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Talk:Christmas tree

Contents of lead section
@79.191.251.168: What you want to add to the lead is not supported in the body of the article. Yes, some aspects of it are briefly mentioned, but you are adding your own ideas. For instance, you state that it was "practiced by a plurality of Christians", which is nowhere in the article. Please discuss this here before adding it again. Also, be aware of Wikipedia's WP:3RR rule. Indyguy (talk) 15:29, 4 July 2023 (UTC)

Evergreen trees in other cultures
In American culture using of evergreen trees are backed to 17th century or Germans back to 15th century. It is of great concern to speak about other civilization that used it as specific ritual and on specific time. please share your Idea about adding older history of Evergreen Trees on Christmas Tree. Light prism2020 (talk) 16:01, 2 October 2023 (UTC)
 * There is already a sourced "Possible precedessors" section for that, where the sources all explicitly mention "Christmas." OhNo itsJamie Talk 16:10, 2 October 2023 (UTC)
 * Ohhh James, great that you are here. Because I added paragraph about one specific civilization that is Persians, that have books and ancient poems and also stone depiction of evergreen trees and symbolizing it as everlasting life and standing against winter coldness and darkness and you delete that!! I added references and pictures of inscription of their tree on stone!! and you deleted it it that specific section!! Light prism2020 (talk) 19:32, 2 October 2023 (UTC)
 * References must explicitly make a connection between what the Persians were doing with trees and the Renaissance-era practices in Europe. The citations you have been using do not make that connection. MrOllie (talk) 20:37, 2 October 2023 (UTC)
 * Great that you are replying. Are we concern about Renaissance-era only period (14th Century onward)? if so, there are paragraphs about ancient Egyptian and Chinese and Jews. I am sure they are not from that era, and you way want to delete that parts from article. If you are connecting it to The Jesus Christ (1st Century) ,you can change topic to "Christianity Tree", but I am pretty sure Jesus did not celebrate his birthday on Dec 25th with Trees. If non of previous sentence are correct and you accept it has rooted before 1st Century and other Cultures had symbolized it as eternal life, you can not eliminate it`s time period just to your desired time and do not look at other periods and Civilizations that had Evergreen Coniform Tree. And By the way, I just looked at one of references and want to know more about that, How can some one accepted The reference No 26 it is clearly a Yellow magazine. I heard they only accept first hand research based article and you deleted my writing because of that! Light prism2020 (talk) 04:07, 3 October 2023 (UTC)
 * The citations about the Egyptions and so on do make an explicit connection. That is not the same as what you are attempting to add. MrOllie (talk) 11:47, 3 October 2023 (UTC)
 * Trees were often (and still are) regarded as sacred in different cultures around the world. I think what has to be shown with reliable sources is a connection between Cypress tree and Yalda in Persia/Iran and the Christmas tree as that is what the article is about. Connections can however, be ancient or a contemporary overlays of an ancient tradition to the Christmas tree. However, it might be better if you work on finding reliable sources for the Cypress tree and Yalda and add it to the article Sacred tree on Wikipedia instead of the Christmas tree article for now. Myotus (talk) 15:10, 3 October 2023 (UTC)

Source for August Imgard's Decoration Using Candy Canes
Hey All, I found a source for the claim of August Imgard decorating a pine tree with candy canes on the Candy Cane page, here is a copy below:

Parker, Rick (2003). Introduction to Food Science. Albany, New York: Delmar/Thomson Learning. ISBN 0-7668-1314-2 – via Google Books. "In 1670, the choirmaster at the Cologne Cathedral gave sugar sticks to his young singers to keep them quiet during the long Living Crèche ceremony. In honor of the occasion, he had the candies bent into the shepherd's crooks. In 1847, a German-Swedish immigrant named August Imgard of Wooster, Ohio decorated a small pine tree with paper ornaments and candy canes." — Preceding unsigned comment added by 2601:603:5401:D6D0:58DF:4CFE:E916:B793 (talk) 23:57, 18 December 2023 (UTC)
 * The source does not say that he was first to use candy canes for decoration, not to say about "popularizing" this. - Altenmann >talk 00:15, 19 December 2023 (UTC)

 * Edited the language to make it less specific, and added the source mentioned above. No longer says the first, but one of the first, and removed the word popularized. Tooncool64 (talk) 00:39, 19 December 2023 (UTC)
 * The source does not say "one of the first" either. - Altenmann >talk 01:00, 19 December 2023 (UTC)
 * Ended up removing that sentence altogether, combining it with the next. The article no longer says he was the first or that he popularized it. Tooncool64 (talk) 01:16, 19 December 2023 (UTC)

Semi-protected edit request on 26 December 2023
Cite 31 (31] Huckabee, Tyler (9 December 2021). "No, Christmas Trees Don't Have 'Pagan' Roots". RELEVANT. Retrieved 5 March 2023. ) in reference to quote “ although there are no historical records of that” should be removed because this is a citation from an OPINION ARTICLE by a young freelance writer who lacks credibility because he does not cite any sources at all. History should not be able to be tampered with and rewritten according to opinion!! Please remove this quote and citation. DigbyDarling (talk) 00:26, 26 December 2023 (UTC)
 * Red information icon with gradient background.svg Not done: He actually does cite his source. The information the journalist wrote about is from Macrobius’ Saturnalia and he credits it as such. You may want to review WP:Reliable Sources, WP:Verifiability and WP:No Original Research for further details about why this source is allowed. Change not done. Thickynugnug (talk) 09:09, 26 December 2023 (UTC)

Photos/Illustrations to illustrate the Podłaźniczka subsection
I have removed the drawing but instead of returning the old photo of the ringed version, I have added one that depicts the most common type. While drawings can are are used in Wikipedia, the drawing you posted is of poor quality and arguably does not do a good job depicting the subject. However, photos of Podłaźniczka posted in Wikipedia Commons are also of poor quality. I have taken one that is marginal and color corrected, cropped, sharpened it to make it at least somewhat better. I strongly suggest if none of the photos are of good enough quality for you that you either take and submit better photos or seek out better photos that can be uploaded to Wikimedia Commons. Myotus (talk) 17:53, 17 May 2024 (UTC)
 * User:Myotus, perhaps this new image is a bit better. --E-960 (talk) 12:18, 22 May 2024 (UTC)
 * 02016 Bielitz-Saybuscher Festspiele "Pastuszki".JPG is dark and blurry but there still isn't much better. While it will do for now, we still should be on the look out for better images. Similar to the main Christmas tree image for the article the should be in "product shot" style. I have added the Template:Photo requested to the Podłaźniczka Talk page. Hopefully a good image will eventually be taken/found.
 * BTW, I love the uncropped photo of the image that is used. It should be used on the main Podłaźniczka page, showing it in context with a holiday activity. Myotus (talk) 14:21, 22 May 2024 (UTC)

title: Talk:Christmas tree


text:
Michael Holroyd

Sir Michael de Courcy Fraser Holroyd (born 27 August 1935) is an English biographer.

Early life and education
Holroyd was born in London, the son of Basil de Courcy Fraser Holroyd (a descendant of Sir George Sowley Holroyd, Justice of the King's Bench, whose ancestor was Isaac Holroyd, younger brother of George, the great-great-grandfather of John Baker Holroyd, 1st Earl of Sheffield), and his wife, Ulla (known as "Sue"), daughter of Karl Knutsson-Hall, a Swedish army officer. His parents having separated- their son "left to grow up in a bewilderingly extended family, shunted back and forth among parents and stepparents and grandparents and uncles and aunts"- Holroyd was raised at his father's family home, Norhurst, at Maidenhead, Berkshire. The Holroyds "for a time enjoyed a small fortune", provided by, amongst other things, an Indian tea plantation; this fortune was eventually "done in by mismanagement of resources and foolish investments" including investment in Lalique glassware, his grandfather having been its sole London agent in the 1920s. The Holroyd family had been "for several centuries" Yorkshire "butchers, clergymen, clothiers, farmers, landowners, soldiers, yeoman (sic) of all kinds".

He was educated at Eton College, though he has often claimed Maidenhead Public Library as his alma mater.

Career
In 1964, Holroyd published his first book, a biography of the writer Hugh Kingsmill; his reputation was consolidated in 1967–68 with the publication of his two-volume life of Lytton Strachey (which the playwright Christopher Hampton later used extensively when writing the screenplay for the 1995 film Carrington). Holroyd has also written biographies of Augustus John and, in four volumes, of Bernard Shaw. His book A Book of Secrets: Illegitimate Daughters, Absent Fathers (2010) concerns the Villa Cimbrone on the Gulf of Salerno and the Edwardian literary and society figures who lived there, such as Ernest Beckett, 2nd Baron Grimthorpe.

Lytton Strachey: A Critical Biography (1967, 1968) became Holroyd's definitive work. He published a revised version in 1994 under the revised subtitle The New Biography.

Holroyd was chairman of the Society of Authors, 1973–83, and from 1985 to 1988 was president of the English branch of PEN. He is also President of the Shaw Society. His awards include the 2001 Heywood Hill Literary Prize and the 2005 David Cohen Prize for literature. In 2006, he was awarded the Golden PEN Award by English PEN for "a Lifetime's Distinguished Service to Literature". He was president of the Royal Society of Literature from 2003 to 2008, and was knighted in the 2007 New Year Honours List. Holroyd is a patron of Dignity in Dying.

Personal life
Holroyd is married to the author Margaret Drabble.

Awards

 * 1968—Yorkshire Post Book Award (Book of the Year): Lytton Strachey: A Critical Biography
 * 1988—Irish Life Arts Award
 * 1989—CBE
 * 1995—Prix du Meilleur Livre Etranger (France)
 * 2001—Heywood Hill Literary Prize
 * 2003—Golden PEN Award
 * 2005—David Cohen British Literature Prize
 * 2007—Knighted for services to English Literature
 * 2008—James Tait Black Memorial Prize
 * 2010—Lifetime Services to Biography Award

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

title: Michael Holroyd


text:
User talk:Hecatonchires

Hello, welcome to Wikipedia. Here's some tips:
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 * If you have any questions, see the help pages, add a question to the village pump or ask me on my talk page.

Other useful pages are: how to edit, how to write a great article, naming conventions, manual of style and the Wikipedia policies.

I hope you enjoy editing here and being a Wikipedian! Angela. 00:13, Feb 24, 2004 (UTC)

Orphaned non-free image File:Simpson Thacher New Logo.gif
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title: User talk:Hecatonchires


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Vijay Anand (filmmaker)

Vijay Anand (22 January 1934 – 23 February 2004), also known as Goldie Anand, was an Indian filmmaker, producer, screenwriter, editor and actor, who is known for acclaimed films such as Guide (1965), Teesri Manzil (1966), Jewel Thief (1967) and Johny Mera Naam (1970). He made most of his films for the in-house banner Navketan Films and was part of the Anand family.

