title: Arabic phonology

text: Super-heavy syllables are usually not allowed except word finally, with the exception of CVV- before geminates creating non-final CVVC- syllables, these can be found in the active participles of geminate Form I verbs, like in ('substance, matter'), ('entirely'), ('poisonous'), ('dry'), ('public, general'), ('private, special'), and ('hot, spicy').


title: Arabic phonology

text: In the pausal form, the final geminates behave as a single consonant, only when preceding another word or with vocalization, the geminates start appearing, belonging to two separate syllables.


title: Arabic phonology

text: Loanwords can break some phonotactic rules like allowing initial consonant clusters (with an initial epenthetic [i] being optional) like in /bluː.toː/ "Pluto" or allowing CVVC syllables non-finally without geminates like in /ruːs.jaː/ "Russia" which can be modified to /ruː.si.jaː/ to fit the phonotactics better.


title: Arabic phonology

text: The placement of word stress in Arabic varies considerably from one dialect to another, and has been the focus of extensive research and debate.


title: Arabic phonology

text: The word stress of Classical Arabic has been the subject of debate. However, there is consensus as to the general rule, even though there are some exceptions. A simple rule of thumb is that word-stress falls on the penultimate syllable of a word if that syllable is closed, and otherwise on the antepenultimate.


title: Arabic phonology

text: A more precise description is J. C. E. Watson's. Here the stressed syllable follows the marker ' and variant rules are in brackets:


title: Arabic phonology

text: Modern Arabic dialects all maintain rules (1) and (2). But if there is neither a final superheavy syllable nor a heavy penultimate syllable, their behaviour varies. Thus in Palestinian, rule (3) is instead 'otherwise stress the first syllable (up to the antepenult): ‘he wrote’, ‘man’', whereas the basic rules of Cairene (to which there are exceptions) are:


title: Arabic phonology

text: Spoken varieties differ from Classical Arabic and Modern Standard Arabic not only in grammar but also in pronunciation. Outside of the Arabian peninsula, a major linguistic division is between "sedentary", largely urban, varieties and rural varieties. Inside the Arabian peninsula and in Iraq, the two types are less distinct; but the language of the urbanized Hejaz, at least, strongly looks like a conservative sedentary variety.


title: Arabic phonology

text: In Modern Standard Arabic (not in Egypt's use), is used as a marginal phoneme to pronounce some dialectal and loan words.


title: Arabic phonology

text: On the other hand, it is considered a native phoneme or allophone in most modern Arabic dialects, mostly as a variant of (as in Arabian Peninsula and Northwest African dialects) or as a variant of (as in Egyptian and a number of Yemeni and Omani dialects). It is also considered a separate foreign phoneme that appears only in loanwords, as in most urban Levantine dialects where is and is .


title: Arabic phonology

text: The phoneme represented by the Arabic letter "" () has many standard pronunciations: in most of the Arabian Peninsula and as the predominant pronunciation of Literary Arabic outside the Arab world, in most of Egypt and some regions in southern Yemen and southwestern Oman. This is also a characteristic of colloquial Egyptian and southern Yemeni dialects. In Morocco and western Algeria, it is pronounced as in some words, especially colloquially. In most north Africa and most of the Levant, the standard is pronounced , and in certain regions of the Persian Gulf colloquially with . In some Sudanese and Yemeni dialects, it may be either or as it used to be in Classical Arabic.


title: Arabic phonology

text: The foreign phonemes and are not necessarily pronounced by all Arabic speakers, but are often pronounced in names and loanwords. and are usually transcribed with their own letters and but as these letters are not present on standard keyboards, they are simply written with and , e.g. both and , or "November", both and "caprice" can be used. The use of both sounds may be considered marginal and Arabs may pronounce the words interchangeably; besides, many loanwords have become Arabized, e.g. or "Pakistan", or "virus".


