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Dempsey and Makepeace

Dempsey and Makepeace is a British television crime drama made by LWT for ITV, created and produced by Ranald Graham. Lead roles were played by Michael Brandon (Lieutenant Dempsey) and Glynis Barber (Sergeant Makepeace), who later married each other in real life in 1989.

Premise
The premise of Dempsey and Makepeace is the oddball pairing of two police detectives: an elegant British noblewoman, Sgt (Lady) Harriet Makepeace, and a streetwise working-class New Yorker, Lt James Dempsey, both working for an elite and armed unit of the London Metropolitan Police.

When his partner Joey dies in a botched drugs operation and he uncovers police corruption at the highest level, Dempsey is under threat of assassination. With help from his colleagues, he hurriedly leaves New York for London, on the pretence of an undercover international police exchange programme.

Harriet "Harry" Makepeace is the daughter of Lord Winfield (Ralph Michael), who owns an English stately home. Reference is made to his having formerly been in the Army or the Secret Service. Makepeace's grandfather is mentioned as having been a Victorian collector of antiques and rare items. Makepeace's mother is mentioned only once, by her maternal uncle Duffy, and it would seem she had died some time ago, also mentioned is her best friend had an affair with Makepeace's ex husband and they now live together. Makepeace has made her way up through the ranks of the police force, despite sexism by her male counterparts and the physical demands of the job.

Although there is initial reluctance on both sides, Dempsey and Makepeace work as partners in a specialised task force, SI 10, and they make a good team. SI 10 is under the command of Gordon Spikings, played by Ray Smith. A fourth regular role is that of Chas, played by Tony Osoba, who provides useful research and communications in the SI 10 office and occasionally has a more active role.

Two double-length episodes were produced, the first being the pilot ("Armed and Extremely Dangerous"), with the second the series 3 two-part opener ("The Burning").

At the height of the series' popularity, and during season 2 particularly, the British tabloid press hounded the lead actors for off-screen stories regarding their then-budding personal relationship.

Much of the show's draw came from the good-natured "will they or won’t they" interplay and a slowly evolving romance between the main protagonists, made possible by the obvious chemistry between the two lead actors. The show ended with an episode directed by Michael Brandon himself where Dempsey and Makepeace are forced to confront at least some of their feelings for one another. Makepeace leaves the force after having a vision of Dempsey being shot and killed in the line of duty. Dempsey tries to get her to return, after Dempsey's new partner—an old female friend of Makepeace—visits Makepeace to have a chat with Harry, it is implied from the conversation Makepeace is in love with Dempsey and can't bear to see anything happen to him. Dempsey gets her to help him when his new partner is injured. In the final scene it looks like they are going to join up as partners again as a call comes over the police radio they both smile at each other.

Main cast

 * Michael Brandon as Lieutenant James Dempsey NYPD
 * Glynis Barber as Detective Sergeant Lady Harriet "Harry" Makepeace
 * Ray Smith as Chief Superintendent Gordon Spikings
 * Tony Osoba as Detective Sergeant Charles ”Chas” Jarvis
 * Colin McFarlane as Detective Sergeant Watson
 * Jonathan Docker-Drysdale as Detective Sergeant Ward

Filming locations
In episode 9 of series 1, "Cry God for Harry", Chilham Castle in Kent becomes Winfield Hall, the grand English estate of Lord Winfield (Ralph Michael), and Chilham Square also makes a brief appearance as Dempsey and Makepeace approach the grand gates to the estate.

Episode 1 of series 2, "Silver Dollar", used London Weekend Television's own studio building and reception area as the location for the fictional company Consolidated Westmore.

As with many films and television programmes of the era, extensive filming was conducted at the disused remains of the East Greenwich Gas Works (the present-day site of The O 2 ).

A shot of Chief Superintendent Gordon Spikings (Ray Smith) in front of Cutty Sark was incorporated into the series' opening credit sequence.

Episodes
Dempsey and Makepeace ran for three series between 11 January 1985 and 1 November 1986. A total of 30 episodes were produced.

Broadcast
The show was originally broadcast on ITV between 11 January 1985 and 1 November 1986. From July 2009, the series was repeated on ITV3 in the UK, and again on ITV4 from July 2020. Forces TV showed it from 1 September 2020.

International broadcast
It was sold to many countries in Europe, including Eastern Bloc Czechoslovakia, Poland and Hungary. The programme was broadcast elsewhere worldwide, such as on Pakistan Television during 1985–86. The series was also syndicated to the U.S. airwaves in the autumn of 1985 (by Tribune Entertainment), usually broadcast on Saturday afternoons or early evenings. However, only the first 20 hours of the series were run in the U.S. By mid-January 1986, it was discontinued, with the 10 episodes of series 3 never being aired. To encourage interest, the show was marketed in the U.S. as being similar to a re-make of The Avengers, but, while well advertised, it never grew a substantial following.

Ratings
The show was also critically acclaimed.

All three series attained great popularity in the UK, achieving good ratings with 20 million viewers in the UK.

Home media

 * In the UK, all three series of Dempsey and Makepeace were released on DVD in 2006 from Network DVD. They include interviews and audio commentaries on selected episodes with Michael Brandon and Glynis Barber.
 * In Portugal, all three series were released in 2004 by Prisvideo. There were no extras but the audio was in English with optional Portuguese subtitles, and the episodes were uncut*. (*Episode 'Judgement' has a scene removed towards the end where Judge Hackett is holding Bates hostage; however, it is believed this edit may have been made shortly after the episode was made, even before its original broadcast).
 * Starting with December 2004, DVDs and VCDs with all the episodes of the series were gradually added in Poland to a TV-guide magazine TV Okey!. They soon re-appeared in another collection series and finally, on 8 December 2008 a box with Season 1 episodes was released.
 * In mid 2000s a DVD was released in the Czech Republic and in Slovakia with Slovak dubbing.

In other media
In the UK, Dempsey and Makepeace merchandise such as jigsaw puzzles, children's annuals and replica toy cars were produced.

title: Dempsey and Makepeace


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User:Ninam~enwiki

& Angelina Marković Interests: IT Law, Linguistics Native Language: Serbian Second Language: English, Polish, Russian and South Slavic languages.

Complete Articles
Milan Budimir Biography, Selected Bibliography,,Photo Ljiljana Crepajac Biography, Selected Bibliography, Vladimir Ćorović Biography, photo Veselin Čajkanović Biography, Selected Bibliography, Milan Damnjanovic Bio-Bibliography Mihailo Djurić Biography, bibliography, Photo Predrag R. Dragić Kijuk Biography, Selected Bibliography, Image Nićifor Dučić HRH Tomislav Karadjordjevic, Biography, Photo Stefan Lazarević Biography, A Homage of Love, Images: Coat of Arms, A Homage to Love Mateja Matejic Biography, Bibliography, photo Dimitrije Mitrinović Biography, Photo Nicolas Moravcevich / Nikola Moravčević Biography Nenad Petrovic Biography, Photo Saint Justin Popović, Biography, Bibilography, Photo, Works on Internet, Tropation Serbs // Extendend List of References on Ancient and Mediaval Serbs Slobodan Rakitić, Biography, Bibliography, Photo. Aleksandar Solovjev Biography, Selected Bibliography Template:Serbia-stub Template:Serbia and Montenegro-stub

Significant Contributions
Alexander I of Yugoslavia Biography additions. Dušan's Code Quotes, Future Reading, image  Hristos of Prizren. Jovan Dučić, Biography rewritins Djra Jakšić, Biography add.s and painting Authoportrait Princess Jelisaveta Biography additions on humanitarian work, educatin,.. some rewritings and Photo Prince Pavle Biography addition facts, Photo HM King Petar II major Biography aditions, Photo Radomir Putnik some Biography additions, Mt. Putnik, Photo. Nikolai Velimirović some Biography additional facts, adds to Bibliography Slobodan Vuksanovic Bibliography, some Biography rewritings, Photo. Gusle, text, photo, media file.

Some Notable Contributions
Jasenovac, Ustase, verification on photos, some additions. Serbia Medieval Serbia 7th - 14th Century: Tsar Dusan's Serbia map  cca 1350 A.D. Serbia Medieval Serbia 7th - 14th Century: Nemanjic's Serbia map cca 1200 A.D. Dušan Kovačević Biography rewritins, filmography translation in English. Vuk Brankovic some biography rewritings Jovan Rašković, Biography rewritings and additions Dr. Archibald Reiss, photo, some additional links. Photos/Images: Biljana Palvšić, Dragan Jočić, Aleksandar Obrenović, Stefan Nemanja, Nikola Pašić, Vladan Batić HRH Princess Olga of Greece and Denmark, Svetozar Marković, Vladimir Jovanović Serbian Cyrillic and Serbian Latin cca. IXX c., German Warrant on gen. Draža Mihailović,  Nemanjić dynasty insignia, HRH Alexander Karadjordjevic, Prince Alexander Karadjordjevic, Petar I Petrovic Njegos (st. Peter of Cetinje), Dušan Kovačević, Pavle Jurišić Šturm, Svetozar Pribićević, Signature of KLA, Devic Monastery, Monastery Devic after the pogrom on March 2004 , Battle on Kosovo by Adam Stefanovic, 1870 , Stevan Sinđelić , Vojislav Vukčević

patrol
Most active -Category:Articles that need to be wikified - Category:Candidates for speedy deletion-Deletion log- Deadend pages, Most_wanted_articles, Copyright_problems, Unusual_articles,

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Resqued pages: BKTV, Fruska Gora National Park, Nenad Prokic, Serbian Contemporary Art

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

title: User:Ninam~enwiki


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Zinc finger inhibitor

Zinc finger inhibitors, or zinc ejectors, are substances or compounds that interact adversely with zinc fingers and cause them to release their zinc from its binding site, disrupting the conformation of the polypeptide chain and rendering the zinc fingers ineffective, thereby preventing them from performing their associated cellular functions. This is typically accomplished through chelation of the zinc binding site. As zinc fingers are known to be involved in m-RNA regulation, reverse transcription, protection of synthesized viral DNA, transcription inhibition, and initial integration processes, prevention of zinc finger function can have drastic effects on the function of the cell or virus.