Background and personal life
Vijay Anand was born in Gurdaspur, Punjab, India, the son of Pishori Lal Anand, a successful and affluent advocate. He was the youngest of nine siblings. The producer and director Chetan Anand and the celebrated actor Dev Anand were his brothers, and among his sister was Sheel Kanta Kapur, mother of film director Shekhar Kapur.

Vijay married his much younger niece, Sushma Kohli, the daughter of his older sister. This uncle-niece pairing is forbidden in much of Indian society and was a scandal when it happened. The couple married in the face of resistance from many quarters, not least their own families, but they had a happy marriage which lasted all their lives. They have a son together named Vaibhav Anand.

Career
Though Vijay Anand has had a career as an actor, screenwriter, editor, and producer, he will primarily be remembered as a director. He made his directorial debut in 1957 superhit Nau Do Gyarah. The film, where Vijay's brother Dev Anand played the leading role, was shot in only 40 days.

Some of Vijay's other successful movies as a director are Kala Bazar (1960), Guide (1965), Teesri Manzil (1966), Jewel Thief (1967), Johny Mera Naam (1970), Tere Mere Sapne (1971), Ram Balram (1980) and Rajput (1982). Nearly all of these films were made by Navketan films, the production company started by the Anand brothers themselves. Notable exceptions wereTeesri Manzil, which was produced by Nasir Hussain," Ram-Balram" produced by Tony Juneja and "Rajput" produced by Mushir-Riaz.The period 1957-1970 must be reckoned the High Noon of Vijay Anand's career, as is evident from the films listed above. Vijay's 1965 film Guide starring Dev Anand and Waheeda Rehman, which was based on R. K. Narayan's novel of the same name, marked the acme of Vijay Anand's career. It was not only his biggest blockbuster but also his most critically acclaimed movie, celebrated by the masses, the classes and music-lovers alike. Navketan attempted an international release of an English-language remake of Guide, but without success.

Vijay Anand is known for his stylish song picturization, such as the numbers; "O Haseena Zulfonwali" (Teesri Manzil), "Aaj Phir Jeene Ki Tamanna Hai" (Guide) and "Honthon Mein Aisi Baat" (Jewel Thief).

He debuted as an actor with the film Agra Road (1957). As an actor, his most memorable roles were in the films like Kala Bazar (1960), Haqeeqat (1964), Kora Kagaz (1974), (in which he starred opposite Jaya Bachchan) and Main Tulsi Tere Aangan Ki (1978). Songless thriller film Chor Chor (1974), in which Leena Chandavarkar was his heroine. He acted in Ghungroo Ki Awaaz (1981) and Double Cross (1972) with Rekha as well as Chhupa Rustam (1973) and Tere Mere Sapne with Dev Anand, Hema Malini & Mumtaz.

To the younger generation of the 1990s he is also known for playing detective Sam in the television series Tehkikaat (1994).

He served a short stint as the chairman of the Central Board of Film Certification, India's censor board, a position from which he resigned, in 2002, after he ran into ideological differences with the government over the introduction of ratings for adult movies.

Goldie, as he was affectionately called, died on 23 February 2004 due to a heart attack. He was aged 70.

Director

 * Nau Do Gyarah (1957)
 * Kala Bazar (1960)
 * Tere Ghar Ke Samne (1963)
 * Guide (1965)
 * Teesri Manzil (1966)
 * Jewel Thief (1967)
 * Kahin Aur Chal (1968)
 * Johny Mera Naam (1970)
 * Tere Mere Sapne (1971)
 * Blackmail (1973)
 * Chhupa Rustam (1973)
 * Bullet (1976)
 * Ek Do Teen Chaar (1980)
 * Ram Balram (1980)
 * Rajput (1982)
 * Main Tere Liye (1988)

Writer

 * Taxi Driver (1954)
 * Hum Dono (1961)

Actor

 * Agra Road (1957) - Sunil
 * Kala Bazar (1960) - Nand Kumar Chattopadhyay
 * Haqeeqat (1964) - Major Pratap Singh
 * Tere Mere Sapne (1971) - Dr. Jagannath Kothari
 * Double Cross (1972) - Ajay Arya / Vijay Arya / Jimmy
 * Chhupa Rustam (1973) - Jimmy Fernandes
 * Kora Kagaz (1974) - Professor Sukesh Dutt
 * Chor Chor (1974) - N/A
 * Main Tulsi Tere Aangan Ki (1978) - Thakur Rajnath Singh Chouhan
 * Ghungroo Ki Awaaz (1981) - Thakur Ranjeet Singh
 * Tehkikaat (1994) - Sam D'Silva

Legacy
Sriram Raghavan's Johnny Gaddar, a Film noir style thriller is dedicated to his influence on the Hindi noir/thriller genre. It also pays tribute to him in a scene in which his movie Johny Mera Naam is being watched by a character and there he takes the name johnny to hide his identity. In another scene, an actor is shown reading the book, The Guide, a reference to one of the most famous films directed by him.

A retrospective of his films was held at International Film Festival of India (IFFI), held at Goa in 2007.

His film Guide has been studied and analyzed by several writers and thinkers. The book Guide the Film Perspectives has an in-depth study on the genius of the director running through the film. He also acted in television serial tehqiqat on Delhi doordarshan.

Awards

 * Filmfare Award for Best Director for Guide (1965)
 * Filmfare Award for Best Dialogue for Guide (1965)
 * Filmfare Award for Best Screenplay for Johnny Mera Naam (1970)
 * Filmfare Award for Best Editing for Johnny Mera Naam (1970)
 * BFJA Awards as Best Editor for Johnny Mera Naam (1970)
 * BFJA Awards as Best Editor for Double Cross (1972)

title: Vijay Anand (filmmaker)


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Non-Partisan Association

The Non-Partisan Association (NPA) is a municipal political party in Vancouver, British Columbia, Canada. It was established by the city's business leaders in 1937 to challenge the democratic socialist Co-operative Commonwealth Federation (CCF) in that year's municipal election. The party has historically been described as centre-right and drawn its strongest support from Vancouver's business community.

In the years following the 2018 municipal election, seven of the NPA's ten elected officials resigned from the party, claiming that it had become right-wing and undemocratic. Several other prominent members, such as the NPA's 2018 mayoral candidate Ken Sim, also resigned. Most of those departing later joined ABC Vancouver in the run-up to the 2022 municipal election, which saw Sim elected as mayor and the NPA lose all its remaining seats.

Early years
The NPA was established by Vancouver's business leaders on November 13, 1937, to counteract the growing influence of the CCF. Fearful of a CCF victory in the Vancouver municipal election on December 8, 1937, provincial politicians from the then-ruling BC Liberal Party launched an initiative to create a pro-business municipal party to challenge the CCF. The NPA's first chairman was Victor Odlum, a prominent member of Vancouver's business and political elite who had served as a Liberal MLA from 1924 to 1928. Other founding members of the NPA include W. C. Woodward of Woodward's department store, Victor Spencer of Spencer's department store, and industrialist Austin Taylor. Despite its party connections, the NPA claimed it was not a party, but rather a "free enterprise coalition" which "oppose[d] the introduction of party politics into Vancouver's civic administration".

The NPA first fielded candidates in the December 9, 1936, municipal election, which saw their mayoral candidate, George Miller, elected to office. Miller later ran in provincial elections for the BC Progressive Conservative Party. Prior to the 1939 election, a member of the NPA's executive, Nelson Spencer, broke away from the party and ran independently after the NPA chose the then-incumbent Miller as its mayoral candidate instead of Spencer. The result was that the right-wing vote was split, and CCF candidate Lyle Telford was elected. Telford would only serve one term before NPA candidate Jack Cornett was elected in the 1940 election, beginning a decades-long period of NPA dominance on Vancouver City Council.

21st century

Jennifer Clarke was chosen to be the NPA's mayoral candidate for the 2002 municipal election, as opposed to the then-incumbent mayor Philip Owen. Owen had been in disagreement with the rest of the party leadership due to his support for harm reduction programs in the Downtown Eastside, although Clarke stated she was also in favour of such programs. The NPA ultimately lost the mayoral race, as well as its majority on city council that it had maintained since 1986.

Long-time city councillor Sam Sullivan was chosen as the NPA's candidate for the 2005 mayoral race, which he later won. The NPA also regained its majority on city council, winning a total of six seats.

Peter Ladner was the NPA's mayoral candidate for the 2008 municipal election but was defeated by Gregor Robertson, the candidate for Vision Vancouver. The NPA's electoral platform during the 2008 election focused on reducing crime, improving housing affordability, leveraging the 2010 Winter Olympics, protecting the environment, advancing the city's arts and culture sector, and working collaboratively with senior levels of government, community groups, and the private sector.

The party, led by Suzanne Anton as the NPA's mayoral candidate, once again lost to Robertson and Vision Vancouver in the 2011 municipal election but elected two members to Vancouver City Council. Two members were also elected to the Park Board, and three members to the Vancouver School Board.

On October 16, 2016, provincial education minister Mike Bernier fired the school trustees elected during the 2014 municipal election for failing to pass a balanced budget. NPA incumbent Fraser Ballantyne was re-elected in the subsequent 2017 municipal by-election, alongside newcomer Lisa Dominato.

City councillor Rebecca Bligh announced on December 6, 2019, that she was leaving the NPA but would continue to serve as an independent. She cited concerns over the NPA's newly elected executive team, which included members publicly opposed to the provincial sexual orientation and gender identification (SOGI) curriculum and former staff of the far-right Rebel Media. Other high profile NPA members, such as city councillor Sarah Kirby-Yung and 2018 mayoral candidate Ken Sim, also voiced concerns over the party's perceived shift to the right.

Three of the NPA's four remaining councillors – Lisa Dominato, Colleen Hardwick, and Sarah Kirby-Yung – announced on April 21, 2021, that they would be leaving the NPA to sit as independents, following the decision of the board to appoint Park Board commissioner John Coupar as the 2022 NPA mayoral candidate, the board's refusal to hold an annual general meeting despite a request to do so from all its elected politicians, and broad accusations of a lack of transparency on the board's behalf. Two days later, all three of the NPA's school trustees resigned from the party as well, leaving an elected caucus of one councillor (Melissa De Genova) and two Park Board commissioners (John Coupar and Tricia Barker). On August 5, 2022, Coupar resigned as the NPA's mayoral candidate, with the party indicating it would nominate a new candidate before the ballot deadline. Fred Harding, a retired police officer who ran for mayor with the Vancouver 1st party in the 2018 election, was subsequently announced as the NPA's new mayoral candidate.

