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Rapa Nui language

Rapa Nui or Rapanui (, Rapa Nui:, Spanish: ), also known as Pascuan or Pascuense, is an Eastern Polynesian language of the Austronesian language family. It is spoken on Easter Island, also known as Rapa Nui.

The island is home to a population of just under 6,000 and is a special territory of Chile. According to census data, there are 9,399 people (on both the island and the Chilean mainland) who identify as ethnically Rapa Nui. Census data does not exist on the primary known and spoken languages among these people. In 2008, the number of fluent speakers was reported as low as 800. Rapa Nui is a minority language and many of its adult speakers also speak Spanish. Most Rapa Nui children now grow up speaking Spanish and those who do learn Rapa Nui begin learning it later in life.

History
The Rapa Nui language is isolated within Eastern Polynesian, which also includes the Marquesic and Tahitic languages. Within Eastern Polynesian, it is closest to Marquesan morphologically, although its phonology has more in common with New Zealand Māori, as both languages are relatively conservative in retaining consonants lost in other Eastern Polynesian languages.

Like all Polynesian languages, Rapa Nui has relatively few consonants. Uniquely for an Eastern Polynesian language, Rapa Nui has preserved the original glottal stop of Proto-Polynesian. It is, or until recently was, a verb-initial language.

One of the most important recent books written about the language of Rapa Nui is Verónica du Feu's Rapanui (Descriptive Grammar) (ISBN 0-415-00011-4).

Very little is known about the Rapa Nui language prior to European contact. The majority of Rapa Nui vocabulary is inherited directly from Proto–Eastern Polynesian. Due to extensive borrowing from Tahitian there now often exist two forms for what was the same word in the early language. For example, Rapa Nui has Tahitian alongside original  for 'to see', both derived from Proto-Eastern Polynesian *kitea. There are also hybridized forms of words such as 'to teach', from native  (causative prefix) and Tahitian.

According to archaeologist José Miguel Ramírez "more than a dozen Mapuche - Rapa Nui cognates have been described", chiefly by Sebastian Englert. Among these are the Mapuche/Rapa Nui words toki/toki (axe), kuri/uri (black) and piti/iti (little).

Language notes from 1770 and 1774
Spanish notes from a 1770 visit to the island record 94 words and terms. Many are clearly Polynesian, but several are not easily recognizable. For example, the numbers from one to ten seemingly have no relation to any known language. They are compared with contemporary Rapa Nui words, in parentheses:

 * 1) cojána
 * 2) corena
 * 3) cogojú
 * 4) quirote
 * 5) majaná
 * 6) teúto
 * 7) tejéa
 * 8) moroqui
 * 9) vijoviri
 * 10) queromata-paúpaca quacaxixiva

It may be that the list is a misunderstanding, and the words not related to numbers at all. The Spanish may have shown Arabic numerals to the islanders who did not understand their meaning, and likened them to some other abstraction. For example, the "moroqui" for number eight would have actually been, a small fish that is used as a bait, since "8" can look like a simple drawing of a fish.

Captain James Cook visited the island four years later, and had a Tahitian interpreter with him, who, while recognizing some Polynesian words (up to 17 were written down), was not able to converse with the islanders in general. The British also attempted to record the numerals and were able to record the correct Polynesian words.

Post-Peruvian enslavement
In the 1860s the Peruvian slave raids began, as Peruvians were experiencing labor shortages and came to regard the Pacific as a vast source of free labor. Slavers raided islands as far away as Micronesia, but Rapa Nui was much closer and became a prime target.

In December 1862 eight Peruvian ships landed their crewmen and between bribery and outright violence they captured some 1,000 Rapanui, including the king, his son, and the ritual priests (one of the reasons for so many gaps in knowledge of the ancient ways). It has been estimated that 2,000 Rapanui were captured over a period of years. Those who survived to arrive in Peru were poorly treated, overworked, and exposed to diseases. Ninety percent of the Rapa Nui died within one or two years of capture.

Eventually the Bishop of Tahiti caused a public outcry and an embarrassed Peru rounded up the few survivors to return them. A shipload headed to Rapa Nui, but smallpox broke out en route and only 15 arrived at the island. They were put ashore. The resulting smallpox epidemic nearly wiped out the remaining population.

In the aftermath of the Peruvian slave deportations in the 1860s, Rapa Nui came under extensive outside influence from neighbouring Polynesian languages such as Tahitian. While the majority of the population that was taken to work as slaves in the Peruvian mines died of diseases and bad treatment in the 1860s, hundreds of other Islanders who left for Mangareva in the 1870s and 1880s to work as servants or labourers adopted the local form of Tahitian-Pidgin. Fischer argues that this pidgin became the basis for the modern Rapa Nui language when the surviving part of the Rapa Nui immigrants on Mangareva returned to their almost deserted home island.

Language notes from 1886
William J. Thomson, paymaster on the USS Mohican, spent twelve days on Rapa Nui from 19 to 30 December 1886. Among the data Thomson collected was the Rapa Nui calendar.

Language notes from the twentieth century
Father Sebastian Englert, a German missionary living on Easter Island during 1935–1969, published a partial Rapa Nui–Spanish dictionary in his La Tierra de Hotu Matua in 1948, trying to save what was left of the old language. Despite the many typographical mistakes, the dictionary is valuable, because it provides a wealth of examples which all appear drawn from a real corpus, part oral traditions and legends, part actual conversations.

Englert recorded vowel length, stress, and glottal stop, but was not always consistent, or perhaps the misprints make it seem so. He indicated vowel length with a circumflex, and stress with an acute accent, but only when it does not occur where expected. The glottal stop is written as an apostrophe, but is often omitted. The velar nasal is sometimes transcribed with a $⟨g⟩$, but sometimes with a Greek eta, $⟨η⟩$, as a graphic approximation of ⟨ŋ⟩.

Rongorongo
It is assumed that rongorongo, a possible undeciphered script once used on Rapa Nui, transcribes the old Rapa Nui language if it is indeed a true writing system.

Hispanisation
The island has been under the jurisdiction of Chile since 1888 and is now home to a number of Chilean continentals. The influence of the Spanish language is noticeable in modern Rapa Nui speech. As fewer children learn to speak Rapa Nui at an early age, their superior knowledge of Spanish affects the 'passive knowledge' they have of Rapa Nui. A version of Rapanui interspersed with Spanish nouns, verbs and adjectives has become a popular form of casual speech. The most well integrated borrowings are the Spanish conjunctions (or),  (but) and y (and). Spanish words such as problema (problem), which was once rendered as poroporema, are now often integrated with minimal or no change.

Spanish words are still often used within Rapanui grammatical rules, though some word order changes are occurring and it is argued that Rapanui may be undergoing a shift from VSO to the Spanish SVO. This example sentence was recorded first in 1948 and again in 2001 and its expression has changed from VSO to SVO.

 * 'They both suffer and weep'
 * 1948: he aroha, he tatagi ararua
 * 2001: ararua he aroha he tatagi

Rapa Nui's indigenous Rapanui toponymy has survived with few Spanish additions or replacements, a fact that has been attributed in part to the survival of the Rapa Nui language. This contrasts with the toponymy of continental Chile, which has lost many of its indigenous names.

Phonology
Rapa Nui has ten consonants and five vowels.

Consonants
As present generation Rapa Nui speak Spanish as their first language in younger years and learn Rapa Nui later in life, flap in word-initial position can be pronounced alveolar trill.

Vowels

 * {| class="wikitable" style="text-align: center;"

! ! Front ! Central ! Back ! High ! Mid ! Low
 * }
 * }
 * }
 * }

All vowels can be either long or short and are always long when they are stressed in the final position of a word. Most vowel sequences are present, with the exception of *uo. The only sequence of three identical vowels is, also spelled ('yes').

Syllable structure
Syllables in Rapa Nui are CV (consonant-vowel) or V (vowel). There are no consonant clusters or word-final consonants.

Orthography
Written Rapanui uses the Latin script. The Latin alphabet for Rapanui consists of 20 letters:

 * A, Ā, E, Ē, H, I, Ī, K, M, N, Ŋ, O, Ō, P, R, T, U, Ū, V,

The nasal velar consonant is generally written with the Latin letter $⟨g⟩$, but occasionally as $⟨ng⟩$. In electronic texts, the glottal plosive may be written with a (always lower-case) saltillo $⟨⟩$ to avoid the problems of using the punctuation mark $⟨'⟩$. A special letter, $⟨ġ⟩$, is sometimes used to distinguish the Spanish, occurring in introduced terms, from the Rapa Nui. Similarly, has been written $⟨g̈⟩$ to distinguish it from Spanish $⟨g⟩$. The IPA letter $⟨ŋ⟩$ is now also coming into use.

Reduplication
The reduplication of whole nouns or syllable parts performs a variety of different functions within Rapa Nui. To describe colours for which there is not a predefined word, the noun for an object of a like colour is duplicated to form an adjective. For example:

 * (mist) → (dark grey)
 * (dawn) → (white)

Besides forming adjectives from nouns, the reduplication of whole words can indicate a multiple or intensified action. For example:

 * (weave) → (fold)
 * (undo) → (take to pieces)
 * (dive) → (go diving)

There are some apparent duplicate forms for which the original form has been lost. For example:
 * (tired)

The reduplication of the initial syllable in verbs can indicate plurality of subject or object. In this example the bolded section represents the reduplication of a syllable which indicates the plurality of the subject of a transitive verb:
 * (dance):
 * E ori ro a (he/she/they is/are dancing)
 * E oori ro a (they are all dancing)

The reduplication of the final two syllables of a verb indicates plurality or intensity. In this example the bolded section represents the reduplication of two final syllables, indicating intensity or emphasis:

 * (tell):
 * Ka haaki (Tell the story)
 * Ka haakiaki (Tell the whole story)

Borrowed words
Rapa Nui incorporates a number of borrowed words in which constructions such as consonant clusters or word-final consonants occur, though they do not occur naturally in the language. Historically, the practice was to transliterate unfamiliar consonants, insert vowels between clustered consonants and append word-final vowels where necessary.

 * e.g.: Britain (English loanword) → Peretane (Rapa Nui rendering)

More recently, loanwords – which come primarily from Spanish – retain their consonant clusters. For example, litro (litre).