Zinc finger inhibitors are typically used to combat HIV. HIV treatments usually rely on targeting reverse transcriptases and proteases. However, these methods are proving to be ineffective due to the development of resistant strains of the virus or due to the stoppage of the treatment. This method of using zinc finger inhibitors to target and destabilize zinc fingers represents a new method of fighting HIV. Other viruses such as SARS, polio, Ebola, measles, human coxsackie, Dengue, rabies, human hepatitis, human parainfluenza and human respiratory syncytical have similar zinc finger motifs and could potentially benefit from zinc finger inhibitor technology.

Zinc ejectors were patented in 2008 and some have entered Phase I/II trials as a HIV drug.

Zinc Finger Inhibitor Target: Nucleocapsid Protein
The HIV-1 nucleocapsid protein 7 (NCp7) is the protein targeted by zinc ejectors. NCp7 is initially formed as part of the gag polypeptide and follows a gag-knuckle zinc finger conformation. In its lifetime, NCp7 facilitates the unwinding of tRNA, acts as a primer for reverse transcription, chaperones nucleic acids within the capsid of HIV-1, helps integrate the viral RNA into budding virions, and is intimately involved in the replication of HIV-1 in both the early phase and late phase. These processes play critical roles in the replication of HIV-1 thus making NCp7 a prime target for drugs seeking to contravene the replication process. NCp7 is a 55-amino acid protein that is highly basic and consists of two gag-knuckle motifs. These motifs contain two peptide units of Cys-X2-Cys-X4-His-X4-Cys (CCHC), where the X represents a substituted amino acid, that make up the zinc (II) ion binding sites. The binding of zinc (II) in the CCHC binding site is necessary for the domain to be functional and for the stabilization of the conformation of the structure, allowing the NCp7 to carry out the processes required for HIV replication. Since the CCHC binding site is mutation resistant and involved in the replication of HIV-1, it makes a prime candidate for the prevention of HIV through zinc ejectors. By inhibiting the function of NCp7, the viral replication is affected and a non-functional virus that is unable to infect its host is produced.

Azodicarbonamide
Azodicarbonamide (ADA) was the first zinc ejector to go into clinical trial for treatment of HIV. ADA inhibits HIV by electrophilically attacking the sulfur atoms of the zinc coordinated cysteine. This electrophilic interaction destabilizes the zinc binding site making it easier for the zinc ion to be withdrawn due to the new arrangement of bonds. The binding site then performs a disulfide exchange, forming new intermolecular disulfide bonds, and rearrangement occurs placing the zinc finger in a conformation that inhibits its function.

C-nitroso
3-nitrosobenzamide (NOBA) and 6-nitroso-1,2-benzopyrone (NOBP) were the first  compounds to demonstrate an ability to inhibit infection of HIV by ejecting zinc from NCp7. In the same manner as ADA, the compounds interact with an 18-residue polypeptide on the N terminal zinc knuckle region of the HIV nucleocapsid protein which causes ejection of the zinc from the region by covalently modifying the cysteine residues. Studies suggest that NOBA and NOBP were able to inhibit HIV-1 infection by inhibiting reverse transcription without an apparent impairment of reverse transcriptase. This reiterates the role of NCp7 in reverse transcription.

2,2’-di-thiobisbenzamide (DIBA)
DIBAs act similarly to ADA, NOBA and NOBP. They react with the cysteine residues on the zinc finger of the NCp7 and cause a covalent conformation change which ejects the zinc from the zinc finger domain. Though DIBAs initially seemed to be promising antiviral candidates, there were clinical issues with their stability. DIBAs tend to cyclize into benzisothiazolones which do not have the same potency when used to combat retroviruses as the original compound. Additionally, glutathione can reduce the disulfide bonds in DIBA thereby restricting its function in vitro.

Mercaptobenzamides
Mercaptobenzamide prodrugs transfer acyl group to 36th cysteine residue of NCp7 and the acyl group then migrates to neighboring lysine residue that triggers the ejection of Zn. The mercaptobenzamide and its corresponding prodrug yielded additivity to synergy when combined with known HIV drugs. Moreover they showed no cytotoxicity.

Pyridinioalkanoyl thiolesters (PATES)
N-[2-(5-pyridiniovaleroylthio)benzoyl]sulfacetamide bromide (referred to as compound 45) is a pyridinioalkanoyl thiolester that can function as a zinc ejector. Once activated with silver, compound 45 uses its pyridinioalkanoyl groups to covalently modify NCp7, specifically altering cysteines 36 and 49 on the carboxyl-terminal zinc finger. It ejects the zinc from the zinc binding sites in a two steps. The zinc in the carboxyl-terminal zinc finger is released first, followed by the ejection of zinc from the amino-terminal zinc finger.

Bis-Thiadizolbenzene-1,2-Diamine
Bis-Thiadizolbenzene-1,2-diamine (NV038) is one of the newer zinc ejectors. NV038 is found to effect the function of the zinc finger after the virus has entered the cell but before reverse transcription is completed. NV038, like other zinc ejector compounds, chelates zinc to remove it from its binding site. However, it is thought to act through a different mechanism than many of the other zinc ejectors due to its structural features. Its structure would not readily allow thiol-disulfide interchange or acyl transfer to cysteine. Instead, NV038 is believed to react with the zinc using its two carbonyl oxygens found in the esters.

Safety Concerns
There was concern over whether these zinc ejectors were safe to use due to the uncertainty as to whether the zinc ejectors had sufficient selectivity to target only the CCHC binding sites of the zinc fingers in NCp7. Zinc finger domains are not unique to HIV but rather are ubiquitous in cell biology, and play important roles in many processes such as cellular replication, protein-protein interactions, and DNA replication. If these zinc ejectors unintentionally bind to the wrong zinc finger domains they have the potential to adversely affect other cellular functions that could be essential for proper bodily functions.

Experimentation and modeling of the selectivity of DIBA-1, ADA, and other zinc ejectors found that this safety concern was essentially unfounded. All zinc ejectors were found to effectively combat the replication of HIV at concentrations that did not exhibit cytotoxic effects denoting that they specifically targeted NCp7 and did not target other zinc fingers. It is thought that factors such as ligand binding affinity, ligand reactive proximity, and the general saddleshape necessary for the compound to fit into the binding pocket all play a role in the selectivity shown by zinc ejectors.

title: Zinc finger inhibitor


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Ballynure

Ballynure is a village and civil parish near Ballyclare in County Antrim, Northern Ireland. It is part of Antrim and Newtownabbey Borough Council and had a population of 677 people in the 2001 census.

Transport

 * Ballynure was formerly served by the Ballymena and Larne Railway, a narrow gauge railway. Ballynure railway station opened on 24 August 1878, but finally closed on 1 October 1930.

Sport
Ballynure Old Boys F.C. plays association football in the Ballymena & Provincial League.

2002 census
Ballynure is classified as a massive village or hamlet by the NI Statistics and Research Agency (NISRA) (i.e. with a population between 500 and 10,000 people). On census day (29 April 2002) there were 677 people living in Ballynure. Of these:
 * 22.3% were aged under 16 and 15.8% were aged 60 and over
 * 48.2% of the population were male and 51.9% were female
 * 0.1% were from a Catholic background and 99.9% were from a Protestant background
 * 0.4% of people aged 16–74 were unemployed.

Places of interest
The Ballynure Elementary School for Primary Education (often known simply as Ballynure Primary School) is only school in the village and surrounding areas until Ballyclare. It is also one of six schools in Northern Ireland classed as "Elementary Schools". The School was founded in 1930.

The Ballynure Cemetery is the oldest cemetery in all Newtownabbey and second oldest in all Antrim.

There are three churches within the village of Ballynure. Christ Church (Church of Ireland), Ballynure Presbyterian Church, and Ballynure Methodist Church.

Additional information
Jonathan Swift, the writer of Gulliver's Travels, was responsible for the Ballynure parish of the Church of Ireland, during his time as prebend of Kilroot.

The Clements family, who lived at Clements Hill outside the village, were the ancestors of Samuel Langhorne Clemens, better known as Mark Twain. Twain, who was author of works including The Adventures of Tom Sawyer, was described by William Faulkner as 'the father of American literature.' His grandfather Samuel Clemens emigrated to America and Twain was born in Florida, Missouri, in November 1835. One of his ancestors, Henry Clements, was Mayor of Carrickfergus in 1696 and another is said to have fought for William of Orange at the Battle of the Boyne six years earlier.

In 2017, the village established "Ballynature Day", currently the largest nature convention in Northern Ireland.

Notable people

 * William Marsden Hind, English botanist
 * Alexander Macomb, American merchant, born in Ballynure
 * James Whiteside McCay (1864–1930), Australian general during WWI, born in Ballynure
 * Jonathan Rea, five-time World Superbike champion; won his titles consecutively in 2015, 2016, 2017, 2018 and 2019, making him the most successful World SBK rider in the competition's history. He also holds the highest number of race wins in the championship.
 * Paddy McNair, a professional footballer with Middlesbrough FC and the Northern Ireland national football team

title: Ballynure


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Wujie, Yilan

Wujie Township is a rural township in the eastern part of Yilan County, Taiwan.

Geography

 * Area: 38.87 km2
 * Population: 40,984 people (September 2023)

Administrative divisions
The township comprises 15 villages: Chengxing, Daji, Erjie, Fuxing, Jinzhong, Jixin, Lize, Sanxing, Shangsi, Sijie, Wujie, Xiaowei, Xiehe, Zengan and Zhongxing.

Tourist attractions

 * Chung Hsing Cultural and Creative Park
 * Dongshan River Water Park
 * Erjie Rice Barn
 * Lizejian Yong'an Temple
 * National Center for Traditional Arts

Festivals

 * Yilan International Children's Folklore and Folkgame Festival

Transportation
The Erjie Station and Zhongli Station of Taiwan Railways is located in the township.

Notable natives

 * Lin Yi-hsiung, Chairperson of Democratic Progressive Party (1998–2000)

title: Wujie, Yilan


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Avascular necrosis

Avascular necrosis (AVN), also called osteonecrosis or bone infarction, is death of bone tissue due to interruption of the blood supply. Early on, there may be no symptoms. Gradually joint pain may develop, which may limit the person's ability to move. Complications may include collapse of the bone or nearby joint surface.