Most of the elected officials who resigned from the NPA later joined ABC Vancouver in the run-up to the 2022 municipal election, which saw Ken Sim elected as mayor and the defeat of all NPA incumbents.

Electoral results
The NPA held a majority on Vancouver City Council from 1941 to 1967, 1970 to 1972, 1978 to 1980, 1986 to 2002, and from 2005 to 2008. It held the mayor's office from 1941 to 1958, from 1963 to 1966, from 1986 to 2002, and from 2005 to 2008. However, it has elected only three of the last eight mayors since 1972. Over the years, its opposition has been The Electors' Action Movement (TEAM) in the 1970s, the left-wing Coalition of Progressive Electors (COPE) in the 1980s and 1990s, and centre-left Vision Vancouver in the 2000s and 2010s.

There have been eleven NPA mayors of Vancouver:
 * Jack (Jonathan Webster) Cornett (1941–1946)
 * Gerry McGeer (1947)
 * Charles E. Jones (1947–1948)
 * George Clark Miller (acting) (1948)
 * Charles Edwin Thompson (1949–1950)
 * Frederick Hume (1951–1958)
 * William Rathie (1963–1966)
 * Tom Campbell (1967–1972)
 * Gordon Campbell (1986–1993)
 * Philip Owen (1993–2002)
 * Sam Sullivan (2005–2008)

title: Non-Partisan Association


text:
Periodogram

In signal processing, a periodogram is an estimate of the spectral density of a signal. The term was coined by Arthur Schuster in 1898. Today, the periodogram is a component of more sophisticated methods (see spectral estimation). It is the most common tool for examining the amplitude vs frequency characteristics of FIR filters and window functions. FFT spectrum analyzers are also implemented as a time-sequence of periodograms.

Definition
There are at least two different definitions in use today. One of them involves time-averaging, and one does not. Time-averaging is also the purview of other articles (Bartlett's method and Welch's method). This article is not about time-averaging. The definition of interest here is that the power spectral density of a continuous function, $$x(t),$$ is the Fourier transform of its auto-correlation function (see Cross-correlation theorem, Spectral density, and Wiener–Khinchin theorem): $$\mathcal{F}\{x(t)\circledast x^*(-t)\} = X(f)\cdot X^*(f) = \left| X(f) \right|^2.$$

Computation

For sufficiently small values of parameter $T,$ an arbitrarily-accurate approximation for $X(f)$ can be observed in the region $$-\tfrac{1}{2T} < f < \tfrac{1}{2T}$$  of the function:

$$X_{1/T}(f)\ \triangleq \sum_{k=-\infty}^{\infty} X\left(f - k/T\right),$$

which is precisely determined by the samples $x(nT)$ that span the non-zero duration of $x(t)$ (see Discrete-time Fourier transform).

And for sufficiently large values of parameter $N$, $$X_{1/T}(f)$$ can be evaluated at an arbitrarily close frequency by a summation of the form:

$$X_{1/T}\left(\tfrac{k}{NT}\right) = \sum_{n=-\infty}^\infty \underbrace{T\cdot x(nT)}_{x[n]}\cdot e^{-i 2\pi \frac{kn}{N}},$$

where $k$ is an integer. The periodicity of $$e^{-i 2\pi \frac{kn}{N}}$$  allows this to be written very simply in terms of a Discrete Fourier transform:

$$X_{1/T}\left(\tfrac{k}{NT}\right) = \underbrace{\sum_{n} x_{_N}[n]\cdot e^{-i 2\pi \frac{kn}{N}},}_\text{DFT} \quad \scriptstyle{\text{(sum over any }n\text{-sequence of length }N)},$$

where $$x_{_N}$$ is a periodic summation: $$x_{_N}[n]\ \triangleq \sum_{m=-\infty}^{\infty} x[n - mN].$$

When evaluated for all integers, $k$, between 0 and $N$-1, the array: $$S\left(\tfrac{k}{NT}\right) = \left| \sum_{n} x_{_N}[n]\cdot e^{-i 2\pi \frac{kn}{N}} \right|^2$$ is a periodogram.

Applications

When a periodogram is used to examine the detailed characteristics of an FIR filter or window function, the parameter $N$ is chosen to be several multiples of the non-zero duration of the $x[n]$ sequence, which is called zero-padding (see ). When it is used to implement a filter bank, $N$ is several sub-multiples of the non-zero duration of the $x[n]$ sequence (see ).

One of the periodogram's deficiencies is that the variance at a given frequency does not decrease as the number of samples used in the computation increases. It does not provide the averaging needed to analyze noiselike signals or even sinusoids at low signal-to-noise ratios. Window functions and filter impulse responses are noiseless, but many other signals require more sophisticated methods of spectral estimation. Two of the alternatives use periodograms as part of the process:
 * The method of averaged periodograms, more commonly known as Welch's method,   divides a long x[n] sequence into multiple shorter, and possibly overlapping, subsequences.  It computes a windowed periodogram of each one, and computes an array average, i.e. an array where each element is an average of the corresponding elements of all the periodograms.  For stationary processes, this reduces the noise variance of each element by approximately a factor equal to the reciprocal of the number of periodograms.
 * Smoothing is an averaging technique in frequency, instead of time. The smoothed periodogram is sometimes referred to as a spectral plot.

Periodogram-based techniques introduce small biases that are unacceptable in some applications. Other techniques that do not rely on periodograms are presented in the spectral density estimation article.

title: Periodogram


text:
Pākehā Māori

Pākehā Māori or Pakeha Maori were early European settlers (known as Pākehā in the Māori language) who lived among the Māori in New Zealand.

History
Many Pākehā Māori were runaway seamen or escaped Australian convicts who settled in Māori communities by choice.

A few Pākehā Māori such as James Caddell, John Rutherford and Barnet Burns even received moko (facial tattoos).

In 1862 and 1863, the early settler Frederick Edward Maning published two books under the pseudonym "A Pakeha Maori" in which he describes how they lived.

Notable Pākehā Māori

 * Kimball Bent
 * Barnet Burns
 * James Caddell
 * Thomas Kendall
 * David MacNish
 * Frederick Edward Maning
 * Jacky Marmon
 * John Rutherford

Similar people in other countries

 * Jim Bridger
 * Caramuru
 * Isaac Davis
 * Gonzalo Guerrero
 * John Young

title: Pākehā Māori


text:
Cranbrook, British Columbia

Cranbrook is a city in southeast British Columbia, Canada, located approximately 10 km southwest of the confluence of the Kootenay River and the St. Mary's River. It is the largest urban centre in the region known as the East Kootenay. As of 2016, Cranbrook's population is 20,499 with a census agglomeration population of 27,040. It is the location of the headquarters of the Regional District of East Kootenay and also the location of the regional headquarters of various provincial ministries and agencies, notably the Rocky Mountain Forest District.

According to the Cranbrook Daily Townsman, dated 9 February 2022, Cranbrook has a population of 20,499. This is also indicated in the latest census data on the Government of Canada website.

Cranbrook is home to the Canadian Museum of Rail Travel which presents static exhibits of passenger rail cars built in the 1920s for the CPR and in the 1900s for the Spokane International Railway.

History
Originally inhabited by Ktunaxa peoples, the land that Cranbrook now occupies was bought by European settlers, notably Colonel James Baker who named his newly acquired land Cranbrook after his home in Cranbrook, Kent, England. In 1890, the Kootenay Indian Residential School, also called St. Eugene's, opened in Cranbrook, and operated until 1975.

In 1898, Baker had successfully convinced Canadian Pacific Railway to establish their Crowsnest Pass line through Cranbrook rather than nearby Gold Rush Boom Town Fort Steele. With that accomplishment Cranbrook became the major centre of the region, while Fort Steele declined; however, the latter is today a preserved heritage town.

On November 1, 1905, Cranbrook was incorporated as a city.

Some of the major industries include mining and forestry services, trades, and health care.

Geography
While much of the city is relatively flat, Cranbrook is surrounded by many rising hills where many residential homes are located. Cranbrook faces the Purcell Mountains to the west and the Rocky Mountains to the north and east. There are many lakes in close proximity to Cranbrook. Some of these lakes include Jim Smith Lake, Wasa Lake, Lazy Lake, Moyie Lake, Monroe Lake, Norbury Lake and Elizabeth Lake. Many of these lakes contain opportunities for boating, fishing and camping. There are public recreational beaches and provincial campgrounds.

Climate
Cranbrook features a humid continental climate (Dfb) under the Köppen climate classification. Environment and Climate Change Canada reports Cranbrook as having the most sunshine hours of any BC city at approximately 2190.5 hours annually. It is a fairly dry city throughout the year, and when precipitation does fall a good percentage of it will be in the form of snow. Environment and Climate Change Canada also states that the city experiences some of the lightest wind speeds year-round, has few foggy days, and has among the highest average barometric pressure of any city in Canada. Frost-free days average 110 days, typically occurring between May 26 to September 14. Mean daily temperatures range from -8.3 C to 18.2 C. However, temperatures can range from -20 C in the winter to 35 C in the summer months. Overall, its climate is extremely similar to that of Kelowna, in the nearby Okanagan Valley to the west - especially in regard to precipitation patterns and total monthly accumulation. However, Kelowna is significantly warmer throughout all seasons.

The highest temperature ever recorded in Cranbrook was 40.5 C on August 10, 2018. The coldest temperature ever recorded was -41.1 C on January 19, 1958.

Demographics
In the 2021 Canadian census conducted by Statistics Canada, Cranbrook had a population of 20,499 living in 8,780 of its 9,058 total private dwellings, a change of NaN% from its 2016 population of 20,047. With a land area of 31.97 km2, it had a population density of in 2021.

Religion
According to the 2021 census, religious groups in Cranbrook included:
 * Irreligion (11,190 persons or 56.4%)
 * Christianity (8,060 persons or 40.6%)
 * Sikhism (155 persons or 0.8%)
 * Hinduism (120 persons or 0.6%)
 * Buddhism (85 persons or 0.4%)
 * Islam (45 persons or 0.2%)
 * Indigenous Spirituality (25 persons or 0.1%)
 * Judaism (15 persons or 0.1%)

Schools
Public schools are run by School District 5 Southeast Kootenay, consisting of seven elementary schools and two middle schools that feed into the city's only high school: Mount Baker Secondary School, home to approximately 1,000 students and 90 staff members. Mount Baker is the largest high school in school district five. Prior to 2004, the middle schools were referred to as junior high schools housing grades 8-10 rather than the current 7–9. However, due to declining enrollment, the school district adopted the new system. There is also a local home-school network.

