text:
Hjallis Harkimo

Harry Juhani "Hjallis" Harkimo (born 2 November 1953) is a Finnish businessman, sportsperson, and a member of the Finnish Parliament. Previously a National Coalition Party MP, he now chairs his own political party, Movement Now.

First elected to the Parliament in 2015 representing NCP, his tenure in the party was cut short following his complaints about leadership in 2018. He then proceeded to establish and register his new political movement simply as an association due to strong disdain toward traditional party politics. Following his successful re-election campaign in 2019, Harkimo decided to register Movement Now as a party afterall, explaining that "the whole system was built so that thriving in it won't be possible without having a party."

In the Parliament, Harkimo sits in opposition, although he voted in favor of swearing in the Rinne Cabinet. He later explained this by saying he wanted to give the government platform a chance, since he considered many of its goals positive. Since then, Harkimo and Movement Now have been more critical of the government, even by joining in on some joint opposition interpellations.

Sailing
In the 1981–82 season Harkimo was a crewmember on the yacht Skopbank of Finland in the Whitbread Round the World Yacht Race.

From 1986 to 1987 he participated in a round-the-world single-handed yacht race, BOC Challenge, and finished third.

In the 1989–90 season he was a crewmember on the yacht Belmont Finland in the Whitbread Round the World Yacht Race.

Political career
In 1988 Finnish presidential election, Harkimo was Harri Holkeri's constituent.

Harkimo was elected to the Eduskunta in 2015 with 11,416 votes in the election. Although he was elected representing the National Coalition Party, in 2018 he left the party and founded a new political movement, Movement Now. In the 2019 parliamentary election, Harkimo was elected to the parliament as the sole representative from Movement Now.

Harkimo told in late August 2020 that he is running for Mayor of Helsinki in 2021 Finnish municipal elections

Presidential election 2024
In 2022, Harkimo was nominated as the Movement Now candidate for the Finnish presidential election of 2024. In the election, he finished last with 0.5% of the votes.

Business
Harkimo was the chairman of the board of the Helsinki-based ice-hockey team Jokerit 1991–2019.

Hjallis had been dreaming of his own ice rink since 1994. At that time, the club was playing in the Helsinki Ice Hall together with HIFK, and Harkimo had understood that there would be no continuity in the operations of the Jokerit, if it continued in the same hall. He as a builder and developer of the team's home arena, Hartwall Areena, and had been an investor in sports.

Harkimo shared a common interest with HJK. Hjallis bought the PK-35 and renamed the club FC Jokerit with the aim of attracting Jokerit hockey fans to the football audience as well. Harkimo had experience in stadium construction after leading the Hartwall Arena project, which was completed in 1997. Harkimo raised FIM 64 million in private funding, the City of Helsinki paid 32 million from the budget and the state 14 million, and so the new football stadium began to rise rapidly along Urheilukatu. Töölö football stadium was completed on 10 June 2000, just in time for the opening match between FC Jokerit and HJK. Eventually, HJK acquired the FC Jokerit football operations and formed the reserve team HJK Klubi 04 when, in March 2004, Hjallis Harkimo announced the closure of FC Jokerit.

Harkimo was a talk show hosted by "With Hjallis" on MTV3. In the program, Harkimo interviewed economic and political figures as well as other public figures.

The first production period of the program was presented from 27 January to 31 March 2011, the second from 8 March to 10 May 2012 and the third from 7 March to 9 May 2013. The fourth season, which was presented from 2 November to 21 December 2013 and the name was changed to "Hjallis". Unlike in the fourth season, there are three guests instead of one. The fifth season of the series was shown from 26 September to 19 December 2014. The sixth production season began on 11 March 2016. In the sixth season, there are two guests in each episode.

In the 2012 presidential election, Harkimo supported the Coalition Party's Sauli Niinistö campaign with 10,000 euros through Hjallis Promotion Oy.

Harkimo hosted the Finnish version of The Apprentice from 2009 until 2013. and made a one-season return in 2018.

In October 2017, Harkimo started to publish YouTube videos, discussing politics, business, sports and other subjects.

In 2019 Harkimo bought the 49% share of Jokerit from Russians Gennady Timchenko and Roman Rotenberg, the owners of Arena Events Oy. Harkimo then sold 100% of Jokerit to Jari Kurri, a long time manager of the club. Harkimo's intent was to exclude the club from the US sanction list drawn upon the annexation of Crimea.

Personal life
Harkimo married his first wife, MP Leena Harkimo in 1989. The pair filed for divorce in 2002. He later married MP Merikukka Forsius-Harkimo in 2004, but they divorced after only a year of marriage. Harkimo has two sons from his first marriage and a third from his second marriage.

Harkimo has been a vegetarian since the beginning of 2018.

title: Hjallis Harkimo


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User:Budloveall

Real name: Bud Loveall Location: Austin, TX USA

Interests: Lots of things, but for here (and for now), mostly Beatles related things.

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

title: User:Budloveall


text:
User:Aranel

Aranel, also known as Sarah, has been an editor of the English Wikipedia since August 2, 2004 and an administrator since November 4, 2004. She has made a ridiculous number of edits, mostly because of her category and other housekeeping work. She also dislikes talking about herself in the third person and is going to stop now.

Name
I am actually named Sarah, but so is your little sister, your great-aunt, your second-grade teacher, and at least three people in your graduating class, the result of which is that the user name Sarah has been one of the first ones taken on every place requiring a user name since the dawn of time¹. Fortunately, it's an extremely durable name with eminently respectable origins. One hundred years from now, I predict that it will still seem like every third of fourth girl is named Sarah.

Sarah means princess and comes from Hebrew שרה. The Quenya word with the same meaning is Aranel, conveniently already appearing in a form that is appropriate for a feminine name.

My current signature contains my name in red because red is the coolest color ever.

¹And usually it was registered and promptly abandoned. See User:Sarah.

Favorite subjects
Having apparently abandoned my degree in physics, I've been nitpicking and expanding Middle-earth and Tolkien-related articles. I was initially quite delighted to have finally found an outlet for my vast stores of completely useless Tolkien knowledge, but then I discovered the joys of working on categories, which is endless entertaining for someone with my organization tendencies.

I don't just work on categories and Tolkien articles. I have also contributed to such subjects as French science fiction (I don't know much, but I can translate) and looms.

Current hobby: Copyright problems and the backlog of DOOM.

Notes for Tolkien articles

 * Hobbit, Dwarf, Man, Elf - not hobbit, dwarf, man, elf. (Unless referring to a generic male of any species.)
 * Link dates to Second Age, Third Age, or Fourth Age (when appropriate, Shire Calendar for explanation of Shire Reckoning). Generally use dating systems of Númenor, Gondor and the New Reckoning at the beginning of the Fourth Age. Format: T.A. 3019, S.R. 1419, etc. as used by Tolkien in LotR. Linking avoids ambiguity of reference to "F.A.". Don't need to include this once time frame has been established.
 * User:Aranel/WelcomeME - I need to update this.

Notes for categories

 * User:Aranel/unresolved - to label archive pages for unresolved CfD entries
 * User:Aranel/resolved

Unexplained disappearances
I seem to have disappeared for a few months. Er...oops? Life happens, I guess. I had no idea it had been so long!

I do have a habit of occasionally disappearing for no apparent reason. Usually I will reappear after a few days or weeks at the most. (This has to do with being a perpetual student and having a wildly erratic schedule.) For the purposes of explaing the most recent (and excessively long) disappearance, I offer you your choice of the following explanations:
 * I was abducted by aliens.
 * I blame end-of-semester stress followed by summer internship.
 * I moved to Antarctica.

If I should happen to disappear again, this list should be handy. (If you have any other ideas that might explain it, please share them on my talk page! I can always use more excuses explanations.)

Other fun and cool stuff
fr:Utilisateur:Aranel

title: User:Aranel


text:
Talk:2112

Untitled
True or false: this article belongs at 2112 (disambiguation). The rule of Wikipedia articles is that numbers between 0 and 10000 exclusive without a suffix are years. 66.245.97.168 23:13, 3 Aug 2004 (UTC)
 * Technically I believe that is correct. However, I personally think it's OK to leave like this for the next 5-7 years, until we actually have something to say about the year. Niteowlneils 16:56, 17 Aug 2004 (UTC)

Years vs. numbers that aren't years.
Classify positive integers into 2 groups:

Group #1: Articles with that number and no suffix are years; articles for that number that aren't years must be identified as so; for example 13 (number)

Group #2: Articles with that number and no suffix should NOT be years for a given reason. Please explain. 66.32.249.176 20:03, 6 Sep 2004 (UTC)

Requested move 7 December 2019

 * The following is a closed discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. Editors desiring to contest the closing decision should consider a move review after discussing it on the closer's talk page. No further edits should be made to this discussion.