Risk factors include bone fractures, joint dislocations, alcoholism, and the use of high-dose steroids. The condition may also occur without any clear reason. The most commonly affected bone is the femur (thigh bone). Other relatively common sites include the upper arm bone, knee, shoulder, and ankle. Diagnosis is typically by medical imaging such as X-ray, CT scan, or MRI. Rarely biopsy may be used.

Treatments may include medication, not walking on the affected leg, stretching, and surgery. Most of the time surgery is eventually required and may include core decompression, osteotomy, bone grafts, or joint replacement.

About 15,000 cases occur per year in the United States. People 30 to 50 years old are most commonly affected. Males are more commonly affected than females.

Signs and symptoms
In many cases, there is pain and discomfort in a joint which increases over time. It can affect any bone, and for in about half of affected people, multiple sites are damaged.

Avascular necrosis most commonly affects the ends of long bones, such as the femur. Other common sites include the humerus (upper arm), knees,  shoulders,  ankles and the jaw.

Causes
The main risk factors are bone fractures, joint dislocations, alcoholism, and the use of high-dose steroids. Other risk factors include radiation therapy, chemotherapy, and organ transplantation. Osteonecrosis is also associated with cancer, lupus, sickle cell disease, HIV infection, Gaucher's disease, and Caisson disease (dysbaric osteonecrosis). Bisphosphonates are associated with osteonecrosis of the mandible (jawbone). The condition may also occur without any clear reason.

Prolonged, repeated exposure to high pressures (as experienced by commercial and military divers) has been linked to AVN, though the relationship is not well understood.

In children, avascular osteonecrosis can have several causes. It can occur in the hip as part of Legg–Calvé–Perthes syndrome, and it can also occur as a result after malignancy treatment such as acute lymphoblastic leukemia and allotransplantation.

Pathophysiology
The hematopoietic cells are most sensitive to low oxygen and are the first to die after reduction or removal of the blood supply, usually within 12 hours. Experimental evidence suggests that bone cells (osteocytes, osteoclasts, osteoblasts etc.) die within 12–48 hours, and that bone marrow fat cells die within 5 days.

Upon reperfusion, repair of bone occurs in two phases. First, there is angiogenesis and movement of undifferentiated mesenchymal cells from adjacent living bone tissue grow into the dead marrow spaces, as well as entry of macrophages that degrade dead cellular and fat debris. Second, there is cellular differentiation of mesenchymal cells into osteoblasts or fibroblasts. Under favorable conditions, the remaining inorganic mineral volume forms a framework for establishment of new, fully functional bone tissue.

Diagnosis
In the early stages, bone scintigraphy and MRI are the preferred diagnostic tools.

X-ray images of avascular necrosis in the early stages usually appear normal. In later stages it appears relatively more radio-opaque due to the nearby living bone becoming resorbed secondary to reactive hyperemia. The necrotic bone itself does not show increased radiographic opacity, as dead bone cannot undergo bone resorption which is carried out by living osteoclasts. Late radiographic signs also include a radiolucency area following the collapse of subchondral bone (crescent sign) and ringed regions of radiodensity resulting from saponification and calcification of marrow fat following medullary infarcts.

Types
When AVN affects the scaphoid bone, it is known as Preiser disease. Another named form of AVN is Köhler disease, which affects the navicular bone of the foot, primarily in children. Yet another form of AVN is Kienböck's disease, which affects the lunate bone in the wrist.

Treatment
A variety of methods may be used to treat the most common being the total hip replacement (THR). However, THRs have a number of downsides including long recovery times and the life spans of the hip joints (often around 20 to 30 years ). THRs are an effective means of treatment in the older population; however, in younger people, they may wear out before the end of a person's life.

Other techniques such as metal on metal resurfacing may not be suitable in all cases of avascular necrosis; its suitability depends on how much damage has occurred to the femoral head. Bisphosphonates which reduce the rate of bone breakdown may prevent collapse (specifically of the hip) due to AVN.

Core decompression
Other treatments include core decompression, where internal bone pressure is relieved by drilling a hole into the bone, and a living bone chip and an electrical device to stimulate new vascular growth are implanted; and the free vascular fibular graft (FVFG), in which a portion of the fibula, along with its blood supply, is removed and transplanted into the femoral head. A 2016 Cochrane review found no clear improvement between people who have had hip core decompression and participate in physical therapy, versus physical therapy alone. There is additionally no strong research on the effectiveness of hip core decompression for people with sickle cell disease.

Progression of the disease could possibly be halted by transplanting nucleated cells from bone marrow into avascular necrosis lesions after core decompression, although much further research is needed to establish this technique.

Prognosis
The amount of disability that results from avascular necrosis depends on what part of the bone is affected, how large an area is involved, and how effectively the bone rebuilds itself. The process of bone rebuilding takes place after an injury as well as during normal growth. Normally, bone continuously breaks down and rebuilds—old bone is resorbed and replaced with new bone. The process keeps the skeleton strong and helps it to maintain a balance of minerals. In the course of avascular necrosis, however, the healing process is usually ineffective and the bone tissues break down faster than the body can repair them. If left untreated, the disease progresses, the bone collapses, and the joint surface breaks down, leading to pain and arthritis.

Epidemiology
Avascular necrosis usually affects people between 30 and 50 years of age; about 10,000 to 20,000 people develop avascular necrosis of the head of the femur in the US each year.

Society and culture
Cases of avascular necrosis have been identified in a few high-profile athletes. It abruptly ended the career of American football running-back Bo Jackson in 1991. Doctors discovered Jackson to have lost all of the cartilage supporting his hip while he was undergoing tests following a hip-injury he had on the field during a 1991 NFL Playoff game. Avascular necrosis of the hip was also identified in a routine medical check-up on quarterback Brett Favre following his trade to the Green Bay Packers in 1992. However, Favre would go on to have a long career at the Packers.

Another high-profile athlete was American road racing cyclist Floyd Landis, winner of the 2006 Tour de France, the title being subsequently stripped from his record by cycling's governing bodies after his blood samples tested positive for banned substances. During that tour, Landis was allowed cortisone shots to help manage his ailment, despite cortisone also being a banned substance in professional cycling at the time.

Rafael Nadal successfully continued his tennis career after having surgery for Mueller–Weiss syndrome (osteonecrosis of the navicular bone in the foot). Youtuber Steve Wallis has revealed he has the condition in his hip. (ref livestream steve wallis step 2 channel 19 December 2020)

title: Avascular necrosis


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Jiaoxi, Yilan

Jiaoxi Township or Chiaohsi Township is a rural township in the northern section of Yilan County, Taiwan.

Geography

 * Area: 101.43 km²
 * Population: 34,932 people (September 2023)

Administrative divisions
The township includes eighteen rural villages:
 * Baiyun, Yushi (Yushih; ), Deyang , Dazhong , Dayi , Liujie , Erlong , Shichao , Yutian , Sanmin , Linmei , Baie , Yuguang , Guangwu , Wusha , Longtan , Paolun and Erjie Village.

Education

 * Fo Guang University
 * Tamkang University Lanyang Campus

Tourist attractions
Jiaoxi is famous for its hot springs. These attract large numbers of visitors so as the result, Jiaoxi has become a favorite weekend resort, mostly people from Taipei, featuring an array of hotels from the budget to the luxurious. There is also a few free public hot springs, mostly sheltered, where visitors can enjoy a leisurely foot bath at any time.

In March 2012, it was named one of the Top 10 Small Tourist Towns by the Tourism Bureau of Taiwan.

Other notable points of interests include:

 * Wufengqi Waterfall

Events

 * Jiaoxi Hot Spring Festival

Transportation
Jiaoxi is served by Jiaoxi Station on the Yilan Line run by the Taiwan Railways Administration. Another convenient way of transportation to/from Taipei and further to Yilan City is by bus route that uses the National Freeway 5 and passes through the Snow Mountain Tunnel. It is operated by Kamalan Bus Inc. and Capital Star (首都之星). The Provincial Highway 9 also serves the township.

Notable natives

 * Chang Chuan-tien, member of Legislative Yuan (1999–2006)
 * Lai In-jaw, President of Control Yuan (2007-2010)
 * Wu Tze-cheng, Minister of Public Construction Commission

title: Jiaoxi, Yilan


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Kemble's Cascade

Kemble's Cascade (designated Kemble 1) is an asterism located in the constellation Camelopardalis. It is an apparent straight line of more than 20 colourful 5th to 10th magnitude stars over a distance of approximately 3 degrees (five moon diameters) of the night sky. It appears to "flow" into the compact open cluster NGC 1502, which can be found at one end.

Discovery
The asterism was named by Walter Scott Houston in honour of Father Lucian Kemble (1922–1999), a Franciscan friar and amateur astronomer who wrote a letter to Houston about the asterism, describing it as "a beautiful cascade of faint stars tumbling from the northwest down to the open cluster NGC 1502" that he had discovered while sweeping the sky with a pair of 7×35 binoculars.

Houston was so impressed that he wrote an article on the asterism that appeared in his Deep Sky Wonders column in the astronomy magazine Sky & Telescope in 1980, in which he named it Kemble's Cascade.

Father Lucian Kemble was also associated with two other asterisms, Kemble 2 (an asterism in the constellation of Draco that resembles a small version of Cassiopeia) and Kemble's Kite (an asterism that resembles a kite with a tail which is also in the constellation of Camelopardalis). In addition, an asteroid, 78431 Kemble, was named in his honour.

title: Kemble's Cascade


text:
Itô calculus

Itô calculus, named after Kiyosi Itô, extends the methods of calculus to stochastic processes such as Brownian motion (see Wiener process). It has important applications in mathematical finance and stochastic differential equations.