Word Classes
Rapa Nui can be said to have a basic two-way distinction in its words, much like other Polynesian languages. That is between full words, and particles. Full words occur in the head of the phrase and are mostly open classes (exceptions like locationals exist). Particles occur in fixed positions before or after the head, and have a high frequency. There also exists an intermediate category, Pro-Forms, which occur in the head of a phrase, and can be preceded or followed by a particle. Unlike full words, they do not have lexical meaning, and like particles, form a closed class. Pro-forms include personal, possessive and benefactive pronouns, as well as interrogative words. Additionally, two other intermediate categories are the negator (ina) and the numerals. While both of them form a closed class, they are able to function as phrase nuclei.

Demonstratives
Rapa Nui does not have one class of demonstratives, instead it has four classes of particles with demonstrative functions. Each class is made up of three particles of different degrees of distance; proximal, medial, or distal. This is a three-way distinction, similar to Samoan and Māori, two closely related languages from the same language family. Tongan, by contrast, has a two-way contrast.

Rapa Nui speakers hence distinguish between entities that are close to the speaker (proximal), something at a medium distance or close to the hearer (medial), and something far away, removed from both the speaker and hearer (distal). This is called a person-oriented system, in which one of the demonstratives denotes a referent in proximity of the hearer. For Rapa Nui speakers, that is the medial distinction, //. This system of spatial contrasts and directions is known as spatial deixis, and Rapa Nui is full of ways to express this, be it through locationals, postverbal or postnominal demonstratives, or directionals.

These four classes that function as demonstratives are similar in form, but differ in syntactic status and have certain differences in functions.

Postnominal Demonstratives
The postnominal demonstratives are used to indicate different degrees of distance. They always occur on the right periphery of the noun phrase.

Postnominal demonstratives are obligatory when following a t-demonstrative (tau/tou/tū) unless the noun phrase contains the identity marker ā/ ana. They can also co-occur with other determiners, like articles in this example:

te kona hare era

ART place house DIST

'home' [R210.021]

Postnominal demonstratives can be used deictically or anaphorically. As deictic markers they are used to point at something visible, while as anaphoric markers they refer to entities in discourse context (entities which have been discussed before or are known by other means). In practice, the anaphoric use is much more common.

Distal/Neutral era
is used deictically to point to something at a distance from both speaker and hearer.

¿Hē te haraoa o te poki era?

WH.Q ART bread of ART child DIST

'Where is the bread of that child (over there)?' from [R245.041]

However, it's more common to see used anaphorically, as a general purpose demonstrative. is often found co-occurring with the neutral t-demonstrative determiner, as the general form tau/tou/tū (N) era, and this combination doubles as a common strategy to refer to a participant mentioned earlier in the discourse. So common, that era is the seventh most common word overall in the text corpus.

For example, the two main characters in this story are simply referred to as tau taŋata era 'that man' and tau vi e era 'that woman'.

He moe rō ꞌavai tau taŋata era. He koromaki ki tau viꞌe era toꞌo era e tōꞌona matuꞌa.

NTR {lie down} EMPH certainly DEM man DIST NTR miss to DEM woman DIST take DIST AG POSS.3SG.INAL parent

"The man slept. He longed for the woman that had been taken back by her father." [Mtx-5-02.057-060]

era is also used in combination anaphorically with te, a more conventional determiner instead of a demonstrative determiner. Rapa Nui uses this combination to refer to something which is known to both speaker and hearer, regardless of whether it has been mentioned in the discourse. This means the te N era construction (Where N is a noun), indicates definiteness, making it the closest equivalent to English (or Spanish) definite article, rather than a demonstrative.

Te N era can also be used to refer to entities which are generally known, or presumed to be present in context. In the example, the cliffs refer to the cliffs in general, which can be presumed to be known by all Rapa Nui speakers on Rapa Nui with the coastline being a familiar feature. No specific cliff is meant.

I naꞌa era a {ꞌOho Takatore} i tū kūpeŋa era, he oho mai ki te kona ꞌōpata era.

PFV hide DIST PROP {Oho Takatore} ACC DEM net DIST NTR go hither to ART place cliff DIST

"When Oho Takatore had hidden that net, he went to the cliffs (lit. the cliffplace)." [R304.110]

Deictic Locationals
Deictic locationals utilize the same form as demonstrative determiners (nei, nā, rā). They can be the head of a phrase as they are locationals, and like other locationals they can be preceded by a preposition, but not by a determiner. They indicate distance with respect to the origo, which is either the speaker or the discourse situation.

E vaꞌu mahana i noho ai ꞌi nei.

IPFV eight day PFV stay PVP at PROX

Pronouns
Pronouns are usually marked for number: in Rapa Nui there are markers for first, second and third personal singular and plural; however, there is only a marker for dual in the first person. The first person dual and plural can mark for exclusive and inclusive. The pronouns are always ahead of the person singular (PRS) a and relational particle (RLT) i or dative (DAT) ki. However, in some examples, they do not have PRS, RLT and DAT.

There is only one paradigm of pronouns for Rapa Nui. They function the same in both subject and object cases.

Here is the table for the pronoun forms in Rapa Nui:

Ko au e  noho  mai  ena  hokotahi  no

PRF 1sg STA stay  TOW  PPD  alone  LIM

'I live here all alone'

He haka ai  i  a  ia  he  suerkao

ACT CAUS EXIST  RLT  PRS  3sg  ±SPE  governor

'They made him governor'

Questions
Yes/no questions are distinguished from statements chiefly by a particular pattern of intonation. Where there is no expectation of a particular answer, the form remains the same as a statement. A question expecting an agreement is preceded by.

Conjunction
Original Rapa Nui has no conjunctive particles. Copulative, adversative and disjunctive notions are typically communicated by context or clause order. Modern Rapa Nui has almost completely adopted Spanish conjunctions rather than rely on this.

Alienable and inalienable possession
In the Rapa Nui, there are alienable and inalienable possession. Lichtenberk described alienable possession as the possessed noun being contingently associated with the possessor, and on the other hand inalienable possession as the possessed noun being necessarily associated with the possessor. The distinction is marked by a possessive suffix inserted before the relevant pronoun. Possessive particles: Alienable possession is used to refer to a person's spouse, children, food, books, work, all animals (except horses), all tools and gadgets (including refrigerators), and some illnesses.
 * (alienable) expresses dominant possession

E tunu au i te kai mo ꞌaku ga poki ko maruaki ꞌa

STA cook 1sg RLT +SPE food BEN POS.1sg.ALIEN GRP child PRF hungry RES

'I must cook dinner for my children who are hungry'

(children) is an alienable possession therefore a is used to indicate that in this sentence, therefore the possessive pronoun a is used instead of ooku.

It is used with parents, siblings, house, furniture, transports (including carts, cars, scooters, boats, airplanes), clothes, feeling, native land, parts of the body (including mind), horses, and their bridles.
 * (inalienable) expresses the subordinate possession

He agi na boꞌi he taina ꞌoꞌoku

STA true LIM EMP -SPE sibling POS.1sg.INAL.

'It is true apparently, he is my brother.' Inalienable possession o is used in this example, therefore ooku instead of aaku is used. It is talking about the speaker's brother, which is an inalienable relation.

There are no markers to distinguish between temporary or permanent possession; the nature of objects possessed; or between past, present or future possession.

A and O possession
A and O possession refer to alienable and inalienable possession in Rapa Nui. marks for alienable possession and marks for inalienable possession. a and o are marked as suffixes of the possessive pronouns; however, they are only marked when the possessive pronoun is in the first, second or third person singular. In (2) above, taina 'sibling' is inalienable and the possessor is first person singular ooku 'my'. However, for all the other situations, a and o are not marked as a suffix of the possessor. He vanaga maua o te meꞌe era

ACT talk 1DU.EX POS +SPE thing PPD

'We'll talk about those matters.'

In the above example, the possessor mee 'those' is not a possessive pronoun of the first, second or third person singular. Therefore, o is marked not as a suffix of the possessor but a separate word in the sentence.

Classifiers
There are no classifiers in the Rapa Nui language.

Exclamation
Ko and ka are exclamatory indicators.
 * suggests a personal reaction:
 * Ko te aroha (Poor thing!)
 * suggests judgement on external events:
 * Ka haakiaki (Tell the whole story!)

Compound words
Terms which did not exist in original Rapa Nui were created via compounding:
 * = ('spear fish') = harpoon
 * = ('spear food') = fork
 * = ('skin foot') = shoe
 * = ('bird spear') = wasp
 * = ('stool horse') = saddle
 * = ('stool stay') = chair

Negation
In Rapa Nui, negation is indicated by free standing morphemes. Rapa Nui has four main negators:

 * ina (neutral)
 * kai (perfective)
 * (e)ko (imperfective)
 * tae (constituent negator)

Additionally there are also two additional particles/ morphemes which also contribute to negation in Rapa Nui:

 * kore (Existential/noun negator)
 * hia / ia (verb phrase particle which occurs in combination with different negators to form the meaning 'not yet')

Negation occurs as preverbal particles in the verb phrase, with the clausal negator kai and (e)ko occurring in first position in the verbal phrase, while the constituent negator (}}tae}}) occurs in second position in the verbal phrase. Clausal negators occur in the same position as aspect markers and subordinators—this means it is impossible for these elements to co-occur. As a result, negative clauses tend to have fewer aspectual distinctions. }}Hia}} occurs in eighth position as a post-verbal marker. Verbal negators precede adjectives. The table below roughly depicts the positions of negators in the Verb Phrase:

{{saltillo}}Ina
Ina is the neutral negator (regarding aspect). It has the widest range of use in a variety of contexts. It usually occurs in imperfective contexts, as well as habitual clauses and narrative contexts, and is used to negate actions and states. It almost always occurs clause initially and is always followed by the neutral aspectual he + noun or he + verb.

ꞌIna he maꞌeha mo uꞌi iga i te kai

NEG PRED light for see NMLZ ACC ART food

'There was no light to see the food.' [R352.070]

In the example above ina is followed by the combination of he + maeha (noun)

ꞌIna he takeꞌa rahi i te tagata

NEG NTR see many/much ACC ART man

'He did not see many people.' [R459.003]

In this example, ina is followed by he + takea (verb)

In addition to negating verbal and nominal clauses, it also functions as the term ꞌnoꞌas shown below:

¿ꞌIna he pepe?...

NEG PRED chair...