title: Arabic phonology

text: The Arabic of Cairo (often called "Egyptian Arabic" or more correctly "Cairene Arabic") is a typical sedentary variety and a de facto standard variety among certain segments of the Arabic-speaking population, due to the dominance of Egyptian media. Watson adds emphatic labials and and emphatic to Cairene Arabic with marginal phonemic status. Cairene has also merged the interdental consonants with the dental plosives (e.g. ثلاثة → , 'three') except in loanwords from Classical Arabic where they are nativized as sibilant fricatives (e.g. ثانوية → , 'secondary school'). Cairene speakers pronounce as and debuccalized to (again, loanwords from Classical Arabic have reintroduced the earlier sound or approximated to with the front vowel around it changed to the back vowel ). Classical Arabic diphthongs and became realized as and respectively. Still, Egyptian Arabic sometimes has minimal pairs like شايلة ('carrying' f.s.) vs شيلة ('burden'). جيب 'pocket' + نا 'our' → collapsing with which means (جبنة 'cheese' or جيبنا 'our pocket'), because Cairene phonology cannot have long vowels before two consonants. Cairene also has as a marginal phoneme from loanwords from languages other than Classical Arabic.


title: Arabic phonology

text: Varieties such as that of Sanaa, Yemen, are more conservative and retain most phonemic contrasts of Classical Arabic. Sanaani possesses as a reflex of Classical (which still functions as an emphatic consonant). In unstressed syllables, Sanaani short vowels may be reduced to . is voiced to in initial and intervocalic positions.


title: Arabic phonology

text: The most frequent consonant phoneme is , the rarest is . The frequency distribution of the 28 consonant phonemes, based on the 2,967 triliteral roots listed by Wehr is (with the percentage of roots in which each phoneme occurs):


title: Arabic phonology

text: This distribution does not necessarily reflect the actual frequency of occurrence of the phonemes in speech, since pronouns, prepositions and suffixes are not taken into account, and the roots themselves will occur with varying frequency. In particular, occurs in several extremely common affixes (occurring in the marker for second-person or feminine third-person as a prefix, the marker for first-person or feminine third-person as a suffix, and as the second element of Forms VIII and X as an infix) despite being fifth from last on Wehr's list. The list does give, however, an idea of which phonemes are more marginal than others. Note that the five least frequent letters are among the six letters added to those inherited from the Phoenician alphabet, namely, , , , , and .


title: Arabic phonology

text: The Literary Arabic sample text is a reading of The North Wind and the Sun by a speaker who was born in Safed, lived and was educated in Beirut from age 8 to 15, subsequently studied and taught in Damascus, studied phonetics in Scotland and since then has resided in Scotland and Kuwait.


title: Arabic phonology

text: The North Wind and the Sun were disputing which was the stronger, when a traveler came along wrapped in a warm cloak. They agreed that the one who first succeeded in making the traveler take his cloak off should be considered stronger than the other. Then the North Wind blew as hard as he could, but the more he blew the more closely did the traveler fold his cloak around him; and at last the North Wind gave up the attempt. Then the Sun shined out warmly, and immediately the traveler took off his cloak. And so the North Wind was obliged to confess that the Sun was the stronger of the two.


title: Black Tie White Noise

text: Black Tie White Noise is the 18th studio album by English musician David Bowie, released on 5 April 1993 through Savage Records in the United States and Arista Records in the United Kingdom. Conceived following the disbandment of Bowie's rock band Tin Machine and his marriage to model Iman, it was recorded throughout 1992 between studios in Montreux, Los Angeles and New York City. Bowie co-produced with his "Let's Dance" (1983) collaborator Nile Rodgers, who voiced dissatisfaction with the project in later decades. The album features several guest appearances, including previous collaborators Mike Garson and Mick Ronson, and new arrivals Lester Bowie and Chico O'Farrill.


title: Black Tie White Noise

text: Inspired to write the title track after witnessing the 1992 Los Angeles riots, "Black Tie White Noise" is primarily separated into themes of racial harmony and David's marriage to Iman. It features prevalent saxophone work from Bowie and a wide variety of musical styles, from art rock, electronic and soul, to jazz, pop and hip-hop influences. It also contains multiple instrumentals and cover versions. The album's lead single "Jump They Say" alludes to Bowie's step-brother Terry, who died in 1985.