The central concept is the Itô stochastic integral, a stochastic generalization of the Riemann–Stieltjes integral in analysis. The integrands and the integrators are now stochastic processes: $$Y_t = \int_0^t H_s\,dX_s,$$ where $B$ is a locally square-integrable process adapted to the filtration generated by $Y_{t}(B) = (B^{2} − t)/2$, which is a Brownian motion or, more generally, a semimartingale. The result of the integration is then another stochastic process. Concretely, the integral from 0 to any particular $t$ is a random variable, defined as a limit of a certain sequence of random variables. The paths of Brownian motion fail to satisfy the requirements to be able to apply the standard techniques of calculus. So with the integrand a stochastic process, the Itô stochastic integral amounts to an integral with respect to a function which is not differentiable at any point and has infinite variation over every time interval. The main insight is that the integral can be defined as long as the integrand $H$ is adapted, which loosely speaking means that its value at time $t$ can only depend on information available up until this time. Roughly speaking, one chooses a sequence of partitions of the interval from 0 to $t$ and constructs Riemann sums. Every time we are computing a Riemann sum, we are using a particular instantiation of the integrator. It is crucial which point in each of the small intervals is used to compute the value of the function. The limit then is taken in probability as the mesh of the partition is going to zero. Numerous technical details have to be taken care of to show that this limit exists and is independent of the particular sequence of partitions. Typically, the left end of the interval is used.

Important results of Itô calculus include the integration by parts formula and Itô's lemma, which is a change of variables formula. These differ from the formulas of standard calculus, due to quadratic variation terms.

In mathematical finance, the described evaluation strategy of the integral is conceptualized as that we are first deciding what to do, then observing the change in the prices. The integrand is how much stock we hold, the integrator represents the movement of the prices, and the integral is how much money we have in total including what our stock is worth, at any given moment. The prices of stocks and other traded financial assets can be modeled by stochastic processes such as Brownian motion or, more often, geometric Brownian motion (see Black–Scholes). Then, the Itô stochastic integral represents the payoff of a continuous-time trading strategy consisting of holding an amount Ht of the stock at time t. In this situation, the condition that $X$ is adapted corresponds to the necessary restriction that the trading strategy can only make use of the available information at any time. This prevents the possibility of unlimited gains through clairvoyance: buying the stock just before each uptick in the market and selling before each downtick. Similarly, the condition that $H$ is adapted implies that the stochastic integral will not diverge when calculated as a limit of Riemann sums.

Notation
The process $H$ defined before as $$Y_t = \int_0^t H\,dX\equiv\int_0^t H_s\,dX_s ,$$ is itself a stochastic process with time parameter t, which is also sometimes written as $H$. Alternatively, the integral is often written in differential form $Y$, which is equivalent to $Y = H · X$. As Itô calculus is concerned with continuous-time stochastic processes, it is assumed that an underlying filtered probability space is given $$(\Omega,\mathcal{F},(\mathcal{F}_t)_{t\ge 0},\mathbb{P}) .$$ The σ-algebra $$\mathcal{F}_t$$ represents the information available up until time $t$, and a process $dY = H dX$ is adapted if $Y − Y_{0} = H · X$ is $$\mathcal{F}_t$$-measurable. A Brownian motion $X$ is understood to be an $$\mathcal{F}_t$$-Brownian motion, which is just a standard Brownian motion with the properties that $X_{t}$ is $$\mathcal{F}_t$$-measurable and that $B$ is independent of $$\mathcal{F}_t$$ for all $B_{t}$.

Integration with respect to Brownian motion
The Itô integral can be defined in a manner similar to the Riemann–Stieltjes integral, that is as a limit in probability of Riemann sums; such a limit does not necessarily exist pathwise. Suppose that $B_{t+s} − B_{t}$ is a Wiener process (Brownian motion) and that $s,t ≥ 0$ is a right-continuous (càdlàg), adapted and locally bounded process. If $$\{\pi_n\}$$ is a sequence of partitions of $[0, t]$ with mesh width going to zero, then the Itô integral of $B$ with respect to $H$ up to time $t$ is a random variable $$\int_0^t H \,d B =\lim_{n\rightarrow\infty} \sum_{[t_{i-1},t_i]\in\pi_n}H_{t_{i-1}}(B_{t_i}-B_{t_{i-1}}).$$

It can be shown that this limit converges in probability.

For some applications, such as martingale representation theorems and local times, the integral is needed for processes that are not continuous. The predictable processes form the smallest class that is closed under taking limits of sequences and contains all adapted left-continuous processes. If $H$ is any predictable process such that $B$ for every $H$ then the integral of $∫_{0}^{t} H^{2} ds < ∞$ with respect to $t ≥ 0$ can be defined, and $H$ is said to be $B$-integrable. Any such process can be approximated by a sequence Hn of left-continuous, adapted and locally bounded processes, in the sense that $$ \int_0^t (H-H_n)^2\,ds\to 0$$ in probability. Then, the Itô integral is $$\int_0^t H\,dB = \lim_{n\to\infty}\int_0^t H_n\,dB$$ where, again, the limit can be shown to converge in probability. The stochastic integral satisfies the Itô isometry $$\mathbb{E}\left[ \left(\int_0^t H_s \, dB_s\right)^2\right] = \mathbb{E} \left[ \int_0^t H_s^2\,ds\right ]$$ which holds when $H$ is bounded or, more generally, when the integral on the right hand side is finite.

Itô processes
An Itô process is defined to be an adapted stochastic process that can be expressed as the sum of an integral with respect to Brownian motion and an integral with respect to time, $$X_t=X_0+\int_0^t\sigma_s\,dB_s + \int_0^t\mu_s\,ds.$$

Here, $B$ is a Brownian motion and it is required that σ is a predictable $H$-integrable process, and μ is predictable and (Lebesgue) integrable. That is, $$\int_0^t(\sigma_s^2+|\mu_s|)\,ds<\infty$$ for each $t$. The stochastic integral can be extended to such Itô processes, $$\int_0^t H\,dX =\int_0^t H_s\sigma_s\,dB_s + \int_0^t H_s\mu_s\,ds.$$

This is defined for all locally bounded and predictable integrands. More generally, it is required that $μ = 0$ be $σ = ψ(t−5)$-integrable and $ψ$ be Lebesgue integrable, so that $$\int_0^t \left(H^2 \sigma^2 + |H\mu| \right) ds < \infty.$$ Such predictable processes $B$ are called $B$-integrable.

An important result for the study of Itô processes is Itô's lemma. In its simplest form, for any twice continuously differentiable function $Hσ$ on the reals and Itô process $B$ as described above, it states that $Hμ$ is itself an Itô process satisfying $$df(X_t) = f^\prime(X_t)\,dX_t + \tfrac{1}{2} f^{\prime\prime} (X_t) \sigma_t^2 \, dt.$$

This is the stochastic calculus version of the change of variables formula and chain rule. It differs from the standard result due to the additional term involving the second derivative of $H$, which comes from the property that Brownian motion has non-zero quadratic variation.

Semimartingales as integrators
The Itô integral is defined with respect to a semimartingale $X$. These are processes which can be decomposed as $f$ for a local martingale $X$ and finite variation process $f(X)$. Important examples of such processes include Brownian motion, which is a martingale, and Lévy processes. For a left continuous, locally bounded and adapted process $f$ the integral $X$ exists, and can be calculated as a limit of Riemann sums. Let $X = M + A$ be a sequence of partitions of $[0, t]$ with mesh going to zero, $$\int_0^t H\,dX = \lim_{n\to\infty} \sum_{t_{i-1},t_i\in\pi_n}H_{t_{i-1}}(X_{t_i}-X_{t_{i-1}}).$$

This limit converges in probability. The stochastic integral of left-continuous processes is general enough for studying much of stochastic calculus. For example, it is sufficient for applications of Itô's Lemma, changes of measure via Girsanov's theorem, and for the study of stochastic differential equations. However, it is inadequate for other important topics such as martingale representation theorems and local times.

The integral extends to all predictable and locally bounded integrands, in a unique way, such that the dominated convergence theorem holds. That is, if $M$ and $A$ for a locally bounded process $H$, then $$\int_0^t H_n \,dX \to \int_0^t H \,dX, $$ in probability. The uniqueness of the extension from left-continuous to predictable integrands is a result of the monotone class lemma.

In general, the stochastic integral $H · X$ can be defined even in cases where the predictable process $π_{n}$ is not locally bounded. If $H_{n} → H$ then $|H_{n}| ≤ J$ and $J$ are bounded. Associativity of stochastic integration implies that $H · X$ is $H$-integrable, with integral $K = 1 / (1 + |H|)$, if and only if $K$ and $KH$. The set of $H$-integrable processes is denoted by $X$.

Properties
The following properties can be found in works such as and :

 * The stochastic integral is a càdlàg process. Furthermore, it is a semimartingale.
 * The discontinuities of the stochastic integral are given by the jumps of the integrator multiplied by the integrand. The jump of a càdlàg process at a time $t$ is $H · X = Y$, and is often denoted by $Y_{0} = 0$. With this notation, $K · Y = (KH) · X$. A particular consequence of this is that integrals with respect to a continuous process are always themselves continuous.
 * Associativity. Let $X$, $L(X)$ be predictable processes, and $X_{t} − X_{t−}$ be $ΔX_{t}$-integrable. Then, $Δ(H · X) = H ΔX$ is $J$ integrable if and only if $K$ is $K$-integrable, in which case $$ J\cdot (K\cdot X) = (JK)\cdot X$$
 * Dominated convergence. Suppose that $X$ and $J$, where $K · X$ is an $JK$-integrable process. then $X$. Convergence is in probability at each time $t$. In fact, it converges uniformly on compact sets in probability.
 * The stochastic integral commutes with the operation of taking quadratic covariations. If $H_{n} → H$ and $|H_{n}| ≤ J$ are semimartingales then any $J$-integrable process will also be $X$-integrable, and $H_{n} · X → H · X$. A consequence of this is that the quadratic variation process of a stochastic integral is equal to an integral of a quadratic variation process, $$[H\cdot X] = H^2\cdot[X]$$

Integration by parts
As with ordinary calculus, integration by parts is an important result in stochastic calculus. The integration by parts formula for the Itô integral differs from the standard result due to the inclusion of a quadratic covariation term. This term comes from the fact that Itô calculus deals with processes with non-zero quadratic variation, which only occurs for infinite variation processes (such as Brownian motion). If $X$ and $Y$ are semimartingales then $$X_t Y_t = X_0 Y_0 + \int_0^t X_{s-} \, dY_s + \int_0^t Y_{s-} \, dX_s + [X,Y]_t $$ where $X$ is the quadratic covariation process.