The following 13 schools are located in Cranbrook.
 * Aqamnik Elementary School (First Nations school located in St. Mary's Band)
 * Amy Woodland Elementary
 * Gordon Terrace Elementary
 * Highlands Elementary School
 * Kootenay Christian Academy
 * Kootenay Orchards Elementary School
 * Laurie Middle School
 * Mount Baker Secondary School
 * Parkland Middle School
 * Pinewood Elementary School
 * St. Mary's Catholic Independent School (private school)
 * Steeples Elementary School
 * T M Roberts Elementary School

Post-secondary education
Cranbrook is home to the main campus of the College of the Rockies, which has over 2,500 full and part-time students from over 21 countries.

Transportation
Cranbrook is at the junction of major highways 3 and 93/95, and due to its close proximity to the borders of Alberta and the United States, it is an important transportation hub. Cranbrook has a major Canadian Pacific Railway yard, which serves as a key gateway for trains arriving from and departing to the United States.

The McPhee Bridge also known as the St. Mary's Bridge rises high above the St. Mary River and is near the Cranbrook/Canadian Rockies International Airport and the Shadow Mountain Golf Community. It supports the thousands of people who travel between Kimberley and Cranbrook on highway 95A.

Approximately 5 NM north is the Cranbrook/Canadian Rockies International Airport, which has recently completed its 12.5 million dollar expansion including the lengthening of its runway from 6000 to 8000 ft feet in order to accommodate a limited number of international flights and an expansion to the Terminal for more passengers. The airport is served by Air Canada Jazz to Vancouver, Pacific Coastal Airlines to Victoria and Kelowna, and WestJet Link to Vancouver and Calgary. On February 11, 1978, Pacific Western Airlines Flight 314, a Boeing 737-200, nearly impacted a snowplow on the runway at the airport in Cranbrook, then lost control and crashed, killing 42 of the 49 people on board.

Cranbrook has a public transit system operated by BC Transit, which runs buses on eight different lines.

Health care
Cranbrook has the largest hospital in the region, the East Kootenay Regional Hospital.

Sports and recreation
Western Financial Place (formerly called the RecPlex) is a pool and hockey arena in Cranbrook that opened in 2000, and was formerly the home to the Kootenay Ice until relocating to Winnipeg, Manitoba, in 2019. Following their departure, the recreational centre became home to the Cranbrook Bucks who play in the BCHL. A paved, two-lane 28 km trail exists between Cranbrook and Kimberley, BC. This trail constitutes a section of the Trans-Canada Trail and is known as the Rails to Trails. Canadian Pacific Railway donated the rail right-of-way and the teardown of the railway began by CP Rail in 2009. In addition to this trail, there are 2000 acres of wilderness to explore in the community forest.

Media

 * Newspapers
 * Cranbrook Daily Townsman - Daily paper

 * Radio stations
 * 101.3 FM - CBRR-FM, CBC Radio One (repeats CBTK-FM, Kelowna)
 * 102.9 FM - CHDR-FM, 102.9 REWIND RADIO
 * 104.7 FM - CHBZ-FM, B-104, Country
 * 107.5 FM - CFSM-FM, 107.5 2day FM, Adult Contemporary

 * Television
 * Channel 5: (Air) Channel 4: (Cable) CFCN-TV-9, CTV (analogue repeater of CFCN-DT Calgary)
 * Shaw TV (community cable channel)

Notable people
The following notable people come from or were born in Cranbrook:

 * Ray Allison, retired NHL player
 * Greg Andrusak, retired NHL player
 * Bowen Byram, NHL player
 * Brent Carver, actor
 * Glen Cochrane, retired NHL player
 * Tanya Fir, Member of the Alberta Leglislature, 2019-
 * James Heilman, doctor
 * Jim Hiller, NHL head coach, retired NHL player
 * Dryden Hunt, NHL player
 * Juggernaut, retired professional wrestler
 * Jon Klemm, retired NHL player
 * Lillix, former pop rock band
 * Bernie Lukowich, retired NHL player
 * Brad Lukowich, retired NHL player
 * Donald C. MacDonald, politician
 * Jason Marshall, retired NHL player
 * Bob McAneeley, former WHA player
 * Ted McAneeley, retired NHL and WHA player
 * Evah McKowan, novelist
 * Bob Murdoch and Don Murdoch, retired NHL players
 * Riley Nelson, retired ECHL player and captain for the Colorado Eagles
 * Rob Niedermayer, retired NHL player
 * Scott Niedermayer, retired NHL player
 * Kate Pullinger, author
 * Tom Renney, former NHL and Olympic ice hockey coach
 * Ben Rutledge, Olympic gold medal rower
 * Joel Savage, retired NHL player
 * Terry Segarty, businessman and BC Minister of Labour
 * Jonathan Shewchuk, computer science professor
 * Corey Spring, retired NHL player
 * Frank Spring, retired NHL player
 * David Sweet, OC, Officer of the Order of Canada for work in forensic odontology
 * Steve Yzerman, retired NHL player
 * Tom Shypitka, three time Provincial Curling Champion (1979, 1991, 2010)

Sister cities
Cranbrook is twinned with
 * Coeur d'Alene, Idaho (United States)

title: Cranbrook, British Columbia


text:
Talk:Chinese martial arts

Qi and Western science
"The existence of qi as a measurable form of energy as discussed in traditional Chinese medicine has no basis in the scientific understanding of physics, medicine, biology or human physiology.[47]" The cited source is " Ernst, Edzard; Simon Singh (2009). Trick or treatment: The undeniable facts about alternative medicine. W. W. Norton & Company. ISBN 978-0393337785." Why is it necessary to include this statement? You might as well include the statement that "however Western science is limited by the tools it has with which to examine the world, as it always has been". Qi of course does have it's "basis" in spiritual and religious understanding of many religions and yogic practices. 83.84.100.133 (talk) 11:41, 7 April 2020 (UTC)

Removal of qi as part of a s pseudoscience, the root meaning of qi can be seen as transformation. Just because something from another culture has not been explained properly does not make it not Science based. To talk as it is better to clarify things like this of a caltural nature than to insight prejudice that will bring more harm than good. The world Heath organisation has just recognised Traditional Chinese Medicine. The understanding of Qi comes with this. When it comes to understanding the nature of qi it is time for those that do not know to go back to study and learn some more. I am happy to talk about the some of the basics of this study. But for me it has been fifty years so far. Amituofo 🙏🏼🙏🏼🙏🏼 Shenqijing (talk) 04:15, 22 September 2020 (UTC)

Discipleship
Most long-term practitioners of traditional Chinese martial arts, and all teachers of them, are familiar with the concept of Discipleship. A fine section has been written on the subject matter, but it is being consistently deleted by a Wikipedia user whose nickname is MrOllie. I call upon professionals in the field and genuine martial artists to intervene and prevent the continuation of this trolling campaign. — Preceding unsigned comment added by 187.244.113.106 (talk) 23:57, 16 May 2021 (UTC)

 * Please have a look at WP:RS. We cannot rely on self published books as citations. Adding a few more citations on top of them does not solve the essential problem that the section depends on unreliable, self published materials. - MrOllie (talk) 00:01, 17 May 2021 (UTC)

 * Your claims are incorrect. The section does not rely solely on these sources, as I have added references to 7 books which are not self-published and to two feature-films which were produced by studios. You are obviously an internet bureaucrat and not a practitioner of traditional Chinese martial arts. You have deleted the section once more without actually reviewing or reading any of the sources which were referenced. Your keyboard bullying does not do justice to this page or to these traditions. How about you google the joint terms "discipleship" and "chinese martial arts". Is it a coincidence you get 42,000 results? No, because this topic is central to the history and lore of these arts, and you are here engaged in a silly power-grab from behind the safety of your screen from far away, enjoying the little game of having control over information which pertains to traditions that you are not a part of. This is literally a no-brainer, as basically ANY and ALL teachers of traditional Chinese martial arts teachers are aware of the facts presented in this section. Every single one of them. It's common knowledge, not special commentary.  187.244.113.106 (talk) 00:08, 17 May 2021 (UTC)

 * If you would like your content to remain on Wikipedia, it will be much more effective to learn our policies and write with them in mind. A paragraph full of personal attacks isn't going to get you anywhere. - MrOllie (talk) 00:11, 17 May 2021 (UTC)