The result of the move request was: moved as requested per the discussion below. Dekimasu よ! 05:40, 16 December 2019 (UTC)

2112 (disambiguation) → 2112 – 2112 is currently a redirect to 22nd century, but I don't really think that's the best option at the moment; there's, of course, very little related to the year on the page, and there probably won't be anything substantial for many, many years. Given that various links to 2112 across Wikipedia mean the Rush album/song, and the disambiguation page is fairly heavily viewed, making it the landing page for now seems like the most sensible option. Nohomersryan (talk) 02:22, 7 December 2019 (UTC) —Relisting. Dekimasu よ! 09:51, 14 December 2019 (UTC)
 * If moved the edit history of the year should be restored and moved to AD 2112 though the logs for "2112" don't show a deletion for some reason (see also AFD).  Crouch, Swale  ( talk ) 10:56, 14 December 2019 (UTC)
 * Support: The year is not a PT, so a primary redirect is not justified. Incoming links are 204 to 2112 (album), 167 to 2112 (song), 153 to 2112: The Birth of Doraemon and single figures for other topics including the year.  |2112_(album)|2112_(song)|2112:_The_Birth_of_Doraemon|2112_Ulyanov|2112_(year)|2112_(disambiguation) Pageviews tell a similar story.  We (or our successors) should revisit this matter once we have a substantial article about the year 2112, but it's well worth making a temporary change for the intervening decades. Certes (talk) 18:42, 14 December 2019 (UTC)
 * Support – More notability for the album/song than for the future year. I think 2112 (album) should be made primary until 2099. — JFG talk 05:19, 16 December 2019 (UTC)

 * The above discussion is preserved as an archive of a requested move. Please do not modify it. Subsequent comments should be made in a new section on this talk page or in a move review. No further edits should be made to this section.

Year links
What should we do with the link to this dab from Leap year starting on Friday? I've unlinked the year elsewhere but wikilinks from articles about years are exceptionally encouraged. One option is to create a redirect AD 2112 → 22nd century, though the topic is barely covered there. This question is trivial now, but there may be many more such cases in future and I'd prefer to get consensus before setting a precedent. Certes (talk) 10:02, 16 December 2019 (UTC)
 * Yes and the deleted history should also be restored and moved to that title.  Crouch, Swale  ( talk ) 18:31, 16 December 2019 (UTC)

title: Talk:2112


text:
User talk:Ifoolyou

No, you don't. :p
 * Your user picture looks particularly tasty. - Fennec (はさばくのきつね) 23:26, 3 Aug 2004 (UTC)
 * Is that a threat? I know from experience to keep well away from foxes of all types. I was even ambushed by one once in a Quailmob dispute, and another time in the Quailrean War and even once in 'Quailnam. It's best to shout "kakahkaha, kakahkaha, kakahkaha!" and then fly far away. Ifoolyou 23:27, 3 Aug 2004 (UTC)
 * Did you know that your username/password are publicly available at htttp://www.bugmenot.com? I would suggest that you change your password lest some random person make edits in your name.  Users with public passwords tend to be used as sock puppets in my experience.  --[[User:Ardonik|Ardonik(talk)]] 08:06, Sep 4, 2004 (UTC)

Tucson, Arizona and more
Hi. I saw that you voted on the RFC regarding Tucson, Arizona, and I thought you might be interested in commenting on a broader application of the formatting to other city articles. The discussion (for now) is at Talk: Tucson, Arizona (It might get moved to WikiProject Cities, if there's interest in doing so.) Thanks! kmccoy (talk) 01:48, 27 Dec 2004 (UTC)

title: User talk:Ifoolyou


text:
John D. Fitzgerald

John Dennis Fitzgerald (February 3, 1906 – May 21, 1988) was an American author, most notable for The Great Brain series of children's books.

Biography
Fitzgerald was born in Price, Utah, the son of an Irish Catholic father and a Scandinavian mother who was a member of the Church of Jesus Christ of Latter-day Saints. He had two older brothers, Thomas (1902-1988; the basis for the character known as the Great Brain) and William; two younger brothers, Charles and Gerald; and an older sister, Isabelle (known as "Belle").

He left Utah in 1925, at the age of 18, and held a variety of jobs, including playing in a jazz band, working at a bank and working for a steel company.

Fitzgerald published his first novel, Papa Married a Mormon, in 1955. Other novels for adults about late nineteenth and early twentieth century Utah followed. Fitzgerald had many stories published in magazines, and he also co-wrote two textbooks about creative writing.

In the 1960s, he turned his attention to books for children, writing the highly successful The Great Brain series, in which his characters are loosely based on people from his own family and community, including himself. The Great Brain is based on his brother, Tom. Fitzgerald changed many family details in the Great Brain series. He omitted his oldest sibling Isabelle and his younger brothers Charles and Gerald, gave his older brother William the name Sweyn, and invented a family custom of giving sons the middle name Dennis (his older brothers were William J. and Thomas N., not Sweyn D. and Tom D.) The Great Brain novels are structured like a collection of short stories, in which Tom either swindles people and then rationalizes it by claiming it was to teach them a lesson, or solves an important problem for the community. There are eight books in the series (one of which was published posthumously).

The Great Brain series

 * The Great Brain (Dial Press, 1967)
 * More Adventures of the Great Brain (Dial Press, 1969)
 * Me and My Little Brain (Dial Press, 1971)
 * The Great Brain at the Academy (Dial Press, 1972)
 * The Great Brain Reforms (Dial Press, 1973)
 * The Return of the Great Brain (Dial Press, 1974)
 * The Great Brain Does It Again (Dial Press, 1976)
 * The Great Brain Is Back (Dial Press, 1995) — published from loose notes after the author's death

Other books

 * Papa Married a Mormon (Prentice-Hall, 1955) — unofficially co-authored with Fitzgerald's sister Belle Fitzgerald Empey
 * Mamma's Boarding House (W.H. Allen, 1958) — sequel to Papa Married a Mormon
 * Uncle Will and the Fitzgerald Curse (Bobbs-Merrill Company, 1961)
 * (with Robert C. Meredith) The Professional Story Writer and His Art (Crowell, 1963)
 * (with Robert C. Meredith) Structuring Your Novel: From Basic Idea to Finished Manuscript (HarperCollins Publishers, 1972)
 * Brave Buffalo Fighter (Bethlehem Books, 1973)
 * Private Eye (T. Nelson, 1974)

title: John D. Fitzgerald


text:
Wikipedia:Articles for deletion/I Hear Ya! Records

I Hear Ya! Records 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 to delete

advert for non-notable record album. also has redirects Jonathan Smith, D.C. Scorpio, EU (band), Rare Essence; only thing i found on google for "I Hear Yeah" (missp) was but Rare Essence is real  Salasks 23:17, Aug 3, 2004 (UTC) This page is now preserved as an archive of the debate and, like other '/delete' pages 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.
 * Weak Delete: It seems like a cut & paste, too. Notability is lacking.  It's possible that clean up could do something, but it's doubtful. Geogre 01:22, 4 Aug 2004 (UTC)
 * Delete - Most of Google's first page of hits is now mirrors of this article, so I agree it doesn't seem that notable. It does look a lot like a cut-'n'-paste too. The redirects show very little on the Googlometer too (except Rare Essence), Jonathan Smith in particular is so generic a name there doesn't seem to be anything to be found on this particular character. Delete them all, except the last, which probably deserves a band entry. TPK 05:28, 4 Aug 2004 (UTC)
 * Keep Weak keep. When I looked at it before and listed it for cleanup, I considered listing it for VFD but discovered it did exist and had some relevance.  It may still be considered lacking in notability, I suppose.  Noisy 08:47, 4 Aug 2004 (UTC)
 * Where did you discover it existed? What relevance? I couldn't find anything to back up the claims in the article.Salasks 01:14, Aug 5, 2004 (UTC)
 * Found one more (weak) reference, which I have recorded on Talk:I Hear Ya! Records. Also, the lable is mentioned on another article. Noisy 15:48, 5 Aug 2004 (UTC)
 * Delete. A few weak references does not a wikipedia article justification make. Timbo


text:
Youngs

Youngs can refer to:

People:
 * Ben Youngs (b. 1989), English rugby union player
 * Elaine Youngs (b. 1970), American beach volleyball player
 * Jenny Owen Youngs (b. 1981), American singer-songwriter
 * Jim Youngs (b. 1956), American actor who appeared in such films as The Wanderers and Footloose
 * John Youngs (minister) (c. 1598–1672), Puritan minister who founded Southold, New York
 * John E. Youngs (1883–1970), American politician
 * John William Theodore Youngs (1910–1970), American mathematician
 * Nick Youngs (b. 1959), former English rugby union footballer
 * Richard Youngs (b. 1966), British musician
 * Ross Youngs (1897–1927), American Major League Baseball outfielder
 * Samuel Youngs (1760–1839), American schoolteacher who served as inspiration for the character Ichabod Crane

Places:
 * Youngs, California, a former town in El Dorado County
 * Youngs Bay, Oregon
 * Youngs River, tributary of the Columbia River in northwest Oregon
 * Youngs Siding, Western Australia, in the City of Albany, Australia

Companies
 * Young's, British pub chain
 * Young's Seafood, British fish company

title: Youngs


text:
Kalskag, Alaska

Kalskag, Alaska may refer to:

 * Lower Kalskag, Alaska
 * Upper Kalskag, Alaska
 * Kalskag Airport, serving both communities

title: Kalskag, Alaska


text:
Divergent series

In mathematics, a divergent series is an infinite series that is not convergent, meaning that the infinite sequence of the partial sums of the series does not have a finite limit.