'There were no chairs?...' [R413.635]

Unlike the other two clausal negators (which are preverbal particles), ina is a phrase head, thus it can form a constituent of its own.

Kai
Kai negates clauses with perfective aspects.

kai ꞌite a au ko ai a ia

NEG.PFV know PROP 1SG PROM who PROP 3SG

'I don't know who she is.' [R413.356]

It is used to negate past events and narrative events, and is usually combined with ina. It is also used to negate stative verbs, and a verb phrase marked with kai may contain various post-verbal particles such as the continuity marker ā / ana. This marker occurs when the clause has perfect aspect (often obligatory with the perfect marker ko). When combined with kai, it indicates that the negative state continues.

Kai haꞌamata a au kai paꞌo ꞌā e tahi miro

NEG.PFV begin PROP 1SG NEG.PFV chop CONT NUM one tree

'I haven't yet started to chop down a tree.' [R363.091]

(E)ko
(E)ko is the imperfective negator, which (like kai) replaces the aspectual marker in front of the verb, and which can occur with the negator ina.

ꞌIna e ko kai i te kahi o tōꞌona vaka

NEG IPFV NEG.IPFV eat ACC ART tuna of POSS.3SG.INAL boat

'(The fisherman) would not eat the tune (caught with) his boat.' [Ley-5-27.013]

It marks negative commands in imperatives (usually with ina) with the e often excluded in imperatives.

ꞌIna ko kai i te kai mata

NEG NEG.IPFV eat ACC ART food raw

'Don't eat raw food.' (Weber 2003b:610)

In other contexts, especially when ina is absent, the e is obligatory.

¿E ko haga ꞌō koe mo ꞌori o Tāua?

NEG.IPFV NEG.IPFV want really 2SG for dance of 1DU.INCL

'Don't you want to dance with me (lit. us to dance)?' [R315.115]

Ta{{saltillo}}e
Tae is a constituent negator used to negate anything other than a main clause. This can be subordinate clauses, prepositional phrases, possessive predicates and other non-verbal clauses. It also negates nominalised verbs and sub-constituents such as adjectives and quantifiers. It does not negate nouns (this is done by the noun negator kore). It is also used to negate locative phrases, actor emphasis constructions, and is also used to reinforce the preposition mai.

ꞌI au he oho rō ꞌai mai taꞌe pō

IMM 1SG NTR go EMPH SUBS from CONNEG night

'I'm going now, before it gets dark.' [R153.042]

Tae is an indicator for subordinate clauses, as it can also negate subordinate clauses without subordinate markers (in which case it usually occurs with an aspect marker).

ꞌI te taꞌe hakarogo, he garo rō atu ꞌai

at ART CONNEG listen NTR lost EMPH away SUBS

'Because (the sheep) did not listen, it got lost.' [R490.005]

It also occurs in main clauses with main clause negators and aspect markers i and e, when the clause has a feature of a subordinate clause such as oblique constituents

Noun negator: kore
kore is a verb meaning 'the absence or lack of something'.

He uꞌi ku kore ꞌā te tagi

NTR look PRF lack CONT ART cry

'He looked (at his wife); the crying was over.' [Ley-9-55.076]

It immediately follows the noun in the adjective position, and is used to indicate that the entity expressed by the noun or noun modifier does not exist or is lacking in the given context.

Te ꞌati he matariki kore mo oro o rā hora

ART problem PRED file lack for grate of DIST time

'The problem was the lack of files to sharpen (the fishhooks) at the time.' [R539-1.335]

Hia / ia
Hia / ia is a morpheme used immediately after negated verbs and co-occurs with a negator to indicate actions or events which are interrupted or are yet to happen.

kai oromatuꞌa hia i oho rō mai era ki nei

NEG.PFV priest yet PFV go EMPH hither DIST to PROX

'When he had not yet become a priest, he came here.' [R423.004]

Double negation
In Rapa Nui, double negation is more frequent than single negation (with the negator ina often co-occurring with another clause negator most of the time). It is often used as a slight reinforcement or emphasis.

Ina can be combined with negators kai and (e)ko, both of these are main clause negators.

¡Ka rua ꞌō mahana ꞌina kai tuꞌu mai!

CNTG two really day NEG NEG.PFV arrive hither

'She hasn't come for two days.' [R229.132]

In the example above we see the negator ina co-occurring with the perfective negator kai.

When tae occurs in double negation, if the other negator is kai or (e)ko, the negative polarity is cancelled out.

kai taꞌe haka ꞌite ko ai a ia hai meꞌe rivariva aga

NEG.PFV CONNEG CAUS know PROM who PROP 3SG INS thing good:REDUP do

'(God) did not fail to make known who he is, by the good things he did.' (Acts 14:17)

Ina only negates main clauses so it never combines with the negator tae, which is a subordinate clause negator. When occurring with ina, negation may be reinforced.

.... ꞌina e ko taꞌe ravaꞌa te ika

{} NEG IPFV NEG.IPFV CONNEG obtain ART fish

'(if the mother does not eat the fish caught by her firstborn son), he will not fail to catch fish.' [Ley-5-27.008]

Double negation occurs very frequently in imperatives in particular.

ꞌIna ko oho ki te tētahi kona

NEG NEG.IPFV go to ART some/other place

'Don't go to another place.' [R161.027]

Numerals
There is a system for the numerals 1–10 in both Rapa Nui and Tahitian, both of which are used, though all numbers higher than ten are expressed in Tahitian. When counting, all numerals whether Tahitian or Rapanui are preceded by ka. This is not used however, when using a number in a sentence.

Word order
Rapa Nui is a VSO (verb–subject–object) language. Except where verbs of sensing are used, the object of a verb is marked by the relational particle.

He hakahu koe i te rama

{} {} {} RL.PTC {} OBJ

"You light the torch"

Where a verb of sensing is used, the subject is marked by the agentive particle.

He tikea e au te poki

{} {} AG.PTC SBJ {} {}

"I can see the child"

Directionals
Spatial deictics is also present in Rapa Nui, in the form of two directionals: mai and atu. They indicate direction with respect to a specific deictic centre or locus.

 * indicates movement towards the deictic centre, hence the gloss 'hither'.
 * atu indicates movement away from the deictic centre, and is as such glossed as 'away'. They are both reflexes of a larger system in Proto-Polynesian.

Postverbal Demonstratives
The postverbal demonstratives (PVDs) have the same form as the postnominal demonstratives, and they have the same meaning:

 * : proximity, close to the speaker
 * : medial distance, close to the hearer
 * : default PVD; farther distance, removed from both speaker and hearer.

How they differ from postnominal demonstratives is their function/where they can appear, as it is quite limited. They can only appear in certain syntactic contexts, listed here:

 * PVDs are common after imperfective e to express a progressive or habitual action.
 * The contiguous marker ka is often followed by a PVD, both in main and subordinate clauses.
 * With the perfect ko V ā, era is occasionally used to express an action which is well and truly finished.
 * PVDs also appear in relative clauses

Overall, their main function is to provide nuance to the aspectual marker they are being used alongside.

title: Rapa Nui language


text:
Torit

Torit is a city of Eastern Equatoria State in South Sudan.

History
On 18 August 1955, the Equatoria Corps mutinied at Torit, starting the First Sudanese Civil War. In 1964 the military government in Khartoum closed "all the Christian mission schools" in the area. Torit was upgraded to Municipality status administered by a mayor on August 19, 2013.

Location
The city is in Torit County in Eastern Equatoria State, in the southeastern part of South Sudan, close to the international border with the Republic of Uganda. It is approximately 150 km east of Juba, the capital and largest city in South Sudan, by road. The coordinates of Torit are: 4° 24' 28.80"N, 32° 34' 30.00"E (Latitude:4.4080; Longitude:32.5750).

Population
The population of Torit was last estimated at 20,050, in 2004, and, according to census results, 33,657 in 2008.

Education
Equatoria International University temporarily opened in Torit on 21 June 2019, although the university is building a permanent site south of the city.

Points of interest
The following points of interest are found in Torit:

 * Fr Saturlino Ohure Mausoleum
 * The offices of Torit Town Council
 * The headquarters of Torit County
 * The headquarters of Eastern Equatoria State
 * Dr John Garang Memorial Secondary School, Torit
 * Torit Day Secondary School
 * Torit East Primary School
 * Torit Hospital
 * Torit State Hospital
 * The Juba-Lokichogio Road - The road, which is the primary land route to and from Kenya, passes through Torit
 * Torit Airport - A small civilian airport
 * Lomoliha Market - The central market for the town.
 * Johnson Akio Secondary School
 * Fr. saturlino Ohure Secondary School

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

title: Torit


text:
Wikipedia:Articles for deletion/Universidad Católica

 This page is an archive of the discussion about the proposed deletion of the article below. 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 KEEP. Deathphoenix 01:58, 26 Feb 2005 (UTC)

Universidad Católica
User:68.126.250.240 created this article to refer to the Universidad Católica de Santa María, in Peru. Then he/she thought better: moved the content to Universidad Católica de Santa María and blanked this article. I reverted it to turn into a stub when I noticed the awkward situation. This sould not redirect to the new article because there are many Catholic universities in Spanish speaking countries which could be called "Universidad Católica", like Universidad Católica de Temuco and Universidad Católica de Valparaíso. JoaoRicardo 06:36, 13 Feb 2005 (UTC) This page is now preserved as an archive of the debate and, like some other VfD subpages, is no longer 'live'. Subsequent comments on the issue, the deletion, or the decision-making process should be placed on the relevant 'live' pages. Please do not edit this page.
 * Then you've just gained a foothold onto making a page, just like Saint John's University.  Why is this in VFD? I don't understand. Uncle G 07:03, 2005 Feb 13 (UTC)
 * Yeah. This should be made into a disambiguation page. — J3ff 07:56, 13 Feb 2005 (UTC)
 * Alright, alright, I'll punish myself for it. Disambig page created. Can I take out the VfD proposal? JoaoRicardo 08:58, 13 Feb 2005 (UTC)
 * Comment: The general ettiquette is to show your desire to remove the nomination by striking through your comments above (using text ). Removing the VfD tag early is severely frowned upon. Too often, it is a tactic used by vandals to try to disrupt the process. At the end of the 5 day discussion period, the nomination will go through the Deletion process. If the consensus is still an overwhelming "keep" at that point, anyone (including you) can follow the process to close the discussion and remove the tag. Rossami (talk) 17:03, 15 Feb 2005 (UTC)
 * Keep, let the VfD run. Wyss 11:19, 13 Feb 2005 (UTC)
 * Keep -- AllyUnion (talk) 12:49, 13 Feb 2005 (UTC)
 * Keep. Carrp | Talk 17:14, 15 Feb 2005 (UTC)
 * Delete, not a useful disambiguation page. Megan1967 05:54, 18 Feb 2005 (UTC)


text:
Legs Diamond

Jack "Legs" Diamond (possibly born John Thomas Diamond, though disputed; July 10, 1897 – December 18, 1931), also known as John Nolan and Gentleman Jack, was an Irish-American gangster in Philadelphia and New York City during the Prohibition era. A bootlegger and close associate of gambler Arnold Rothstein, Diamond survived a number of attempts on his life between 1916 and 1931, causing him to be known as the "clay pigeon of the underworld". In 1930, Diamond's nemesis Dutch Schultz remarked to his own gang, "Ain't there nobody that can shoot this guy so he don't bounce back?"

