2" | Party ! Votes ! % ! +/- ! Seats ! +/- ! Seats % ! colspan=8| ! align=right colspan=2| Total ! align=right| 1,160,985 ! align=right| 100.0 ! align=right| ! align=right| 115 ! align=right| 1 ! align=right| ! align=right colspan=2| Voter turnout ! align=right| ! align=right| 56.5 ! align=right| 15.0 ! align=right| ! align=right| ! align=right|
 * bgcolor=|
 * align=left | Christian Democratic Union (CDU)
 * align=right| 433,521
 * align=right| 37.3
 * align=right| 15.3
 * align=right| 48
 * align=right| 20
 * align=right| 41.7
 * bgcolor=|
 * align=left | Party of Democratic Socialism (PDS)
 * align=right| 236,484
 * align=right| 20.4
 * align=right| 0.8
 * align=right| 25
 * align=right| 0
 * align=right| 21.7
 * bgcolor=|
 * align=left | Social Democratic Party (SPD)
 * align=right| 231,732
 * align=right| 20.0
 * align=right| 15.9
 * align=right| 25
 * align=right| 22
 * align=right| 21.7
 * bgcolor=|
 * align=left | Free Democratic Party (FDP)
 * align=right| 154,145
 * align=right| 13.3
 * align=right| 9.1
 * align=right| 17
 * align=right| 17
 * align=right| 14.8
 * align=right| 9.1
 * align=right| 17
 * align=right| 17
 * align=right| 14.8
 * bgcolor=#63B8FF|
 * align=left | Party for a Rule of Law Offensive (Schill party)
 * align=right| 52,589
 * align=right| 4.5
 * align=right| New
 * align=right| 0
 * align=right| New
 * align=right| 0
 * bgcolor=|
 * align=left | Alliance 90/The Greens (Grüne)
 * align=right| 22,696
 * align=right| 2.0
 * align=right| 1.2
 * align=right| 0
 * align=right| ±0
 * align=right| 0
 * bgcolor=|
 * align=left | Others
 * align=right| 29,818
 * align=right| 2.6
 * align=right|
 * align=right| 0
 * align=right| ±0
 * align=right| 0
 * align=right| 0
 * align=right| ±0
 * align=right| 0
 * }

Outcome
The SPD suffered a major defeat, falling to third place behind both the CDU and PDS. The CDU became the largest party with 37% of the vote. The FDP achieved an unexpected victory with 13% of the vote. The Party for a Rule of Law Offensive (Schill party) failed to win seats, despite polling suggesting they would narrowly enter the Landtag.

While polls before the election indicated the SPD and PDS would likely retain a slim majority, the success of the FDP at the SPD's expense meant that the CDU and FDP held a comfortable majority between them. Thus, the PDS-backed SPD government no longer had the numbers to retain power. The CDU and FDP negotiated a coalition, with CDU leader Wolfgang Böhmer heading the new government.

The election, which took place five months before the 2002 federal election, was a major defeat for the federal SPD–Green government, and weakened its standing in the Bundesrat.

title: 2002 Saxony-Anhalt state election


text:
Stockland

Stockland Corporation Limited is a diversified Australian property development company. It has business in shopping centres, residential estates, industrial estates and manufactured housing communities.

History
Stockland was founded in 1952 by Albert Scheinberg and Ervin Graf. In 1957 Stockland listed on the Australian Stock Exchange by acquiring a controlling interest in Simon Hickey Industries Ltd, the smallest company then listed.

In the same year, Stockland's activities became more diversified, moving into commercial development, initially with retail projects in suburbs of Sydney. In 1965 Stockland opened its first big commercial development - the redeveloped Imperial Arcade, Sydney in Sydney's CBD, which offered the first underground link to David Jones, four retail levels and six levels of office space.

Its current activities include: The current managing director is Tarun Gupta, and the board chairman is Tom Pockett.
 * management of shopping centres, 41 centres valued at $5 billion across Australia.
 * development of 65 residential communities with end-market value of approximately $21.2 billion.
 * ownership and management of 16 offices in Australian capital cities
 * 13 distribution and industrial centres
 * 59 established retirement living villages.

In 2022, Stockland launched its ecommerce platform, Stockland Marketplace, expanding its retail operations to e-commerce. Stockland Marketplace connects local stores and online channels to extend the shopping experience. Shop Stockland Marketplace at: https://marketplace.stockland.com.au

New South Wales

 * Stockland Forster
 * Stockland Glendale
 * Stockland Green Hills
 * Stockland Merrylands
 * Stockland Piccadilly
 * Stockland Shellharbour
 * Stockland Shellharbour Retail Park
 * Stockland Wetherill Park

Queensland

 * Stockland Baringa
 * Stockland Birtinya
 * Stockland Burleigh Heads
 * Stockland Hervey Bay
 * Rockhampton

Victoria

 * Stockland Point Cook
 * Wendouree

Western Australia

 * Baldivis
 * Harrisdale

E-Commerce

 * Stockland Marketplace - https://marketplace.stockland.com.au

title: Stockland


text:
Telling Stories (album)

Telling Stories is the fifth album by American singer-songwriter Tracy Chapman, released on February 14, 2000, by Elektra Records.