If a series converges, the individual terms of the series must approach zero. Thus any series in which the individual terms do not approach zero diverges. However, convergence is a stronger condition: not all series whose terms approach zero converge. A counterexample is the harmonic series

 * $$1 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \frac{1}{5} + \cdots =\sum_{n=1}^\infty\frac{1}{n}.$$

The divergence of the harmonic series was proven by the medieval mathematician Nicole Oresme.

In specialized mathematical contexts, values can be objectively assigned to certain series whose sequences of partial sums diverge, in order to make meaning of the divergence of the series. A summability method or summation method is a partial function from the set of series to values. For example, Cesàro summation assigns Grandi's divergent series

 * $$1 - 1 + 1 - 1 + \cdots$$

the value $1⁄2$. Cesàro summation is an averaging method, in that it relies on the arithmetic mean of the sequence of partial sums. Other methods involve analytic continuations of related series. In physics, there are a wide variety of summability methods; these are discussed in greater detail in the article on regularization.

History
Before the 19th century, divergent series were widely used by Leonhard Euler and others, but often led to confusing and contradictory results. A major problem was Euler's idea that any divergent series should have a natural sum, without first defining what is meant by the sum of a divergent series. Augustin-Louis Cauchy eventually gave a rigorous definition of the sum of a (convergent) series, and for some time after this, divergent series were mostly excluded from mathematics. They reappeared in 1886 with Henri Poincaré's work on asymptotic series. In 1890, Ernesto Cesàro realized that one could give a rigorous definition of the sum of some divergent series, and defined Cesàro summation. (This was not the first use of Cesàro summation, which was used implicitly by Ferdinand Georg Frobenius in 1880; Cesàro's key contribution was not the discovery of this method, but his idea that one should give an explicit definition of the sum of a divergent series.) In the years after Cesàro's paper, several other mathematicians gave other definitions of the sum of a divergent series, although these are not always compatible: different definitions can give different answers for the sum of the same divergent series; so, when talking about the sum of a divergent series, it is necessary to specify which summation method one is using.

Examples

 * 1 - 1 + 1 - 1 + ⋯$$\text{ “ = ” }\frac{1}{2}$$
 * 1 − 2 + 3 − 4 + ⋯$$\text{ “ = ” }\frac{1}{4}$$
 * 1 − 1 + 2 − 6 + 24 − 120 + ⋯$$\text{ “ = ” }\!\!\int_0^\infty \frac{e^{-x}}{1+x} \, dx \approx 0.596\,347\ldots$$
 * 1 − 2 + 4 − 8 + ⋯$$\text{ “ = ” }\frac{1}{3}$$
 * 1 + 2 + 4 + 8 + ⋯$$\text{ “ = ” }-1$$
 * 1 + 1 + 1 + 1 + ⋯$$\text{ “ = ” }-\frac{1}{2}$$
 * 1 + 2 + 3 + 4 + ⋯$$\text{ “ = ” }-\frac{1}{12}$$

Theorems on methods for summing divergent series
A summability method M is regular if it agrees with the actual limit on all convergent series. Such a result is called an Abelian theorem for M, from the prototypical Abel's theorem. More subtle, are partial converse results, called Tauberian theorems, from a prototype proved by Alfred Tauber. Here partial converse means that if M sums the series Σ, and some side-condition holds, then Σ was convergent in the first place; without any side-condition such a result would say that M only summed convergent series (making it useless as a summation method for divergent series).

The function giving the sum of a convergent series is linear, and it follows from the Hahn–Banach theorem that it may be extended to a summation method summing any series with bounded partial sums. This is called the Banach limit. This fact is not very useful in practice, since there are many such extensions, inconsistent with each other, and also since proving such operators exist requires invoking the axiom of choice or its equivalents, such as Zorn's lemma. They are therefore nonconstructive.

The subject of divergent series, as a domain of mathematical analysis, is primarily concerned with explicit and natural techniques such as Abel summation, Cesàro summation and Borel summation, and their relationships. The advent of Wiener's tauberian theorem marked an epoch in the subject, introducing unexpected connections to Banach algebra methods in Fourier analysis.

Summation of divergent series is also related to extrapolation methods and sequence transformations as numerical techniques. Examples of such techniques are Padé approximants, Levin-type sequence transformations, and order-dependent mappings related to renormalization techniques for large-order perturbation theory in quantum mechanics.

Properties of summation methods
Summation methods usually concentrate on the sequence of partial sums of the series. While this sequence does not converge, we may often find that when we take an average of larger and larger numbers of initial terms of the sequence, the average converges, and we can use this average instead of a limit to evaluate the sum of the series. A summation method can be seen as a function from a set of sequences of partial sums to values. If A is any summation method assigning values to a set of sequences, we may mechanically translate this to a series-summation method AΣ that assigns the same values to the corresponding series. There are certain properties it is desirable for these methods to possess if they are to arrive at values corresponding to limits and sums, respectively.

 * Regularity. A summation method is regular if, whenever the sequence s converges to x, A(s) = x. Equivalently, the corresponding series-summation method evaluates AΣ(a) = x.
 * Linearity. A is linear if it is a linear functional on the sequences where it is defined, so that A(k r + s) = k A(r) + A(s) for sequences r, s and a real or complex scalar k. Since the terms an+1 = sn+1 − sn of the series a are linear functionals on the sequence s and vice versa, this is equivalent to AΣ being a linear functional on the terms of the series.
 * Stability (also called translativity). If s is a sequence starting from s0 and s′ is the sequence obtained by omitting the first value and subtracting it from the rest, so that s′n = sn+1 − s0, then A(s) is defined if and only if A(s′) is defined, and A(s) = s0 + A(s′). Equivalently, whenever a′n = an+1 for all n, then AΣ(a) = a0 + AΣ(a′). Another way of stating this is that the shift rule must be valid for the series that are summable by this method.

The third condition is less important, and some significant methods, such as Borel summation, do not possess it.

One can also give a weaker alternative to the last condition.
 * Finite re-indexability. If a and a′ are two series such that there exists a bijection $$ f: \mathbb{N} \rightarrow \mathbb{N} $$ such that ai = a′f(i) for all i, and if there exists some $$ N \in \mathbb{N} $$ such that ai = a′i for all i > N, then AΣ(a) = AΣ(a′).  (In other words, a′ is the same series as a, with only finitely many terms re-indexed.)  This is a weaker condition than stability, because any summation method that exhibits stability also exhibits finite re-indexability, but the converse is not true.)

A desirable property for two distinct summation methods A and B to share is consistency: A and B are consistent if for every sequence s to which both assign a value, A(s) = B(s). (Using this language, a summation method A is regular iff it is consistent with the standard sum Σ.) If two methods are consistent, and one sums more series than the other, the one summing more series is stronger.

There are powerful numerical summation methods that are neither regular nor linear, for instance nonlinear sequence transformations like Levin-type sequence transformations and Padé approximants, as well as the order-dependent mappings of perturbative series based on renormalization techniques.

Taking regularity, linearity and stability as axioms, it is possible to sum many divergent series by elementary algebraic manipulations. This partly explains why many different summation methods give the same answer for certain series.

For instance, whenever r ≠ 1, the geometric series
 * $$\begin{align}

G(r,c) & = \sum_{k=0}^\infty cr^k & & \\ & = c + \sum_{k=0}^\infty cr^{k+1} & & \text{ (stability) } \\ & = c + r \sum_{k=0}^\infty cr^k & & \text{ (linearity) } \\ & = c + r \, G(r,c), & & \text{ hence } \\ G(r,c) & = \frac{c}{1-r} ,\text{ unless it is infinite} & & \\ \end{align}$$ can be evaluated regardless of convergence. More rigorously, any summation method that possesses these properties and which assigns a finite value to the geometric series must assign this value. However, when r is a real number larger than 1, the partial sums increase without bound, and averaging methods assign a limit of infinity.

Classical summation methods
The two classical summation methods for series, ordinary convergence and absolute convergence, define the sum as a limit of certain partial sums. These are included only for completeness; strictly speaking they are not true summation methods for divergent series since, by definition, a series is divergent only if these methods do not work. Most but not all summation methods for divergent series extend these methods to a larger class of sequences.

Absolute convergence
Absolute convergence defines the sum of a sequence (or set) of numbers to be the limit of the net of all partial sums ak 1 + ... + ak n, if it exists. It does not depend on the order of the elements of the sequence, and a classical theorem says that a sequence is absolutely convergent if and only if the sequence of absolute values is convergent in the standard sense.

Sum of a series
Cauchy's classical definition of the sum of a series a0 + a1 + ... defines the sum to be the limit of the sequence of partial sums a0 + ... + an. This is the default definition of convergence of a sequence.

Nørlund means
Suppose pn is a sequence of positive terms, starting from p0. Suppose also that
 * $$\frac{p_n}{p_0+p_1 + \cdots + p_n} \rightarrow 0.$$

If now we transform a sequence s by using p to give weighted means, setting
 * $$t_m = \frac{p_m s_0 + p_{m-1}s_1 + \cdots + p_0 s_m}{p_0+p_1+\cdots+p_m}$$

then the limit of tn as n goes to infinity is an average called the Nørlund mean Np(s).

The Nørlund mean is regular, linear, and stable. Moreover, any two Nørlund means are consistent.