Early life
Jack Diamond was born July 10, 1897, to Sara and John Moran, who emigrated from Ireland to Philadelphia, Pennsylvania, in 1891. In 1899, Jack's younger brother Eddie was born. Jack and Eddie both struggled through grade school, and Sara suffered from severe arthritis and other health problems. Sara passed away on December 24, 1913, following complications brought on by a bacterial infection and a high fever. John Moran then moved his family to Brooklyn, New York.

Diamond soon joined a Manhattan street gang called the Hudson Dusters. His first arrest for burglary occurred when he broke into a jewelry store on February 4, 1914. Diamond served in the United States Army in World War I, but was convicted and jailed for desertion in 1918 or 1919. He served two years of a three- to five-year sentence at Leavenworth Military Prison. After being released in 1921, Diamond became a hired thug and later personal bodyguard for crime boss Arnold Rothstein.

Lifestyle
Diamond was known for leading a rather flamboyant lifestyle. He was an energetic individual—his nickname "Legs" derived either from his being a good dancer or from how fast he could escape his enemies. His wife Alice was never supportive of his life of crime but did not do much to dissuade him from it. Diamond was a womanizer; his best-known mistress was showgirl and dancer Marion "Kiki" Roberts.

Prohibition and the Manhattan Bootleg Wars
In the late 1920s, Prohibition was in force, and the sale of beer and other alcoholic beverages was illegal in the United States. Diamond traveled to Europe to acquire beer and narcotics but failed. However, he did obtain liquor, which was dumped overboard in partially full barrels that floated to Long Island as ships entered New York Harbor. Diamond paid children a nickel for every barrel they brought to his trucks.

Following the death of Jacob "Little Augie" Orgen, Diamond oversaw illegal alcohol sales in downtown Manhattan via the Hotsy Totsy Club, an establishment partly-owned by Diamond on Broadway. This work brought him into conflict with Dutch Schultz, who wanted to move beyond his base in Harlem. He also ran into trouble with other gangs in the city. On July 14, 1929, Diamond and fellow gang member Charles Entratta shot three drunken brawlers in the Hotsy Totsy Club; two of the brawlers, William Cassidy and Simon Walker, were killed, while the survivor, Peter Cassidy, was severely wounded. The club's bartender, three waiters, and the hat check girl "vanished" (one of them was found shot dead in New Jersey). Diamond was not charged, but he was forced to close the club.

In 1930, Diamond and two henchmen kidnapped truck driver Grover Parks in Cairo, New York, demanding to know where he had obtained his load of hard cider. When Parks denied carrying anything, Diamond and his men beat and tortured Parks, eventually letting him go. A few months later, Diamond was charged with the kidnapping of James Duncan. He was sent to Catskill, New York, for his first trial, but he was acquitted. However, he was convicted in a federal case on related charges and sentenced to four years in jail. Diamond was tried in December 1931 in Troy, New York, also for kidnapping, he was once again acquitted.

Trip to Europe
On August 23, 1930, Diamond, under the false name John Nolan, boarded the ocean liner SS Belgenland (1914), bound for Europe. The New York City Police Department (NYPD) suspected that he might have left the U.S. aboard RMS Olympic or RMS Baltic (1903), but he was not found on either ship when they reached Europe. The NYPD then sent a wireless telegraph message to the crew of Belgenland, who replied that a man similar to Diamond's description was among the passengers. Diamond spent much of the voyage in the ship's smoking room playing poker; one report claimed that he won thousands of dollars in this game. Belgenland's officers, however, refuted this, saying his winnings were small.

The NYPD telegraphed police in England, France and Belgium with the warning that Diamond was an undesirable character. When Belgenland reached Plymouth on August 31, Scotland Yard officers told Diamond he would not be allowed to land in England. Diamond told reporters that he wanted to travel to the French spa town of Vichy for "the cure". Diamond disambarked in Antwerp on September 1, where Belgian police took him to their headquarters. Eventually, Diamond agreed to voluntarily leave Belgium and was put on a train to Germany. When his train reached Aachen, German police arrested him. On September 6, the German government decided to deport Diamond; he was driven to Hamburg and put on the cargo ship Hannover for passage to Philadelphia.

On September 23, Hannover arrived in Philadelphia, and Diamond immediately was arrested by the Philadelphia police. At a court hearing that day, the judge said he would release Diamond if he left Philadelphia within the hour. Diamond agreed.

Assassination attempts and prosecution
On October 24, 1924, Diamond was shot and wounded by shotgun pellets, reportedly after trying to hijack liquor trucks belonging to a rival crime syndicate.

On October 16, 1927, Diamond tried to stop the murder of "Little Augie" Orgen. Diamond's brother Eddie was Orgen's bodyguard, but Diamond substituted for Eddie that day. As Orgen and Diamond were walking down a street on Manhattan's Lower East Side, three young men approached them and started shooting. Orgen was fatally wounded, and Diamond was shot twice below the heart. Diamond was taken to Bellevue Hospital, where he eventually recovered. Police interviewed Diamond in the hospital, but he refused to identify any suspects or help the investigation in any way. Police initially suspected that Diamond was an accomplice and charged him with homicide, but the charge was dropped. The assailants were supposedly hired by Louis Buchalter and Gurrah Shapiro, who were seeking to encroach on Orgen's garment-district labor rackets.

On October 12, 1930, Diamond was shot and wounded at the Hotel Monticello on Manhattan's West Side. Two men forced their way into Diamond's room and shot him five times. Still in his pajamas, Diamond staggered into the hallway and collapsed. When asked later by the police commissioner how he managed to walk out of the room, Diamond said he drank two shots of whiskey first. Diamond was rushed to the Polyclinic Hospital, where he eventually recovered. He was discharged from Polyclinic on December 30, 1930.

On April 21, 1931, Diamond was arrested in Catskill on assault charges for the Parks beating in 1930. Two days later, he was released from the county jail on $25,000 bond. Five days later, Diamond was again shot and wounded at the Aratoga Inn, a road house near Cairo. After eating in the dining room with three companions, Diamond was shot three times and collapsed by the front door. A local resident drove Diamond to a hospital in Albany, where he was reputed to have told the attending surgeon, "they have not yet made the bullet that will kill me." Diamond eventually recovered. On May 1, while Diamond was still in the hospital, the New York State Police seized over $5,000 worth of illegal beer and alcohol from his hiding places in Cairo and at the Aratoga Inn.

In August 1931, Diamond and Paul Quattrocchi went on trial for bootlegging. The same month, Diamond was convicted and sentenced to four years in state prison. In September 1931, Diamond appealed his conviction.

Death
On December 18, 1931, Diamond's enemies finally caught up with him. Diamond had been staying in a rooming house on Dove Street in Albany while on trial for kidnapping in Troy. On the night of his acquittal, on December 17, Diamond, his family and friends visited a restaurant in Albany. At 1 a.m., Diamond and mistress, Marion "Kiki" Roberts, entertained themselves at the Rain-Bo Room of the Kenmore Hotel on North Pearl Street.

At 4:30 a.m., Diamond drunkenly went back to the rooming house and passed out on his bed. Two gunmen entered his room around an hour later. One man held Diamond down, and the other shot him three times in the back of the head.

There has been much speculation as to who was responsible for the murder. Likely candidates include Schultz, the Oley Brothers, the Albany Police Department, and relatives of Red Cassidy, another Irish American gangster at the time. According to author William Kennedy in his book O Albany, Dan O'Connell, who ran the local Democratic political machine, ordered Diamond's execution, which was carried out by the Albany police. The following are Dan O'Connell's own words recorded during a 1974 interview by Kennedy, which appear on pages 203 and 204:

In order for the Mafia to move in they had to have protection, and they know they'll never get it in this town. We settled that years ago. Legs Diamond...called up one day and said he wanted to go into the 'insurance' business here. He was going to sell strong-arm 'protection' to the merchants. I sent word to him that he wasn't going to do any business in Albany and we didn't expect to see him in town the next morning. He never started anything here.

Prior brought him around here...but brought him around once too often. Fitzpatrick finished Legs.

O'Connell added that William Fitzpatrick (a police sergeant at the time and later chief) and Diamond were "sitting in the same room and (Fitzpatrick) followed him out. Fitzpatrick told him he'd kill him if he didn't keep going.

Given the power that the O'Connell machine held in Albany and its determination to prevent organized crime, other than their own, from threatening their monopoly of vice in the city, some accept this account of the story. For those believing this theory, Fitzpatrick's promotion to chief of police is said to have been a reward for executing Diamond. In 1945, Chief Fitzpatrick was shot and killed in his own office by John McElveney, an Albany police detective. McElveney was sentenced to 20 years to life in prison. He was released in 1957 when his sentence was commuted by Governor W. Averell Harriman.

On December 23, 1931, Diamond was buried at Mount Olivet Cemetery in Maspeth, Queens. There was no church service or graveside ceremony. Family and spectators numbering 200 attended the interment; no criminal figures were spotted.

On July 1, 1933, Alice Kenny Diamond (age 33), Diamond's widow, was found shot to death in her Brooklyn apartment. It was speculated that she was shot by Diamond's enemies to keep her quiet.