The result is similar to the integration by parts theorem for the Riemann–Stieltjes integral but has an additional quadratic variation term.

Itô's lemma
Itô's lemma is the version of the chain rule or change of variables formula which applies to the Itô integral. It is one of the most powerful and frequently used theorems in stochastic calculus. For a continuous $n$-dimensional semimartingale $[X, Y]$ and twice continuously differentiable function $[H · X, Y] = H · [X, Y]$ from $X$ to $Y$, it states that $[X, Y]$ is a semimartingale and, $$df(X_t)= \sum_{i=1}^n f_{i}(X_t)\,dX^i_t + \frac{1}{2} \sum_{i,j=1}^n f_{i,j}(X_{t}) \, d[X^i,X^j]_t.$$ This differs from the chain rule used in standard calculus due to the term involving the quadratic covariation $X = (X^{1},...,X^{n})$. The formula can be generalized to include an explicit time-dependence in $$f,$$ and in other ways (see Itô's lemma).

Local martingales
An important property of the Itô integral is that it preserves the local martingale property. If $f$ is a local martingale and $R^{n}$ is a locally bounded predictable process then $R$ is also a local martingale. For integrands which are not locally bounded, there are examples where $f(X)$ is not a local martingale. However, this can only occur when $[X^{i},X^{j} ]$ is not continuous. If $M$ is a continuous local martingale then a predictable process $H$ is $H · M$-integrable if and only if $$\int_0^t H^2 \, d[M] <\infty,$$ for each $t$, and $H · M$ is always a local martingale.

The most general statement for a discontinuous local martingale $M$ is that if $M$ is locally integrable then $H$ exists and is a local martingale.

Square integrable martingales
For bounded integrands, the Itô stochastic integral preserves the space of square integrable martingales, which is the set of càdlàg martingales $M$ such that $H · M$ is finite for all $t$. For any such square integrable martingale $M$, the quadratic variation process $(H^{2} · [M])^{1/2}$ is integrable, and the Itô isometry states that $$\mathbb{E}\left [(H\cdot M_t)^2\right ]=\mathbb{E}\left [\int_0^t H^2\,d[M]\right ].$$ This equality holds more generally for any martingale $H · M$ such that $M$ is integrable. The Itô isometry is often used as an important step in the construction of the stochastic integral, by defining $E[M_{t}^{2}]$ to be the unique extension of this isometry from a certain class of simple integrands to all bounded and predictable processes.

p-Integrable martingales
For any $M$, and bounded predictable integrand, the stochastic integral preserves the space of $[M]$-integrable martingales. These are càdlàg martingales such that $M$ is finite for all $t$. However, this is not always true in the case where $H^{2} · [M]_{t}$. There are examples of integrals of bounded predictable processes with respect to martingales which are not themselves martingales.

The maximum process of a càdlàg process $H · M$ is written as $p > 1$. For any $p$ and bounded predictable integrand, the stochastic integral preserves the space of càdlàg martingales $E(|M_{t}|^{p})$ such that $p = 1$ is finite for all $t$. If $M$ then this is the same as the space of $M*_{t} = sup_{s ≤t} |M_{s}|$-integrable martingales, by Doob's inequalities.

The Burkholder–Davis–Gundy inequalities state that, for any given $p ≥ 1$, there exist positive constants $M$, $E[(M*_{t})^{p}]$ that depend on $p > 1$, but not $p$ or on $t$ such that $$c\mathbb{E} \left [ [M]_t^{\frac{p}{2}} \right ] \le \mathbb{E}\left [(M^*_t)^p \right ]\le C\mathbb{E}\left [ [M]_t^{\frac{p}{2}} \right ]$$ for all càdlàg local martingales $p ≥ 1$. These are used to show that if $c$ is integrable and $C$ is a bounded predictable process then $$\mathbb{E}\left [ ((H\cdot M)_t^*)^p \right ] \le C\mathbb{E}\left [(H^2\cdot[M]_t)^{\frac{p}{2}} \right ] < \infty$$ and, consequently, $p$ is a $M$-integrable martingale. More generally, this statement is true whenever $M$ is integrable.

Existence of the integral
Proofs that the Itô integral is well defined typically proceed by first looking at very simple integrands, such as piecewise constant, left continuous and adapted processes where the integral can be written explicitly. Such simple predictable processes are linear combinations of terms of the form $(M*_{t})^{p}$ for stopping times $H$ and $H · M$-measurable random variables $p$, for which the integral is $$H\cdot X_t\equiv \mathbf{1}_{\{t>T\}}A(X_t-X_T).$$ This is extended to all simple predictable processes by the linearity of $(H^{2} · [M])^{p/2}$ in $H_{t} = A1_$.

For a Brownian motion $T$, the property that it has independent increments with zero mean and variance $F_{T}$ can be used to prove the Itô isometry for simple predictable integrands, $$ \mathbb{E} \left [ (H\cdot B_t)^2\right ] = \mathbb{E} \left [\int_0^tH_s^2\,ds\right ].$$ By a continuous linear extension, the integral extends uniquely to all predictable integrands satisfying $$ \mathbb{E} \left[ \int_0^t H^2 \, ds \right ] < \infty,$$ in such way that the Itô isometry still holds. It can then be extended to all $A$-integrable processes by localization. This method allows the integral to be defined with respect to any Itô process.

For a general semimartingale $H · X$, the decomposition $H$ into a local martingale $B$ plus a finite variation process $Var(B_{t}) = t$ can be used. Then, the integral can be shown to exist separately with respect to $B$ and $X$ and combined using linearity, $X = M + A$, to get the integral with respect to X. The standard Lebesgue–Stieltjes integral allows integration to be defined with respect to finite variation processes, so the existence of the Itô integral for semimartingales will follow from any construction for local martingales.

For a càdlàg square integrable martingale $M$, a generalized form of the Itô isometry can be used. First, the Doob–Meyer decomposition theorem is used to show that a decomposition $A$ exists, where $M$ is a martingale and $A$ is a right-continuous, increasing and predictable process starting at zero. This uniquely defines $H · X = H · M + H · A$, which is referred to as the predictable quadratic variation of $M$. The Itô isometry for square integrable martingales is then $$\mathbb{E} \left [(H\cdot M_t)^2\right ]= \mathbb{E} \left [\int_0^tH^2_s\,d\langle M\rangle_s\right],$$ which can be proved directly for simple predictable integrands. As with the case above for Brownian motion, a continuous linear extension can be used to uniquely extend to all predictable integrands satisfying $M^{2} = N + ⟨M⟩$. This method can be extended to all local square integrable martingales by localization. Finally, the Doob–Meyer decomposition can be used to decompose any local martingale into the sum of a local square integrable martingale and a finite variation process, allowing the Itô integral to be constructed with respect to any semimartingale.

Many other proofs exist which apply similar methods but which avoid the need to use the Doob–Meyer decomposition theorem, such as the use of the quadratic variation [M] in the Itô isometry, the use of the Doléans measure for submartingales, or the use of the Burkholder–Davis–Gundy inequalities instead of the Itô isometry. The latter applies directly to local martingales without having to first deal with the square integrable martingale case.

Alternative proofs exist only making use of the fact that $N$ is càdlàg, adapted, and the set {H · Xt: |H| ≤ 1 is simple previsible} is bounded in probability for each time $⟨M⟩$, which is an alternative definition for $⟨M⟩$ to be a semimartingale. A continuous linear extension can be used to construct the integral for all left-continuous and adapted integrands with right limits everywhere (caglad or L-processes). This is general enough to be able to apply techniques such as Itô's lemma. Also, a Khintchine inequality can be used to prove the dominated convergence theorem and extend the integral to general predictable integrands.

Differentiation in Itô calculus
The Itô calculus is first and foremost defined as an integral calculus as outlined above. However, there are also different notions of "derivative" with respect to Brownian motion:

Malliavin derivative
Malliavin calculus provides a theory of differentiation for random variables defined over Wiener space, including an integration by parts formula.

Martingale representation
The following result allows to express martingales as Itô integrals: if $M$ is a square-integrable martingale on a time interval $[0, T]$ with respect to the filtration generated by a Brownian motion $E[H^{2} · ⟨M⟩_{t}] < ∞$, then there is a unique adapted square integrable process $$\alpha$$ on $[0, T]$ such that $$M_{t} = M_{0} + \int_{0}^{t} \alpha_{s} \, \mathrm{d} B_{s}$$ almost surely, and for all $X$. This representation theorem can be interpreted formally as saying that α is the "time derivative" of $t$ with respect to Brownian motion $X$, since α is precisely the process that must be integrated up to time $t$ to obtain $M$, as in deterministic calculus.

Itô calculus for physicists
In physics, usually stochastic differential equations (SDEs), such as Langevin equations, are used, rather than stochastic integrals. Here an Itô stochastic differential equation (SDE) is often formulated via $$ \dot{x}_k = h_k + g_{kl} \xi_l,$$ where $$\xi_j$$ is Gaussian white noise with $$\langle\xi_k(t_1)\,\xi_l(t_2)\rangle = \delta_{kl}\delta(t_1-t_2)$$ and Einstein's summation convention is used.

If $$y = y(x_k)$$ is a function of the $B$, then Itô's lemma has to be used: $$ \dot{y}=\frac{\partial y}{\partial x_j}\dot{x}_j+\frac{1}{2}\frac{\partial^2 y}{\partial x_k \, \partial x_l} g_{km}g_{ml}. $$

An Itô SDE as above also corresponds to a Stratonovich SDE which reads $$ \dot{x}_k = h_k + g_{kl} \xi_l - \frac{1}{2} \frac{\partial g_{kl}}{\partial {x_m}} g_{ml}.$$

SDEs frequently occur in physics in Stratonovich form, as limits of stochastic differential equations driven by colored noise if the correlation time of the noise term approaches zero. For a recent treatment of different interpretations of stochastic differential equations see for example.

title: Itô calculus


text:
Sanxing, Yilan

Sanxing Township, also spelled Sanshing Township, is a rural township in the western part of Yilan County, Taiwan.