Cesàro summation
The most significant of the Nørlund means are the Cesàro sums. Here, if we define the sequence pk by
 * $$p_n^k = {n+k-1 \choose k-1}$$

then the Cesàro sum Ck is defined by Ck(s) = N( pk )(s). Cesàro sums are Nørlund means if k ≥ 0, and hence are regular, linear, stable, and consistent. C0 is ordinary summation, and C1 is ordinary Cesàro summation. Cesàro sums have the property that if h > k, then Ch is stronger than Ck.

Abelian means
Suppose λ = {λ0, λ1, λ2,...} is a strictly increasing sequence tending towards infinity, and that λ0 ≥ 0. Suppose
 * $$f(x) = \sum_{n=0}^\infty a_n e^{-\lambda_n x}$$

converges for all real numbers x > 0. Then the Abelian mean Aλ is defined as
 * $$A_\lambda(s) = \lim_{x \rightarrow 0^{+}} f(x).$$

More generally, if the series for f only converges for large x but can be analytically continued to all positive real x, then one can still define the sum of the divergent series by the limit above.

A series of this type is known as a generalized Dirichlet series; in applications to physics, this is known as the method of heat-kernel regularization.

Abelian means are regular and linear, but not stable and not always consistent between different choices of λ. However, some special cases are very important summation methods.

Abel summation
If λn = n, then we obtain the method of Abel summation. Here

 * $$f(x) = \sum_{n=0}^\infty a_n e^{-nx} = \sum_{n=0}^\infty a_n z^n,$$

where z = exp(−x). Then the limit of f(x) as x approaches 0 through positive reals is the limit of the power series for f(z) as z approaches 1 from below through positive reals, and the Abel sum A(s) is defined as

 * $$A(s) = \lim_{z \rightarrow 1^{-}} \sum_{n=0}^\infty a_n z^n.$$

Abel summation is interesting in part because it is consistent with but more powerful than Cesàro summation: A(s) = Ck(s) whenever the latter is defined. The Abel sum is therefore regular, linear, stable, and consistent with Cesàro summation.

Lindelöf summation
If λn = n log(n), then (indexing from one) we have

 * $$f(x) = a_1 + a_2 2^{-2x} + a_3 3^{-3x} + \cdots .$$

Then L(s), the Lindelöf sum, is the limit of f(x) as x goes to positive zero. The Lindelöf sum is a powerful method when applied to power series among other applications, summing power series in the Mittag-Leffler star.

If g(z) is analytic in a disk around zero, and hence has a Maclaurin series G(z) with a positive radius of convergence, then L(G(z)) = g(z) in the Mittag-Leffler star. Moreover, convergence to g(z) is uniform on compact subsets of the star.

Analytic continuation
Several summation methods involve taking the value of an analytic continuation of a function.

Analytic continuation of power series
If Σanxn converges for small complex x and can be analytically continued along some path from x = 0 to the point x = 1, then the sum of the series can be defined to be the value at x = 1. This value may depend on the choice of path. One of the first examples of potentially different sums for a divergent series, using analytic continuation, was given by Callet, who observed that if $$1 \leq m < n$$ then

$$\frac{1-x^m}{1-x^n} = \frac{1 + x + \dots + x^{m-1}}{1 + x + \dots x^{n-1}} = 1 - x^m + x^n - x^{n+m} + x^{2n} - \dots$$

Evaluating at $$x=1 $$, one gets

$$1 - 1 + 1 - 1 + \dots = \frac{m}{n} .$$

However, the gaps in the series are key. For $$m=1, n=3$$ for example, we actually would get

$$1-1+0+1-1+0+1-1+\dots = \frac{1}{3} $$, so different sums correspond to different placements of the $$0 $$'s.

Another example of analytic continuation is the divergent alternating series $$ \sum_{k \ge 0} (-1)^{k+1}\frac{1}{2k-1}\binom{2k}{k} =1+2-2+4-10+28-84+264-858+2860-9724+\cdots $$ which is a sum over products of $$\Gamma$$-functions and Pochhammer's symbols. Using the duplication formula of the $$\Gamma$$-function, it reduces to a generalized hypergeometric series $$ \ldots = \sum_{k \ge 0} (-4)^k\frac{(-1/2)_k}{k!} ={}_1F_0(-1/2;;-4) = \sqrt{5}. $$

Euler summation
Euler summation is essentially an explicit form of analytic continuation. If a power series converges for small complex z and can be analytically continued to the open disk with diameter from $−1⁄q + 1$ to 1 and is continuous at 1, then its value at q is called the Euler or (E,q) sum of the series Σan. Euler used it before analytic continuation was defined in general, and gave explicit formulas for the power series of the analytic continuation.

The operation of Euler summation can be repeated several times, and this is essentially equivalent to taking an analytic continuation of a power series to the point z = 1.

Analytic continuation of Dirichlet series
This method defines the sum of a series to be the value of the analytic continuation of the Dirichlet series

 * $$f(s) = \frac{a_1}{1^s} + \frac{a_2}{2^s} + \frac{a_3}{3^s}+ \cdots $$

at s = 0, if this exists and is unique. This method is sometimes confused with zeta function regularization.

If s = 0 is an isolated singularity, the sum is defined by the constant term of the Laurent series expansion.

Zeta function regularization
If the series

 * $$f(s) = \frac{1}{a_1^s} + \frac{1}{a_2^s} + \frac{1}{a_3^s}+ \cdots $$

(for positive values of the an) converges for large real s and can be analytically continued along the real line to s = −1, then its value at s = −1 is called the zeta regularized sum of the series a1 + a2 + ... Zeta function regularization is nonlinear. In applications, the numbers ai are sometimes the eigenvalues of a self-adjoint operator A with compact resolvent, and f(s) is then the trace of A−s. For example, if A has eigenvalues 1, 2, 3, ... then f(s) is the Riemann zeta function, ζ(s), whose value at s = −1 is −$1⁄12$, assigning a value to the divergent series 1 + 2 + 3 + 4 + .... Other values of s can also be used to assign values for the divergent sums ζ(0) = 1 + 1 + 1 + ... = −$1⁄2$, ζ(−2) = 1 + 4 + 9 + ... = 0 and in general
 * $$\zeta(-s)=\sum_{n=1}^\infty n^s=1^s + 2^s + 3^s + \cdots = -\frac{B_{s+1}}{s+1}\, ,$$

where Bk is a Bernoulli number.

Integral function means
If J(x) = Σpnxn is an integral function, then the J sum of the series a0 + ... is defined to be
 * $$\lim_{x\rightarrow\infty}\frac{\sum_np_n(a_0+\cdots+a_n)x^n}{\sum_np_nx^n},$$

if this limit exists.

There is a variation of this method where the series for J has a finite radius of convergence r and diverges at x = r. In this case one defines the sum as above, except taking the limit as x tends to r rather than infinity.

Borel summation
In the special case when J(x) = ex this gives one (weak) form of Borel summation.

Valiron's method
Valiron's method is a generalization of Borel summation to certain more general integral functions J. Valiron showed that under certain conditions it is equivalent to defining the sum of a series as
 * $$ \lim_{n\rightarrow +\infty}\sqrt{\frac{H(n)}{2\pi}}\sum_{h\in Z} e^{-\frac12 h^2H(n)}(a_0+\cdots+a_h)$$

where H is the second derivative of G and c(n) = e−G(n), and a0 + ... + ah is to be interpreted as 0 when h < 0.

Moment methods
Suppose that dμ is a measure on the real line such that all the moments

 * $$\mu_n=\int x^n \, d\mu$$

are finite. If a0 + a1 + ... is a series such that

 * $$a(x)=\frac{a_0x^0}{\mu_0}+\frac{a_1x^1}{\mu_1}+\cdots$$

converges for all x in the support of μ, then the (dμ) sum of the series is defined to be the value of the integral

 * $$\int a(x) \, d\mu$$

if it is defined. (If the numbers μn increase too rapidly then they do not uniquely determine the measure μ.)

Borel summation
For example, if dμ = e−x dx for positive x and 0 for negative x then μn = n!, and this gives one version of Borel summation, where the value of a sum is given by
 * $$\int_0^\infty e^{-t}\sum\frac{a_nt^n}{n!} \, dt.$$

There is a generalization of this depending on a variable α, called the (B′,α) sum, where the sum of a series a0 + ... is defined to be

 * $$\int_0^\infty e^{-t}\sum\frac{a_nt^{n\alpha}}{\Gamma(n\alpha+1)} \, dt$$

if this integral exists. A further generalization is to replace the sum under the integral by its analytic continuation from small t.

BGN hyperreal summation
This summation method works by using an extension to the real numbers known as the hyperreal numbers. Since the hyperreal numbers include distinct infinite values, these numbers can be used to represent the values of divergent series. The key method is to designate a particular infinite value that is being summed, usually $$\omega$$, which is used as a unit of infinity. Instead of summing to an arbitrary infinity (as is typically done with $$\infty$$), the BGN method sums to the specific hyperreal infinite value labeled $$\omega$$. Therefore, the summations are of the form

 * $$\sum_{x=1}^\omega f(x)$$

This allows the usage of standard formulas for finite series such as arithmetic progressions in an infinite context. For instance, using this method, the sum of the progression $$1 + 2 + 3 + \ldots$$ is $$\frac{\omega^2}{2} + \frac{\omega}{2}$$, or, using just the most significant infinite hyperreal part, $$\frac{\omega^2}{2}$$.

Hausdorff transformations
.

