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Leo VI the Wise

Leo VI, also known as Leo the Wise (, 19 September 866 – 11 May 912), was Byzantine Emperor from 886 to 912. The second ruler of the Macedonian dynasty (although his parentage is unclear), he was very well read, leading to his epithet. During his reign, the renaissance of letters, begun by his predecessor Basil I, continued; but the empire also saw several military defeats in the Balkans against Bulgaria and against the Arabs in Sicily and the Aegean. His reign also witnessed the formal discontinuation of several ancient Roman institutions, such as the separate office of Roman consul.

Early life
Born on 19 September 866 to the empress Eudokia Ingerina, Leo was either the illegitimate son of Emperor Michael III  or the second son of Michael's successor, Basil I the Macedonian. Eudokia was both Michael III's mistress and Basil's wife. In 867, Michael was assassinated by Basil, who succeeded him as emperor. As the second-eldest son of the Emperor, Leo was associated on the throne in 870 and became the direct heir on the death of his older half-brother Constantine in 879. However, Leo and Basil did not like each other; a relationship that only deteriorated after Eudokia's death, when Leo, unhappy with his marriage to Theophano, took up a mistress in the person of Zoe Zaoutzaina. Basil married Zoe off to an insignificant official, and later almost had Leo blinded when he was accused of conspiring against him. On 29 August 886, Basil died in a hunting accident, though he claimed on his deathbed that there was an assassination attempt in which Leo was possibly involved.

Domestic policy
One of the first actions of Leo VI after his succession was the reburial, with great ceremony, of the remains of Michael III in the imperial mausoleum within the Church of the Holy Apostles in Constantinople. This contributed to the suspicion that Leo was (or at least believed himself to be) in truth Michael's son. Seeking political reconciliation, the new emperor secured the support of the officials in the capital, and surrounded himself with bureaucrats like Stylianos Zaoutzes (the father of his mistress, Zoe Zaoutzaina) and the eunuch Samonas, an Arab defector whom Leo raised to the rank of patrikios and who stood in as godfather to Leo's son, Constantine VII. His attempts to control the great aristocratic families (e.g., the Phokadai and the Doukai) occasionally led to serious conflicts, the most significant being the revolt of Andronikos Doukas in 906. Leo also attempted to involve himself in the church through his arbitrary interference with the patriarchate. Using his former tutor Patriarch Photios's excommunication by Pope John VIII as an excuse, Leo dismissed him and replaced him with his own 19-year-old brother Stephen in December 886. On Stephen's death in 893, Leo replaced him with Zaoutzes' nominee, Antony II Kauleas, who died in 901. Leo then promoted his own Imperial secretary (mystikos) Nicholas, but suspicions that he was involved in the failed assassination attempt against Leo in 903 as well as his opposition to Leo's fourth marriage saw Nicholas replaced with Leo's spiritual father Euthymios in 907. The magnificent Church of Agios Lazaros in Larnaca was constructed during the rule of Leo VI in the late 9th century, and it was built after the relics of St. Lazaros were transported from Crete to Constantinople. The church is one of the best examples of Byzantine architecture. Leo also completed work on the Basilika, the Greek translation and update of the law code issued by Justinian I, which had been started during the reign of Basil.

Bishop Liutprand of Cremona gives an account similar to those about Caliph Harun al-Rashid, to the effect that Leo would sometimes disguise himself and go about Constantinople looking for injustice or corruption. According to one story, he was even captured by the city guards during one of his investigations. Late in the evening, he was walking alone and disguised. Though he bribed two patrols with 12 nomismata and moved on, a third city patrol arrested him. When a terrified guardian recognized the jailed ruler in the morning, the arresting officer was rewarded for doing his duty, while the other patrols were dismissed and punished severely.

Foreign policy
Leo VI's fortune in war was more mixed than Basil's had been. In indulging his chief counselor Stylianos Zaoutzes, Leo provoked a war with Simeon I of Bulgaria in 894, but he was defeated. Bribing the Magyars to attack the Bulgarians from the north, Leo scored an indirect success in 895. However, deprived of his new allies, he lost the major Battle of Boulgarophygon in 896 and had to make the required commercial concessions and to pay annual tribute. Although he won a victory in 900 against the Emirate of Tarsus, in which the Arab army was destroyed and the Emir himself captured, in the west the Emirate of Sicily took Taormina, the last Byzantine outpost on the island of Sicily, in 902. Nevertheless, Leo continued to apply pressure on his eastern frontier through the creation of the new thema of Mesopotamia, a Byzantine invasion of Armenia in 902, and the sacking of Theodosiopolis, as well as successful raids in the Arab Thughur. Then, in 904 the renegade Leo of Tripolis sacked Thessalonica with his pirates—an event described in The Capture of Thessalonica by John Kaminiates—while a large-scale expedition to recover Crete under Himerios in 911–912 failed disastrously. Nevertheless, the same period also saw the establishment of the important frontier provinces (kleisourai) of Lykandos and Leontokome on territory recently taken from the Arabs. In 907 Constantinople was attacked by the Kievan Rus' under Oleg of Novgorod, who was seeking favorable trading rights with the empire. Leo paid them off, but they attacked again in 911, and a trade treaty was finally signed.

Marriages
Leo VI caused a major scandal with his numerous marriages which failed to produce a legitimate heir to the throne. His first wife Theophano, whom Basil had forced him to marry on account of her family connections to the Martinakioi, and whom Leo hated, died in 897, and Leo married Zoe Zaoutzaina, the daughter of his adviser Stylianos Zaoutzes, though she died as well in 899. Upon this marriage Leo created the title of basileopatōr ("father of the emperor") for his father-in-law.

After Zoe's death a third marriage was technically illegal, but he married again, only to have his third wife Eudokia Baïana die in 901. Instead of marrying a fourth time, which would have been an even greater sin than a third marriage (according to the Patriarch Nicholas Mystikos) Leo took as mistress Zoe Karbonopsina. He married her only after she had given birth to a son in 905, but incurred the opposition of the patriarch. Replacing Nicholas Mystikos with Euthymios, Leo got his marriage recognized by the church (albeit with a long penance attached, and with an assurance that Leo would outlaw all future fourth marriages).

Succession
The future Constantine VII was the illegitimate son born before Leo's uncanonical fourth marriage to Zoe Karbonopsina. To strengthen his son's position as heir, Leo had Constantine crowned as co-emperor on 15 May 908, when he was only two years old. Leo VI died on 11 May 912. He was succeeded by his younger brother Alexander, who had reigned as emperor alongside his father and brother since 879.

Alexander died thirteen months later, and Constantine succeeded him. Shortly before Constantine reached the age of maturity, one of his regents made himself senior co-emperor as Romanos I. Romanus married his daughter to Constantine, and their son became emperor as Romanos II on Constantine's death in 959.

Works
Leo VI was a prolific writer, and he produced works on many different topics and in many styles, including political orations, liturgical poems, and theological treatises. On many occasions he would personally deliver highly wrought and convoluted sermons in the churches of Constantinople.

In the subject matter of legal works and treatises, he established a legal commission that carried out his father's original intent of codifying all of existing Byzantine law. The end result was a six-volume work consisting of 60 books, entitled the Basilika. Written in Greek, the Basilika translated and systematically arranged practically all of the laws preserved in the Corpus Juris Civilis, thereby providing a foundation upon which all later Byzantine laws could be built. Leo then began integrating new laws issued during his reign into the Basilika. Called "Novels", or "New Laws", these were codes that dealt with current problems and issues, such as the prohibition on fourth marriages. Both the Basilika and the Novels were concerned with ecclesiastical law (canon law) as well as secular law. Most importantly, from a historical perspective, they finally did away with much of the remaining legal and constitutional architecture that the Byzantine Empire had inherited from the Roman Empire, and even from the days of the Roman Republic. Obsolete institutions such as the Curiae, the Roman Senate, even the Consulate, were finally removed from a legal perspective, even though these still continued in a lesser, decorative form.

The supposed Book of the Prefect and the Kletorologion of Philotheos were also issued under Leo's name and testify to his government's interest in organization and the maintenance of public order. The Book of the Eparch described the rules and regulations for trade and trade organizations in Constantinople, while the Kletorologion was an attempt to standardize officials and ranks at the Byzantine court. Leo is also the author, or at least sponsor, of the Tactica, a notable treatise on military operations.

Succeeding generations saw Leo as a prophet and a magician, and soon a collection of oracular poems and some short divinatory texts, the so-called Oracles of Leo the Wise, at least in part based on earlier Greek sources, were attached to the Emperor's name in later centuries and were believed to foretell the future of the world.

Finally, Leo is credited with translating the relics of St. Lazarus to Constantinople in the year 890. There are several stichera (hymns) attributed to him that are chanted on Lazarus Saturday in the Eastern Orthodox Church. He also composed hymns that are sung on the Great Feast of the Exaltation of the Cross.