In popular culture

 * Released on February 3, 1960, the film The Rise and Fall of Legs Diamond was directed by director Budd Boetticher and stars Ray Danton and Warren Oates. The film was nominated for AFI's Top 10 Gangster Films list.
 * On October 20, 1960, Diamond was played by Steven Hill in the episode "Jack 'Legs' Diamond" of the series The Untouchables starring Robert Stack.
 * The 1963 Looney Tunes short The Unmentionables features an appearance by "Jack 'Legs' Rhinestone," who is shown to feature a pair of ladylike legs. His last name is a reference to the diamond simulant of the same name.
 * A Terry Gilliam animation sequence from the British TV show Monty Python's Flying Circus (1969-1973) features a gangster chicken by the name of "Eggs" Diamond.
 * Legs, the first book in author William Kennedy's Albany cycle, was released in 1975. It follows Diamond to his death.
 * The Broadway show Legs Diamond was a musical starring Peter Allen. It ran briefly in late 1988 through early 1989. It lasted just 64 performances, and it is regarded as one of Broadway's legendary high-profile flops.
 * Josh Mosby portrayed Legs Diamond in the 1993 film The Outfit.
 * Wu-Tang Clan member Raekwon the Chef's 1995 debut hip hop album Only Built for Cuban Linx features a mafioso theme in which he and each guest artist assume a "Wu-Gambino" nickname. Raekwon's nickname is Lex Diamond, an homage to Legs Diamond.
 * Legs Diamond provides the background to the 1996 short story "Running from Legs" by Ed McBain.

title: Legs Diamond


text:
Template:Music of Greece

{{Documentation|content=

title: Template:Music of Greece


text:
Little Cornwallis Island

Little Cornwallis Island is one of the Queen Elizabeth Islands in the Canadian Arctic islands in Nunavut, Canada. It is located at 75°30'N 96°30'W, between Cornwallis Island and Bathurst Island in McDougall Sound, and measures 412 km2. It is uninhabited.

Little Cornwallis Island was the home to Polaris Mine, the most poleward base-metal mine in the world. In 1960 a vast concentration of zinc and lead was discovered on the island during mapping for oil permits. Cominco acquired land in the area and a gravity survey in 1970 detected a large anomaly. By 1973 surface drilling and underground development had outlined the Polaris ore body and defined reserves of about 25 million tons grading approximately 14% zinc and 4% lead. A mining facility was constructed on a barge at Trois-Rivières, Quebec and towed to the island; arriving in mid August 1981. Production commenced in 1982. The mile-long gravel runway allowed aircraft as large as the Boeing 727 and Boeing 737 to service the mine. The mine was closed in August 2002 as forecast due to depletion of the ore body. From 1982 to 2002 the mine processed 21 million tons of ore grading 3.72% lead and 15.81% zinc, producing 733,800 tons of lead metal and 2.8 million tons of zinc metal in concentrate. A two-year, $53 million decommissioning and reclamation program was completed in September 2004.

During the operating lifetime of the mine, there was a company-owned camp to provide lodgings to miners, and the community and mine was serviced by Bell Canada and then by Northwestel.

title: Little Cornwallis Island


text:
Talk:Music of Crete

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title: Talk:Music of Crete


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Talk:Alicia Silverstone

Lead and lead sentence
Just want to point out that WP:BLPLEAD states: "avoid overloading the lead paragraph with various sundry roles; instead, emphasize what made the person notable. Incidental and non-notable roles (i.e. activities that are not integral to the person's notability) should usually not be mentioned in the lead paragraph"

and "In general, a position, activity, or role should not be included the lead paragraph if: a) the role is not otherwise discussed in the lead (per MOS:LEAD, don't tease the reader), b) the role is not significantly covered in the body of the article, or, c) the role is auxiliary to a main profession of the person (e.g. do not add "textbook writer", if the person is an academic)."

LK (talk) 01:03, 4 July 2017 (UTC)

Nationality
If Silverstone's parents were both British citizens, then unless she has since renounced it, she is also a British citizen, no matter where she was born.

When Clueless came out she was on a UK TV interview programme where she mentioned that she was actually in fact British and not American. — Preceding unsigned comment added by 95.150.10.248 (talk) 11:36, 12 August 2017 (UTC)

Today's edits

 * The following has been ported over and combined from Ronz's and Tenebrae's talk pages as background for today's major edits, and probably should have taken place here centrally anyway.--Tenebrae (talk) 00:09, 14 May 2018 (UTC)

I didn't even think I was involved in an edit war with you; never my intention, and to be honest, it's not even an interest to be involved in one. I thought it would be appropriate to mention her other film roles as a whole timeline. As for her stage credits, the woman has constantly starred in plays, so I thought it was also noteworthy. I'd love to add something else in the lead, as it only addresses specifically her film trajectory until her Batgirl role, and her 'Golden Globe nomination' sentence seems a little isolated. Hope we can agree on something and warm greetings to you, regardless of my miscommunication. 190.249.179.87 (talk) 00:36, 11 May 2018 (UTC)
 * The lede should summarize and introduce, identifying why she's notable. She's done a lot of work, but she doesn't seem to get much press or other coverage beyond initial publicity campaigns. Disputes over what should belong in the lede have been a huge problem with article for a long time. Quality references are scarce, especially anything written from a historical context. I'm happy to help you, but I'm mostly just keeping an eye on the article so we don't backslide with the latest publicity campaign or controversy. --Ronz (talk) 02:11, 11 May 2018 (UTC)
 * Overall, I think the edits by the ip are an improvement. The ip contacted me (User_talk:Ronz), and I contacted Davey2010 (User_talk:Davey2010). Could you take another look? --Ronz (talk) 19:06, 13 May 2018 (UTC)
 * Happy to leave it up you, Ronz. I saw he was edit-warring and making unexplained major changes, so I thought it prudent to pull back on them until they could be discussed, as is happening now. --Tenebrae (talk) 20:19, 13 May 2018 (UTC)

title: Talk:Alicia Silverstone


text:
Category:British memoirists

This category is for people from the United Kingdom who have written a memoir.

title: Category:British memoirists


text:
Talk:Notebook processor

The following was moved from the article page Weaponofmassinstruction 06:45, 13 Feb 2005 (UTC) (FIXME: how exactly does the choice of a notebook processor effect wireless networking ?) (FIXME: incomplete list -- should we just include *companies*? Or all notebook processors that have Wikipedia articles ?)

Irrelevant wireless networking mention removed.

Requested move

 * Notebook processor → mobile processor – more common name, more generic, and not linked to notebook (originally a type of stationery) —Mulad (talk) June 30, 2005 16:51 (UTC)

 * Oppose. In my limited experience, I've always heard it called a notebook processor, and it's hard to support moving an article to a title that's not even mentioned in the article. I'm not sure I understand why "not linked to notebook" is a reason to move the page. I'm open to changing my vote though. — Knowledge Seeker দ 1 July 2005 02:56 (UTC)

 * Support if moved to mobile computing microprocessor or portable computing CPU or mobile computing CPU or portable computing microprocessor 67.68.64.213 2 July 2005 00:10 (UTC)

It was requested that this article be renamed but there was no consensus for it be moved. I think the name is perhaps a better name but it is probably best to go via the WP:DA route. violet/riga (t) 19:53, 11 July 2005 (UTC)

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title: Talk:Notebook processor


text:
Richmond Power Station

Richmond Power Station was a coal fired power station which operated on the banks of the Yarra River in Richmond, Victoria, Australia from its construction in 1891 until its closure in 1976. It was one of the first alternating current (AC) electricity generation plants in the state. It has since been converted into office space and is the headquarters of international fashion brand Country Road and advertising agency CHE Proximity. The area in which it is located is now called Cremorne.

The former power station is listed on the Victorian Heritage Register.

History
The Richmond Power Station was completed in 1891 by the New Australian Lighting & Traction Company. It was one of the first alternating current (AC) electricity generation plants in Victoria. The building was designed by Charles D'Ebro, one of Melbourne's premier architects of the time. Initially the station provided power to Melbourne and the suburbs of Richmond, Prahran and South Melbourne. The main competitor was the Electric Light & Motive Power Company. Early equipment was a 750 kW Elwell-Parker alternator. Power was supplied at 2 kV and 97 Hz. The set was driven by a Robey compound steam engine rated at 200 hp. In 1899, the two companies were taken over by Brush Electrical and were combined to form the Electric Lighting and Traction Company of Australia. In 1901, two Brush-Universal 500 kW sets were added.

As demand increased, the plant went through a series of upgrades, the first being an expansion to the engine house. In 1905, the first of two Parsons-Brush 1 MW single-phase turbo-alternators, with a terminal voltage of 4.2 kV, were added. A Curtis-Thompson 1.5 MW turbo alternator was bought in 1907.

The company's name was changed in 1908 to the Melbourne Electric Supply Company. In 1910, two Belliss & Morcom high-speed triple-expansion engines, coupled to Brush alternators, were added. Another four turbo alternators were installed from 1911 onwards, with the engine room extended to the east to accommodate the 10MW increase in power output. Also, several Babcock & Wilcox boilers were added in 1912, and a new 150 ft chimney stack was built in 1913. In 1919, a second chimney stack was erected, and in 1922, a second floor was added to the office block. By 1924, installed capacity had increased to 17 MW.

In 1929, the station was taken over by the State Electricity Commission of Victoria, which relegated Richmond to a peak-load facility. A 15 MW turbo-alternator was installed on the site of the older plant in 1930. That machine ran at 3000 RPM at 6.6 kV at 50 Hz. It was of great value to Melbourne during the power shortages of the 1950s and was still in service in the 1960s.

After World War II, Melbourne experienced severe power shortages. There was no way of procuring steam plant from the usual English manufactures for several years, but a Swiss firm came to the rescue in 1950. A Brown Boveri three-cylinder steam turbo alternator, with a capacity of 38 MW, was installed. That plant was very cheap to run in the 1950s with 180,000 lb/h of steam supplied by each of the two Velox oil-fired boilers, at 600 psi and 850 F.

Although obsolete by the 1970s, the station continued to operate very reliably as a peak-load plant until 1982, when its inefficiency, dilapidated condition and pollution led to its closure.

Redevelopment
The building lay derelict in a large pocket of SECV owned land for many years. Its chimney stacks were demolished soon after closure due to structural faults. It was a popular location for film and television makers during this time. Some scenes for Bangkok Hilton were shot there, some of which incongruously showed the Bryant and May Factory in the background, as were scenes for the police drama Phoenix.