Hutton's method
In 1812 Hutton introduced a method of summing divergent series by starting with the sequence of partial sums, and repeatedly applying the operation of replacing a sequence s0, s1, ... by the sequence of averages $s_{0} + s_{1}⁄2$, $s_{1} + s_{2}⁄2$, ..., and then taking the limit.

Ingham summability
The series a1 + ... is called Ingham summable to s if

 * $$\lim_{x\rightarrow \infty} \sum_{1\le n\le x} a_n\frac{n}{x}\left[\frac{x}{n}\right] = s.$$

Albert Ingham showed that if δ is any positive number then (C,−δ) (Cesàro) summability implies Ingham summability, and Ingham summability implies (C,δ) summability.

Lambert summability
The series a1 + ... is called Lambert summable to s if
 * $$\lim_{y\rightarrow 0^+} \sum_{n\ge 1} a_n\frac{nye^{-ny}}{1-e^{-ny}} = s. $$

If a series is (C,k) (Cesàro) summable for any k then it is Lambert summable to the same value, and if a series is Lambert summable then it is Abel summable to the same value.

Le Roy summation
The series a0 + ... is called Le Roy summable to s if

 * $$\lim_{\zeta\rightarrow 1^-} \sum_{n} \frac{\Gamma(1+\zeta n)}{\Gamma(1+ n)} a_n = s. $$

Mittag-Leffler summation
The series a0 + ... is called Mittag-Leffler (M) summable to s if
 * $$\lim_{\delta\rightarrow 0} \sum_{n} \frac{a_n}{\Gamma(1+\delta n)} = s.$$

Ramanujan summation
Ramanujan summation is a method of assigning a value to divergent series used by Ramanujan and based on the Euler–Maclaurin summation formula. The Ramanujan sum of a series f(0) + f(1) + ... depends not only on the values of f at integers, but also on values of the function f at non-integral points, so it is not really a summation method in the sense of this article.

Riemann summability
The series a1 + ... is called (R,k) (or Riemann) summable to s if

 * $$\lim_{h\rightarrow 0} \sum_{n} a_n\left(\frac{\sin nh}{nh}\right)^k = s.$$

The series a1 + ... is called R2 summable to s if

 * $$\lim_{h\rightarrow 0} \frac{2}{\pi}\sum_n \frac{\sin^2 nh}{n^2h}(a_1+\cdots + a_n) = s.$$

Riesz means
If λn form an increasing sequence of real numbers and

 * $$A_\lambda(x)=a_0+\cdots+a_n \text{ for } \lambda_n<x\le \lambda_{n+1}$$

then the Riesz (R,λ,κ) sum of the series a0 + ... is defined to be

 * $$\lim_{\omega\rightarrow\infty} \frac{\kappa}{\omega^\kappa} \int_0^\omega A_\lambda(x)(\omega-x)^{\kappa-1} \, dx.$$

Vallée-Poussin summability
The series a1 + ... is called VP (or Vallée-Poussin) summable to s if

 * $$\lim_{m\rightarrow \infty} \sum_{k=0}^{m} a_k\frac{[\Gamma(m+1)]^2}{\Gamma(m+1-k)\,\Gamma(m+1+k)} = \lim_{m\rightarrow \infty} \left[a_0+a_1\frac{m}{m+1}+a_2\frac{m(m-1)}{(m+1)(m+2)}+\cdots\right] = s, $$

where $$\Gamma(x)$$ is the gamma function.

Zeldovich summability
The series is Zeldovich summable if

 * $$\lim_{\alpha\to 0^+}\sum_n c_n e^{-\alpha n^2} = s.$$

title: Divergent series


text:
Melisende Psalter

The Melisende Psalter (London, British Library, Egerton MS 1139) is an illuminated manuscript commissioned around 1135 in the crusader Kingdom of Jerusalem, probably by King Fulk for his wife Queen Melisende. It is a notable example of Crusader art, which resulted from a merging of the artistic styles of Roman Catholic Europe, the Eastern Orthodox Byzantine Empire and the art of the Armenian illuminated manuscript.

Seven scribes and illuminators, working in the scriptorium built by the crusaders in the Church of the Holy Sepulchre in Jerusalem, were involved in the creation of the psalter. It measures 21.6 centimetres by 14 centimetres.

This manuscript forms part of the Egerton Collection in the British Library in London.

The New Testament cycle
The first twenty-four illustrations (on each side of the first twelve folios) depict scenes from the New Testament. New Testament images were commonly found at the beginning of western psalters, unlike in eastern psalters, but in this case the images depict scenes more common in the Eastern Orthodox liturgy. The scenes depicted are the Annunciation, Visitation, the Nativity, the Adoration of the Magi, the Presentation of Jesus at the Temple, the Baptism of Jesus, the Temptation of Christ, the Transfiguration, the Raising of Lazarus, the triumphal entry into Jerusalem (see illustration), the Last Supper, the Washing of the Feet, the Agony in the Garden, the Betrayal of Judas, the Crucifixion of Jesus, the Descent from the Cross, the Lamentation, the Harrowing of Hell, the Three Marys at the Tomb, and the Deesis.

These illustrations were made by an illuminator named Basilius, who signed the last illustration (pictured above) Basilius me fecit (Latin for "Basilius made me"), and is the only named illuminator or scribe of this manuscript. Nothing is known about Basilius, but because of his Greek name it has been suggested that he was a Byzantine artist; it is also possible that he was a western artist who had been trained in a Greek style, maybe in Constantinople; or he may have been an Armenian Catholic, familiar with both Catholic and Orthodox traditions.

The calendar
Folios 13-21 contain the calendar, which is strikingly similar to psalter calendars produced in England in the same period. It appears to be based on a calendar of St. Swithun's church in Winchester. The calendar is filled with English saint days rather than those more popular in Jerusalem, and one name, St. Martin of Tours, a saint popular throughout Europe, is written in gold, for unknown reasons. Three crusader-specific dates are mentioned in the calendar: the capture of Jerusalem on July 15, the death of Baldwin II on August 21, and the death of his wife Morphia on October 1. Each month also has a medallion with a sign of the Zodiac, illustrated in a Romanesque style with heavy Islamic influences.

The psalter
Folios 22-196 contain the Latin psalms written in a northern French script. A third illuminator painted the initial letters of each psalm. Some initials take up the entire side of a leaf, and are drawn with gold lettering on a purple background. They show influence from Italian and Islamic art, possibly suggesting that the artist was trained in Muslim-influenced southern Italy.

Prayers to the saints
The scribe who wrote the psalms also wrote a series of prayers on folios 197–211, dedicated to nine saints: the Virgin Mary, St. Michael, St. John the Baptist, St. Peter, St. John the Evangelist, St. Stephen, St. Nicholas, St. Mary Magdalene, and St. Agnes. The prayers are accompanied by paintings of the saints by a fourth illuminator trained in a Romanesque style, but his technique also shows an attempt to incorporate a Byzantine style. There are a few blank and undecorated spaces in this section of the psalter, and it may be incomplete.

The covers
The ivory covers, decorated with some small turquoise beads, show scenes from the life of King David and from the Psychomachia of Prudentius on the front side, and another king performing the six works of mercy from the Gospel of Matthew on the back side, both showing influence from Byzantine, Islamic, and western art. The geometric designs on the covers are especially influenced by Islamic art. The king on the back side is dressed in Byzantine imperial clothes, but most likely represents a crusader king, perhaps Fulk. There is a carving of a falcon above him, which is possibly a clue that the king is Fulk, as "falcon" and "Fulk" in Old French were both Fouque. Another bird name,, was possibly also implied here as a pun on the king's name. Underneath the falcon, the word is carved, Latin for gyrfalcon. The artist has not signed in the same way Basilius has.

The spine of the psalter is decorated with Byzantine silk and silver thread, as well as red, blue, and green Greek crosses (which are also found in the royal arms of the kingdom). The spine was stitched by an artisan who was perhaps a westerner trained in a Byzantine style, as his stitching is not as smooth as other examples of Byzantine silk spines made by native Greeks.

Date and recipient
The exact date of the psalter, and for whom it was made, is unknown, although it is obviously made for a noblewoman of the kingdom, based on the use of Byzantine styles (considered to be "aristocratic" by the crusaders), the depictions of kings, and the use of feminine word endings in the Latin prayers. Through circumstantial evidence Queen Melisende can probably be identified as the recipient. The English influence in the calendar and elsewhere likely comes from King Fulk, who was related to the English royal family by marriage. It is also notable that aside from the capture of Jerusalem, the only crusader-specific dates in the calendar are the deaths of Melisende's parents, King Baldwin II and Queen Morphia. The mixture of Catholic and Orthodox elements in the psalter may reflect Melisende's mixed upbringing (Baldwin was Catholic and Morphia was an Armenian of the Greek Orthodox faith).

If Melisende was indeed the recipient, then the psalter was most likely commissioned by Fulk, probably around 1135. Prior to this, Fulk and Melisende had been fighting for superiority in the kingdom, and Melisende had allied with rebels against Fulk; by 1134 they had reconciled, and the psalter had to have been written after 1131, the date of Baldwin II's death. On the other hand, it could have been written anytime before Melisende's death in 1161. Palaeographical comparisons to other texts produced in Jerusalem suggest it was written in the 1140s or even 50s, but the later texts may have used the Melisende Psalter as a source.