Family
By his first wife, Theophano Martinakia, Leo VI had one daughter: By his second wife, Zoe Zaoutzaina, Leo had one daughter: By his third wife, Eudokia Baïana, Leo had one son: By his fourth wife, Zoe Karbonopsina, Leo had two children:
 * Eudokia, who died in 892.
 * Anna, betrothed and married to the Holy Roman Emperor Louis the Blind.
 * Basil, who survived for only a few days.
 * Anna
 * Constantine VII.

title: Leo VI the Wise


text:
Talk:Levi-Civita connection

Stub history
Why did you kill this page? -- Anon

 * The problem is the article as it was written doesn't make sense. The text was: " The unique torsion free connection, preserving a riemannian metric".  What does that mean?  What does this relate to?  Is it physics?  biology?  fiction?  Remember you are writing for a non-specialist audience.

 * A quick Google tells me this is something to do with mathematics. The Anome gave a great example of how to write a good article on mathematical topics:

 * "(Mathematician) invented the concept of X in 18xx to represent (squeezy-pully-twisty things). A simple example, using modern notation is (example). (Explain notation). The idea has now been generalized to (stuff), which has uses in (other fields of math and science). The idea of X can be formalized as follows: let there be objects X such that (notation). Then (notation) (notation) (notation)..." (from this talk page)

 * See also WikiProject Mathematics

 * If this article has nothing to do with mathematics, then that shows the problem even more clearly. In a case like this it is usually thought better to remove the article rather than have a confusing sub-stub.  But much better is to improve the article, and if you can do that it would be great! I hope you stick around and give it a go.  Regards -- sannse 19:30 26 Jun 2003 (UTC)

Formal definition

 * This section needs to be reviewed. With a firm background in vector calculus, I cannot interpret what the two equations are trying to express.  Please explain where the RHS and LHS are coming from, and be more explicit with notation.  I can only assume that X(g(Y,Z)) is supposed to mean the scalar multiplication of the vector field X with the inner product of the fields Y and Z, but this yields a vector quantity, and the RHS, which is the sum of inner products, would be a scalar. 98.235.167.113 (talk) 18:26, 8 March 2012 (UTC)

 * It is common for Xf to represent the Lie derivative of the function f by the vector field X (so that Xf is a function). This is not the same as the product of f and X, which would be written fX and would be a vector. Thus X(g(Y,Z)) means the Lie derivative of the function g(Y,Z), and the equations in this section make sense. — Preceding unsigned comment added by 83.104.131.53 (talk) 11:16, 3 May 2012 (UTC)

 * To say "It is common ..." is perhaps a bit strong, especially in this encyclopedic context. The notation strikes me as highly context-specific, and since the term "Lie derivative" does not occur once in the article, it is appropriate to add something like "... where Xf denotes the Lie derivative of ...".  I would go so far as to say that a more explicit notation such as $$\mathcal{L}_{\!X} g(Y,Z) $$ should be used, plus the mention that this represents the Lie derivative.  — Quondum☏ 13:09, 3 May 2012 (UTC)

 * there is no need to introduce lie drivatives here. to make the notation more intuitive replace Xf by $$\partial_X f$$ which is if necessary easily explained as df(X).Peter Grabs (talk) 06:28, 2 August 2018 (UTC)

Derivative along curve
i suggest to replace this sections by something like this, because the given definition is not applicable for vectorfields along curves (as i know that notion):

The Levi-Civita connection (like any affine connection) also defines a derivative along curves, sometimes denoted by $$D$$.

Given a smooth curve $$\gamma$$ on $$(M,g)$$ we consider vector fields along $$\gamma$$, i.e. smooth sections $$V\in\Gamma(\gamma^{\ast}TM)$$ of the pullback bundle $$\gamma^{\ast}TM$$, and define their derivative by
 * $$D_tV:=(\gamma^{\ast}\nabla)_1 V|_t$$.

For $$V=X\circ \gamma\in\Gamma(TM)\circ \gamma \subset \Gamma(\gamma^{\ast}TM)$$ this pullback connection specializes to
 * $$D_tV = \nabla_{\dot\gamma(t)}X|_{c(t)}$$.

In particular, $$\dot{\gamma}$$ is a vector field along the curve $$\gamma$$ itself. If $$D_t\dot\gamma$$ vanishes, the curve is called a geodesic of the covariant derivative. If the covariant derivative is the Levi-Civita connection of a certain metric, then the geodesics for the connection are precisely those geodesics of the metric that are parametrised proportionally to their arc length.

-- Peter Grabs (talk) 19:17, 29 April 2012 (UTC)

Connection preserves metric
The expression $$\nabla g=0$$ does not make sense to me. Isn't the property of metric preservation exactly $$X g(Y,Z)=g(\nabla_XY,Z)+g(Y,\nabla_XZ)$$? — Preceding unsigned comment added by 2003:6B:A1E:4801:4000:2B7E:EC01:A50 (talk) 10:06, 25 May 2015 (UTC)

 * if you have a notion of derivation for functions ($$\nabla_X f=\partial_X f=df(X)$$) and vectors ($$\nabla_X Y$$, e.g. Levi Civita of TM), you can carry it over to arbitrary tensors like $$g\in\Gamma(T^*M\otimes T^*M)$$ by requiring the leibniz rule, i.e. $$\nabla_X (g(Y,Z)) = (\nabla_X g)(Y,Z) + g(\nabla_X Y,Z) + g(Y,\nabla_X Z)$$, this defines $$\nabla g$$ and lets you read off the equivalence of the two definitions of metricity.Peter Grabs (talk) 06:56, 2 August 2018 (UTC)

Animation of parallel transport
The animation in the section on parallel transport indicates that it shows parallel transport of a vector under two different metrics. However, the metrics are simply both the flat metric, but in Cartesian and polar coordinates. I'm not sure how the right-side animation is supposed to be interpreted. If the axes still represent Cartesian coordinates $$x,y$$ then the animation is clearly wrong as parallel transport should be identical to that in the left image. If the coordinate axes are for $$r,\theta$$ really, then the parallel transport curve (unit circle) passes through the coordinate singularity at $$r = 0$$ and secondly the length of the vector is not preserved with respect to the metric. Jeldering (talk) 22:18, 20 January 2016 (UTC)

This turned out to be an erroneous anonymous edit that I reverted. Still, I think this section is not clear and needs rewriting/improvement. I may have a go at it if I find time. Jeldering (talk) 14:18, 21 January 2016 (UTC)

I spent a long time thinking about this section and it still confuses me. Part of the problem is that we are not used to "see" non-euclidean metrics on the plane. Also, if I'm not mistaken, both metrics should be the same in S^1, which is the situation shown here. I would appreciate it if someone took the time to explain in more detail (possibly in charts) how the different parallel transports arise. Emilparole (talk) 13:08, 20 February 2018 (UTC)

Some other people edited this page and screwed up the metrics again. I've tried my best, with the limited time and understanding I currently have, to make it at least a little bit clearer that $$dx^2 + dy^2 = dr^2 + r^2d\theta^2$$ and that the second transport is for a completely different metric. It still needs a rewrite, though. 73.114.132.157 (talk) 02:56, 18 July 2018 (UTC)

Parallel transport example is wrong
First the whole discussion about a singularity in the origin is besides the point, because both have this singularity, the big scary formula although not wrong is distracting and pointless and should be removed. The error is in the claim that both connections are "different" Levi-Civita connections, the one on the left is indeed a Levi-Civita connection but the one on the right is NOT! (this error is also present on the file page of the animation.) The animation on the right has a connection but it's not a Levi-Civita connection, i.e. it's non-symmetrical in the last two indices. The connection can be found by using the general formula for the Connection coefficients in a nonholonomic basis using the formula given in this article will result in all zero coefficients and parallel transport that does not change the vector and so identical to the animation on the left. --DelftUser (talk) 15:24, 25 February 2020 (UTC)

The metric used in the right image is wrong! the right image does not use the coordinates basis and so the metric can't be written as $$ds^{2}=dr^{2}+d\theta ^{2}$$. Here is how the title & captions of the two animations should be:

Because the basis vectors are different it's wrong to write the metric with ($$dr, d\theta$$), so this is my fix; I'll wait a while for comments before changing the article.--DelftUser (talk) 09:31, 29 February 2020 (UTC)
 * The example is correct, interpreting r and theta as functions on R^2. The former defines the standard metric on R^2 and the latter defines an incomplete metric on R^2-{(0,0)} which is isometric to the standard circular cone. I think it should be explained more clearly though, and there is probably a better example to use. Gumshoe2 (talk) 23:04, 5 January 2022 (UTC)

The Asymmetric Metric
Consider an asymmetric metric, as it relates to Relativity. In Einstein's The Meaning of Relativity, 5th Edition, 1953, on page 71, equations 69 and 70 show the Christoffel symbols, the Levi-Civita connection being equation 70. I propose some alternative definitions by swapping the indices of the 2nd term on the right of equation 69:

$$ { [(g)ij,k]\equiv\frac{1}{2} (g_{ik,j}+g_{kj,i}-g_{ij,k}) } $$

The swapping makes no difference for a symmetric metric, but better serves the case for an asymmetric metric (Notice a new notation, where this alternate Christoffel symbol of the 1st kind is now an operator, on a rank 2 covariant tensor). For the case of the symmetric metric, the normal results ensue. When $$t$$ is nondegenerate I propose the following connection:

$$ { \Gamma^k{}_{ij} \equiv s^{mk} [(s)ij,m] + t^{mk}[(t)ij,m], (RP, 1Feb1993) } $$

where $$g_{ij}=s_{ij}+t_{ij}$$, $$s_{ij}=s_{ji}$$, $$t_{ij}=-t_{ji}$$, and similarly for the associated contravariant metric.