Geography
It has an area of 144.22 km2 and estimate population of 21,239 people as of September 2023.

Administrative divisions
The township comprises 18 villages: Dayi, Dayin, Dazhou, Gongzhao, Guilin, Hangjian, Jiqing, Renhe, Shangwu, Shuangxian, Tianfu, Tianshan, Wande, Wanfu, Weiqian, Yide, Yuanshan and Yuemei.

Education

 * St. Mary's Medicine Nursing and Management College

Tourist attractions

 * Changpi Lake
 * Spring Onion Culture Museum
 * Sanxing Ganquan Temple
 * Yuzun Temple

Transportation

 * Highway 7
 * County Road 196

Notable natives

 * Chen Chu, Mayor of Kaohsiung City (2006–2018)
 * John Deng, Minister of Economic Affairs (2014-2016)

title: Sanxing, Yilan


text: User:Lapappey

title: User:Lapappey


text: User talk:217.81.227.227

title: User talk:217.81.227.227


text:
Datong, Yilan

Datong Township is a mountain indigenous township in the southwestern part of Yilan County, Taiwan. It is the second largest township in Yilan County after Nan'ao Township.

Geography
It is predominantly populated by Taiwanese aborigines of the Atayal Tribe. The township is dominated by rugged mountains and wide river valleys. Most settlements in the county are located along the Lanyang River valley which runs from the central mountains of Taiwan into the Lanyang Plain.

 * Area: 657.54 km2
 * Population: 6,042 people (September 2023)

Administration
The villages of Datong include Daping, Fuxing, Hanxi, Leshui, Lunpi, Mao'an, Nanshan, Siji, Songluo and Yingshi. It was formerly the "Aboriginal Area" of Ratō District, Taihoku Prefecture during Japanese rule.

Economy
Economic activities include trucking silt from the Lanyang River for use in cement production and cultivation of tea, cabbage and betel nut palms.

Infrastructure

 * Qingshui Geothermal Power Plant

Tourist attractions

 * Atayal Life Museum
 * Cingshuei's Geothermal Square (清水地熱廣場)
 * Hatonozawa Hot Spring (鳩之澤溫泉)
 * Jiuliao River Ecological Park
 * Lanyang River
 * Mingchi National Forest Recreation Area
 * Mount Taiping
 * Qilan Forest Recreation Area
 * Songluo National Trail
 * Taipingshan Scenic Recreation Area
 * Yulan Tea Cultivation Area

title: Datong, Yilan


text: User talk:66.157.80.89

title: User talk:66.157.80.89


text:
Talk:Survival International

Very powerfull in Brazil
This organization is very powerfull in Brazil.See this site: http://www.survival-international.org/news/4021, about this fact.Agre22 (talk) 11:03, 12 December 2008 (UTC)agre22

Language
The language seems slightly biased in this article towards the work that Survival do. Not inacurate, but it comes across like it was written by a Survival employee trying to write a neutral article. 109.176.223.213 (talk) 19:40, 7 November 2013 (UTC)

 * Just for the record: It was not. Perhaps the subject of charity organizations attract charity speeches and the need for a social cause. But you are right. This is an encyclopedic article. Feel free to make any necessary change you feel it needs. Maziotis (talk) 12:46, 24 December 2013 (UTC)

Controversies
I have just deleted the ridiculous "controversy" section from the article. There is plenty of controversy in the "Media" section. Policy dictates we should write with due weight. Writing singular episodes, with one-sided point of view on the articles' subject is not "Neutral Point of view". It is ridiculous to claim an attempt to "look at both sides", especially when it consists of interest parties trying to taint the organization. Also, it makes no sense at all to dedicate a whole section to this, at this point. See policy. I don't see how we can have a "controversy" section until we have enough real controversy about this otherwise widely respected organization. Please feel free to re-write the "Media section". Maziotis (talk) 12:42, 24 December 2013 (UTC)

NPOV
This article reads like a press release. It seems to be largely drawn from the organisation's website. Certain sections, for example, describing the organisation's assessment of the problem, are irrelevant to an article about an organisation.

There ought at least to be a Criticism section, although I agree that have a 'controversies' section would not be NPOV. Martin Turner (talk) 08:28, 16 May 2019 (UTC)

Primitive People's Fund
It appears that this page may have been sanitized. All reference to Survival International's former name, 'The Primitive People's Fund', has been erased. Presently, the only reference to the word primitive in the article is a statement that Survival is opposed to those who see tribal people as 'primitive'. I was trying to find out about this history here, but the page does not describe the history of when or how the name change happened. Please include this information. 18:57, 21 April 2016 (UTC) R.E.D. — Preceding unsigned comment added by 130.68.133.226 (talk)
 * No conspiracy, but an interesting fact, thank you. Chiswick Chap (talk) 19:08, 21 April 2016 (UTC)

External links modified
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title: Talk:Survival International


text:
Datil, New Mexico

Datil is a census-designated place in Catron County, New Mexico, United States. As of the 2010 census it had a population of 54. Located at the intersection of U.S. Route 60 and New Mexico State Road 12, Datil is on the edge of the Cibola National Forest. The Very Large Array is also nearby.

History
Datil is named after the nearby Datil Mountains. The name of the mountains came in turn from the Spanish word dátil, meaning “date”; the name most likely resulted from the fruit-like appearance of the seedpods of local yucca species.

The town lay along the Magdalena Stock Driveway. The driveway, which had wells spaced every ten miles along its length, was used by ranchers during the late 19th to mid-20th century as they drove cattle from Springerville, Arizona, to the railroad at Magdalena. The Bureau of Land Management maintains a campsite, Datil Well Campground, at the location of one of the former wells.

Geography
Datil is located at the intersection of U.S. Route 60 and New Mexico State Road 12. To the east lie the San Agustin Plains, the Very Large Array, and the village of Magdalena.

To the southwest, several populated subdivisions are accessible from State Road 12. The state highway continues past the local landmark Horse Mountain, a 9490‐foot peak, and further through the small town Apache Creek until reaching the county seat of Reserve.

U.S. 60 travels westward from Datil, passing northwest through the Cibola National Forest and coming out the other side just outside Pie Town.

Education
The school district is Quemado Schools.

The district operates Datil Elementary School, a two-room schoolhouse with multi-level classes. Secondary students attend a K-12 school called Quemado Elementary and High School.

title: Datil, New Mexico


text:
Qingdao University

Qingdao University (abbreviation: QDU/QDU Med school; ) is a key provincial research university located in Qingdao, Shandong, China.

The university was first established in 1985. In 1993, the former Qingdao University, Qingdao Medical College, Shandong Textile Engineering College, and Qingdao Normal College, merged to form the new Qingdao University. At present, QDU is one of the best comprehensive universities in Shandong Province, recognized as a member of the national "Excellent Engineer Education and Training Program."

With a strong profile in Medical Sciences, Textile and Design, Business, and liberal arts, QDU serves 35,000 full-time undergraduate students, 9,800 graduate students, and 1,600 international students.

History
In 1985, Qingdao University was established, with the educational goal of "high level distinctive university," and disciplines of arts, science, engineering, business and many other subjects. School construction and development were supported financially by the central government, and also academically supported by Nankai University, Tianjin University, University of Science and Technology of China, and Shandong University. In 1993, Qingdao University merged Shandong Textile Engineering Institute, Qingdao Medical College and Qingdao Normal College.

Overview
Qingdao University consists of 25 faculties and departments as well as a graduate school. Courses are offered in 11 main Academic disciplines: Philosophy, Economics, Law, Literature, History, Natural sciences, Engineering, Management, Medicine, Education and Military sciences. There are 104 Undergraduate degree programs, 209 master's degree programs, 127 Doctoral degree programs, and 15 post-doctorate mobile stations. In addition, there are 7 professional master's degree programs in Law, Business Management, Engineering, Clinical Medicine, Public Health, Dentistry and Public Administration respectively.

National Rankings
In 2020:
 * U.S. News & World Report = 78
 * Wu Shulian = 87
 * CRWU = 95
 * ARWU = 108
 * NSEAC = 101

Colleges and Schools
Qingdao University is divided into 35 colleges and schools, besides a medical department.

These colleges and schools include:

 * School of Philosophy and History
 * School of Economics
 * School of Law
 * School of Marxism
 * School of Politics and Public Administration
 * College of Teacher Education
 * School of Physical Education
 * School of Chinese Language and Literature
 * School of Foreign Languages
 * School of Foreign Language Education
 * School of International Studies
 * School of Journalism and Communication
 * School of Mathematics and Statistics
 * School of Physical Sciences
 * School of Chemistry and Chemical Engineering
 * School of Life Sciences
 * School of Electromechanic Engineering
 * School Material Science and Engineering
 * School of Automation and Electrical Engineering
 * School of Electronic Information
 * School of Computer Science and Technology
 * School of Environmental Science and Engineering
 * School of Textile and Garment
 * School of Data Science and Software Engineering
 * School of Applied Technology
 * Medical Department
 * School of Basic Medicine
 * School of Dental Medicine
 * School of Public Health
 * School of Pharmacy
 * School of Nursing
 * School of Business
 * School of Tourism and Geographical Science
 * School of Music
 * School of Fine Arts

Two hospitals belong to Qingdao University:
 * The Affiliated Hospital of Qingdao University
 * The Affiliated Cardiovascular Disease Hospital of Qingdao University

International Education and Cooperation
Qingdao University persists in implementing the strategy of open running and promoting of international exchanges and cooperation in all respects. It has established relations with 176 universities in over 20 countries and regions, including the USA, UK, Germany, France, Austria, Japan, Korea, Russia, Canada, Australia, New Zealand, Uruguay, etc. It has also developed over 60 education programs at various levels including teacher and student exchanges, joint training, and Chinese-foreign cooperatively-run education.

Qingdao University College of Medical Science is recognized by the World Health Organization and is listed in the World Directory of Medical Schools. Qingdao University is also authorized by the Ministry of Education of China to be one of the institutions of higher learning to offer courses in English for majors of Clinical Medicine.