 * Look... I would agree with you that concerning matters of personal commentary or interpretation about a topic, one needs to bring forth sound evidence, and support for any claims being made. But on the subject of traditional Chinese martial arts, to state that Discipleship exists and to portray it in the manner that I did, is akin to suggesting that a car has wheels. Really. Check out the sources, by all means. I referenced a book by professor Peter Lorge, for instance. He is an internationally renown authority of the history of Chinese martial arts and related cultural aspects. His book alone, which has an enormous pile of academically-valid references, could support that section all by itself. But the other books, and the experts who wrote them, do a job just as good in my opinion. Take another example - Jess O'Brien's book, 'Nei Jia Quan'. That book includes in-depth scholarly interviews with over a dozen masters of traditional Chinese martial arts, and most of them refer to Discipleship either directly or indirectly. Please, read the books! You have dismissed such works but you are not familiar with the source material and the subject at hand. Discipleship is a tradition that goes back over 3000 years in China, and is strongly rooted in Confucianism. In martial arts you see it being referenced as a concept as far back as The Romance of the Three Kingdoms, which is one of the most important books in Chinese history, whose plot is referring to Chinese customs as they were nearly 2000 years ago. 00:20, 17 May 2021 (UTC)
 * Why cite trash-level sources from the likes of createspace and amazon selfpublished ebooks, then? Just write a version based on what Lorge has to say about it and leave out the rest. - MrOllie (talk) 00:27, 17 May 2021 (UTC)
 * The point about this social construct of 'Discipleship' is to manifest the Confucian relationship between father-son/master-disciple, which cannot be formally manifested without proper ceremony. Confucius taught that the ceremonies and rituals were of utmost importance for social order, and in The Analects, a book about his teachings, are explained the social virtues expected in this relationship of father-son/master-disciple. To have a Discipleship is means by which teachers of traditional Chinese martial arts are often able to build better trust and a stronger bond with students, in a paradigm which was originally devoid of rank or financial incentives. This is a very Chinese idea about relationships, that they ought to be formalized with ritual and ceremony, and embody a 'family-like dynamic' in order to deepen. The bowing thrice comes from feudal traditions in China, and the offering of tea, and sometimes a gift, is meant to symbolize the student 'feeding' his 'new parent'. 187.244.113.106 (talk) 00:48, 17 May 2021 (UTC)
 * May I ask you - by what judgement or account do you refer to these sources as 'trash', via the sole virtue of them being self-published? I have read these works in the past and found them to be excellent and up to standard - which is why they are referenced. I googled now and found the following article: https://selfpublishingadvice.org/famous-self-publishing-authors/   .  It claims the following famous authors were all self-published:  Margaret Atwood, Frank Baum, William Blake ,Ken Blanchard, Robert Bly, Beatrix Potter Alfred, Lord Byron, Willa Cather, Julia Cameron, Pat Conroy, Stephen Crane,  e.e. cummings, Charles Dickens, Roddy Doyle W.E.B. DuBois, Alexander Dumas, T.S. Eliot, Lawrence Ferlinghetti, Benjamin Franklin, and many others (listed at the link). How would they fare in their time, if Wikipedia existed and someone was to comment that their works are "trash" because they are self-published, and he had not read them?
 * Adding to this, I would argue that with this particular section, some bias is actually due. We are here overall discussing a prevalent tradition which includes similar concepts and actions, such as the father-son/master-disciple relationship, the tea-offering and the bowing. However, there is variance between the schools, sects and lineages. It is therefore important to have sources which showcase their bias - such is evidence to their special minor divergences from the norm in terms of practice and ceremony.
 * Furthermore, the world of traditional martial arts (not solely the Chinese ones) is non-academic by nature. These are traditions being promoted by families and lineages. None of these people sits in a laboratory or quotes by the standards of Academia. Wikipedia is not going to change the manner in which this has been carried out for thousands of years. Most articles of Chinese culture on Wikipedia reflect this.
 * The notion that one could simply ignore a key thematic concept pertaining this this broad subject, borders on cultural racism. Not that I blame your for it, but please allow me to explain. There are certain things in a culture which are a given. Any Chinese person alive who lives in China, knows that the Shifu-Tudi relationship exists in these traditions. It is a cultural given. It is a given about as much as the fact that there was/is Italian Mafia in New York City, or that there are tensions between Native Americans and the US Government over land and oil. However, it would be ludicrous for anyone on Wikipedia to doubt that the Italian Mafia or Native American tensions over land or oil exist, because all Americans know this, as do most people who were born and live in English-speaking countries. You are herein casting doubt on a cultural element which is a given, because of your unfamiliarity with Chinese traditional culture. See what I mean?... Of course one needs sources to back up more detailed claims concerning even cultural givens, but some things do not need a special justification.
 * Instead of attacking the sources and the subject matter as such, please do a little bit of research. Google the thing and read about it for a few hours. Or better yet - randomly approach teachers of traditional Chinese martial arts, and ask them about it. You will then see that the section is perfectly reasonable, and that the sources are valid. 187.244.113.106 (talk) 00:48, 17 May 2021 (UTC)
 * I would like to add, that one cannot make a case for the supposedly 'objective' nature of works put out through publishers, as compared with those which are self-published. A publishing house is usually a private or public company. The majority of Western nations have corporate laws which strictly state that the sole or primary goal of a commercial company is to make money. This goal is not necessarily in-line with either objectivity or truth. A publishing house is not akin or equivalent to the environment provided by a peer-reviewed journal. That being said, with respect to cultural elements pertaining to chinese martial arts, there are no peer-reviewed journals, and the publishing houses, as stated before, are primarily motivated by what will sell more copies - the corporate laws require this of them, unless they are a non-profit, and most of them are not. The only valid way therefore to make an estimate of the references in such a case is to consider what is written, and who were the authors. The entire premise for the deletion of this section therefore, was not based on sound logic, but rather on rules and regulations which are irrelevant to the subject at hand. Yet even if we were to accept this argument, it seems to me that Wikipedia is still lenient with self-published sources, as long as they were authored by 'experts'. I do believe that everyone who authored the sources which had been referenced here were indeed experts. 187.244.113.106 (talk) 00:58, 17 May 2021 (UTC)
 * Again, please read WP:RS. With only very limited exceptions, self published sources are not used on Wikipedia. The whole point of WP:V is that we do not expect our readers to go ask a bunch of people in person if our articles are accurate. The way we do this is by using only sources that have a reputation for fact-checking and editorial control. That includes academic publishers, and excludes the likes of createspace, where anyone can write anything and get it published. If this field is 'non-academic by nature' it may not be a good fit for Wikipedia. Perhaps you could start a blog or something, there you would not be responsible for meeting Wikipedia's sourcing standards. If you'd like instead to argue that Wikipedia's sourcing requirements are illogical and should be changed, you can bring that up at WP:RSN, but you should not expect your content to remain on Wikipedia if you are going to simply ignore our content policies. - MrOllie (talk) 01:01, 17 May 2021 (UTC)
 * You are once more ignoring all of the facts and arguments I have placed before you, by plainly and solely appealing to 'protocol' as an escape. Read above: Alexander Dumas and Benjamin Franklin were self-published. So they are "not a good fit for Wikipedia" because "they have no editorial control" and "are not academic"?... This is beyond silly. These two gentlemen, and the many others I have listed and linked to above, were self-published before they were famous. Which means, that they gained fame, and rightfully so, because society was not bickering over the fact that they were self-published, but rather judged them by the contents of what they wrote, said and did.
 * Much as "anyone can publish on CreateSpace" (which is not entirely true, by the way), anyone with something that sells well can have their work picked up by a big publisher. A porn star with no gray matter (and no offense to the smart ones among them) can get anything printed through a publisher if she is famous. Anything. As a matter of fact, unlike self-published authors, he or she would often who not even have to write the book themselves. Thus, a self-published author who is an expert in a field of interest, has much more credibility with respect to facts as compared with an author with a big publisher who was selected due to their fame.
 * Then what of this statement of yours, that "if something 'non-academic by nature' it may not be a good fit for Wikipedia". Are you kidding me? You just ruled out the existence of pages concerning Jimmy Hendrix, Recreational Fishing, Carpentry and Stamp Collecting. Something does not have to be 'academic' to be on Wikipedia.
 * Furthermore, this appeal to 'fact-checkers' is an entirely new fashion, not even 5 years old. Are you truly proposing that we negate Chinese cultural traditions which are thousands of years old because they have to give way to 'fact-checkers'? Again, this stinks of cultural racism, mind you.
 * Then when you say "our policies"... Excuse me? This is a free enterprise for all people. This website does not belong to you or to them, it belong to us - to me as well. This is not a privately owned business, and neither is it intended solely for academics.  187.244.113.106 (talk) 03:03, 17 May 2021 (UTC)

I would like to point out several additional arguments as to why this section on Discipleship is relevant and important for this page:

1. The Discipleship section is directly preceded by the section on Wu De - Martial Morality. I have not chosen that location on the page by coincidence. Wu De is a concept which is strongly linked with the institution of the Shifu-Tudi discipleship relationship. One is usually required to abide by Wu De to become a disciple, and is expected to be an exemplar of Wu De after having become a disciple.

2. Chinese Culture is inherently a Confucian Culture, a fact agreed upon universally by all East-Asian scholars. The Shifu-Tudi relationship of discipleship is dictated by Confucian values and social norms and expectations.

3. The institution of Discipleship is intrinsically woven into the history of traditional Chinese martial arts, and is the source of much lore and political intricacies.

4. Lineages of traditional Chinese martial arts are based on the discipleship model. This is apparent and exemplified, for example, in Xing Yi Quan, Bagua Zhang and Taiji Quan, and discussed on their respective pages on Wikipedia.

5. Several of the teachers mentioned in the extant section of 'Notable Teachers' were disciples, such as Ip Man, Gu Ruzhang, Yang Luchan, etc.

6. Discipleship is a main theme in the literary genre of Wuxia, which was already previously mentioned and referenced on this page.

7. Discipleship is a main theme in the cinematic genre of Kung fu Films, which was already previously mentioned and referenced on this page. 187.244.113.106 (talk) 04:46, 17 May 2021 (UTC)

 * Yes, you are correct, I am not engaging with arguments that are not based on Wikipedia policies. They amount to special pleading. If you think the policies are no good, you can get them changed, but you cannot just filibuster on the talk page and then ignore them. - MrOllie (talk) 11:09, 17 May 2021 (UTC)

 * Your bureaucratic megalomania with which you are trying to eliminate prominent and important aspects of traditional Chinese culture, is most improper. As I have noted before, this borderlines cultural racism. It is like suggesting Baseball should not be on Wikipedia.

 * There are now as references:

 * * 10 Books and 6 articles - only a minority of which are self-published, but are nonetheless valid and useful. All of the books and articles were written by experts, and I challenge you to refute that.

 * * 12 films and 2 television series whose plots CENTER around the concept of Discipleship in Traditional Chinese Martial Arts. You cannot pretend that films and series which were watched by hundreds of millions of people worldwide, are not sufficient evidence for the existence of a phenomenon.

 * * 3 famous actors who portrayed disciples in several films: Bruce Lee, Jet Li, and Jackie Chan.

 * What else do you need as proof in order to cease your trolling? Why should he general readership on Wikipedia suffer from a campaign to hide useful and important information about Chinese culture, because a self-appointed bureaucrat thinks he can forgo mountains of evidence out of personal spite? 187.244.113.106 (talk) 17:18, 17 May 2021 (UTC)

 * I have opened a discussion about this at Reliable_sources/Noticeboard so hopefully more editors will weigh in shortly. - MrOllie (talk) 17:19, 17 May 2021 (UTC)

Fictional films can be RS for the plot, not for that plot being factually correct. If that were true Ares fought in WW1 and Chinese Gordon was an Amercian.Slatersteven (talk) 17:40, 17 May 2021 (UTC)
 * And let us not forget the tragedy of Darth Plagueis the Wise... ᛗᛁᛟᛚᚾᛁᚱPants   Tell me all about it.  18:46, 17 May 2021 (UTC)

 * Mr IP, are you associated with the Blue Jade Society or Jonathan Bluestein in any way? - MrOllie (talk) 23:26, 17 May 2021 (UTC)

Training
Have 3 kids need training no phone to contact need them to become experts JoeanaLGarza (talk) 02:48, 8 June 2021 (UTC)

Unsourced Material has not Been Addressed
Many moons ago i contributed to Wikipedia almost daily, I enjoyed doing so and it was therapeutic for a person who had just discovered I will be disabled for life. Then it became an arduous and anger inducing chore because of the dogged manner in which Wikipedia's self-appointed police would pock every sentence with citation needed tags and the entire page would be marked for deletion. Now it is common to find unsourced material, pages that have been flagged as containing: unsourced material, self published work, citation needed etc. some of which date back years and yet nothing is done about it. Why? 2600:1700:8A90:ECF0:5456:2293:933F:B3B0 (talk) 05:00, 4 December 2021 (UTC) Perhaps in bad etiquette, I am responding to my own talk topic. I completely understand now why no one addresses these issues, it is insanely difficult to comprehend the instructions for nomination for deletion, or even to nominate for discussion of deletion. This is absolutely absurd and completely counterintuitive to what Wikipedia is supposed to be about. Before i finally published the above paragraph I self-edited an entire paragraph about how difficult it had become to continue contributing to Wikipedia, after trying to wade through all of the B.S. on how to nominate an already flagged for unsourced material article for deletion, I wish I had kept the entire thing in. Wikipedia has become it's own worse enemy by making it nearly impossible for the average person to even begin to figure out how to do anything for or to an existing article, that is other than to get frustrated and vandalize the damned thing. And Wikipedia has the audacity to ask me for a donation? The damned thing tells me this is the 2nd time we've interrupted you please give $2.25 For what? Nearly everything I personally look up is cited for unsourced material! As far as i am concerned Wikipedia was a great idea, then it became a monster, and now it is a failed experiment. Best of Luck to You All.