For the case of an asymmetric metric these alternative definitions provide for Torsion with metricity (the covariant derivative of the metric is identically zero), and the Bianchi identity remains valid.

Regards, Ric Peregrino Ric.Peregrino (talk) 20:42, 18 April 2024 (UTC)

 * In an attempt to further develop the results of an asymmetric metric towards a potentially modified Einstein tensor, it seems the Bianchi identity doesn't simplify the same way. Taking a step back, I had started studying the remaining symmetries of the resulting curvature tensor in an effort to arrive at a better result for such an Einstein tensor. As you may have noticed, this was decades ago.
 * I've shared this topic here, in an effort to get someone who might understand what I'm trying to propose with an asymmetric metric, the alternative connection which reduces to the Levi-Civita connection with a symmetric metric, and the ensuing results, if any, towards an alternative Einstein tensor. Hopefully this makes sense to someone and they might comment. Or perhaps this has already been dealt with, in which case some pointers would be appreciated.
 * I have more information with some details of my claims, which I'd gladly share upon request.
 * At this time, there's been some feedback, and I'm no longer considering posting such a chapter to the article.
 * Regards, Ric Ric.Peregrino (talk) 02:56, 19 April 2024 (UTC)
 * Please don't edit the article, this isn't the right place for original research. Regardless, I believe your formula for Γ^k_ij doesn't make sense since t is generally not nondegenerate, so t^mk is meaningless. (Certainly this is at least the case in the most important special case, t=0.)
 * There is some work out there on nonsymmetric metrics, notably by Einstein. Gumshoe2 (talk) 17:30, 28 April 2024 (UTC)
 * Regarding that work by Einstein, it seems to suggest that if |t|!=0 at any point in spacetime, it's nonzero every where and when. So to be more precise, I should state the formula only applies if |t|!=0, and else if |t|=0 revert to Levi-Civita formula. I think they further arrive at there being only 2 unique components of t in 4d spacetime, and arrive at a complicated set of formula for the connection which I may or may not be able to eventually understand.
 * The result I provided seems simply stated, and may or may not be valid, and if valid may or may not be equivalent to Einstein's quoted work. I hope I can find out.
 * I'd like to ask you, where might be a good place to discuss this topic? Perhaps here in this talk is ok, at least to start? I may poke around different topics and see if another one makes more sense... Ric.Peregrino (talk) 20:00, 28 April 2024 (UTC)
 * Wikipedia isn't a good place for such discussion, since the focus here is on writing exposition and very much against doing novel work. I would suggest math stackexchange or math overflow. Gumshoe2 (talk) 20:17, 28 April 2024 (UTC)
 * Roger wilco, and thanks for the response.
 * Thanks so much for that reference! Looks like I have some homework.
 * Indeed t^mk is meaningless if t_ij=0, but I suggest the redefinition of the Christoffel symbol of the 1st kind, results in the ensuing connection resolving to the Levi-Civita connection.
 * Cheers,
 * Ric Ric.Peregrino (talk) 17:51, 28 April 2024 (UTC)

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

title: Talk:Levi-Civita connection


text:
Alexander (Byzantine emperor)

Alexander (, Alexandros, 23 November 870 – 6 June 913) was briefly Byzantine emperor from 912 to 913, and the third emperor of the Macedonian dynasty.

Life
Born in the purple, Alexander was the third son of Emperor Basil I and Eudokia Ingerina. Unlike his older brother Leo VI the Wise, his paternity was not disputed between Basil I and Michael III because he was born years after the death of Michael. As a child, Alexander was crowned as co-emperor by his father in early 879, following the death of Basil's son Constantine. Upon the death of his brother Leo on 11 May 912, Alexander succeeded as senior emperor alongside Leo's young son Constantine VII. He was the first Byzantine emperor to use the term "autocrator" (αὐτοκράτωρ πιστὸς εὑσεβὴς βασιλεὺς) on coinage to celebrate the ending of his thirty-three years as co-emperor. Alexander promptly dismissed most of Leo's advisers and appointees, including the admiral Himerios, the patriarch Euthymios, and the empress Zoe Karbonopsina, the mother of Constantine VII, whom he locked up in a nunnery. The patriarchate was again conferred on Nicholas Mystikos, who had been removed from this position due to his opposition to Leo's fourth marriage. During his short reign, Alexander found himself attacked by the forces of Al-Muqtadir of the Abbasid Caliphate in the east, and provoked a war with Simeon I of Bulgaria by refusing to send the traditional tribute on his accession. Alexander died soon after, allegedly from a stomach disease caused by excessive eating and alcohol. The sources are uniformly hostile towards Alexander, who is depicted as lazy, lecherous, drunk, and malignant, including the rumor that he planned to castrate the young Constantine VII in order to exclude him from the succession. He did not, but Alexander did leave his successor a hostile regent (Nicholas Mystikos) and the beginning of a long war against Bulgaria. The sources also accused the emperor of idolatry, including making pagan sacrifices to the golden statue of a boar in the Hippodrome, and providing it with new teeth and genitals, in hope of curing his impotence.

title: Alexander (Byzantine emperor)


text:
Talk:Matti Vanhanen

Untitled
Moved here from the article:
 * The special thing in Vanhanen is, that he doesn't speak Swedish which is one of the two national languages of Finland.

Anyone got some proof of this? -- Jniemenmaa 19:10 26 Jun 2003 (UTC)

In the last Nordic council meeting he answered all the questions of the press in Swedish. The Hufvudstadsbladet [www.hbl.fi] repoter described his Swedish in a positive manner. So I assume his Swedish is good enough. -- Caid Raspa
 * And even if it was so, there wouldn't be anything "special" about it. --Jaakko Sivonen 20:02, 7 October 2006 (UTC)

This seems to be outdated, but according to David Arter he did not speak Swedish at his first foreign meeting (with the Swedish King). Source: David Arter (2007). "The End of the Social Democratic Hegemony? The March 2007 Finnish General Election.", in West European Politics, Vol 30, No 5, November 2007. The section about his 2nd cabinet also needs a language clean up. I tried making a few improvements at least. --85.164.7.217 (talk) 20:45, 2 January 2009 (UTC)

When going to Matti Vanhanen's webpage, take special care that the URL ends in. It has been lately mentioned in the Finnish press that http://mattivanhanen.com (note the TLD) is a porn site. Is there anything the Finnish government can do about this? — J I P  | Talk 11:09, 21 November 2005 (UTC)

Hehe, I hear carp give up their lives at the mention of Matti's name, they can sense bad leadership... Conan is so funny --203.59.204.141 05:20, 6 January 2006 (UTC)

Picture
Doesn't anyone have a normal picture of this guy floating around? -Yupik 08:22, 11 October 2006 (UTC)
 * It looks like he's pissed off with the text -Clapaucius 00:10, 19 March 2007 (UTC)

Personality

 * Anti-Democratic Tendencies?

I added a few arguments of Matti Vanhanen against supporting the Baltic independence and democracy from the Suomenmaa 30.7.1985 article. (I also changed the reference from the carreer section, so that there is a link to his piece) In addition, I added his statement that West should take an example of the Chinese policy making.

They are translations from his own words, from Finnish to English, but if someone wants verify my NPOV in translating, please do so. I also added a link to Aamulehti where his opinions have been analysed as being against Estonian independence. (I also re-arranged this discussion a little bit .. I hope nobody minds) Pprkl007 (talk) 17:34, 12 May 2009 (UTC)

I think we should mentioned Susan Kuronen. She appears to be linked well enough with the PM that it deserves a mention. This link may be helpful. I assume it's a Finnish tabloid that the PM doesn't like but IMHO it still merits inclusion Nil Einne 13:43, 7 December 2006 (UTC)
 * Susan Kuronen

 * wasn't it berlusconi?

the current article states that jaques chirac claimed Vanhanen was the sexiest man in europe, i hacve a distinct memory that the person to utter those accolades was the italian premier Berlusconi, ... I might be wrong... -- cimon —The preceding unsigned comment was added by 88.112.45.229 (talk) 08:50, 19 March 2007 (UTC).