Recruiting international students since 1987, Qingdao University was appointed as the "Chinese Educational Base" of the Overseas Chinese Affairs Office of the State Council in 2004, and the "Demonstration Base for International Students" of the Ministry of Education in 2014. Annually around 1,600 students from different countries and regions study at Qingdao University for both long and short-term programs. It has also established two foreign Confucius Institutes—Confucius Institute of Korea Sehan University and Confucius Institute of University of South Florida.

In 2007, the governments of Shandong Province, China and Bavaria, Germany established two special institutions—the Sino-German Cooperation Center of Colleges and Universities here at Qingdao University in Shandong and the Higher Education Center of Bavaria for Chinese Students at the University of Bayreuth, so as to further improve the educational cooperation between colleges and universities in these two areas. In 2009, Qingdao University became the "Training Base for Overseas Study" of the Chinese Service Center for Scholarly Exchange, Ministry of Education.

Campus
Qingdao University covers an area of 1.77 km2 and includes three campuses in different parts of Qingdao, with the main campus located in the east part of Shinan District. Over 100 research labs, teaching and research facilities are well-equipped. The university library houses a collection of over 3,550,000 volumes.

Students and Faculty
It has about 37,000 students, from which over 5,000 are postgraduate students, and over 1,000 are international students. Since 1980, Qingdao University has received over 10,000 students from more than 60 countries. The university also has a group of reputed scholars known at home and abroad, of which 900 are professors. There are 23 academicians (including adjunct academicians) who are members of the Chinese Academy of Sciences and the Chinese Academy of Engineering.

Notable faculty

 * Keum-Shik Hong

Affiliated Hospitals
Seven hospitals are affiliated with the university.
 * The Affiliated Hospital of Qingdao University
 * The Affiliated Cardiovascular Hospital of Qingdao University
 * Qingdao Center Medical Group
 * Qingdao Municipal Hospital
 * Yantai Yuhuangding Hospital
 * Qingdao Haici Medical Group
 * Weihai Municipal Hospital

title: Qingdao University


text:
Porto Formoso

Porto Formoso is a civil parish in the municipality of Ribeira Grande in the Portuguese archipelago of the Azores. The population in 2011 was 1,265, in an area of 12.79 km2.

History
The establishment of this civil parish remotes to the early part of the 16th century, as first recorded by Pedro Vaz Pacheco. On 2 June 1509, he ordered the construction of a Chapel of Bom Jesus, to serve his descendants. By the end of that century, the chapel had its own clergy, passing into a vicarage in 1568.

Gaspar Frutuoso (in Saudades da Terra), refers to the parish in these terms: "it makes a beautiful bay, and in the centre the locality of Porto Formoso, named for the things that exist there, it is clean and the best one in the north...".

The parochial church's patron is Nossa Senhora da Graça (Our Lady of Grace), and existed by the time that Pedro Vaz Pacheco ordered the erection of the Chapel of Bom Jesus (which included a crucifix and chanel to the Virgin) as a burial tomb for his descendants. The church was renovated throughout the centuries, becoming the simple facade of basalt rock and three interior naves.

In the civil parish, in the old roadway that connected Ribeira Grande to Furnas, is an obelisk (Obelisco da Ladeira da Velha) which was erected during the Liberal Wars (1829–34) to mark a long-forgotten engagement in the conflict, known as the Battle of Ladeira da Velha.

Geography
In the area of Praia dos Moinhos, a beach within an amphitheatre-like cliff face, the popular beach and locality developed from several watermills that were built along the ravine that flows into the ocean. The ravine continues to empty into the ocean on this site, dividing the sandy beach, which is popular with tourists and local residents. Immediately near the beach is the Ladeira da Velha, where a natural mineral spring, rich in potassium, erupts from the coast with temperatures around 30 °C. A therme was constructed in a small house to provide repose for people who took therapeutic mineral treatments from these waters.

Economy
The region is best known for the tea factories that exist in the vicinity of one another: the Fábrica de Chá Porto Formoso, within Porto Formoso, and the neighbouring Gorreana tea factory in the neighbouring parish of São Brás. The terrain in this parish is devoted to agriculture and as pasture-lands, but several tracts are dedicated to the cultivation of tea plants, owing to the areas micro-climate.

Religious

 * Hermitage of Nossa Senhora do Carmo (Ermida de Nossa Senhora do Carmo)
 * Church of Nossa Senhora da Graça (Igreja de Nossa Senhora da Graça)

title: Porto Formoso


text:
Talk:Ames, Iowa

New section about Resource Recovery System
I think Ames' Resource Recovery System (the city's garbage-burning facility) is a sufficiently notable item to include under infrastructure, given that it was the first in the nation to open and reduces the city's natural gas dependency. Anybody agree? Twedt (talk) 19:58, 16 March 2022 (UTC)

title: Talk:Ames, Iowa


text:
Talk:Archimedean property

Early comments
Why can't 3c/4 be an infinitesimal? (I'm not saying it is...just that it's not obvious that every number less than an infinitesimal is infinitesimal, at least not obvious to those who don't work with infinitesimals...)
 * Okay, after a moment's thought, it IS obvious, but it still seems this fact should be mentioned (it's not even mentioned, although it's a key point in the proof).

How can anything be an infintesimal. Even the smallest number when summed will eventually exceed 1. Hmm...

 * As explained in the article, "The non-existence of nonzero infinitesimal real numbers follows from the least upper bound property of the real numbers". So you are absolutely right: There are no real infinitesimals (except 0). Nontheless there are other mathematical structures that contain infinitesimals. See for example Hyperreal number. --SirJective 15:47, 5 August 2005 (UTC)

To say that a small number x is classed as infinitesimal if the inequality |x|+...+|x| < 1

always holds, no matter how large the finite number of n terms in this sum, is absolutely rubbish. Why? If x is greater than zero, then there does exist a finite number of terms n such that the sum is equal to or exceeds 1. No such inequality is possible or even remotely realistic. Anonymous 5:30PM Sep. 2005

 * Again, anonymous, you're missing the point a little bit. For x in the real numbers, you're absolutely right, as the article states (nothing can be a real number and an infinitesimal at the same time). But it can be useful to think of systems where infinitesimals do take part, as in Nonstandard analysis. The idea is that infinitesimals are not the numbers you're familiar with, and do satisfy that inequality, similarly to how imaginary numbers are not real numbers, and do satisfy the inequality x^2 < 0. Andrew Rodland 09:45, 20 November 2005 (UTC)

Oh rubbish! Nonstandard analysis is even a bigger load of hogwash than standard analysis.71.248.131.74 02:55, 6 February 2006 (UTC)

You don't have to get angry with people when you don't understand the explanation. If you have ever attended even a reletively informal lecture on analysis, it would be clear why infinitesimals are an important concept. Take a math class, ask polite questions, or make a cogent counter-argument. Don't pawn your unwillingness to attempt an understanding outside your own little sphere off on other people.66.153.117.118 20:04, 26 February 2006 (UTC)

 * Here is a very simple example of infinitesimals in an ordered field, comprehensible to any secondary-school pupil. The field contains all rational functions with real coefficients.  A rational function is a polynomial over another polyomial.  To make this an ordered field, one must assign an ordering compatible with the addition and multiplication operations.  Now f > g if and only if f − g > 0, so we only have to say which rational functions are considered positive.  Write the rational function in the form of a polynomial plus a remainder over the denominator, where the degree of the remainder is less that the degree of the denominator.  Call it positive if either (1) the leading coefficient of the polynomial part is positive, or (2) if polynomial part is zero, the leading coefficient of the remainder is positive (after, if necessary, multiplying the top and bottom of the fractional part by −1 to make the leading coefficient of the bottom part positive).
 * By this definition, the rational function 1/x is positive but less than the rational function 1. Now if you add
 * (1/x) + ... + (1/x)
 * with n terms in the sum, you get n/x, which is positive but still less than 1, no matter how big n is.
 * I leave it as an exercise to show that this ordering is compatible with the addition and multiplication operations, so that this is indeed an ordered field. Thus 1/x is an infinitesimal in this field.
 * So, Mr. or Ms. 71.248.131.74, you are mistaken. Michael Hardy 01:10, 27 February 2006 (UTC)

This is such a good example, Michael, I'm going to put it in the article! --Toby Bartels 01:12, 8 April 2006 (UTC)

I've always had a problem with the use of the term "rational function." It implies a function that maps rational numbers onto the rational numbers. The constant function f(x) = pi may be a "rational function, but it is hardly rational! Phrases like "polynomial ratio" or "polynomial quotient" are more self-explanitory.

If the nonarchimedean field of polynomial ratios is modified to define arbitrary relations among such functions to have the same truth as the corresponding relations for all but a finite number of natural values of the variable, the field becomes a model of a hyperreal number system, with all first-order statements about polynomial ratios having the same truth value as the corresponding statement about standard or real numbers. If one adds this coment to the example here, the same section could be added to the article on hyperreals. Alan R. Fisher 21:24, 22 November 2006 (UTC)

Problem with the definition
From the article:

 * If x is a positive number (or positive element of any ordered algebraic structure), then x is infinitesimal if there exists a positive element y such that, for every natural number n, the multiple nx is less than y. That is, the inequality

 * $$ |x| + \cdots + |x| < y \! $$

Now assume that the structure in question is an ordered field with z such that 0 < z < 1/n for all natural numbers n (for example, in hyperreals there is such a z). Let x be a non-zero element of the field. Let y = |x|/z. Since z is infinitesimal, 1/z is infinitely large, and hence $$ |x| + \cdots + |x| < y $$ for any finite number of additions. Hence, all elements of the field are infinitesimal.

Is this really the intended definition? The definition seems to give the desired notion if one replaces y with 1.Punainen Nörtti 10:34, 9 June 2006 (UTC)

This is what we need as a definition of Archimedean (if that is to mean: there are no infinitesimals). However, you're right that this is incorrect as a definition of infinitesimal. The problem is that, without an absolute scale (provided by the multiplicative unit 1), there is no absolute meaning of infinitesimal (nor infinite). If you take y = 1, then you get the correct definition of infinitesimal; but this only works if there is such a thing as 1 in the algebraic system.