The manuscript was perhaps owned by Grande Chartreuse, Grenoble, in the early 19th century. By about 1840 it was owned by Ambroise Comarmond, director of the Museum of Fine Arts of Lyon. Its next owner was Guglielmo Libri (b. 1802, d. 1869), who is most famous for stealing medieval manuscripts from French public libraries; he sold it to the London bookdealers Payne and Foss, who in turn sold to the British Museum in November 1845.

In popular culture
In the historical grand strategy simulation game, Crusader Kings III, the Melisende Psalter is an object the ruler can collect if their spouse or lover is cheating on them, as a reference to Fulk's attempt to win back Melisende's favor with the gift during her affair with Hugh II of Jaffa. It is called 'The Psalter of Cuckoldry', with a description of the detailing of the ivory front and its turquoise beads to define the object as the Melisende Psalter.

title: Melisende Psalter


text:
Kick Off (series)

The Kick Off franchise is a series of football simulation video games created by Dino Dini. Kick Off was published by Anil Gupta's publishing house Anco Software for the Atari ST and Commodore Amiga. First released in 1989, Kick Off was well-received and won awards.

After the release of Kick Off several sequels were released. Player Manager was released in 1990. The game was the first game to combine a management environment (including tactics, league play, transfers, and detailed player attributes) with a football game engine (based on that of Kick Off). Kick Off 2 was released in 1990 as a sequel to Kick Off. The game introduced a number of new features as well as several small alterations.

In 1992, Dino Dini left Anco and signed a contract for Virgin Games, which released Goal! in 1993. Anco released several further editions of the Kick Off series between 1994 and 1997, but these games had little in common with Kick Off and Kick Off 2. In 2001–2003, the KOA collaborated closely with Anco developer Steve Screech in an attempt to relaunch the Kick Off and Player Manager series. Kick Off 2002 was released. Anco started to work on another sequel Kick Off 2004 which reached beta status. The attempt came to a halt when Anco closed in 2003.

History
Kick Off was released in 1989. Kick Off was first developed for the Atari ST and then ported to the Amiga. Several expansion disks were released for Kick Off 2. In 1992, Dino Dini left Anco and signed a contract for Virgin Games, which released Goal! in 1993. Anco released Kick Off 3 in 1994. The game used a side view instead of a top-down view and bore little resemblance to Kick Off 2 apart from the name. Anco Software published the first versions of Kick Off for the Amiga and Atari ST.

Gameplay
With Kick Off the ball did not stick to the player's feet but instead was realistically kicked ahead from the players, in a manner similar to that of Nintendo's Soccer, released in 1985 on the NES. This added a degree of difficulty and skill requirement at the same time. Other attributes, such as action replays, players with different characteristics, different tactics, fouls, yellow cards, red cards, injuries, injury time and various referees with different moods are also featured.

Reception

 * ST Action – Highest accolade they could give.
 * Amiga User Int – "Best computer game ever" 97%
 * The One – "Ultimate soccer simulation" 96%
 * ACE – "Brilliant, BUY BUY BUY" 92%
 * Amiga Format – "Best footy game to have appeared on any machine" 94%
 * ST Format – "What a game! gem to play. Magic" 90%
 * C&VG - "Championship winning material" 95%
 * The Games Machine – "Probably the best sports game ever" 92%
 * Commodore User – "No other footy game can touch it" 90%
 * Amiga Action – "Surpasses all other football games" 93%
 * PCW - "Nothing short of brilliant"
 * New Comp Express – "Computer football event of the year"
 * Zzap!64 – "So realistic, so fun, and soooo addictive" 96%

Awards

 * Awarded UK: 1989 INDIN Best 16 Bit Product
 * Nominated UK: 1989 INDIN Best Programmer (2nd place, the winner was "Bullfrog" for Populous)
 * Awarded 1989 EMAP Images Golden Joystick Award Best 16 Bit Product (EMAP is a major UK magazine publisher)
 * Voted the 7th best game of all time in Amiga Power.

Kick Off 2
In 1990, Kick Off 2 was released by Anco. Kick Off 2 retains the pace and accuracy of Kick Off, with a full size multi directional scrolling pitch and the players, markings, goals etc., in correct proportions. Both teams play the game strictly according to tactics. Players move into position to receive passes and gain possession. The ball, as in real game, travels ahead of the player.

There is a league and a cup tournament with sudden death penalty shoot outs, in case of a draw. The teams in the league are on the whole evenly matched but with different styles of play and the player skills to match, that style. There is an option to load player's team from Player Manager along with player's tactics, to play against another team in a single game or enter league and cup tournament.

The special events selection in the main menu allows data disks to be loaded. Kick Off 2 also provides the facility to change strip colours and on expanded Atari ST's (1 MB or above) there are additional sound effects. The "Action Replay" facility allows goals to be viewed at normal pace or in "Slow Motion" and saved to disk. There are 24 referees and have their own distinctive temperaments.

Super Kick Off
Super Kick Off is one of the follow-ups of Kick Off and Kick Off 2 for the Master System, Game Boy, Mega Drive, and Super Nintendo Entertainment System. Super Kick Off was slower than the original games. The Mega Drive version knocked PGA Tour Golf II from the top of the charts. MegaTech gave the game 94% and a Hyper Game Award, saying that the "feel and playability is unrivalled by any other footy game so far", but criticising the high price of £45.

Goal!
In 1992, a sequel, Kick Off 3, was in development. The game wasn't released in this form though, as Dino Dini left Anco in 1992 for Virgin Games, where he developed Goal!, released in 1993. Goal! featured similar gameplay to Kick Off 2 but also added one-touch passing as seen in Sensible Soccer, player acceleration, and more advanced menu systems and options. Goal! received generally good reviews but did not enjoy the same lasting popularity as Kick Off 2.

Kick Off 3
In 1994, Anco released Kick Off 3 developed by Steve Screech, a totally new game with nothing in common with Kick Off 2. The game didn't receive as good reviews as its predecessors and didn't gain the same popularity. An Atari Jaguar port was in development but never released.

Kick Off 96, 97 & 98
In 1996, Toka Nono released Kick Off 96 for Amiga and Windows. The game received average reviews. In 1997, Kick Off 97 was released for Windows. The game received better reviews than Kick Off 96 but still didn't become popular. Later the same year, Anco released Kick Off 98 for the PC which received poor reviews. In 1998 Kick Off World was released for the original PlayStation, again developed by Toka and published by Funsoft.

Kick Off 2002
In 2001, Steve Screech started a project called Ultimate Kick Off with the help of an early established Kick Off Association. The game was built using the Gamebryo engine, released by Anco in 2002 for PC and Mac with the name Kick Off 2002. The game received poor reviews and only sold 5000 copies. Later a sequel called Kick Off 2004 was planned. It reached beta status but was never released. The project ended when Anco closed in 2003.

Kick Off Revival
A new entry in the series, with a control system designed for the use with an analog stick, Kick Off Revival, was released in June 2016 for PlayStation 4 with poor reviews from the main game websites. PlayStation Vita version was released nine months later in 2017 with bad reviews. A PC version is available on Steam.

Games in the series
The Kick Off series includes the following games:

Games by Dino Dini:
 * Kick Off (1989)
 * Kick Off 2 (1990)
 * Kick Off 2 1MB (1990)
 * Kick Off Revival (2016)

Games by Steve Screech:
 * Kick Off 97 (1997)
 * Kick Off 3 (1994)
 * Kick Off 2002 (2002)

Expansion disks:
 * Kick Off Extra Time (Data disk) (1989)
 * Kick Off 2: Giants of Europe (Data disk) (1990)
 * Kick Off 2: The Final Whistle (Expansion disk) (1991)
 * Kick Off 2: Return To Europe (Expansion disk) (1991)
 * Kick Off 2: Winning Tactics (Data disk) (1991)
 * Kick Off 2: Super League (Expansion disk) (1991) Games by others:
 * Franco Baresi World Cup Kick Off (1990)
 * Player Manager (1990)
 * Kick Off 2 World Cup 90 (1990)
 * Kick Off 2: Maths Disk (Expansion disk) (1991)
 * Super Kick-Off (1991)
 * Kick Off 98 (1997)

Ports

 * World League Soccer (Super NES)

title: Kick Off (series)


text: User talk:203.98.31.76

title: User talk:203.98.31.76


text:
229 (number)

229 (two hundred [and] twenty-nine) is the natural number following 228 and preceding 230.

In mathematics
It is a prime number, and a regular prime. It is also a full reptend prime, meaning that the decimal expansion of the unit fraction 1/229 repeats periodically with as long a period as possible. With 227 it is the larger of a pair of twin primes, and it is also the start of a sequence of three consecutive squarefree numbers. It is the smallest prime that, when added to the reverse of its decimal representation, yields another prime: 229 + 922 = 1151.

There are 229 cyclic permutations of the numbers from 1 to 7 in which none of the numbers is mapped to its successor (mod 7), 229 rooted tree structures formed from nine carbon atoms, and 229 triangulations of a polygon formed by adding three vertices to each side of a triangle. There are also 229 different projective configurations of type (123123), in which twelve points and twelve lines meet with three lines through each of the points and three points on each of the lines, all of which may be realized by straight lines in the Euclidean plane.