Cantonese and Mandarin
This article speaks as if Chinese is a language and it would be nice to specifically state Cantonese or Mandarin for the etymology aspects. 12.149.115.58 (talk) 02:26, 21 May 2024 (UTC)

title: Talk:Chinese martial arts


text:
Regional District of Kootenay Boundary

The Regional District of Kootenay Boundary (RDKB) is one of 28 regional districts in the province of British Columbia, Canada. As of the 2016 Canadian census, the population was 31,447. The area is 8,095.62 km2 (3,125.74 sq mi). The RDKB was incorporated in 1966 and consists of eight incorporated municipalities and five unincorporated electoral areas. The regional district's offices are in the City of Trail, with secondary offices in the City of Grand Forks. Other major population centres include the cities of Rossland and Greenwood, and the villages of Fruitvale, Warfield, and Montrose. The region also encompasses electoral areas A (east of Fruitvale extending just past Champion Lakes and south to Waneta and the Pend d'Oreille River), B/Lower Columbia-Old Glory, C/Christina Lake, D/Rural Grand Forks and E/West Boundary including Rock Creek, Bridesville, Beaverdell and Big White Ski Resort.

Local government services provided by the RDKB to residents in the region include recreation and culture, planning, building inspection, environmental programs, economic development and public safety services for fire and other emergencies.

Demographics
As a census division in the 2021 Census of Population conducted by Statistics Canada, the Regional District of Kootenay Boundary had a population of $33,152$ living in $15,190$ of its $18,998$ total private dwellings, a change of NaN% from its 2016 population of $31,447$. With a land area of 8080.76 km2, it had a population density of in 2021.

 * Note: Totals greater than 100% due to multiple origin responses.

title: Regional District of Kootenay Boundary


text:
Leslie Frost

Leslie Miscampbell Frost (September 20, 1895 – May 4, 1973) was a politician in Ontario, Canada, who served as the province's 16th premier from May 4, 1949, to November 8, 1961. Due to his lengthy tenure, he gained the nickname "Old Man Ontario"; he was also known as "the Silver Fox".

Early years

Born in Orillia, Ontario, he was the son of William Sword Frost and Margaret Jane Barker. His father was a jeweller and mayor of Orillia; his mother was an important figure in the early days of The Salvation Army. He attended the University of Toronto and Osgoode Hall Law School. During World War I, he was an officer with "C"Company 157th Battalion (Simcoe Foresters), CEF, and served with the 20th Battalion, Queen's York Rangers in France and Belgium. In 1918, after being wounded, he was discharged with the rank of Captain. He was called to the Bar in 1921.

In 1926, he married Gertrude Jane Carew. They had no children. The couple lived in Lindsay, Ontario, but Frost preferred his property at Pleasant Point on Sturgeon Lake north of Lindsay. When Frost and his brother, Cecil Gray Frost, first moved to Lindsay to establish a law practice, they rented a building at Pleasant Point that had been the community store and commuted to town by steamer. Frost bought the property in 1925 and, in about 1950, bought adjacent property where he built the winterized log cabin that was his refuge while he was premier and in retirement.

Early political career
In 1937, he was first elected to the Ontario legislature and thereafter never lost an election. He was the Treasurer of Ontario and Minister of Mines from 1943 to 1955. Frost was chosen as leader of the Ontario Progressive Conservative Party (the "Tories") following Premier George Drew's decision to enter federal politics.

Premier of Ontario
Dubbed "The Old Man Ontario" and "The Laird of Lindsay", Frost led the province during the economic boom of the 1950s. His low-key approach garnered him the nickname "The Great Tranquilizer". Combining small-town values with progressive policies, he took the Tories through three successive electoral victories winning majority governments in 1951, 1955 and 1959.

Economic policy
Frost's government also attempted to wrest control of the income tax from the federal government, but failed, resulting in the introduction of a provincial sales tax. Frost expanded health care coverage for Ontarians through the creation of the Hospital Services Commission of Ontario Act and the Ontario Hospital Insurance Plan. By 1960, 94% of the population of Ontario was enrolled in the Ontario Hospital Insurance Plan.

Frost's government oversaw substantial expansion in public services and substantially increased public investment in the economy, as well as through strong fiscal policies.

Education policy
Under Frost, the number of universities in Ontario increased from four to twelve. As finance minister in 1943, the total provincial investment in education was just over $13 million. Upon his retirement in 1961, the education budget for Ontario was $250 million.

Social policy
The Frost government was the first to pass laws providing penalties for racial, ethnic, and gender discrimination on private property; these laws, introduced in the early 1950s as the Fair Employment Practices Act and Fair Accommodation Practices Act, started a movement in Ontario politics that produced the Ontario Human Rights Code in 1962 and later legislation. Frost's government also introduced legislation to ensure women received equal wages. His government also introduced voting rights for First Nations. When confronted by J.A. McGibbon, a judge from Lindsay and fellow fishing companion, regarding an anti-discrimination law about property, Frost told him that his attitudes towards people of color were out of date.

Frost's government oversaw great expansion in the role of government. Under his leadership, Ontario greatly expanded its schools, highways and hospitals. Under his leadership Ontario created the 400 series of superhighways, most notably the Macdonald-Cartier Freeway better known as Highway 401.

Frost's government oversaw the federation of the old City of Toronto with twelve surrounding municipalities to become Metropolitan Toronto.

Retirement
Frost resigned in 1961, and was succeeded as Tory leader and Premier by John Robarts.

After politics
Upon retirement from politics, Frost served on the Board of Governors of the University of Toronto. As well, he was a member of the Board of Directors of the Bank of Montreal, KVP, Canada Life, and Trans Canada Air. Between 1954 and 1969 he also served as Vice-President of the Champlain Society and as its Honorary Vice-President from 1969 to 1973. He served as Chancellor of Trent University from 1967 to 1973. In retirement, he continued his interest in the outdoors. Near the end of his life, he undertook for the government of Ontario an exhaustive investigation of the state and potential of Algonquin Provincial Park. In the last interview he gave, just before he died, to the Toronto Star, he declared: "I am an environmentalist."

Frost was an excellent amateur historian. His book Fighting Men covered the history of the 35th Regiment of Simcoe Foresters from Orillia, Ontario in the context of the First World War. Within that he connects the Canadian home front to the war front in France, and connects the events within the regiment to the bigger picture of the war and Canada's subsequent role in world affairs. His Forgotten Pathways of the Trent (published just after he died) challenged historians' previous conclusions about Indian trade and warfare routes in southern Ontario. He was an avid U.S. Civil War buff and kept on the mantelpiece in his large library a piece of wood that was supposed to have come from Abraham Lincoln's original log cabin.

Honours
In 1969, he was made a Companion of the Order of Canada, Canada's highest civilian honour.

Various places across Ontario are named for Frost:

 * Frost Building, Toronto - houses the Ontario Ministry of Finance and the Ontario Management Board Secretariat, at Queen's Park, was named in his honour.
 * Frost Centre for Canadian Studies and Indigenous Studies, Peterborough, Ontario - at Trent University,
 * Leslie Frost Library at Glendon College (York University), Toronto
 * Frost Campus at Fleming College, Lindsay, Ontario
 * Leslie Frost Public School, Lindsay, Ontario - a school
 * Leslie Frost Place - a street in Lindsay, Ontario
 * Frost Centre Institute - formerly the Leslie M. Frost Natural Resource Centre, operated a private educational facility in Haliburton County offering secondary school credits.
 * Portrait of Frost resides at Trent University

title: Leslie Frost


text:
Mail Call (TV series)

Mail Call is a television program that aired on the History Channel. It was hosted by R. Lee Ermey, a retired United States Marine Corps staff sergeant and honorary gunnery sergeant. The show debuted on August 4, 2002 as part of the "Fighting Fridays" lineup. Most episodes were 30 minutes, but from 2007 through the show's end in 2009 some episodes were 60 minutes.

Description
During each episode, Ermey read and answered questions submitted by viewers regarding weapons, equipment, customs, and terminology used by all branches of the U.S. military now or in the past, as well as by other armed forces in history. Ermey often took his viewers on location to military training areas to film demonstrations and consult with experts. When not on location, Ermey broadcast from a set resembling a military outpost, including a tent, a Jeep, and various other pieces of military gear which changed throughout the series. At times, he would also have a bulldog – usually symbolic of Marines – on his show as well.

Ermey often provided comic relief in the form of light-hearted DI-style verbal abuse aimed at viewers; testing the effects of weapons on assorted objects (most often watermelons, which he described as his "sworn enemy"); and occasional appearances of "Mini-Lee", an action figure styled in Ermey's likeness, often seen berating a luckless G.I. Joe figure. His demeanor in character as host was similar to that of Gunnery Sergeant Hartman, the character he portrayed in the Stanley Kubrick film Full Metal Jacket. However, he only showed this attitude toward viewers, such as ordering them to return in time for the end of a commercial break.

The program had several DVD video releases, including selected episodes from the first seven seasons, as well as a blooper video called Mail Call: S.N.A.F.U. Reruns continue to be aired on the Military History Channel.