Small error
The article states that Vanhanen wanted the retirement age to be lifted from 63 to 65. This is slightly incorrect, because 1)The idea first came from the National coalition leader, Jyrki Katainen, and 2) The talk was about the minimum retirement age. At the moment the retirement age varies from 63 to 68, with people staying longer at work (after a certain age) getting an addition to their pension. 101090ABC (talk) 21:18, 23 December 2009 (UTC)

Religion
What is his religion? —Preceding unsigned comment added by 59.23.88.2 (talk) 21:35, 2 February 2010 (UTC)

 * I would assume that he is evangelic-lutheran, seeing that 79,7 per cent belong to the Evangelic Lutheran church of Finland. 101090ABC (talk) 10:59, 1 March 2010 (UTC)

Controversies
While controversy chapters are always controversial (sorry, couldn't resist), I think this article would merit one. Vanhanen's credibility has been questioned over and over again in the press as of late. He has been a central figure in the election funding issue. Perhaps someone who's followed politics more closely (and ideally from other viewpoints than that of press') could write up something about all this. Pasi (talk) 07:09, 16 April 2010 (UTC)

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External links modified (January 2018)
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A Commons file used on this page or its Wikidata item has been nominated for deletion
The following Wikimedia Commons file used on this page or its Wikidata item has been nominated for deletion: Participate in the deletion discussion at the nomination page. —Community Tech bot (talk) 05:53, 26 April 2020 (UTC)
 * Vanhasen II hallitus.JPG

title: Talk:Matti Vanhanen


text:
Almost

In set theory, when dealing with sets of infinite size, the term almost or nearly is used to refer to all but a negligible amount of elements in the set. The notion of "negligible" depends on the context, and may mean "of measure zero" (in a measure space), "finite" (when infinite sets are involved), or "countable" (when uncountably infinite sets are involved).

For example:
 * The set $$ S = \{ n \in \mathbb{N}\,|\, n \ge k \} $$ is almost $$\mathbb{N}$$ for any $$k$$ in $$\mathbb{N}$$, because only finitely many natural numbers are less than $$k$$.
 * The set of prime numbers is not almost $$\mathbb{N}$$, because there are infinitely many natural numbers that are not prime numbers.
 * The set of transcendental numbers are almost $$\mathbb{R}$$, because the algebraic real numbers form a countable subset of the set of real numbers (which is uncountable).
 * The Cantor set is uncountably infinite, but has Lebesgue measure zero. So almost all real numbers in (0, 1) are members of the complement of the Cantor set.

title: Almost


text:
Locomobile Company of America

The Locomobile Company of America was a pioneering American automobile manufacturer founded in 1899, and known for its dedication to precision before the assembly-line era. It was one of the earliest car manufacturers in the advent of the automobile age. For the first two years after its founding, the company was located in Watertown, Massachusetts. Production was transferred to Bridgeport, Connecticut, in 1900, where it remained until the company's demise in 1929. The company manufactured affordable, small steam cars until 1903, when production switched entirely to internal combustion-powered luxury automobiles. Locomobile was taken over in 1922 by Durant Motors and eventually went out of business in 1929. All cars ever produced by the original company were always sold under the brand name Locomobile.

History

The Locomobile Company of America was founded in 1899, the name coined from "locomotive" and "automobile". John B. Walker, editor and publisher of Cosmopolitan, bought the plans for an early steam-powered vehicle produced by Francis and Freelan Stanley for a price they could not resist, US$250,000. At the time, one car had been built, and 199 more had been ordered. Walker promptly sold half of his interest to paving contractor Amzi L. Barber for the same price as he had purchased the entire company. Walker and Barber's partnership lasted two weeks. Walker went on to found Mobile Company of America at the Stanley works in Tarrytown, New York, while Barber moved house to Bridgeport, Connecticut, as Locomobile, where the Stanley twins were named general managers. The Stanley twins founded the Stanley Motor Carriage Company in 1902, becoming the sharpest rival to Locomobile.

Locomobile began by producing steam cars. The steam Locomobiles were unreliable, finicky to operate, prone to kerosene fires, had small water tanks (getting only 20 mi per tank), and took time to raise steam; author Rudyard Kipling described one example as a "nickel-plated fraud". Initially, they were offered with a single body style only, an inexpensive runabout at $600. Nevertheless, they were a curiosity and middle-class Americans clamoured for the latest technology. Salesmen, doctors, and people needing quick mobility found them useful. More than 4,000 were built between 1899 and 1902.

In 1901, Locomobile offered seven body styles at prices between $600 and $1,400. Most Locomobiles had simple twin-cylinder engines (3x4 in, 76.2x102 mm; 57 in3, 927 cm3) and a wire-wrapped 300-psi boiler, and burned the liquid fuel naphtha to create steam. Typical of the product was the 1904 Runabout, which seated two passengers and sold for $750. The two-cylinder steam engine was situated amidships of the wood-framed car. By now, the car had improved boilers and a new water pump, manufactured by the Overman Wheel Company in Chicopee Falls, Massachusetts. This company itself built the Victor Steamer.

During the Boer War, Locomobile did establish a new mark of sorts, becoming the first automobile to be used in war; it was a generator and searchlight tractor used to dismantle the Klein Nek minefield. It also served as a catering vehicle, with the useful ability (in British eyes, at least) of being able to brew a cup of tea by tapping the boiler.

This was, unfortunately, not a sure way to guarantee commercial success, even in Britain, and Locomobile started experimenting with gasoline internal combustion engines in 1902, starting with a four-cylinder, steel-chassis model designed by Andrew L. Riker. This encouraged the firm to drop steam vehicles the following year, selling the Stanley brothers back their rights for $20,000. In 1903, Barber relinquished his position to his son-in-law Samuel Todd Davis, Jr., who became President of the Locomobile Company.

Switch to internal combustion engines
The 1904 internal combustion Locomobile Touring car had a tonneau and space for five passengers, and sold for $4500, quite a change from the low-priced steam buggies. The front-mounted, vertical, water-cooled straight-four engine produced 16 hp. A three-speed sliding transmission was used, as on the Système Panhard cars with which it competed. The angle steel-framed car weighed 2200 lb. The 1908 Locomobile 40 Runabout was a 60 hp two-seater and sold for $4,750. On the strength of recent competition successes, Locomobile soon became known for well-built and speedy luxury cars.

In competition
Like other early marques, Locomobile entered motor racing, contesting the 1905 Gordon Bennett Cup with a 17.7 L racer; after suffering a transmission gear failure, and with no spare available, driver Joe Tracy only managed two circuits of Auvergne before the transmission packed up entirely. Tracy did better for the company at the Vanderbilt Cup, placing third. A 90 hp, 16.2 L F-head was damaged by tire trouble, so Tracy failed again in the 1906 Vanderbilt, but in 1908, George Robertson (wearing number 16) took the win in this car, ahead of fellow Locomobile pilot Joe Florida in third, becoming the first United States-built car to win in international competition. This was the high-water mark for Locomobile racing, and they soon faded from the scene, though Orin Davis did score a win in the Los Angeles–Phoenix rally in 1913. A Locomobile was raced by Eva Mudge, believed to be the first female driving licence holder and first female racing driver. In 1925, the Locomobile team entered a front-wheel-drive Miller car called the "Junior Eight Special" after their recently introduced smaller car at the Indianapolis 500, but there was nothing Locomobile about it aside from the name.

Model 48 and the Durant years
The most important model for the marque became the impressive Model 48. Introduced in 1911 as the "type M," it had a very conservative, perhaps dated, concept. It had a conventional but huge chassis with a wheelbase of 143 in. Its engine was a straight six with side valves; cylinders were still cast in pairs and it featured a nonremovable cylinder head. Displacement was 429.4 cuin, from a 4+1/2 x bore and stroke, giving it a 48.6-hp tax rating by the North American Chamber of Commerce. While called the "M" internally, this car is usually referred to by its tax hp rating. The brake horsepower rating was somewhere north of 90 for the original model, higher in the later versions. Quality of materials and workmanship were impeccable and among the best in the world. Such was also its pricing: A typical open-body cost about $10,000 when the average Model T Ford Phaeton cost about $300. Locomobile also offered custom designs for the lamps and metal work, carried out by Tiffany Studios. Until 1915, left- or right-hand drive could be specified; afterwards, left-hand drive became standard. Right-hand drive cars were meant for export and sat on a chassis four inches shorter. Around 1919, the engine was updated with a longer 5+1/2 in stroke, for 525 cuin displacement while retaining the same tax hp rating.

A smaller "38 hp" model, very similar to the Model 48, was added in 1913. The model 38 has a 425 cuin, 62 bhp version of the T-head six and sits on a somewhat shorter 140 in wheelbase. By 1914, Locomobile had stopped selling all four-cylinder models to concentrate exclusively on sixes.

In July 1922, Locomobile was acquired by Durant Motors, which not only continued using the Locomobile brand name for their top-of-the-line autos until 1929, but also still produced the Model 48 until its demise in 1929. Until the mid-1920s, this car was Locomobile's only offering. In 1925, the marque brought out their first new model, the 8-66 Junior Eight, with a more contemporary straight-eight engine, and more importantly, a lower price of $1,785.

Introduction of the even smaller Junior Six was in 1926, but this car stayed only for one model year. The larger Model 90 that appeared in the same year was produced until 1929.

With the 8-70 of 1927, Locomobile added one more eight-cylinder car. Using an off the shelf Lycoming engine, this was not accepted as a true Locomobile in the marketplace and served to damage the company's reputation. In the following year, the Junior Eight 8-66 was phased out.

For 1929, a new 8-86 and 8-88 came out, but it was too late to save the company. Locomobile production ended in 1929.