The complete graph K13 has 229 crossings in its straight-line drawing with the fewest possible crossings.

title: 229 (number)


text:
Ministry of Education, Culture, Sports, Science and Technology

The Ministry of Education, Culture, Sports, Science and Technology (文部科学省) is one of the eleven ministries of Japan that composes part of the executive branch of the government of Japan. Its goal is to improve the development of Japan in relation with the international community. The ministry is responsible for funding research under its jurisdiction, some of which includes: children's health in relation to home environment, delta-sigma modulations utilizing graphs, gender equality in sciences, neutrino detection which contributes to the study of supernovas around the world, and other general research for the future.

History
The Meiji government created the first Ministry of Education in 1871. In January 2001, the former Ministry of Education, Science, Sports and Culture and the former Science and Technology Agency (科学技術庁) merged to become the present MEXT.

Organization
The Ministry of Education, Culture, Sports, Science and Technology currently is led by the minister of education, culture, sports, science and technology. Under that position is two state ministers, two parliamentary vice-ministers, and administrative vice-minister, and two deputy ministers. Beyond that the organization is divided as follows.

Minister's Secretariat
The Minister's Secretariat is the department that manages general policies that affect the Ministry of Education, Culture, Sports, Science and Technology as a whole. These functions include many administrative jobs such as auditing policies, community relations, and overall human resource management for domestic and international relations alike.

Director-General for International Affairs
The Director-General for International Affairs, according to Ministry of Education, Culture, Sports, Science and Technology's site, is the main point of contact between Japan's National Commission and United Nations Educational Scientific and Cultural Organization (UNESCO). The collective goal of the two organizations is to create mutual, sustainable development through education, science, and culture.

Department of Facilities Planning and Disaster Prevention
The Department of Facilities Planning and Disaster Prevention is in charge of focusing on the ability of school facilities to reduce damage caused by disasters such as earthquakes. On top of this, Ministry of Education, Culture, Sports, Science and Technology's site, also describes part of their duties as promoting universities' endeavors in educational and research activities.

Education departments
These are the segments of the ministry with focus on the education portions of organization.

Education Policy Bureau
The Education Policy Bureau as a department upholds the concept of lifelong learning, introduced in the Basic Act on Education. Ministry of Education, Culture, Sports, Science and Technology describes this department's duties as designing educational policy based on comprehensive and objective evidence.

Elementary and Secondary Education Bureau
The Elementary and Secondary Education Bureau is in charge of enhancing the educational development of students progressing through preschool to upper secondary schools, or any equivalent.

Higher Education Bureau
The Ministry of Education, Culture, Sports, Science and Technology describes the Higher Education Bureau as a department that focuses on promoting the education of undergraduate and graduate schools. This includes overseeing permission of grants, teacher quality, as well as the selection and admission of both domestic and abroad students.

Sports and culture departments
These are the segments of the ministry with focus on the sports and culture portions of organization.

Japan Sports Agency
The Japan Sports Agency is tasked with the promotion of physical education and health, as well as maintaining the country's ability to compete in international athletics.

Agency for Cultural Affairs
The Japanese Agency for Cultural Affairs tries to create a culture in the country that encourages participation in cultural activities and the arts. Their goal is to achieve a "Nation Based on Culture and Art".

Science and technology departments
These are the segments of the ministry with focus on the science and technology portions of organization.

Science and Technology Policy Bureau
The Ministry of Education, Culture, Sports, Science and Technology's site regards the duties of the Science and Technology Policy Bureau as the department in charge of the promotion of science and technology in the country. The scope of the department includes students as well as established professionals.

Research Promotion Bureau
The Research Promotion Bureau is a department that focuses on development of scientific research, as well as research in fields including technology and physics.

Research and Development Bureau
The Research and Development Bureau is slightly different from the Research Promotion Bureau as this department focuses on social problems including energy and the environment. Consequentially, this department would focus on exploration in space and deep sea.

Activities and funded research
While the Ministry of Education, Culture, Sports, Science and Technology currently contains multiple agencies, primarily a congregation of Education, Culture, Sports, Science and Technology, it actually began as the Ministry of Education. Over the years, Japan separately created each of the agencies that would eventually combine to make the current organization. Nonetheless, each department of the Ministry of Education, Culture, Sports, Science and Technology researches programs and institutions to fund.

Children's health in relation to home environment
During this research, the Ministry of Education, Culture, Sports, Science and Technology concluded there were many intertwined dependencies between family homes, their environment, and how it impacts a child's growth and maturity.

Delta-sigma conversion for graphing
The Ministry of Education, Culture, Sports, Science and Technology have also been responsible in directly, although not fully, funding research into delta-sigma modulation, which in summary describes the graphing of analog-digital information to aid in the conversion of the two means.

Educational research
The Ministry of Education, Culture, Sports, Science and Technology, were able to get their funding increased successfully through the years. They did so with the aid of one of their subgroups, the Japan Society for the Promotion of Science. The additional funds were likely aided in approval due to their source coming from national bonds rather than taxes. The programs, funded by the increased budget, include projects in new materials, molecular-scale surface dynamics, next-generation process technology, computer science, synthesis-based chemical engineering science, micro-mechatronics (micromachinery), biotechnology, human genome research, cell signaling, bioinformatics, brain research, Structural biology, life sciences, developmental biology, and biomedical engineering.

Educational programs
MEXT is one of three ministries that run the JET Programme. It also offers the Monbukagakusho Scholarship, also known as the MEXT or Monbu-shō scholarship. The Ministry sets standards for the romanization of Japanese.

In cooperation with the Japanese Student Services Organization (JASSO), the ministry further funds the prestigious JASSO scholarship for international students which has been described as the "Japanese Fulbright program". It offers financial support of up to 80.000¥ per month for the top 1% of students of any foreign country for studies at a Japanese university.

MEXT provides the Children Living Abroad and Returnees Internet (CLARINET) which provides information to Japanese families living abroad.

MEXT sends teachers around the world to serve in nihonjin gakkō, full-time Japanese international schools in foreign countries. The Japanese government also sends full-time teachers to hoshū jugyō kō supplementary schools that offer lessons that are similar to those of nihonjin gakkō or those which each have student bodies of 100 students or greater. In addition, MEXT subsidizes weekend schools which each have over 100 students.

Japanese Government MEXT scholarship 2022 Japanese Government MEXT Scholarship 2021 Embassy Recommendation. The scholarship programs are for students who wish to study in Japan as Research Student (Masters/Ph.D./ Research), Undergraduate student, College of Technology student, or Specialized Training student.


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Wikipedia:Articles for deletion/Beaumanor Garats HaY ARS

Beaumanor Garats HaY ARS 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.

Advertisement --Rlandmann 23:32, 3 Aug 2004 (UTC) This page is now preserved as an archive of the debate and, like other '/delete' pages 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.
 * Delete: Ad for a social hall/club. Geogre 01:32, 4 Aug 2004 (UTC)
 * Delete: advert, and what's more, a copy-'n'-paste from http://beaumanor.hosted.pipemedia.net/info.htm TPK 06:56, 4 Aug 2004 (UTC)
 * I redirected it before to Beaumanor Hall, which is where they are and most of the content of which was provided by the guy from this group. They possibly deserve a mention in Beaumanor Hall, but are not deserving of a Wikipedia article.  Delete nicely with thanks for info at Beaumanor Hall. Dunc_Harris|☺ 15:55, 4 Aug 2004 (UTC)
 * the previous copy and paste was at Beaumanor & Garats HaY Amateur Radio Society Dunc_Harris|☺ 15:58, 4 Aug 2004 (UTC)


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Jewish mysticism

Academic study of Jewish mysticism, especially since Gershom Scholem's Major Trends in Jewish Mysticism (1941), draws distinctions between different forms of mysticism which were practiced in different eras of Jewish history. Of these, Kabbalah, which emerged in 12th-century southwestern Europe, is the most well known, but it is not the only typological form, nor was it the first form which emerged. Among the previous forms were Merkabah mysticism (c. 100 BCE – 1000 CE), and Ashkenazi Hasidim (early 13th century) around the time of the emergence of Kabbalah.

Kabbalah means "received tradition", a term which was previously used in other Judaic contexts, but the Medieval Kabbalists adopted it as a term for their own doctrine in order to express the belief that they were not innovating, but were merely revealing the ancient hidden esoteric tradition of the Torah. This issue has been crystalized until today by alternative views on the origin of the Zohar, the main text of Kabbalah, attributed to the circle of its central protagonist Rabbi Shimon Bar Yochai in the 2nd century CE, for opening up the study of Jewish Mysticism. Traditional Kabbalists regard it as originating in Tannaic times, redacting the Oral Torah, so do not make a sharp distinction between Kabbalah and early Rabbinic Jewish mysticism. Academic scholars regard it as a synthesis from the Middle Ages, when it appeared between the 13th-15th centuries, but assimilating and incorporating into itself earlier forms of Jewish mysticism, possible continuations of ancient esoteric traditions, as well as medieval philosophical elements.