Show name origin
The title of Mail Call for the series was drawn from the military practice of the same name, in which soldiers assemble to receive mail from a designated person who calls out each recipient's name in turn.

title: Mail Call (TV series)


text:
War of the Three Henrys

The War of the Three Henrys (Guerre des trois Henri), also known as the Eighth War of Religion (Huitième guerre de Religion), took place during 1585–1589, and was the eighth conflict in the series of civil wars in France known as the French Wars of Religion. It was a three-way war fought between:
 * King Henry III of France, supported by the royalists and the politiques;
 * King Henry of Navarre, later Henry IV of France, heir presumptive to the French throne and leader of the Huguenots, supported by Elizabeth I of England and the German protestant princes; and
 * Henry of Lorraine, Duke of Guise, leader of the Catholic League, funded and supported by Philip II of Spain.

The underlying cause of the war was the looming royal succession crisis from the death of heir presumptive, Francis, Duke of Anjou (Henry III's brother), on 10 June 1584, which made the Protestant Henry of Navarre heir to the throne of the childless Henry III, whose death would extinguish the House of Valois. On 31 December 1584, the Catholic League allied itself with Philip II of Spain by the Treaty of Joinville.

The war began when the Catholic League convinced (or forced) King Henry III to issue the Treaty of Nemours (7 July 1585), an edict outlawing Protestantism and annulling Henry of Navarre's right to the throne. Henry III was possibly influenced by the royal favorite, Anne de Joyeuse. In September 1585, Pope Sixtus V excommunicated both Henry of Navarre and his cousin and leading general Condé to remove them from the royal succession.

1585
For the first part of the war, the royalists and the Catholic League were uneasy allies against their common enemy, the Huguenots. Philippe Emmanuel, Duke of Mercœur, a prominent member of the Catholic League and governor of Brittany since 1582, conducted campaigns against the Protestants in 1585, 1587 and 1588, but was repeatedly defeated and forced to flee, thereby establishing his reputation as a poor warrior (he was jokingly nicknamed "duc de Recule" (the "Duke of Retreat") by Brantôme). In the opening phase, Mercœur invaded Poitou in 1585 and fought against Henri, Prince of Condé (1552–1588) in the battle of Fontenay-le-Comte. Condé forced him to retreat back across the river Loire, capturing most of his baggage train and the spoils of war Mercœur had obtained at the beginning of his campaign, as well as taking several groups of Mercœur's soldiers prisoner of war. In October 1585, Condé conducted the Siege of Brouage, but had to lift it when the castle of Angers was seized by treason, and then descended into fighting between various factions. By the time Condé arrived at Angers on 21 October, the castle was in the hands of 6,000 royalist enemies. He quickly retreated as his Protestant army was thrown into confusion, disarray and harassed by royalist forces. Condé's army fell apart during his flight, with some escaping, while those captured were frequently put to death by Catholic forces.

1586
In early 1586, Henry of Navarre's forces were far inferior to his opponents, and he sought to strengthen his position and build his army by buying time and avoiding a general engagement. To that end, Navarre published several declarations in which he lamented the miseries of war, denounced those fighting, and argued that he himself was not to be blamed for it, addressing the clergy (in reference to Pontius Pilate washing his hands in Matthew 27:24–25) with the words: "If war delights you so much, if you prefer a battle to an argument, and a conspiracy to a council, I wash my hands of it, and the blood which may be shed shall be on your heads." In February 1586, the Prince of Condé occupied La Rochelle and the isle of Oléron and turned them into Huguenot strongholds. In early April 1586, St. Luc, the governor of Brouage, attacked La Rochelle for 24 hours with 5,000 troops, but was forced to retreat by the Protestant defenders, losing 400 soldiers and much of his baggage. Condé won a costly Huguenot victory at Saintes afterwards. In late 1586, Armand de Gontaut, baron de Biron besieged Marans, an important town providing access to La Rochelle, during which he was wounded. Henry of Navarre personally came to reinforce the region's fortifications and boost morale. A messenger from Henry III requested both parties to cease hostilities and hold peace talks, leading Biron to withdraw and Navarre to promise to meet Henry III. The negotiations soon broke down amidst mistrust, not only between the two Henrys, but also between Henry III and the Catholic League (including Charles, Duke of Mayenne, one of his leading generals who failed to accomplish anything in the field and blamed Henry III for his failures).

1587
The Battle of Jarrie (19 August 1587) was a Catholic victory. Henry III sent Joyeuse into the field against Navarre, while he himself intended to meet the approaching German and Swiss armies. At the Battle of Coutras (20 October 1587), Navarre, with English fiancial aid, defeated the royal army led by Joyeuse; the duke himself was slain at the battle. It was the first victory won by the Huguenots in the battlefield. For his part, Henry III successfully prevented the junction of the German and Swiss armies. The Swiss were his allies, and had come to invade France to free him from subjection; but Henry III insisted that their invasion was not in his favor, but against him, forcing them to return home. The Germans, led by Fabien I, Burgrave of Dohna, wanted to fight against the Duke of Guise, in order to win a victory like Coutras. He recruited some of the retreating Swiss, who had no scruple fighting against Guise. But at the Battle of Vimory (26 October 1587), Guise took the Germans by surprise, and routed them.

1588
In Paris, the glory of repelling the German and Swiss Protestants all fell to the Duke of Guise. The king's actions were viewed with contempt. They thought that the king had invited the Swiss to invade, paid them for coming, and sent them back again. The king, who had really performed the decisive part in the campaign, and expected to be honored for it, was astounded that public voice should thus declare against him. The Catholic League had put its preachers to good use. In the meantime, the governments of Normandy and Picardy were vacated by the deaths of Joyeuse and Condé. Guise demanded Normandy for himself, and Picardy for his kinsman Aumale. The king denied both requests. The Catholic League was mobilized to resist the royal appointees in these provinces. Guise was forbidden from entering the capital. Guise ignored the prohibition and entered Paris. In the normal course of affairs this would have cost him his life, but the duke was popular with the masses. Further, after the Day of the Barricades, an uprising planned in part by the Spanish diplomat Bernardino de Mendoza, the king decided to flee to Blois.

After the defeat of the Spanish Armada in 1588, the king called the Estates-General in the midst of intrigue and plotting. Henry of Guise planned to assassinate the king and seize the throne, but the king struck first by having Guise killed by his guards, The Forty-Five.

1589
Open war erupted between the royalists and the Catholic League. Charles, Duke of Mayenne, Guise's younger brother, took over the leadership of the League. At the moment it seemed that Henry III could not possibly resist his enemies. His power was effectively limited to Blois, Tours, and the surrounding districts. In these dark times the King of France finally reached out to his cousin and heir, the King of Navarre. Henry III declared that he would no longer allow Protestants to be called heretics, while the Protestants revived the strict principles of royalty and divine right. As on the other side ultra-Catholic and anti-royalist doctrines were closely associated, so on the side of the two kings the principles of tolerance and royalism were united. Henry III sought the aid of the Swiss, who were ready to join his cause. The Catholic royalists revived in their allegiance. At Pontoise the king saw himself at the head of 40,000 men. His newly recovered power may have inspired him with great designs; he planned to take Paris, in order to end the League's power once and for all. The surrender of Paris seemed likely, even to the inhabitants. The preachers of the League sanctioned regicide, to avenge the murder of Guise. Jacques Clément, a fanatical Catholic friar, assassinated King Henry III at Saint-Cloud in August 1589.

With Henry III's death, the coalition broke up. Many Catholic royalists were unwilling to serve the Protestant Henry IV, and the army retreated from Paris.

Aftermath
In the spring, the extant Henry III of Navarre returned to the field; he won significant victories at Ivry and Arques and laid siege to Paris (despite being greatly outnumbered), but a Spanish army under Alexander Farnese, Duke of Parma lifted the siege.

Deciding that further fighting was not worth the cost, Henry converted to Catholicism in 1593. The people of Paris were weary of war and disillusioned with the leaders of the League, and welcomed him amidst jubilation.

The French Wars of Religion lasted several more years, as League diehards and Spanish troops continued to resist the reunification of France. But once those were dealt with, the new king Henry IV's reign inaugurated a time of commerce and peace, commonly regarded as a golden age, and he remains one of France's most beloved kings.

title: War of the Three Henrys


text:
Hénon map

In mathematics, the Hénon map, sometimes called Hénon–Pomeau attractor/map, is a discrete-time dynamical system. It is one of the most studied examples of dynamical systems that exhibit chaotic behavior. The Hénon map takes a point $a = 1.4$ in the plane and maps it to a new point

 * $$\begin{cases}x_{n+1} = 1 - a x_n^2 + y_n\\y_{n+1} = b x_n.\end{cases}$$

The map depends on two parameters, $a$ and $b$, which for the classical Hénon map have values of $b = 0.3$ and $a = 1.4$. For the classical values the Hénon map is chaotic. For other values of $a$ and $b$ the map may be chaotic, intermittent, or converge to a periodic orbit. An overview of the type of behavior of the map at different parameter values may be obtained from its orbit diagram.

The map was introduced by Michel Hénon as a simplified model of the Poincaré section of the Lorenz model. For the classical map, an initial point of the plane will either approach a set of points known as the Hénon strange attractor, or diverge to infinity. The Hénon attractor is a fractal, smooth in one direction and a Cantor set in another. Numerical estimates yield a correlation dimension of 1.21 ± 0.01 or 1.25 ± 0.02 (depending on the dimension of the embedding space) and a Box Counting dimension of 1.261 ± 0.003 for the attractor of the classical map.

Attractor
The Hénon map maps two points into themselves: these are the invariant points. For the classical values of a and b of the Hénon map, one of these points is on the attractor:

 * $$ x = \frac{\sqrt{609}-7}{28} \approx 0.631354477, $$
 * $$ y = \frac{3\left(\sqrt{609}-7\right)}{280} \approx 0.189406343.$$

This point is unstable. Points close to this fixed point and along the slope 1.924 will approach the fixed point and points along the slope -0.156 will move away from the fixed point. These slopes arise from the linearizations of the stable manifold and unstable manifold of the fixed point. The unstable manifold of the fixed point in the attractor is contained in the strange attractor of the Hénon map.

The Hénon map does not have a strange attractor for all values of the parameters a and b. For example, by keeping b fixed at 0.3 the bifurcation diagram shows that for a = 1.25 the Hénon map has a stable periodic orbit as an attractor.

Cvitanović et al. have shown how the structure of the Hénon strange attractor can be understood in terms of unstable periodic orbits within the attractor.

Relationship to bifurcation diagram
If multiple Hénon maps are plotted, for each map varying the value of b, then stacking all maps together, a Bifurcation diagram is produced. A Bifurcation diagram that is folded like a taco. Hence its boomerang shape when viewed in 2D from the top.

Decomposition
The Hénon map may be decomposed into the composition of three functions acting on the domain one after the other.