Locomobile model specifications

 * Locomobile Model 48 Sportif

Locomobiles in fiction
A Locomobile is the setting for one of the final scenes of F. Scott Fitzgerald's first novel, This Side of Paradise, in which the protagonist, Amory Blaine, argues for socialism to the father of a college friend, who staunchly defends the capitalist ideal.

In the spring and summer of 1946, a seven-passenger 1911 Locomobile touring car was driven from Boston to Los Angeles and back as a promotional tour for the Columbia Pictures film Gallant Journey. While not appearing in the movie, the Locomobile attracted much attention for the picture on the tour.

In Thomas Savage's 1967 novel The Power of the Dog, set in the 1920s, the Locomobile is esteemed by protagonist Peter Gordon as a peer to the Pierce-Arrow: "... Those were the vehicles of the high and mighty, and he knew that only the Locomobile (fancied by old General Pershing, among others) rivaled the Pierce."

Clive Cussler's 2007 novel, The Chase, as well as his 2010 novel The Spy, featured a 1906 Locomobile.

In Dashiell Hammett's 1925 mystery story "Scorched Face", the rich girls for whom the Continental Op is looking, were driving a Locomobile "with a special cabriolet body" when they disappeared.

Papa LaBas from Ishmael Reed's 1972 novel Mumbo Jumbo drives a Locomobile.

The Locomobile is central to the 2015 historical novel by Lisa Begin-Kruysman titled Around the World in 1909: Harriet White Fisher and Her Locomobile. The novel is based on Harriet White Fisher's circumnavigation of the globe; the Locomobile is driven, hauled, pushed, and floated in places where no man, let alone woman, had yet explored, certainly not on wheels.

title: Locomobile Company of America


text:
User talk:Ed Griebel

Hello Ed, welcome to Wikipedia. I hope you enjoy editing here and being a Wikipedian. You can learn more on the how to edit page. The naming conventions and manual of style pages are also useful. Feel free to experiment at the Sandbox. If you have any questions about the project then check out Help or add a question to the Village pump. Angela

title: User talk:Ed Griebel


text:
User talk:Boots

Hello Boots, welcome to Wikipedia. I hope you enjoy editing here and being a Wikipedian. You can learn more on the how to edit page. The naming conventions and manual of style pages are also useful. Feel free to experiment at the Sandbox. If you have any questions about the project then check out Help or add a question to the Village pump. Angela

Hi Boots,

I am afraid your renaming of Carlos of Portugal to Charles was wrong. The rule is not to translate the name into english but to use the form of name used to refer to that person in english. Hence we have Wilhelm II of Germany, Nicholas II of Russia etc. Most english language users use the last German kaiser's german name, not an english translation. So we call him Wilhelm not William. But most english language users use Nicholas II, not Nikolai, and Victor Emmanuel not Victorio Emanuele. If people generally used Nikolai in preference to Nicholas, then he would be in as Nikolai. Similarly we call the fifth Irish president's gaelic name, Cearbhall Ó Dálaigh not the english translation, Charles Daly, because his gaelic name was used widely to refer to him in preference to any translation. The rule is not to translate things into english but use the form of name used in that person's case by english speakers. If you have redirected any other people to the english translation of their name rather than the version used by english speakers to refer to them then they will all have to be changed back. Otherwise, as in the case of Charles of Portugal, Charles Daly etc we would have forms of names that few people would recognise. lol. FearÉIREANN 19:39 2 Jul 2003 (UTC)

I see you have redirected a lot of portuguese royal names. You are going to have to reverse all the redirects. Petro V is not known in english as Peter V but as Pedro V. Please stop redirecting royal names and restore them all to the agreed format. FearÉIREANN 19:49 2 Jul 2003 (UTC)

Yeah I agree the Portuguese royal names are a mess. All royal names on wiki used to be an absolute mess. Some months ago a gang of us systematically sorted out the mess but either we missed these names or they were put on since and no one noticed them. I did last week but have been away for a while and so had not a chance to fix them. As you appear to be interested in this area you might be interested in Naming conventions (names and titles) for some of the conventions we worked on last January for royal names. Don't worry, we all make mistakes but I am so glad to see another user is into consistency too. Keep an eye out for User:Deb. She is a great worker in the area. And a guy called John. (I forget his user name. Best of luck. FearÉIREANN 20:12 2 Jul 2003 (UTC)

Please do not rename them at present. Renaming pages can throw links into chaos. More than two links caused by renaming and the links go crazy. One person did this on Japanese emperors and the result took weeks of work by a large number of users to untangle the mess. Only rename them when there is agreement on what they should be. There is no point renaming Petro to Peter when it is going to have to be renamed back to Pedro and the move to Peter may break links and mess up associated articles. Please restore them to the version used by english speakers. That is where the links are connected to with the short chain. It is better to have a mess of names (which personally I hate) than have links broken all over the place. All the pages should be moved if they need to be moved to the version english encyclopædia users use, not the english language version. If you move them then tonight, tomorrow and all during the week people will simply end up changing them back anyway and all your time will be wasted. Don't make extra work for everyone else untangling broken links and renaming pages you have renamed to the wrong version. You will only make the mess in Portuguese names worse. FearÉIREANN 20:33 2 Jul 2003 (UTC)

I agree with jtdirl here. It doesn't make any sense to set it up with a "consistency" that you already acknowledge is going to have to be changed. Leave the pages where they are for the moment, if you're not ready to move the ones at an English name to the Portuguese name. "Peter IV of Portugal" is just bizarre, and never used, so far as I know. A wrong consistency is much worse than an inconsistency that at least gets some of the names right. john 23:54 2 Jul 2003 (UTC)

Okay, I'll leave you be for now, if you have a system...But be sure you finish what you start. As far as names, Pedro not Peter, João not John (I tend towards, at least), certainly Maria not Mary, Carlos not Charles. I'd say either Alfonso or Afonso (Affonso?) for those kings. Err... I'm not sure about King Joseph/José. I've probably seen Joseph more frequently in English. Certainly Miguel, and not Michael, for the pretender. Diniz and not Dennis (or whatever his name was). For King Henry/Henrique, I'm not sure. Again, I've seen both. Sebastian and not Sebastião, I think... john 00:29 3 Jul 2003 (UTC)

Dear Boots

I am so glad to hear you are not a banned user. I hope your owner isn't a banned user, either.

LOL Deb 19:35 3 Jul 2003 (UTC)

Boots, I don't know how incognito you or your owner wish to remain, but there's talk of a meetup in Seattle (notes on my talk page and several other users -- you'll see who if you glance at my talk page) and I thought of mentioning it to you. It's November 6th -- perhaps we'll see you there. :-) Jwrosenzweig 22:30, 30 Sep 2004 (UTC)

title: User talk:Boots


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User:Pauld

I am Paul Doherty, and I live in Surrey, England.

I design and give courses on various technology subjects (especially from a intelligent layman's point-of-view), and on communication subjects such as effective writing and presenting.

I'm 50, I have four children and a partner, all lovely!

title: User:Pauld


text:
User talk:Slathering

Hello Slathering, welcome to Wikipedia. I hope you enjoy editing here and being a Wikipedian. You can learn more on the how to edit page. The naming conventions and manual of style pages are also useful. Feel free to experiment at the Sandbox. If you have any questions about the project then check out Help or add a question to the Village pump. Angela

J.D. title Dr.
For your information, J.D. does entitle the degree holder to use the title Dr. Both the ABA and many state bars have stated that attorneys having a J.D. may legally and properly use the title Dr. Additionally, the degree itself often states that it confers the title "Doctor of Law". Drdouma 17:23, 30 March 2006 (UTC)

Wikipedia Ambassador Program at MSU
Hi! I'm leaving you this message because you're listed as a Wikipedian associated with Michigan State University. The Wikipedia Ambassador Program is currently looking for Campus Ambassadors to help with Wikipedia assignments at MSU, which will be participating in the Public Policy Initiative for the Spring 2011 semester. The role of Campus Ambassadors will be to provide face-to-face training and support for students on Wikipedia-related skills (how to edit articles, how to add references, etc.). This includes doing in-class presentations, running workshops and labs, possibly holding office hours, and in general providing in-person mentorship for students.

Prior Wikipedia skills are not required for the role, as training will be provided for all Campus Ambassadors (although, of course, being an experienced editor is a plus).

If you are interested in being a Wikipedia Campus Ambassador, or know someone in the East Lansing area who might be, please email me or leave a message on my talk page.--Sage Ross - Online Facilitator, Wikimedia Foundation (talk) 20:27, 1 December 2010 (UTC)

Article for Deletion: Michigan State Miracle
Hello! There is an article that has been nominated for deletion regarding the Michigan State football team. I noticed you were an alumni, so I thought I would let you know in case you have any interest in participating with the discussion. If so, please just click on the Title as I have linked it straight to the page's deletion review. If you wish to see the article itself, it is titled Michigan State Miracle. Any thoughts, ideas, or edits that would help improve the page itself would also be appreciated!