In the early 1990s, Victoria's electricity industry was privatised by the Kennett Liberal State Government. This saw this the sale of much of the SECV's surplus assets. The station and surrounding buildings were sold for development as an office park. All surrounding buildings, most of which dated from the 1930s and 1940s were demolished.

Under architects Metier 3 the original station building and turbine hall, which is listed on the Victorian Heritage Register was restored with a modern extension added to the section which formerly housed the old Babcock + Wilcox water tube boilers. The building, designed for Country Road, won a merit award from the Royal Australian Institute of Architects in 1997. The area around the station has also been fully developed.

title: Richmond Power Station


text:
Projection-slice theorem

In mathematics, the projection-slice theorem, central slice theorem or Fourier slice theorem in two dimensions states that the results of the following two calculations are equal:
 * Take a two-dimensional function f(r), project (e.g. using the Radon transform) it onto a (one-dimensional) line, and do a Fourier transform of that projection.
 * Take that same function, but do a two-dimensional Fourier transform first, and then slice it through its origin, which is parallel to the projection line.

In operator terms, if then
 * F1 and F2 are the 1- and 2-dimensional Fourier transform operators mentioned above,
 * P1 is the projection operator (which projects a 2-D function onto a 1-D line),
 * S1 is a slice operator (which extracts a 1-D central slice from a function),
 * $$F_1 P_1 = S_1 F_2.$$

This idea can be extended to higher dimensions.

This theorem is used, for example, in the analysis of medical CT scans where a "projection" is an x-ray image of an internal organ. The Fourier transforms of these images are seen to be slices through the Fourier transform of the 3-dimensional density of the internal organ, and these slices can be interpolated to build up a complete Fourier transform of that density. The inverse Fourier transform is then used to recover the 3-dimensional density of the object. This technique was first derived by Ronald N. Bracewell in 1956 for a radio-astronomy problem.

The projection-slice theorem in N dimensions
In N dimensions, the projection-slice theorem states that the Fourier transform of the projection of an N-dimensional function f(r) onto an m-dimensional linear submanifold is equal to an m-dimensional slice of the N-dimensional Fourier transform of that function consisting of an m-dimensional linear submanifold through the origin in the Fourier space which is parallel to the projection submanifold. In operator terms:

 * $$F_mP_m=S_mF_N.\,$$

The generalized Fourier-slice theorem
In addition to generalizing to N dimensions, the projection-slice theorem can be further generalized with an arbitrary change of basis. For convenience of notation, we consider the change of basis to be represented as B, an N-by-N invertible matrix operating on N-dimensional column vectors. Then the generalized Fourier-slice theorem can be stated as

 * $$F_m P_m B = S_m \frac{B^{-T}}{|B^{-T}|} F_N$$

where $$B^{-T}=(B^{-1})^T$$ is the transpose of the inverse of the change of basis transform.

Proof in two dimensions

The projection-slice theorem is easily proven for the case of two dimensions. Without loss of generality, we can take the projection line to be the x-axis. There is no loss of generality because if we use a shifted and rotated line, the law still applies. Using a shifted line (in y) gives the same projection and therefore the same 1D Fourier transform results. The rotated function is the Fourier pair of the rotated Fourier transform, for which the theorem again holds.

If f(x, y) is a two-dimensional function, then the projection of f(x, y) onto the x axis is p(x) where

 * $$p(x)=\int_{-\infty}^\infty f(x,y)\,dy.$$

The Fourier transform of $$f(x,y)$$ is

F(k_x,k_y)=\int_{-\infty}^\infty \int_{-\infty}^\infty f(x,y)\,e^{-2\pi i(xk_x+yk_y)}\,dxdy. $$

The slice is then $$s(k_x)$$

 * $$s(k_x)=F(k_x,0)

=\int_{-\infty}^\infty \int_{-\infty}^\infty f(x,y)\,e^{-2\pi ixk_x}\,dxdy $$
 * $$=\int_{-\infty}^\infty

\left[\int_{-\infty}^\infty f(x,y)\,dy\right]\,e^{-2\pi ixk_x} dx $$
 * $$=\int_{-\infty}^\infty p(x)\,e^{-2\pi ixk_x} dx

$$

which is just the Fourier transform of p(x). The proof for higher dimensions is easily generalized from the above example.

The FHA cycle
If the two-dimensional function f(r) is circularly symmetric, it may be represented as f(r), where r = |r|. In this case the projection onto any projection line will be the Abel transform of f(r). The two-dimensional Fourier transform of f(r) will be a circularly symmetric function given by the zeroth-order Hankel transform of f(r), which will therefore also represent any slice through the origin. The projection-slice theorem then states that the Fourier transform of the projection equals the slice or

 * $$F_1 A_1 = H,$$

where A1 represents the Abel-transform operator, projecting a two-dimensional circularly symmetric function onto a one-dimensional line, F1 represents the 1-D Fourier-transform operator, and H represents the zeroth-order Hankel-transform operator.

Extension to fan beam or cone-beam CT
The projection-slice theorem is suitable for CT image reconstruction with parallel beam projections. It does not directly apply to fanbeam or conebeam CT. The theorem was extended to fan-beam and conebeam CT image reconstruction by Shuang-ren Zhao in 1995.

title: Projection-slice theorem


text:
Talk:Acute pancreatitis

Bowel Rest
I feel that this section is quite misleading not inline with current evidence or bsg guidance. Currently early feeding is preferred. See BSG guidline re:pancreatitis 2005 SN R (talk) 22:32, 13 July 2012 (UTC)

Laparoscopy
I changed the text which implied that endoscopy is a treatment. It's a diagnostic procedure. Although useful to help figure out what's going on, endoscopy can actually trigger pancreatitis attacks.

The ERCP (endoscopic retrograde cholangiopancreatography) referred to later in the article is an procedure that utilizes endoscopy, but its not endoscopy. By comparison, although you might use a flashlight to change a lightbulb in a dark closet, you wouldn't say that the flashlight changed the lightbulb.

I replaced endoscopy with laparoscopy.

A specific laparoscopic treatment I know of has been used in the last decade by Dr. Peter Banks (Past President of the American Pancreatic Association, President of the International Association of Pancreatology, Past Chair of the Pancreatic Disorders Section of the American Gastroenterological Association, etc.) at Brigham and Women's Hospital in Boston. It involves making an incision in the sphincter of Oddi so that pancreatic secretions enter the descending duodenum more easily rather than accumulating and causing trouble. -- House of Scandal 14:11, 24 October 2006 (UTC)

 * What is the source of your assertion? Some advocate early ERCP to establish whether gallstone disease is the cause of the pancreatitis. The use of sphincterotomy should be supported with citations. Laparoscopy is not useful unless for the specific purpose of draining a pseudocyst. JFW | T@lk  21:29, 6 February 2007 (UTC)

Reply
I mentioned the sphincterotomy proceedure used by Banks here rather than in the article because I don't have citations regarding it, only personal experience. Statements made in talk pages don't need citations and without citations may be weighed accordingly.

Regarding the statement that "Laparoscopy is not useful unless for the specific purpose of draining a pseudocyst", please note:

Diagnostic laparoscopy is a minimally invasive surgical procedure that allows the visual examination of intra abdominal organs in order to detect pathology. The video image of the liver, stomach, intestines, gallbladder, spleen, peritoneum, and pelvic organs can be viewed on a monitor after insertion of a telescope into the abdomen. Manipulation and biopsy of the viscera is possible through additional ports. Heres's another description: Diagnostic laparoscopy is a procedure that allows a health care provider to look directly at the contents of a patient's abdomen or pelvis, including the fallopian tubes, ovaries, uterus, small bowel, large bowel, appendix, liver, and gallbladder. The purpose of this examination is to actually see if a problem exists that has not been found with noninvasive tests. Inflammation of the gallbladder (cholecystitis), appendix (appendicitis), pelvic organs (pelvic inflammatory disease), or tumors of the ovaries may be diagnosed laparoscopically. Use of a search engine for "Diagnostic Laparoscopy" and similar words will return many thousands of results.

I may have missed your point if your point was that laparoscopy shouldn't be mentioned as a treatment option. My concern was that endoscopy was listed as a treatment option and looking at something isn't treatment. Laparoscopy, on the other hand, may involve cutting, etc.

However, note that there are a number of pancreatitis treatment proceedures besides the draining of a pseudocyst you mentioned and the sphincterotomy I mentioned. The most obvious of these is cholecystectomy. Based on that, the intro seems to still make sense.--House of Scandal 04:26, 14 February 2007 (UTC)

Tests
- a useful review of blood tests. JFW | T@lk  21:29, 6 February 2007 (UTC)

Antibiotics
"Prophylactic antimicrobials should not be used." is bit of a strong statement. See edits.

Epidemiology
I removed wrongdiagnosis.com as the primary reference for epidemiology. This is an unreliable site. In fact, I was unable to corrobate the USA incidence data. I added some well-established data from Europe, which is not much different.

I removed completely the claims re. prevalence. For an acute medical condition, prevalence is a completely meaningless number. This would indicate the number of people in the population presently suffering from acute pancreatitis. Prevalence becomes relevant only in more chronic conditions. JFW | T@lk  14:14, 9 July 2007 (UTC)

use of mepedrine
The information in this article concerning use of meperidine/pethidine/demerol is outdated, and contradicts information in the article on the drug, particularly regarding antispasmodic effects. In the U.S., use of demerol is actively discouraged. From what I've been able to gather, hydromorphone is commonly used to treat the pain associated with acute pancreatitis. Suspect other infomation in the article is dated as well. —Preceding unsigned comment added by 70.253.195.89 (talk) 15:00, 15 November 2007 (UTC)

Use of hydromorphone--from a survivor
My personal experience in pain relief for hemorrhagic pancreatits was that I was put on a 100 mcg Fentanyl patch and, following frequent IV injections of 2mg hydromorphine, a dispensing pump. Alhtough I had myself convinced that I was only using the hydromorphine for euphoria, it was because the Fentanyl would mask the pain well past the point that dependent cravings set in. It was only about a year later, on my initial attempt to stop Fentanyl (hydromorphone having been stopped six months earlier) that I discovered how much pain I was really in. In my case, due to a large dose following a rupture in a transplanted kidney, morphine was as effective as water. The main benefit I see to the Fentanyl/hydromorphone combination is that either can be stopped without withdrawal symptoms if the other is continued, and Fentanyl is probably more conducive to the weaning process. In my case I found that the hydromorphone caused hallucinations and vivid dreams which I could not distinguish from reality, as well as short periods of altered reality that I did not recognize when interacting with others: Fentanyl had no such effect.