1) an area-preserving bend:
 * $$(x_1, y_1) = (x, 1 - ax^2 + y)\,$$,

2) a contraction in the x direction:
 * $$(x_2, y_2) = (bx_1, y_1)\,$$,

3) a reflection in the line y = x:
 * $$(x_3, y_3) = (y_2, x_2)\,$$.

One-dimensional decomposition
The Hénon map may also be deconstructed into a one-dimensional map, defined similarly to the Fibonacci Sequence.
 * $$x_{n+1} = 1-a x_n^2 + b x_{n-1}$$

Four-dimensional extension
Although the Hénon map can be plotted on the x- and y-axes, by varying a and b, we obtain two additional dimensions for plotting. The Hénon map therefore, can be plotted in four-dimensional space. We can visualize such a plot by viewing one hyperplane (i.e. one cube of space) at a time representing three axes, then moving along the fourth axis as time passes.

In the video example to the right, the three axes for each image in the video are x, y, and b. As time passes, it is the a axis that is moved through.

Special cases and low-period orbits
If one solves the one-dimensional Hénon map for the special case:
 * $$X = x_{n-1} = x_n = x_{n+1}$$

One arrives at the simple quadradic:
 * $$X = 1-a X^2 + b X$$

Or
 * $$0 = -a X^2 + (b-1) X + 1$$

The quadratic formula yields:
 * $$X = {b-1 \pm \sqrt{b^2-2b+1+4a} \over 2a}$$

In the special case b=1, this is simplified to
 * $$X = {\pm \sqrt{a} \over a} $$

If, in addition, a is in the form $${1 \over c^n}$$ the formula is further simplified to
 * $$X = \pm c^{n/2}$$

In practice the starting point (X,X) will follow a 4-point loop in two dimensions passing through all quadrants.

 * $$(X,X) = (X,-X)$$
 * $$(X,-X) = (-X,-X)$$
 * $$(-X,-X) = (-X,X)$$
 * $$(-X,X) = (X,X)$$

History
In 1976 France, the Lorenz attractor is analyzed by the physicist Yves Pomeau who performs a series of numerical calculations with J.L. Ibanez. The analysis produces a kind of complement to the work of Ruelle (and Lanford) presented in 1975. It is the Lorenz attractor, that is to say, the one corresponding to the original differential equations, and its geometric structure that interest them. Pomeau and Ibanez combine their numerical calculations with the results of mathematical analysis, based on the use of Poincaré sections. Stretching, folding, sensitivity to initial conditions are naturally brought in this context in connection with the Lorenz attractor. If the analysis is ultimately very mathematical, Pomeau and Ibanez follow, in a sense, a physicist approach, experimenting with the Lorenz system numerically.

Two openings are brought specifically by these experiences. They make it possible to highlight a singular behavior of the Lorenz system: there is a transition, characterized by a critical value of the parameters of the system, for which the system switches from a strange attractor position to a configuration in a limit cycle. The importance will be revealed by Pomeau himself (and a collaborator, Paul Manneville) through the "scenario" of Intermittency, proposed in 1979.

The second path suggested by Pomeau and Ibanez is the idea of realizing dynamical systems even simpler than that of Lorenz, but having similar characteristics, and which would make it possible to prove more clearly "evidences" brought to light by numerical calculations. Since the reasoning is based on Poincaré's section, he proposes to produce an application of the plane in itself, rather than a differential equation, imitating the behavior of Lorenz and its strange attractor. He builds one in an ad hoc manner which allows him to better base his reasoning.

In January 1976, Pomeau presented his work during a seminar given at the Côte d'Azur Observatory, attended by Michel Hénon. Michel Hénon uses Pomeau’s suggestion to obtain a simple system with a strange attractor.

Koopman modes
In dynamical system, the Koopman operator is a natural linear operator on the space of scalar fields. For general nonlinear systems, the eigenfunctions of this operator cannot be expressed in any nice form. Instead one must compute them numerically. These modes can give insight into the symbolic dynamics of chaotic maps like the Hénon map. In the mode provided, the stable manifold of the strange attractor can be clearly seen.

Generalizations
A 3-D generalization for the Hénon map was proposed by Hitz and Zele. It is given by

$$\mathbf{s}(n+1)=

\begin{bmatrix}

s_1(n+1) \\

s_2(n+1) \\

s_3(n+1)

\end{bmatrix}

=

\begin{bmatrix}

-\alpha s_1^2(n)+s_3(n)+1\\

-\beta s_1(n)\\

\beta s_1(n) + s_2(n)

\end{bmatrix}$$.

For $$\alpha=1.07$$ and $$\beta=0.3$$ it can be shown that almost all initial conditions inside the unit sphere generate chaotic signals with largest Lyapunov exponent $$0.23$$.

Many other generalizations have been proposed in the literature. One can generate, for example, band-limited chaotic signals using digital filters in the feedback loop of the system.

title: Hénon map


text:
Talk:Interest rate swap

PROJECT FINANCE
This article is part of project finance and has recently been part of a wide review of interest rate derivative amendments. Some very old comments on this talk page have now been removed as either now obsolete or addressed. Below talk comments have been left temporarily for further consideration ahead of deletion.

Users with new comments about this article please submit below within section new comments.

Attack68 (talk) 08:31, 3 July 2017 (UTC)

Adding an external link to this article
I would like to add an external link to http://thinxlabs.com/blog/interest-rate-swaps-pricing-and-bootstrapping-the-yield-curve/ however this could be violating point 11 of the "links to normally be avoided" in the external links guidelines. This isn't a blog much as it is a growing list of articles we are creating sharing 15 years inside investment banking. This one I felt complemented the article however contains multimedia so I cannot add it straight in. Anyway what are the feelings on my adding the external link to this article as I would like to respect the culture of wikipedia and it could represent a conflict of interest as we sell an app on the iPad ( but I am not linking to this of course). DEGoodall (talk) 13:58, 17 August 2012 (UTC)

Most swaps are interest rates swaps per ISDA
The ISDA semi annual survery shows that the plain vanilla interest rate swap exceeds other derivatives by far. Why does this article say that most swaps have a fixed equity leg?

The only possible reason is that there is option pricing model shown as a reference and they work best with equities. But the fact is that equity derivatives lag far behind interest rate swaps in volume.

 * Probably because of the narrow perspective of the writer. I know in the past I have written things from a pure IR derivatives point of view and then realised (or been told) later what a narrow view I espoused. Feel free to change things so that they are right. Pcb21| Pete 11:42, 11 Dec 2004 (UTC)

Removed Tax Purposes Section
''Another common use of the swap was to avoid the British stamp tax on short sales. Unlike the SEC in the US, in the UK only the short sells are taxed, and in order to raise enough money to pay for the exchange, taxed at a fairly high rate. To avoid this tax it is possible to simply swap out a position, paying a small fee to the other counterparty instead of a larger fee to the British exchanges.''

This whole section is inaccurate. Firstly, the UK stamp duty applies on equity purchases, not sales. Thus, in a short sale it applies on the close-out of the position. The money raised is not used to "pay for the exchange", it's levied by the UK government under the Finance Act 1986 (see the entry on Stamp Duty for more). Finally, the instrument used to avoid paying Stamp Duty on purchases is an Equity swap or Total return swap. I added these two items to the See Also section..--Andrew G Ross 23:33, 23 Apr 2005 (UTC)

It would actually be nice if this whole article had a section on the HISTORY of interest rate swaps: how, when, and why did such a complicated financial instrument emerge. The historical dimension is important, I think, if for no other reason than the fact that exploitative swaps have been implicated in the budgetary disaster of Jefferson County, Alabama; and several city and national governments in Europe. —Preceding unsigned comment added by 24.163.35.236 (talk) 20:42, 15 September 2010 (UTC)

Clarifying the Math in Introductory Paragraphs
As a newcomer to swaps, I cannot make the net payment amount of 1.70% square with the 3.00% swap rate and the variable rate of (LIBOR + 50 bps)if LIBOR = 1.30%  in the following paragraph:

''Consider the following swap in which Party A agrees to pay Party B periodic fixed interest rate payments of 3.00%, in exchange for periodic variable interest rate payments of LIBOR + 50 bps (0.50%). Note that there is no exchange of the principal amounts and that the interest rates are on a "notional" (i.e. imaginary) principal amount. Also note that the interest payments are settled in net (e.g. if LIBOR is 1.30% then Party B receives 1.70% (LIBOR + 50bps) and Party A pays 1.70%). The fixed rate (3.00% in this example) is referred to as the swap rate.[1]''

It seems to me that LIBOR + 50 bps = 1.80% and the net payment would be (3.00% -1.80%) or 1.20%. Can some veteran clarify this, please? Thanks. Christian424 (talk) 15:35, 27 October 2008 (UTC)

I agree with Christian, a potentially interesting article but so badly explained in the Structure section that none of the rest of the article has any meaning.

So, consider that I am new to swaps, I'm reading the article because I want to learn about them and yet I have to contend with the following curiosities:

1. In the first figure both parties are shown to win by some positive amount. If it wasn't meant to show that, e.g. that both parties pay and receive some amount, with the possibility that one party is at a net loss, it should say so.

2. The calculation in the text in the Structure section currently reads: "Party A pays (LIBOR + 1.50%)+8.65% - (LIBOR+0.70%) = 9.45% net.". Now just think about it, if the variable LIBOR is cancelled out of this equation then Party A's net position is constant regardless of LIBOR, and in fact 9.45% has miraculously been given to them. I think the author didn;t mean "net" but of course it isn't explained so I can't tell.

3. The second figure is even funnier. The caption states that "the bank takes a spread from the swap payments" and yet the net figures have actually increased, at 9.6% and LIBOR + 0.7% respectively, so it can be concluded that the bank makes money from some mysterious fourth source that also dishes out some risk free profit to the counter parties as well. Once again I suspect the author has a specialised definition of net.

Hope this helps, I would be interested to see the final explanation. mildly_odd (talk) 07:01, 27 May 2010 (UTC)

Interest Rate Swap mis-selling scandal
Am I right in thinking that subject of this article is related to the "Interest Rate Swap Mis-selling Scandal" (or similar names)? If so, I think that this article should have a section on it - or possibly it should have its own article. I don't feel I have enough knowledge in this area to start it.

Here are some references: ,, , FrankSier (talk) 18:57, 23 May 2013 (UTC)

Uses — not evading exchange controls
> Interest rate swaps were originally created to allow multi-national companies to evade exchange controls.

This is unsourced nonsense, so has been deleted. Amongst other problems, IRS wouldn’t be an effective means of avoiding those. If re-adding, please cite reputable source. JDAWiseman (talk) 16:22, 16 February 2014 (UTC)

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title: Talk:Interest rate swap