ArbCom elections are now open!
MediaWiki message delivery (talk) 08:52, 23 November 2015 (UTC)

title: User talk:Slathering


text:
Well-defined expression

In mathematics, a well-defined expression or unambiguous expression is an expression whose definition assigns it a unique interpretation or value. Otherwise, the expression is said to be not well defined, ill defined or ambiguous. A function is well defined if it gives the same result when the representation of the input is changed without changing the value of the input. For instance, if $$f$$ takes real numbers as input, and if $$f(0.5)$$ does not equal $$f(1/2)$$ then $$f$$ is not well defined (and thus not a function). The term well-defined can also be used to indicate that a logical expression is unambiguous or uncontradictory.

A function that is not well defined is not the same as a function that is undefined. For example, if $$f(x)=\frac{1}{x}$$, then even though $$f(0)$$ is undefined, this does not mean that the function is not well defined; rather, 0 is not in the domain of $$f$$.

Example
Let $$A_0,A_1$$ be sets, let $$A = A_0 \cup A_1$$ and "define" $$f: A \rightarrow \{0,1\}$$ as $$f(a)=0$$ if $$a \in A_0$$ and $$f(a)=1$$ if $$a \in A_1$$.

Then $$f$$ is well defined if $$A_0 \cap A_1 = \emptyset\!$$. For example, if $$A_0:=\{2,4\}$$ and $$A_1:=\{3,5\}$$, then $$f(a)$$ would be well defined and equal to $\operatorname{mod}(a,2)$.

However, if $$A_0 \cap A_1 \neq \emptyset$$, then $$f$$ would not be well defined because $$f(a)$$ is "ambiguous" for $$a \in A_0 \cap A_1$$. For example, if $$A_0:=\{2\}$$ and $$A_1:=\{2\}$$, then $$f(2)$$ would have to be both 0 and 1, which makes it ambiguous. As a result, the latter $$f$$ is not well defined and thus not a function.

"Definition" as anticipation of definition
In order to avoid the quotation marks around "define" in the previous simple example, the "definition" of $$f$$ could be broken down into two logical steps: 1. The definition of the binary relation. In the example:
 * $f := \bigl\{(a,i) \mid i \in \{0,1\} \wedge a \in A_i \bigr\}, $

(which so far is nothing but a certain subset of the Cartesian product $A \times \{0,1\}$.)

2. The assertion. The binary relation $f$ is a function; in the example: While the definition in step 1 is formulated with the freedom of any definition and is certainly effective (without the need to classify it as "well defined"), the assertion in step 2 has to be proved. That is, $$f$$ is a function if and only if $$A_0 \cap A_1 = \emptyset$$, in which case $$f$$ – as a function – is well defined.
 * $f: A \rightarrow \{0,1\}.$

On the other hand, if $$A_0 \cap A_1 \neq \emptyset$$, then for an $$a \in A_0 \cap A_1$$, we would have that $$(a,0) \in f$$ and $$(a,1) \in f$$, which makes the binary relation $$f$$ not functional (as defined in Binary relation) and thus not well defined as a function. Colloquially, the "function" $$f$$ is also called ambiguous at point $$a$$ (although there is per definitionem never an "ambiguous function"), and the original "definition" is pointless.

Despite these subtle logical problems, it is quite common to use the term definition (without apostrophes) for "definitions" of this kind, for three reasons:

 * 1) It provides a handy shorthand of the two-step approach.
 * 2) The relevant mathematical reasoning (i.e., step 2) is the same in both cases.
 * 3) In mathematical texts, the assertion is "up to 100%" true.

Independence of representative
Questions regarding the well-definedness of a function often arise when the defining equation of a function refers not only to the arguments themselves, but also to elements of the arguments, serving as representatives. This is sometimes unavoidable when the arguments are cosets and when the equation refers to coset representatives. The result of a function application must then not depend on the choice of representative.

Functions with one argument
For example, consider the following function:

\begin{matrix} f : & \Z/8\Z        & \to     & \Z/4\Z\\ & \overline{n}_8 & \mapsto & \overline{n}_4, \end{matrix}$$ where $$n\in\Z, m\in \{4,8\}$$ and $$\Z/m\Z$$ are the integers modulo m and $$\overline{n}_m$$ denotes the congruence class of n mod m.

N.B.: $$\overline{n}_4$$ is a reference to the element $$n \in \overline{n}_8$$, and $$\overline{n}_8$$ is the argument of $$f$$.

The function $$f$$ is well defined, because:

 * $$n \equiv n' \bmod 8 \; \Leftrightarrow \; 8 \text{ divides } (n-n') \Rightarrow \; 4 \text{ divides } (n-n') \; \Leftrightarrow \; n \equiv n' \bmod 4.$$

As a counter example, the converse definition:

\begin{matrix} g : & \Z/4\Z        & \to     & \Z/8\Z\\ & \overline{n}_4 & \mapsto & \overline{n}_8, \end{matrix}$$ does not lead to a well-defined function, since e.g. $$\overline{1}_4$$ equals $$\overline{5}_4$$ in $$\Z/4\Z$$, but the first would be mapped by $$g$$ to $$\overline{1}_8$$, while the second would be mapped to $$\overline{5}_8$$, and $$\overline{1}_8$$ and $$\overline{5}_8$$ are unequal in $$\Z/8\Z$$.

Operations
In particular, the term well-defined is used with respect to (binary) operations on cosets. In this case, one can view the operation as a function of two variables, and the property of being well-defined is the same as that for a function. For example, addition on the integers modulo some n can be defined naturally in terms of integer addition.
 * $$[a]\oplus[b] = [a+b]$$

The fact that this is well-defined follows from the fact that we can write any representative of $$[a]$$ as $$a+kn$$, where $$k$$ is an integer. Therefore,

 * $$[a]\oplus[b] = [a+kn]\oplus[b] = [(a+kn)+b] = [(a+b)+kn] = [a+b];$$

similar holds for any representative of $$[b]$$, thereby making $$[a+b]$$ the same, irrespective of the choice of representative.

Well-defined notation
For real numbers, the product $$a \times b \times c$$ is unambiguous because $$(a \times b)\times c = a \times (b \times c)$$; hence the notation is said to be well defined. This property, also known as associativity of multiplication, guarantees the result does not depend on the sequence of multiplications; therefore, a specification of the sequence can be omitted. The subtraction operation is non-associative; despite that, there is a convention that $$a-b-c$$ is shorthand for $$(a-b)-c$$, thus it is considered "well-defined". On the other hand, Division is non-associative, and in the case of $$a/b/c$$, parenthesization conventions are not well established; therefore, this expression is often considered ill-defined.

Unlike with functions, notational ambiguities can be overcome by means of additional definitions (e.g., rules of precedence, associativity of the operator). For example, in the programming language C, the operator  for subtraction is left-to-right-associative, which means that   is defined as , and the operator   for assignment is right-to-left-associative, which means that   is defined as. In the programming language APL there is only one rule: from right to left – but parentheses first.

Other uses of the term
A solution to a partial differential equation is said to be well-defined if it is continuously determined by boundary conditions as those boundary conditions are changed.

title: Well-defined expression


text:
User talk:JackSchitt

Hello Jason, welcome to Wikipedia. I hope you enjoy editing here and being a Wikipedian. You can learn more on the how to edit page. The naming conventions and manual of style pages are also useful. Feel free to experiment at the Sandbox. If you have any questions about the project then check out Help or add a question to the Village pump. Angela

Dbpf (file format)
Welcome to Wikipedia. I've seen that you left a comment on dbpf (file format) saying that you didn't know how to do categories. The text you have to enter is shown below:

Note: don't copy what I put into the source (what shows up when you click "edit this page"; just follow the format directly from the page. -- King of Hearts | (talk) 01:15, 18 February 2006 (UTC)

Master PC (Universe)
Master PC (Universe) has been proposed for deletion. An editor felt the subject might not be notable enough for an article. Please review What Wikipedia is not and Notability for the relevant concerns. An example of notability guidelines can be found at Notability (websites). If you can improve the article to address these concerns, please do so.

If no one objects to the deletion within five days by removing the "prod" notice, the article may be deleted without further discussion. If you remove the prod notice, the deletion process will stop, but if an editor is still not satisfied that the article meets Wikipedia guidelines, it may be sent to Articles for deletion for consensus. NickelShoe (Talk) 18:51, 24 July 2006 (UTC)

Proposed deletion of Talisman Desktop

The article Talisman Desktop has been proposed for deletion  because of the following concern:
 * Lacks reliable independent secondary sources offering significant coverage as required by WP:GNG and WP:CORPDEPTH. The only "coverage" is a one-paragraph note on the CNET site where it can be downloaded.

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Proposed deletion of Talisman Desktop

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Nomination of Talisman Desktop for deletion
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title: User talk:JackSchitt


text:
Lesley Choyce

Lesley Choyce (born 21 March 1951) (m. Linda Choyce) is a Canadian author of novels, non-fiction, children's books, young adult novels, and poetry.

He is the author of more than 100 books for adults, teens and children, and teaches in the English department and transition year program at Dalhousie University. He is a year-round surfer and founding member of the 1990s spoken word rock band The SurfPoets. Choyce also runs Pottersfield Press, a small literary publishing house. He hosted the national TV show Off The Page for many years. His books have been translated into Spanish, French, German and Danish, and he has been awarded the Dartmouth Book Award and the Ann Connor Brimer Award.