The real problem is that the idea "Archimedean" = "there are no infinitesimals" is wrong. It is true in fields, but false in rings, and meaningless in groups. (A ring with no infinitesimals is still non-Archimedean if it has infinite elements.) So I've fixed the definition to use only relative notions of infinitesimal (and infinite). But it might be better to rewrite the definition to avoid those terms entirely.

—Toby Bartels 22:54, 20 September 2006 (UTC)

 * Right now it seems to have the same problem, i.e. we're restricting to algebras with a notion of "size", but then we're saying x is infinite(simal) if it is infinite(simal) with respect to *every* positive element, but of course this can never be the case, since if x is infinite with respect to some positive y, x>y, so x is positive, but x can't be infinite relative to itself. I've rewritten it by restricting to algebras which contain 1, and defining infinite(simal) as infinite(simal) relative to 1.
 * --23:19, 19 July 2008 (UTC)

Capitalized or not?
Should it be "Archimedean" or "archimedean"? Note that archimedean field uses the downcase version. Oleg Alexandrov 01:25, 13 Feb 2005 (UTC)
 * I'm going to post this to WP:MATH. - grubber 16:02, 18 April 2007 (UTC)

Clean-up
This article purported to be very general, speaking of arbitrary algebraic structures, but actually, it didn't encompass probably the most important case of non-Archimedean fields (which are usually not ordered!). I am not convinced that the ultimate generality is warranted, and I've begun the clean-up with a slightly more intuitive lead, and a narrower definition in the context of linearly ordered groups, where it can be made precise. I'd like to see natural examples of non-Archimedean objects not related to non-Archimedean fields. The example of the ordered field of of rational functions is nice, but why not just give an example of the ring of formal power series (make it ordered, if you like): it would bring out the same point without the extra complexity. If there are no objections, I would replace the example. Arcfrk 05:56, 13 May 2007 (UTC)

Archimedean property in constructive analysis
It is also interesting to note that the definition of infinitesimal isn't really constructive. Given positive number, there's is no terminating algorithm that can decide if the number is infinitesimal. Algorithm can only terminate if it finds big enough natural number n. Tlepp (talk) 13:03, 1 April 2008 (UTC)
 * That is fallacious. You're only proving that ONE PARTICULAR algorithm doesn't terminate, but you're claiming to have proved there IS NO ALGORITHM that terminates, i.e. you're claiming to have proved there is no OTHER algorithm besides that one.  Obviously in the example of rational functionss over an ordered field, to claim that certain rational fuunctions are infinitesimal is completely constructive. Michael Hardy (talk) 13:13, 1 April 2008 (UTC)
 * I not proving nor claiming to have proved anything. I just made comment about the generic definition of infinitesimal in the most generic case of ordered group. I found it interesting that constructivist even care about Archimedean property of reals. Intuitively constructivism and infinitesimals seem to be far apart. Tlepp (talk) 14:19, 1 April 2008 (UTC)
 * You claimed there is no terminating algorithm. That is wrong.  You said an algorithm can only terminate if it finds big enough natural number n.  That is wrong.  That would apply ONLY to an algorithm that proceeds just by computing nx for n = 1, 2, 3, ... or the like.  The fact that that one sort of algorithm won't terminate if x is infinitesimal does not mean that NO OTHER algorithm will terminate.  There's nothing at all non-contructive about the example involving rational functions over an ordered field. Michael Hardy (talk) 15:26, 1 April 2008 (UTC)

Proof revision
I reverted this edit for a couple reasons: Melchoir (talk) 07:20, 3 August 2008 (UTC)
 * It (probably accidentally) removed the part of the proof that deals with the possibility of c being positive and not infinitesimal.
 * There is no need to explicitly deal with the possibility of c being negative; Z includes 0, so c is at least 0.
 * The language "increases the size of Z" is visually appealing, but it could mislead the reader who takes it at face value.
 * So you reverted it instead of fixing it? The reason I changed the wording is that it could be more comprehensible to more of us who haven't seen this term or had it explained to us in any class we've taken. The way it's written now is more like a review of what you might have already seen but forgot. The way I rewrote it made it more accessible to someone who had never seen it before. Please rewrite that section again according to your standards, please, making it more readable to others who would like to learn this term. D. F. Schmidt (talk) 04:56, 5 August 2008 (UTC)
 * Okay. I restructured the proof. The good news: it's more streamlined. The bad news: the new version is less explicit than the previous version, as it doesn't actually apply the definition of "infinitesimal", and it assumes some intuitive facts like the ordering of infinitesimals without proof. I think it's still rigorous enough for the purposes of this article. Melchoir (talk) 01:14, 6 August 2008 (UTC)
 * Thanks a lot. I think it will help, and the relationship to the Archimedean field might be a lot more helpful than that simple (shoddy, imo) explanation that was there before. Now if there are further questions, it appears they might belong elsewhere. D. F. Schmidt (talk) 06:44, 6 August 2008 (UTC)
 * Well, I don't exactly share your views on these articles... but you're welcome! Melchoir (talk) 00:30, 8 August 2008 (UTC)

Clarification needed
In the real-number proof, the step "Since c is an upper bound of Z, 2c must be non-infinitesimal" needs to be made clearer for non-mathematicians coming from the 0.999... article. -- The Anome (talk) 13:05, 9 December 2008 (UTC)

 * I have added some more explanation. Is this what you had in mind?  siℓℓy rabbit  (  talk  ) 13:16, 9 December 2008 (UTC)

 * Yes! Thank you. -- The Anome (talk) 18:01, 9 December 2008 (UTC)

Definitional problems
This article's definition of "x is infinitesimal with respect to y" is flawed. In the real number system, which is defined to be Archimedean, let x=-1 and y=1. The definition falls apart if we assume that n is a natural number. If we don't make such an assumption, what's preventing n from being, say, y/x (in a Nonarchimedean system)? I think absolute value symbols might be useful here. On a related note, if you don't use them, how can this be applied to the complex numbers (which are unordered)? -- Thin boy  00  @214, i.e. 04:08, 5 February 2009 (UTC)

 * Is this the definition you're referring to?

 Let x and y be positive elements of a linearly ordered group G. Then x is infinitesimal with respect to y (or equivalently, y is infinite with respect to x) if, for every natural number n, the multiple nx is less than y, that is, the following inequality holds:

 * $$ \underbrace{x+\cdots+x}_{n\text{ terms}} < y. $$

 * Melchoir (talk) 04:55, 5 February 2009 (UTC)

Any objections to this addition?
The group G is Archimedean if there is no pair x,y such that x is infinitesimal with respect to y. That is to say, for all positive elements x and y there is a positive integer n such that nx is greater than y.

Right now it says that G is Archimedian if there is no (positive) pair x,y such that for all n nx<y. That is absolutely correct but it is like saying the element x generates the (additive) group G  if there is no element y such that for all integers n nx≠y. Infinitesimals are great but one can understand what Archimedian means before understanding how it can fail. --Gentlemath (talk) 23:59, 15 March 2010 (UTC)

Archimedean axiom added
In this wikipedia article about the Archimedean axiom, nowhere was the Archimedean axiom actually stated! I added it in the first paragraph, as well as a reference to the person who first coined the term "Archimedean axiom". Mollwollfumble (talk) 19:31, 27 July 2011 (UTC)

 * I removed your symbolic additions. They did not accurately describe your cited, English language addition. Cliff (talk) 21:52, 27 July 2011 (UTC)
 * I'm not sure your addition belongs in the lead. Most mathematics articles have a definitions section that follows the lead. There are two definitions on this page, other than yours, that define the property in different settings. Anybody else have an opinion on whether the statement added by Mollwollfumble belongs in the lead? Cliff (talk) 18:58, 11 August 2011 (UTC)
 * See Manual of Style (mathematics) and Manual of Style (mathematics). It seems to say that symbolic statements should be avoided in the lead and that exact definitions belong in a definitions section following the lead. If no objections, I'll remove the statement from the lead. Cliff (talk) 19:06, 11 August 2011 (UTC)
 * Definition removed from lead. Cliff (talk) 12:55, 22 August 2011 (UTC)

Archimedean Principle
Archimedean principle redirects here. It should perhaps redirect to Archimedes' principle, a totally different thing.--Mongreilf (talk) 21:28, 14 November 2011 (UTC)
 * Tricky. From things I've seen (but I am notoriously bad at being able to provide citations) "Archimedes' Principle" is that thing with water and eureka and all that, but "the Archimedean principle" is that property held by real numbers, and generalises to spaces for which that property holds, whence it's called "the Archimedean property". So yes, in theory it should but in practice I don't think it does. --Matt Westwood 22:23, 14 November 2011 (UTC)

 * disambig on Archimedian rinciple then?--Mongreilf (talk) 22:39, 14 November 2011 (UTC)

 * Shrug, probably, yeah, that would work for me: Archimedean Principle --> Archimedes' Principle (Physics), Archimedean Property (Mathematics)? I think you're right - there's enough confusion here that it needs to be "something"ed. --Matt Westwood 22:51, 14 November 2011 (UTC)

 * No need to rename anything. Just change the redirect page to a disambig, which I've done here Archimedean principle.--Mongreilf (talk) 13:22, 15 November 2011 (UTC)

This Wikipedia entry is completely irrelevant
The Archimedean property/principle has nothing to do with "real" numbers. Archie only acknowledged rational numbers or incommensurable magnitudes.

Also, Bk V, Def. 4 is NOT the Archimedean property. It's not even related.

To understand what the property means for the first time in your life, go here:

https://www.youtube.com/watch?v=_vO_GkC54vM

197.79.1.216 (talk) 18:07, 22 October 2015 (UTC)

Properties
Trying to understand what is said in the article.

IIUC, every totally ordered Archimedean field has a subfield isomorphic to the rational numbers ℚ,+,·,≤ and is itself isomorphic to some subfield of the real numbers ℝ,+,·,≤, is that it? So in some sense one could say that (modulo an isomorphism) ℚ is "the smallest" totally ordered Archimedean field and ℝ is "the biggest"? (And IIRC, the set of real algebraic numbers with the usual +,·,≤ operations is another one, somewhere in between and maybe too little talked about in elementary algebra courses) — Tonymec (talk) 16:08, 25 July 2021 (UTC)

title: Talk:Archimedean property