A two-disc special edition was released in Europe in 2000. The album is composed of contemporary rock songs in the first half, and folk songs in the second half.

The record marked a return to shorter songs for Tracy; on New Beginning they had been somewhat longer.

Background and Writing
In 1999, Chapman began working on her first new record in four years, her longest ever hiatus at the time. For the record, she reunited with producer David Kershenbaum, the producer of her first album, Tracy Chapman (1988), and co-producer of her second album, Crossroads (1989). The song "Unsung Psalm" was originally written for her previous album, New Beginning (1995), but it didn't make it onto the album.

Track listing
All songs written by Tracy Chapman.

Cover versions

 * "Three Little Birds" is a Bob Marley cover. The song was originally released on the album Exodus in 1977.
 * "House of the Rising Sun" is a cover of a traditional folk song. It was firstly released by Ashley and Foster on the single Rising Sun Blues under the same title in 1933.

Trivia

 * "Three Little Birds" was recorded at the TNT concert and television special One Love: An All Star Tribute to Bob Marley in Oracabessa on December 4, 1999.
 * "House of the Rising Sun" was recorded at the Greek Theatre, Berkeley and the A&M Studios in Los Angeles in 1990. It seems, that it is actually more a live in the studio recording than a real live recording because you don't hear any crowd noise.
 * "Mountains o' Things" was recorded at the Montreux Jazz Festival on July 4, 1988.
 * "Behind the Wall" was recorded at The Donmar Warehouse in London on March 25, 1988.
 * "Baby Can I Hold You" is the same version as the one that was originally released on the album Tracy Chapman in 1988.

Musicians
• Tracy Chapman – acoustic guitar, bouzouki, harp, vocals, background vocals, baritone guitar, record producer, mixing, art design

• Alex Acuña – percussion

• Rock Deadrick – vocals, background vocals

• Tommy Eyre – organ, keyboard

• Mike Finnigan – organ

• Denny Fongheiser – percussion, drums

• Emmylou Harris – vocals

• Howard Hersh – bass guitar

• Steve Hunter – dulcimer, lap steel guitar, baritone guitar

• Larry Klein – bass guitar

• JayDee Mannes – pedal steel guitar

• John Pierce – bass guitar

• Tim Pierce – acoustic guitar, dobro, mandolin, sitar, baritone guitar

• Eric Rigler – Uilleann pipes, low whistle

• Scarlet Rivera – violin

• Glenys Rogers – percussion, vocals, background vocals

• Andy Stoller – bass guitar

• Patrick Warren – keyboard, Chamberlin

Technical personnel
• Duane Baron – engineering, mixing

• Tim Hailand – artwork

• Jeri Heiden – design

• John Heiden – design

• Renata Kanclerz – production coordination

• David Kershenbaum – mixing, production

• Martie Kolbl – production coordination

• Curt Kroeger – assistant engineering

• Iki Levy – drum programming

• Bob Ludwig – mastering

• Herb Ritts – portraits

• Roger Sommers – assistant engineering

Singles
Billboard (United States)

title: Telling Stories (album)


text:
Talk:Telling Stories (album)

Why the long wait?
Why isn't there a background and writing section explaining why the album took so long to come out? — Preceding unsigned comment added by 24.18.113.3 (talk) 01:51, 21 February 2012 (UTC)

External links modified
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 * Added archive https://web.archive.org/20090723000035/http://www.rollingstone.com:80/artists/tracychapman/albums/album/304324/review/5947018/telling_stories to http://www.rollingstone.com/artists/tracychapman/albums/album/304324/review/5947018/telling_stories

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title: Talk:Telling Stories (album)


text:
User talk:Strokingman

Not funny. Do it again and you'll be blocked. And I have a sneaky suspicion that your name is intended to mock me. --Slowking Man 05:47, Dec 13, 2004 (UTC)
 * You have been blocked indefinitely for vandalizing my User pages and for an improper username. --Slowking Man 06:16, Dec 14, 2004 (UTC)

title: User talk:Strokingman


text: User talk:63.164.255.57

title: User talk:63.164.255.57


text: User talk:138.25.2.22

title: User talk:138.25.2.22