He lives at Lawrencetown Beach, Nova Scotia.

title: Lesley Choyce


text:
Talk:Ecoregion conservation status

I put back the links to make the redirects.These are necessary for the ecoregion project. Anthere

No problem. But then I think you should create less ambiguous titles, like "endangered ecoregion", etc. "vulnerable", in particular, is vulnerable to ambiguity... FVDP.

this is not refering to an endangered ecoregion, but to species endangered, which are to be found in an ecoregion.

perhaps, we could rename them vulnerable species ? what do you think ?

Really, when I re-read your article: ''Ecoregions vary in their biological particularities, as well as in their conservation status. This latter represent an estimation of the current and future ability of the ecoregion to sustain ecological viability and to react to environmental changes. '' it seems to talk about the region, which I may then interpret as "the current ecosystem in that region and the species that constitute it". Whereas a "vulnerable species" can live in several distinct regions. It really depends on what you want to tell. --FvdP 19:59 26 Jun 2003 (UTC)

"region" is administrative, ecoregion is ecological. Look at the ones below

the one on the left was defined by national geographic, the one on the right represent the "régions biogéographiques" as defined in "Directive Habitat" from the EU (which is why Switzerland is in grey).

The species status is defined by the IUCN (look at Liste Rouge de l'IUCN et Espèce menacée. The IUCN propose lists of all species included in these categories. Look at http://www.redlist.org/

So, what I want to do, is perhaps one day (if I find time :-)) first to define clearly each of these categories, second to provide the update list of all species in each of these categories (well, at least the most important ones), then for each ecoregion to indicate the general status of the area, which perhaps means the relative proportion (or number) of threatened species. With a list of some of the threatened species for each ecoregion. Well, at least, I will try to take care of the ones covered by France (and Belgium :-)). I have not decided yet how to fit la Directive Habitat with the other one.

So, I think vulnerable species is the right title. That is perhaps the status as it is defined in the ecoregion that needs to be reworked. Bah, do as you want; As soon as I have time, I will try to come back to that topic and fix this. Right now, it does not harm anything anyway. :-)))

Hum, Bruxelles, c est dans le bleu ou dans le vert ???

User:anthere

 * A vue de nez, c'est dans le bleu (ou le vert pomme, selon la carte). Bruxelles est un peu plus au nord que le milieu de la Belgique (normal, c'est en Flandres ;-)

 * de mes souvenirs (j'ai habité à Antwerpen il y a qlq années), le pays était plutot plat. Meme type climatique. Je ne sais pas ce qui défini le passage de l un a l autre dans ce cas...Note que j habite aussi a la limite bleu vert.

 * So, all these mountainous violet zones (on the right-hand map) define a unique ecoregion ?

 * Zone biogeographique is the terminology used by Directive Habitat. Note that the DH areas are larger and more rough than the ones of NG. They are meant to be usable. But since noone has the unique definition of what an ecoregion is (on the contrary of ecozone pretty well defined) I guess you can say the zones biogeographiques are ecoregions also. So, yes, the violet area is an area considered quite coherent in terms of climate, soil and life.

 * About the other problems, I'll leave it up to you as you are the one who is doing the hard work. Most of my wikipedia interventions are of the "inspection des travaux finis" kind ;-) + :-(. As you say, there's currently no harm.

 * --FvdP 00:06 27 Jun 2003 (UTC)

 * the least I can say is that it is not a "done" project. Hardly starting :-) and :-( But you are more than welcome to provide a pure and innocent eye on it. ant

Wiki Education assignment: Conservation Genetics
— Assignment last updated by PaigeHerkemij (talk) 02:34, 2 February 2024 (UTC)

title: Talk:Ecoregion conservation status


text:
Vulnerable

Vulnerable may refer to:

General

 * Vulnerability
 * Vulnerability (computing)
 * Vulnerable adult
 * Vulnerable species

Albums

 * Vulnerable (Marvin Gaye album), 1997
 * Vulnerable (Tricky album), 2003
 * Vulnerable (The Used album), 2012

Songs

 * "Vulnerable" (Roxette song), 1994
 * "Vulnerable" (Selena Gomez song), 2020
 * "Vulnerable", a song by Secondhand Serenade from Awake, 2007
 * "Vulnerable", a song by Pet Shop Boys from Yes, 2009
 * "Vulnerable", a song by Tinashe from Black Water, 2013
 * "Vulnerability", a song by Operation Ivy from Energy, 1989

Other uses

 * Climate change vulnerability, vulnerability to anthropogenic climate change used in discussion of society's response to climate change
 * Vulnerable, a scoring feature of the game of contract bridge where larger bonuses and penalties apply; see Glossary of contract bridge terms

title: Vulnerable


text:
User talk:Pauld

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title: User talk:Pauld


text:
User talk:Sir Paul

archive

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Invitation to support the creation of WikiProject Effective altruism
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Your submission at Articles for creation: Centre for Effective Altruism (September 23)
 Your recent article submission to Articles for Creation has been reviewed! Unfortunately, it has not been accepted at this time. The reason left by Numberguy6 was:

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title: User talk:Sir Paul


text:
User talk:Kostasge~enwiki

Hello Kostasge, welcome to Wikipedia!

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I am afraid I am one of the few admins without a computing background. I can get Poros directly, but not through search. I think search is static at present, and doesn't add new ppages automatically until it is updated by a developer. Try Village pump, just to check this.

jimfbleak

Kalimera! eimai ellinas kai se vrika apo ti selida Wikipedians/Greece. apla anarotiomoun an ise akomi energos stin wikipedia kai ean mas episkeptese. ean nai, tha xarw na doulepsoume mazi gia na veltiosoume tin elliniki Wikipedia sto mellon. euxaristw, Optim 21:43, 10 Jan 2004 (UTC)

hello
hello. molis eida to minima sou kathws eimoun ki egw apasxolimenos auto ton kairo. egw prosopika tha elega oti ta ksena onomata tha prepei na grafontai sto titlo me tin kseni grafi tous (Martyn Jacques) kai oxi me tin elliniki (Μάρτιν Τζακιουές me to skeptiko pws den boroume na eimaste sigouroi pws na "metagrapsoume" to kathe onoma (to egrapsa swsta sta ellinika? de kserw pragmatika). mesa sto arthro tha grafoume kai tin elliniki metagrafi. stin pragmatikotita auti ti stigmi den iparxei kapoia politiki panw se auto to thema, opote boreis na kaneis oti sou aresei esena kalitera. Optim 16:28, 19 Feb 2004 (UTC)

 * episis na prosthesw oti tha itan kalo na prostheteis Redirections gia ta onomata. px i elliniki metagrafi tou Martyn Jacques borei na einai ena redirect sto arthro pou exei san titlo to kseno onoma tou. gia na ftiakseis ena redirect grafeis "#REDIRECT Martyn Jacques" . Optim 16:31, 19 Feb 2004 (UTC)

Literature Collaboration of the Week
Patrida, I'm rallying up support for Alexandros Papadiamantis in Literature Collaboration of the Week. So, go vote! :D

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Need Help
The article vanavsos is up for deletion. Can you please help in this regard. Second, I am having difficulty with Wikinfo:Classical definition of republic and am having trouble on Talk:Republic because they won't allow an external link. It was deleted off of Wikipedia, and I believe it needs to come back on. A serious mistake in deleting this article. Thanks for your time.WHEELER 18:30, 8 Mar 2005 (UTC)

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If you are interested, there's a poll going on: Talk:Macedonian_Slavs Etz Haim 20:15, 21 Jun 2005 (UTC)

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title: User talk:Kostasge~enwiki


text:
Austin Clarke (novelist)

Austin Ardinel Chesterfield "Tom" Clarke, (July 26, 1934 – June 26, 2016), was a Barbadian novelist, essayist, and short story writer who was based in Toronto, Ontario, Canada. Among his notable books are novels such as The Polished Hoe (2002), memoirs including Membering (2015), and two collections of poetry, Where the Sun Shines Best (2013) and In Your Crib (2015).

Early life and education
Austin Clarke was born in 1934 in St. James, Barbados, where he received his early education in Anglican schools. He taught at a rural school for three years. In 1955, he moved to Canada and attended the University of Toronto's Trinity College for two years.

Career
Clarke was a reporter at the Timmins Daily Press and the Globe and Mail, before joining the Canadian Broadcasting Corporation as a freelance journalist. He subsequently taught at several American universities, including Yale University (Hoyt fellow, 1968–70), Duke University (1971–72), and the University of Texas (visiting professor, 1973) and helped establish black studies programs at several universities.

In 1973, he was designated cultural attaché at the Barbadian embassy in Washington, DC. He was later General Manager of the Caribbean Broadcasting Corporation in Barbados (1975–77). He was writer in residence at Concordia University, Montreal, Quebec (1977), and at the University of Western Ontario (1978). He became a Canadian citizen in 1981. From 1988 to 1993 he served on the Immigration and Refugee Board of Canada.