Causes Section Needs Improvement
I do not have enough background to edit this article, but as a user I observe that the "Causes" section is of very poor quality. In particular:

The cause listed as the sole "Major Cause" is a side effect of the diabetes drug Byetta. Reading the article, this seems a decidedly uncommon cause to me. The "Causes by demographic" section notes that for adults in Western countries 85% of cases are caused by gallstones and alcoholism, yet neither of these causes is listed in either the "Major Causes" or "Minor Causes" sections.

It would be good if someone with expertise would clean up this section. —Preceding unsigned comment added by Galletto (talk • contribs) 18:00, 10 June 2009 (UTC)

FYI, I have undone an edit to the "Major Causes" section that was done five days ago. That edit deleted a listing of several major causes and left only the "Byetta" paragraph. While this list I restored is not high quality prose, it is far more informative that what was left. —Preceding unsigned comment added by Galletto (talk • contribs) 18:12, 10 June 2009 (UTC)

 * I agree with the above. In my opinion, Byetta should not start the "Major Causes" as it is a minor cause. Additionally, Byetta should probably just be lumped into the Drugs category of the mnemonic that is given. Lastly, I think that it would be helpful if the most common causes (Gallstones, ethanol, ERCP, Drug-related, hypertriglyceridemia, etc.) had percentages given with them to give better context. I will get to this soon if no one else beats me to it. Thoughts? justin.kirkham (talk) 23:52, 20 April 2010 (UTC)

 * The war within describes research on how the disease/damage develops but may be more suitable for the Pathogenesis section. - Rod57 (talk) 03:29, 10 February 2012 (UTC)

Removed the following from ERCP section
"It's not always true that people die during sleep. Sometimes, they are conscious when pain occurs but is too weak to move or ask for help."

I have no idea why this was in this article :s —Preceding unsigned comment added by 92.24.101.87 (talk) 15:29, 21 December 2009 (UTC)

British Guideline
10.1136/gut.2004.057026 JFW | T@lk  15:17, 24 February 2011 (UTC)

Classification
... has been revised (modified Atlanta 2012) 10.1136/gutjnl-2012-302779 JFW | T@lk  21:33, 11 December 2012 (UTC)

..what about new atlanta 2013 vs balthazar vs new IMC scoring? ( view petrov et al writings) --88.10.91.189 (talk) 19:16, 1 December 2013 (UTC)

Ranson score
The Ranson score section seems copied from the Ranson criteria article (in read mode, judging by the reference numbers without link). However, the phrase
 * It is applicable to non-gallstone pancreatitis. For gallstone pancreatitis, the parameters are:

is changed to
 * It is applicable to both gallstone and alcoholic pancreatitis.

the gallstone parameters are omitted, and after the sentence
 * Alternatively, pancreatitis severity can be assessed by any of the following:[2]

where the original article lists APACHE score and others, here you get a section with the titel Ranson's score (the 's added because section names must be unique perhaps??)

Later in the Glasgow criteria section, one reads the Glasgow criteria is valid for both gallstone and alcohol induced pancreatitis, whereas the Ranson score is only for alcohol induced pancreatitis.  Ssscienccce (talk) 19:03, 25 June 2013 (UTC)

Causes by demographic
This section makes some highly dubious unreferenced claims - alcohol is the primary etiology in 60% of US cases and only 5% of UK cases, despite broadly similar ethnicity, lifestyle and alcohol consumption? Maybe there's a good explanation, but if so we need to know about it. I've added a citation request. --Ef80 (talk) 14:35, 5 May 2015 (UTC)

Scores are still a bit weak
10.7326/M16-0650 - Annals of Internal Medicine. JFW | T@lk  07:57, 26 July 2016 (UTC)

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NEJM
10.1056/NEJMra1505202 JFW | T@lk  00:27, 17 November 2016 (UTC)

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Flathead Lake

Flathead Lake is a large natural lake in northwest Montana, United States.

The lake is a remnant of the ancient, massive glacial dammed lake, Lake Missoula of the era of the last interglacial. Flathead Lake is a natural lake along the mainline of the Flathead River. It was dammed in 1930 by Kerr Dam at its outlet on Polson Bay, slightly raising the lake level; the dam generates electricity. The hydroelectric has been owned and operated by the Confederated Salish and Kootenai Tribes since 2015. It is one of the cleanest lakes in the populated world for its size and type.

Geography
Located in the northwest corner of the state of Montana, 7 mi south of Kalispell, it is approximately 30 mi long and 16 mi wide, covering 197 sqmi. It is a similar size as Minnesota's Mille Lacs Lake, but smaller than Red Lake. It is about half the area of San Francisco Bay (main bay). It is larger in surface area than Lake Tahoe, but it is much smaller in volume due to Tahoe's depth. Flathead Lake has a maximum depth of 370.7 ft, and an average of 164.7 ft. This makes Flathead Lake deeper than the average depths of the Yellow Sea or the Persian Gulf. Flathead Lake is in a scenic part of Montana, 30 mi southwest of Glacier National Park and is flanked by two scenic highways, which wind along its curving shoreline. On the west side is U.S. Route 93, and on the east, is Route 35. The lake is bordered on its eastern shore by the Mission Mountains and on the west by the Salish Mountains. The Flathead valley was formed by the glacial damming of the Flathead River and sustains a remarkably mild climate for a region located this far north and inland; the Pacific Ocean is almost 400 mi to the west. The mild climate allows for cherry orchards on the east shore and vineyards for wine production on the west shore. There are also apple, pear and plum orchards around the lake as well as vegetables, hay, honey, nursery tree, Christmas tree, sod/turf, and wheat production bordering or near the lake.

The lake has an irregularly shaped shoreline and a dozen small islands cover 5.5 sqmi. Wild Horse Island is the largest at 2164 acre. Melita Island is a 64 acre island on Flathead Lake, located about one-half mile off the west lakeshore. At its highest point Melita is 80 ft above water level. The closest access is from Walstad Landing (one and a half miles), a state-maintained landing off Highway 93, approximately 15 minutes north of Polson. The island is owned by the Montana Council of the Boy Scouts of America, and is home to Camp Melita Island, and is used and for other activities; there is a project for woodland rehabilitation run by the Montana Council. There is also a bald eagle reserve which is protected by the Native Americans. Boy Scouts began using the island in the 1940s.

Geology
Flathead Lake lies at the southern end of a geological feature called the Rocky Mountain Trench. The trench, which formed with the Rocky Mountains, extends north into the southern Yukon as a straight, steep valley, which also holds the headwaters of the Columbia River. During the last ice age this trench was filled by an enormous glacier. As the glacier moved southward it carved out the trench. The Polson Moraine, near present-day Polson, Montana, marks the southernmost extent of the glacier during the last ice age and thus is the site of the glacier's terminal moraine.

The large size of the Polson Moraine indicates that the glacier stalled here for many years before retreating. As the climate warmed, a portion of the glacier in the Mission Valley receded more slowly than the main body, which kept the lake basin from being filled with sediment. Eventually this ice also melted, forming a lake behind the moraine. Once the water reached the top of this moraine dam, it began to cut a channel through it. Most moraine dammed lakes drain quickly because water cuts entirely through the moraine. Flathead Lake remained because a bedrock hill buried underneath the Polson Moraine prevented the moraine from being completely cut through so the meltwater never completely drained.

At one time, probably when the valley was partially filled by a glacier, the level of Flathead Lake was about 500 ft higher and drained through the valley west of Elmo, Montana, which is at the end of Big Arm Bay, bottom center in the aerial photo above. Water carved out a wide, flat-bottomed pass with a deeper, narrow channel at the south edge of the pass. The deeper channel and traces of the dry riverbed are still visible from Route 28.

Management
The Flathead River and the Swan River (known also as the Bigfork River where it enters the lake) are the major tributaries of the five tributaries that are within the Flathead Watershed. Numerous small streams flow into the lake, particularly on the wetter east shore. The Seli’š Ksanka Qlispe’ Dam, formerly known as Kerr Dam and built near Polson, controls the top 10 feet, generates hydroelectric power, and provides water for irrigation to support a federal irrigation project in the area. Minimum outflow levels from Flathead Lake are designated by the Federal Energy Regulatory Commission (FERC) and are based on flood risk management, power generation requirements, and biological needs to support aquatic life in river systems.

The lake is downstream of Hungry Horse Dam on the South Fork Flathead River. The Hungry Horse Dam is managed by the Bureau of Reclamation to provide beneficial flow conditions and to provide safe passage for migrating juvenile fish to reach the Columbia River Estuary and the Pacific Ocean. The Columbia River Technical Management Team makes operational recommendations to the agencies that control federal dams. Made up of representatives from four states, five federal agencies and six tribal nations, it prioritizes fish and wildlife above other system benefits. The Columbia River system has 14 projects that must be operated to meet congressionally authorized purposes.

History
Once known as "Salish Lake", this body of water was named for the Salish Indians. Early European explorers, like David Thompson, called them the Flathead Indians because of a misinterpretation of early Native American sign language. In 1855 the United States (US) made the Treaty of Hellgate, by which it set aside the Flathead Reservation solely for use of the Flathead, encompassing an area including much of Flathead Lake.

The summer of 2023 saw abnormally low water levels. Variations to the Flood Risk Management Plan were approved by the U.S. Army Corp of Engineers in 2024 in response to the continuing dry conditions.

Fauna
Flathead Lake is home to a number of native and non-native fishes, and is managed cooperatively by both Montana Fish, Wildlife and Parks and the Confederated Salish and Kootenai Tribes. The lake is inhabited by the native bull trout and cutthroat trout, as well as the non-native lake trout, yellow perch, and lake whitefish. Local residents have reported sighting other aquatic fauna in the lake as well, such as sturgeon and the Flathead Lake Monster.

The non-native opossum shrimp, (Mysis diluviana), were introduced by Montana Department of Fish, Wildlife and Parks in the Flathead drainage basin to encourage production of larger kokanee salmon; they migrated into Flathead Lake and have altered the ecosystem.