The theosophical aspect of Kabbalah itself developed through two historical forms: "Medieval/Classic/Zoharic Kabbalah" (c.1175 – 1492 – 1570), and Lurianic Kabbalah (1569 – today) which assimilated Medieval Kabbalah into its wider system and became the basis for modern Jewish Kabbalah. After Luria, two new mystical forms popularised Kabbalah in Judaism: antinomian-heretical Sabbatean movements (1666 – 18th century), and Hasidic Judaism (1734 – today). In contemporary Judaism, the only main forms of Jewish mysticism which are practiced are esoteric Lurianic Kabbalah and its later commentaries, the variety of schools of Hasidic Judaism, and Neo-Hasidism (incorporating Neo-Kabbalah) in non-Orthodox Jewish denominations.

Two non-Jewish syncretic traditions also popularized Judaic Kabbalah through their incorporation as part of general Western esoteric culture from the Renaissance onwards: theological Christian Cabala (c. 15th – 18th century) which adapted Judaic Kabbalistic doctrine to Christian belief, and its diverging occultist offshoot Hermetic Qabalah (c. 19th century – today) which became a main element in esoteric and magical societies and teachings. As separate traditions of development outside Judaism, drawing from, syncretically adapting, and different in nature and aims from Judaic mysticism, they are not listed on this page.

Three aims
The Kabbalistic form of Jewish mysticism itself is divided into three general streams: the Theosophical/Speculative Kabbalah (seeking to understand and describe the divine realm), the Meditative/Ecstatic Kabbalah (seeking to achieve a mystical union with God), and the Practical Kabbalah (seeking to theurgically alter the divine realms and the World). These three different, but inter-relating, methods or aims of mystical involvement are also found throughout the other pre-Kabbalistic and post-Kabbalistic stages in Jewish mystical development, as three general typologies. As in Kabbalah, the same text can contain aspects of all three approaches, though the three streams often distill into three separate literatures under the influence of particular exponents or eras.

Within Kabbalah, the theosophical tradition is distinguished from many forms of mysticism in other religions by its doctrinal form as a mystical "philosophy" of Gnosis esoteric knowledge. Instead, the tradition of Meditative Kabbalah has similarity of aim, if not form, with usual traditions of general mysticism; to unite the individual intuitively with God. The tradition of theurgic Practical Kabbalah in Judaism, censored and restricted by mainstream Jewish Kabbalists, has similarities with non-Jewish Hermetic Qabalah magical Western Esotericism. However, as understood by Jewish Kabbalists, it is censored and forgotten in contemporary times because without the requisite purity and holy motive, it would degenerate into impure and forbidden magic. Consequently, it has formed a minor tradition in Jewish mystical history.

title: Jewish mysticism


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Lawrence Aubrey Wallace

Sir Lawrence Aubrey Wallace  (2 February 1857 - 26 February 1942) was a British colonial administrator. He was administrator of North-Eastern Rhodesia from April 1907 to January 1909, administrator of Barotziland-North-Western Rhodesia from January 1909 to August 1911, and administrator of Northern Rhodesia from August 1911 until March 1921.

He made an exploratory journey round Lake Tanganyika in August 1897, for which he received the Back Award of the Royal Geographical Society in 1912.

He died on 26 February 1942 in Le Mans due to natural causes. He's buried in the Grand Cimetière, Le Mans.

Works

 * 'The Beginnings of Native Administration in Northern Rhodesia', Journal of the African Society, 16 (1922), pp. 165–176
 * 'Rhodesia', in The dominions and dependencies of the Empire. Vol. I of Hugh Gunn, ed., The British Empire: A survey, Collins, 1924
 * 'Northern Rhodesia and the last phase of the war in Africa'. In vol. 4 (1926) of Charles Prestwood Lucas, ed., The Empire at War, Oxford University Press, 1921–26.

title: Lawrence Aubrey Wallace


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Immanuel Jakobovits, Baron Jakobovits

Immanuel Jakobovits, Baron Jakobovits (8 February 1921 – 31 October 1999) was the Chief Rabbi of the United Hebrew Congregations of the Commonwealth from 1967 to 1991. Prior to this, he had served as Chief Rabbi of Ireland and as rabbi of the Fifth Avenue Synagogue in New York City. In addition to his official duties he was regarded as an authority in medical ethics from a Jewish standpoint. He was knighted in 1981 and became the first Chief Rabbi to enter the House of Lords in 1988 as Baron Jakobovits.

Biography
Jakobovits was born in Königsberg, East Prussia, Germany (now Kaliningrad, Russia), where his father Julius (Yoel) was a community rabbi. The family moved to Berlin in the 1920s, where his father became rabbinical judge on the beth din of the Grossgemeinde, but fled Germany in 1938 to escape Nazi persecutions. In the United Kingdom he completed his higher education, including a period at the Etz Chaim Yeshiva in London, studying under and receiving semicha (rabbi ordination) from the Rabbis Elya Lopian, Leib Gurwicz and Nachman Shlomo Greenspan. He also studied in Jews' College and the University of London (BA and PhD, University College).

He married Amélie Munk of Paris, the daughter of a prominent rabbi, who would support his community work throughout his life. The couple had six children. Lady Jakobovits died in May 2010, and was buried alongside her husband, on Jerusalem's Mount of Olives.

His first position was as rabbi of the Brondesbury synagogue. In 1949, at the relatively young age of 27, he was appointed Chief Rabbi of the declining Jewish community of Ireland. This was to be a stepping stone towards a greater rabbinical career, and in 1958 he assumed the rabbinate of Hermann Merkin's Fifth Avenue Synagogue in New York, a position he held until 1966, when he was called to the Chief Rabbinate of the United Hebrew Congregation of the British Commonwealth. He held this position until his retirement in 1991.

He was knighted on 22 July 1981 and was created a life peer on 5 February 1988, as Baron Jakobovits, of Regent's Park in Greater London, becoming the first rabbi to receive this honour. In 1987 he was given a Lambeth DD by the Archbishop of Canterbury, the first Jew to receive such a degree. In 1991 he received the Templeton Prize for Progress in Religion.

In the House of Lords he became known as a campaigner for traditional morality. Jakobovits aroused considerable controversy when, after the discovery of a possible genetic explanation for homosexuality, he suggested that he saw no "moral objection for using genetic engineering to limit this particular trend". While he did not advocate abortion, he did describe homosexuality as "a grave departure from the natural norm which we are charged to overcome like any other affliction"; if there were genetic explanations for homosexuality, "the errant gene" should be "removed or repaired" to prevent the "disability". In a speech in the House of Lords, Jakovites made a speech saying that homophobia was an invented term that aimed to "uproot existing moral order."

Jakobovits died of a cerebral haemorrhage on 31 October 1999, and was buried on the Mount of Olives in Jerusalem.

Other functions
Jakobovits was also the president of the Conference of European Rabbis, in which capacity he worked on standardising and regulating religious conversion to Judaism.

Ideas and philosophy
Jakobovits was a firm adherent of the "German-Jewish" Torah im Derech Eretz philosophy, having a broad knowledge of religious subjects as well as secular culture and philosophy. This made him a unique spokesperson for Orthodox Judaism, as he was able to transmit ideas to a wide audience which would otherwise not have achieved dissemination.

Jakobovits was the most prominent figure in 20th century Jewish medical ethics, a field he virtually created on his own. He was also a pioneer in religious bioethics. His speciality was the interaction between medical ethics and halakha. Thanks to his academic training in Ireland, Rabbi Jakobovits approached his comprehensive volume, Jewish Medical Ethics, in light of Roman Catholic medical ethics, with which he often compares Jewish ethics. Whether developing or disputing his analysis, subsequent Jewish bioethicists have utilised his work on abortion, euthanasia, the history of Jewish medical ethics, palliative care, treatment of the sick, and professional duties. Likewise, he is credited with popularizing the viewpoint that Judaism supports the nearly absolute sanctity of life.

Jakobovits' political stance was conservative, and he was particularly close to Margaret Thatcher. When a Church of England report titled Faith in the City was published in December 1985 criticising Thatcher's policies, Jakobovits responded by attacking its underlying philosophy. Jakobovits argued that work rather than welfare should be the over-riding aim of government policy: "Cheap labour is better than a free dole". More controversially, he contended that inner-city black people should learn from Jewish experiences in America. There, he argued, Jews had worked themselves out of poverty, educated themselves, integrated into the host culture and nurtured a "trust in and respect for the police, realising that our security as a minority depended on law and order being maintained". Jakobovits also took a conservative view on trade unions, criticised Faith in the City for not mentioning the role of trade unions, arguing that "The selfishness of workers in attempting to secure better conditions at the cost of rising unemployment and immense public misery can be just as morally indefensible as the rapaciousness of the wealthy in exploiting the working class".

Within Judaism, Jakobovits held mildly Zionist views. He maintained that sooner or later Israel would need to negotiate the territory it conquered during the Six-Day War; which made him a controversial figure, as he mentioned these views publicly.

Works

 * Jewish Medical Ethics (1959/1975)
 * Jewish Law Faces Modern Problems (1965)
 * Journal of a Rabbi (1966)
 * The Timely and The Timeless: Jews, Judaism and Society in a Storm-tossed Decade (1977)
 * If Only My People: Zionism in My Life (1984)
 * Dear Chief Rabbi: From the Correspondence of Chief Rabbi Immanuel Jakobovits on Matters of Jewish Law, Ethics and Contemporary Issues, 1980–1990 (1995)
 * Lord Jakobovits in Conversation (2000)

title: Immanuel Jakobovits, Baron Jakobovits