He was not the first Canadian writer of African origin, that distinction belonging to 19th-century author Amelia E. Johnson. However, George Elliott Clarke says that Clarke was "the author of African descent in English, in Canada, that anyone who was interested in being a writer would have to be aware of, to challenge as well." In September 2012, at the International Festival of Authors, Clarke was announced as the winner of the $10,000 Harbourfront Festival Prize "on the merits of his published work and efforts in fostering literary talent in new and aspiring writers". Previous recipients of the award (established in 1984) include: Dionne Brand, Wayson Choy, Christopher Dewdney, Helen Humphreys, Paul Quarrington, Peter Robinson, Seth, Jane Urquhart, and Guy Vanderhaeghe. Clarke was reported as saying: "I rejoiced when I saw that Authors at Harbourfront Centre had named me this year's winner of the Harbourfront Festival Prize. I did not come to this city on September 29, 1959, as a writer. I came as a student. However, my career as a writer buried any contention of being a scholar and I thank Authors at Harbourfront Centre for saving me from the more painful life of the 'gradual student.' It is an honour to be part of such a prestigious list of authors."

An outspoken intellectual, he avoided talking about multiculturalism, hoping his own term omniculturalism could be accepted by people from both the political left and right. He ran as a Progressive Conservative candidate in the 1977 Ontario general election.

Clarke died on June 26, 2016, at the age of 81, in Toronto.

Selected awards and honours

 * 1980, Casa de las Américas Prize, Cuba
 * 1992, Toronto Arts Award for Lifetime Achievement in Literature
 * 1997, Lifetime Achievement Award from Frontier College in Toronto
 * 1998, Member of the Order of Canada.
 * 1999, Martin Luther King Jr. Achievement Award for Excellence in Writing.
 * 1999, W. O. Mitchell Literary Prize
 * 2002, Giller Prize, for The Polished Hoe
 * 2003, Commonwealth Writers' Prize
 * 2009, Toronto Book Award, for More.
 * 2012, Harbourfront Festival Prize

Novels

 * The Survivors of the Crossing (Toronto: McClelland & Stewart, 1964)
 * Amongst Thistles and Thorns (Toronto: McClelland & Stewart, 1965)
 * The Meeting Point (Toronto: Macmillan, 1967; Boston: Little, Brown, 1972)
 * Storm of Fortune (Boston: Little, Brown, 1973)
 * The Bigger Light (Boston: Little, Brown, 1975)
 * The Prime Minister (Don Mills, Ont.: General Publishing, 1977)
 * Proud Empires (London: Gollancz, 1986; Penguin-Viking, 1988, ISBN 978-0670817566)
 * The Origin of Waves (McClelland & Stewart, 1997; winner of the Rogers Writers' Trust Fiction Prize)
 * The Question (Toronto: McClelland & Stewart, 1999; nominated for a Governor General's Award)
 * The Polished Hoe (Toronto: Thomas Allen, 2002; winner of the Giller Prize and the Commonwealth Writers' Prize)
 * More (2008, winner of the City of Toronto Book Award)

Short story collections

 * When He Was Free and Young and He Used to Wear Silks (Toronto: Anansi, 1971; revised edition Little, Brown, 1973)
 * When Women Rule (Toronto: McClelland & Stewart, 1985)
 * Nine Men Who Laughed (Toronto: McClelland & Stewart, 1986)
 * In This City (Toronto: Exile Editions, 1992)
 * There Are No Elders (Toronto: Exile Editions, 1993)
 * The Austin Clarke Reader, ed. Barry Callaghan (Toronto: Exile Editions, 1996)
 * Choosing His Coffin: The Best Stories of Austin Clarke (Toronto: Thomas Allen, 2003)
 * They Never Told Me: and Other Stories (Holstein, ON: Exile Editions, 2013)
 * Canadian Experience (Toronto: Exile Editions, 1994)

Poetry

 * Where the Sun Shines Best (Toronto: Guernica Editions, 2013)
 * In Your Crib (Toronto: Guernica Editions, 2015)

Memoirs

 * Growing Up Stupid Under the Union Jack: a Memoir (Toronto: McClelland & Stewart, 1980; Thomas Allen, 2005, ISBN 978-0887621888)
 * "A Stranger In A Strange Land", The Globe and Mail, Toronto, 15 August 1990, p. 30.
 * Public Enemies: Police Violence and Black Youth (Toronto: HarperCollins, 1992)
 * A Passage Back Home: A Personal Reminiscence of Samuel Selvon (Toronto: Exile Editions, 1994)
 * Pigtails 'n Breadfruit: A Culinary Memoir (New Press, 1999); as Pigtails 'n' Breadfruit: The Rituals of Slave Food, A Barbadian Memoir (Toronto: Random House, 1999; University of Toronto Press, 2001); Pig Tails 'n' Breadfruit - Anniversary Edition (Ian Randle Publishers, 2014, ISBN 978-9766378820)
 * Love and Sweet Food: A Culinary Memoir (Toronto: Thomas Allen, 2004; ISBN 978-0887621536)
 * ′Membering (Toronto: Dundurn Press, 2015)

title: Austin Clarke (novelist)


text:
Francis Rogallo

Francis Melvin Rogallo (January 27, 1912 – September 1, 2009) was an American aeronautical engineer inventor born in Sanger, California, U.S. Together with his wife, he is credited with the invention of the Rogallo wing, or "flexible wing", a precursor to the modern hang glider and paraglider. His patents were ranged over mechanical utility patents and ornamental design patents for wing controls, airfoils, target kite, flexible wing, and advanced configurations for flexible wing vehicles.

Career
Francis Rogallo earned an aeronautical engineering degree at Stanford University in 1935. Since 1936, Rogallo worked for the National Advisory Committee for Aeronautics (NACA) as an aeronautics project engineer at the wind tunnels. During 1948, he and his wife, Gertrude Rogallo, invented and patented a self-inflating flexible kite. They called this kite the "flexible wing". Rogallo had originally invented the wing with the idea to create an aircraft which would be simple enough and inexpensive enough that anyone could have one. The wing was flown by Rogallo as a model glider with small payloads hung beneath the wing (thus model hang glider) and as a kite.

The Rogallo wing is one of the simplest airfoils ever created. A wing using the airfoil could be used to carry payloads, undercarriage devices, pilot-control assemblies, etc. For the next six years, the Rogallos tried ceaselessly to attract both government and industry interest in their flexible wing, and they licensed a manufacturer in Connecticut to sell a kite based on it. When the DuPont company announced the development of Mylar in 1952, Rogallo immediately saw how superior it would be for his kite, and the five-dollar toy "Flexikite" became one of the first products to use the plastic material. The Rogallos found themselves traveling to kiting events around the Northeast to fly and promote the toy, with moderate success.

On October 4, 1957, the Russian Sputnik began beeping its message from orbit, and everything changed. The space race caught the imagination of the newly formed NASA and Rogallo was in position to seize the opportunity. The Rogallos released their patent to the government, and with Rogallo's help at the wind tunnels, NASA began a series of experiments testing the Parawing (NASA renamed the Rogallo wing the Parawing, and modern hang glider pilots often refer to it as the flexible Rogallo wing) at altitudes up to 200,000 feet and as fast as Mach 3 in order to evaluate them as alternative recovery system for the Gemini space capsules and used rocket stages. By 1960, NASA had made test flights of a framed Parawing powered aircraft, called the "flying Jeep" or Fleep, and of a weight shift Parawing glider, called Paresev, in a series of several shapes and sizes, manned and unmanned. A key wing configuration applying Francis Rogallo's leadership that gave base to kited gliders with hung pilots using weight-shift control was designed by Charles Richards and constructed by the Richards team in 1961–2; such wing became a template for recreational use or Rogallo's inventions, ending up mechanically and ornamentally in Skiplane, ski-kites, and hang gliders of the 1960–1975.

In 1967, projects focused on the Parasev were stopped by NASA in favor of round parachutes. NASA was not in the business of applying Rogallo's family of airfoils to personal aircraft such as kites, hang gliders, and powered light aircraft; however what was already in the Paresev series of aircraft provided all the fundamental mechanics that could be simplified to lighter personal aircraft. That task of lightening and tweaking what the Paresev team had done with the Rogallo wing was taken up by independent designers around the world: Barry Palmer in 1961, Richard Miller, Thomas Purcell, and Australian Mike Burns were among the first to tap the technology for manned personal-craft glider/kite use.

As of 2003, Rogallo had new designs for kites.

Tens of thousands of people have taken hang gliding lessons in Rogallo wing type hang gliders at Jockey's Ridge State Park, an enormous sand dune which is located five miles from the site of the first powered aircraft flight. Mr. Rogallo was frequently seen at the park flying his own hang glider in the 1970s and 1980s.

Francis Rogallo died at home on September 1, 2009, in Southern Shores, North Carolina, near Kitty Hawk, the birthplace of aviation. Gertrude died on January 28, 2008.

The Rogallo name lives on as members of the United States Hang Gliding and Paragliding Association are called "Rogallo" members.

title: Francis Rogallo