Fishermen had introduced lake trout 80 years prior but remained at low densities until the non-native Mysis became established. The bottom-dwelling mysids eliminated a recruitment bottleneck for lake trout by providing a deep water source of food where little was available previously. Lake trout subsequently flourished on mysids; this voracious piscivore now dominates the lake fishery. The formerly abundant kokanee were extirpated, and native bull and westslope cutthroat trout are imperiled. Predation by Mysis has shifted zooplankton and phytoplankton community size structure. Bayesian change point analysis of primary productivity (27-y time series) showed a significant step increase of 55 mg C m−2 d−1 (i.e., 21% rise) concurrent with the mysid invasion, but little trend before or after despite increasing nutrient loading. Mysis facilitated predation by lake trout and indirectly caused the collapse of kokanee, redirecting energy flow through the ecosystem that would otherwise have been available to other top predators (bald eagles).

Like the majority of other nonnative species, the lake trout (Salvelinus namaycush) became established in the lake from the late 1800s-early 1900s. The introduction of lake trout has placed increased pressure on the ecologically similar threatened native bull trout (Salvelinus confluentus). The semi-annual "Mack Days" Lake Trout fishing contest aims to reduce the non-native "Mackinaw trout" or lake trout populations, as well as educate people about the Flathead Lake Fisheries Management Plan. Since the inception of this event in 2002, over 402,000 lake trout have been harvested.

 * Native
 * 1) Cutthroat Trout
 * 2) Northern Pikeminnow
 * 3) Bull Trout
 * 4) Mountain Whitefish
 * 5) Westslope Cutthroat Trout
 * Nonnative
 * 1) Brown Trout
 * 2) Lake Trout
 * 3) Golden Trout
 * 4) Yellowstone Cutthroat Trout
 * 5) Brook Trout
 * 6) Rainbow Trout
 * 7) Kokanee Salmon
 * 8) Northern Pike
 * 9) Yellow Perch
 * 10) Largemouth Bass
 * 11) Smallmouth Bass
 * 12) Sturgeon (sp)

In addition to these commonly-pursued game fish, the lake is also home to other native species that currently are not actively managed by government fish and wildlife agencies, including the longnose sucker (Catostomus catostomus), redside shiner (Richardsonius balteatus), and slimy sculpin (Cottus cognatus).

title: Flathead Lake


text:
Abel transform

In mathematics, the Abel transform, named for Niels Henrik Abel, is an integral transform often used in the analysis of spherically symmetric or axially symmetric functions. The Abel transform of a function f(r) is given by

 * $$F(y) = 2 \int_y^\infty \frac{f(r)r}{\sqrt{r^2 - y^2}} \,dr.$$

Assuming that f(r) drops to zero more quickly than 1/r, the inverse Abel transform is given by

 * $$f(r) = -\frac{1}{\pi} \int_r^\infty \frac{dF}{dy} \,\frac{dy}{\sqrt{y^2 - r^2}}.$$

In image analysis, the forward Abel transform is used to project an optically thin, axially symmetric emission function onto a plane, and the inverse Abel transform is used to calculate the emission function given a projection (i.e. a scan or a photograph) of that emission function.

In absorption spectroscopy of cylindrical flames or plumes, the forward Abel transform is the integrated absorbance along a ray with closest distance y from the center of the flame, while the inverse Abel transform gives the local absorption coefficient at a distance r from the center. Abel transform is limited to applications with axially symmetric geometries. For more general asymmetrical cases, more general-oriented reconstruction algorithms such as algebraic reconstruction technique (ART), maximum likelihood expectation maximization (MLEM), filtered back-projection (FBP) algorithms should be employed.

In recent years, the inverse Abel transform (and its variants) has become the cornerstone of data analysis in photofragment-ion imaging and photoelectron imaging. Among recent most notable extensions of inverse Abel transform are the "onion peeling" and "basis set expansion" (BASEX) methods of photoelectron and photoion image analysis.

Geometrical interpretation

In two dimensions, the Abel transform F(y) can be interpreted as the projection of a circularly symmetric function f(r) along a set of parallel lines of sight at a distance y from the origin. Referring to the figure on the right, the observer (I) will see

 * $$F(y) = \int_{-\infty}^\infty f\left(\sqrt{x^2 + y^2}\right) \,dx,$$

where f(r) is the circularly symmetric function represented by the gray color in the figure. It is assumed that the observer is actually at x = ∞, so that the limits of integration are ±∞, and all lines of sight are parallel to the x axis. Realizing that the radius r is related to x and y as r2 = x2 + y2, it follows that

 * $$dx = \frac{r\,dr}{\sqrt{r^2 - y^2}}$$

for x > 0. Since f(r) is an even function in x, we may write

F(y) = 2 \int_0^\infty f\left(\sqrt{x^2 + y^2}\right) \,dx = 2 \int_{|y|}^\infty f(r)\,\frac{r\,dr}{\sqrt{r^2 - y^2}}, $$

which yields the Abel transform of f(r).

The Abel transform may be extended to higher dimensions. Of particular interest is the extension to three dimensions. If we have an axially symmetric function f(ρ, z), where ρ2 = x2 + y2 is the cylindrical radius, then we may want to know the projection of that function onto a plane parallel to the z axis. Without loss of generality, we can take that plane to be the yz plane, so that

F(y, z) = \int_{-\infty}^\infty f(\rho, z) \,dx = 2 \int_y^\infty \frac{f(\rho, z) \rho \,d\rho}{\sqrt{\rho^2 - y^2}}, $$

which is just the Abel transform of f(ρ, z) in ρ and y.

A particular type of axial symmetry is spherical symmetry. In this case, we have a function f(r), where r2 = x2 + y2 + z2. The projection onto, say, the yz plane will then be circularly symmetric and expressible as F(s), where s2 = y2 + z2. Carrying out the integration, we have

F(s) = \int_{-\infty}^\infty f(r) \,dx = 2 \int_s^\infty \frac{f(r) r \,dr}{\sqrt{r^2 - s^2}},$$

which is again, the Abel transform of f(r) in r and s.

Verification of the inverse Abel transform
Assuming $$f$$ is continuously differentiable and $$f$$, $$f'$$ drop to zero faster than $$1/r$$, we can set $$u=f(r)$$ and $$ v=\sqrt{r^2-y^2} $$. Integration by parts then yields

 * $$F(y) = -2 \int_y^\infty f'(r) \sqrt{r^2-y^2} \, dr.$$

Differentiating formally,

 * $$F'(y) = 2 y \int_y^\infty \frac{f'(r)}{\sqrt{r^2-y^2}} \, dr.$$

Now substitute this into the inverse Abel transform formula:

 * $$-\frac{1}{\pi} \int_r^\infty \frac{F'(y)}{\sqrt{y^2-r^2}} \, dy = \int_r^\infty \int_y^\infty \frac{-2 y}{\pi \sqrt{(y^2-r^2) (s^2-y^2)}} f'(s) \, ds dy.$$

By Fubini's theorem, the last integral equals

 * $$\int_r^\infty \int_r^s \frac{-2 y}{\pi \sqrt{(y^2-r^2) (s^2-y^2)}} \, dy f'(s) \,ds = \int_r^\infty (-1) f'(s) \, ds = f(r).$$

Generalization of the Abel transform to discontinuous F(y)
Consider the case where $$F(y)$$ is discontinuous at $$y=y_\Delta$$, where it abruptly changes its value by a finite amount $$\Delta F$$. That is, $$y_\Delta$$ and $$\Delta F$$ are defined by $$\Delta F \equiv \lim_{\epsilon\rightarrow 0} [ F(y_\Delta-\epsilon) - F(y_\Delta+\epsilon) ]$$. Such a situation is encountered in tethered polymers (Polymer brush) exhibiting a vertical phase separation, where $$F(y)$$ stands for the polymer density profile and $$f(r)$$ is related to the spatial distribution of terminal, non-tethered monomers of the polymers.

The Abel transform of a function f(r) is under these circumstances again given by:

 * $$F(y)=2\int_y^\infty \frac{f(r)r\,dr}{\sqrt{r^2-y^2}}.$$

Assuming f(r) drops to zero more quickly than 1/r, the inverse Abel transform is however given by

f(r)=\left[ \frac{1}{2}\delta(r-y_\Delta)\sqrt{1-(y_\Delta/r)^2} - \frac{1}{\pi} \frac{H(y_\Delta-r)}{\sqrt{y_\Delta^2-r^2}} \right] \Delta F-\frac{1}{\pi}\int_r^\infty\frac{d F}{dy}\frac{dy}{\sqrt{y^2-r^2}}. $$

where $$\delta$$ is the Dirac delta function and $$H(x)$$ the Heaviside step function. The extended version of the Abel transform for discontinuous F is proven upon applying the Abel transform to shifted, continuous $$F(y)$$, and it reduces to the classical Abel transform when $$\Delta F=0$$. If $$F(y)$$ has more than a single discontinuity, one has to introduce shifts for any of them to come up with a generalized version of the inverse Abel transform which contains n additional terms, each of them corresponding to one of the n discontinuities.

Relationship to the Fourier and Hankel transforms
The Abel transform is one member of the FHA cycle of integral operators. For example, in two dimensions, if we define A as the Abel transform operator, F as the Fourier transform operator and H as the zeroth-order Hankel transform operator, then the special case of the projection-slice theorem for circularly symmetric functions states that

 * $$FA = H.$$

In other words, applying the Abel transform to a 1-dimensional function and then applying the Fourier transform to that result is the same as applying the Hankel transform to that function. This concept can be extended to higher dimensions.

Relationship to the Radon transform
Abel transform can be viewed as the Radon transform of an isotropic 2D function f(r). As f(r) is isotropic, its Radon transform is the same at different angles of the viewing axis. Thus, the Abel transform is a function of the distance along the viewing axis only.

title: Abel transform


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Talk:Kluang District

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Wikipedia:Articles for deletion/Supremegames

 This page is an archive of the discussion about the proposed deletion of the article below. 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. Joyous 20:06, Feb 19, 2005 (UTC)

Supremegames
Wikipedia is not a web directory. Uncle G 06:50, 2005 Feb 13 (UTC)
 * Delete, ad. Wyss 11:18, 13 Feb 2005 (UTC)
 * Delete advertisement. Non-notability established in the article: "Supremegames is a small basic website".  Google agrees with 31 hits; about half are domain registrars saying it's free, and half of the rest are different Supremegameses. —Korath (Talk) 02:27, Feb 16, 2005 (UTC)

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


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