title: Black Tie White Noise

text: Released amidst the rise of Britpop in the UK, "Black Tie White Noise" initially received favourable reviews from music critics, who praised its experimentation but criticised its lack of cohesion. It debuted at number one on the UK Albums Chart, with each of its three singles reaching the UK top 40. Its promotion in America was stalled following the dissolution of Savage Records, resulting in the album's rarity until later reissues. Instead of touring, Bowie released an accompanying film to support it.


title: Black Tie White Noise

text: Despite mixed assessments from critics in subsequent decades, "Black Tie White Noise" marked the beginning of Bowie's commercial revival and improved critical standing following a string of poorly received projects. An interactive CD-ROM based on the album was released in 1994. It was reissued by EMI in 2003 and remastered in 2021 as part of the box set "Brilliant Adventure (1992–2001)".


title: Black Tie White Noise

text: David Bowie began recording material with his former "Let's Dance" (1983) collaborator Nile Rodgers months after disbanding the rock band Tin Machine. The pair, who had reconnected in New York City after a 1991 Tin Machine concert, first recorded "Real Cool World" for the animated film "Cool World". Released as a single in August 1992, it appeared on the film's accompanying soundtrack album and featured a sound that foreshadowed Bowie's direction for his next solo record, his first since "Never Let Me Down" six years earlier.


title: Black Tie White Noise

text: In October 1990, Bowie met Somalian model Iman in Los Angeles as he resumed recording with Tin Machine following the Sound+Vision Tour. They married on 24 April 1992 in a private ceremony in Lausanne, Switzerland. Five days later, the two returned to Los Angeles on the day the 1992 Los Angeles riots began, forcing the newly-weds to stay in a hotel and witness the violence from inside. Bowie later reflected: "It was an extraordinary feeling. I think the one thing that sprang into our minds was that it felt more like a prison riot than anything else. It felt as if innocent inmates of some vast prison were trying to break out, break free from their bonds." According to biographer Nicholas Pegg, both the wedding and racial divide influenced Bowie's next album.


title: Black Tie White Noise

text: With Bowie and Rodgers co-producing, recording for "Black Tie White Noise" took place between April and November 1992, alternating between Mountain Studios in Montreux, Switzerland and the Hit Factory in New York City, with additional recording done at 38 Fresh studio in Los Angeles. According to biographer Chris O'Leary, Bowie composed beats and patterns at 38 Fresh, which he sent to Rodgers at the Hit Factory to transpose into songs. Rodgers described Bowie's attitude as calmer than "Let's Dance", "a hell of a lot more philosophical and just in a state of mind where his music was really, really making him happy".


title: Black Tie White Noise

text: Both Bowie and Rodgers gave positive statements regarding the sessions in contemporary interviews. Speaking with "Rolling Stone", both said they were not looking to do "Let's Dance II", Bowie remarking they "would have done [that] years ago". Nevertheless, Rodgers made several unfavourable comparisons between the two records, including statements about Bowie's involvement and how "Black Tie" was more difficult to produce and took longer to record than "Let's Dance". In the ensuing years, Rodgers expressed disappointment in "Black Tie", brushing it off as "an exercise in futility" that was not as good than "Let's Dance". Tin Machine member Reeves Gabrels later said Bowie felt coerced into hiring Rodgers, who was intent on creating a "Let's Dance" follow-up, while Bowie wanted to pursue other musical directions. Decades later, Rodgers commented that he wanted a more commercial record, while Bowie was trying to "make this artistic statement about this period in his life".


title: Black Tie White Noise

text: During the sessions, Bowie signed a record contract with the American label Savage Records, affiliated with Arista Records and owned by BMG. Savage offered him the "artistic freedom" that he was craving: "[Studio head] David Nemran ... encouraged me to do exactly what I wanted to do, without any kind of indication that it would be manipulated, or that my ideas would be changed, or that other things would be required of me. That made me feel comfortable and that was the deciding factor." Nemran replied that Bowie would be the label's breakthrough: "He's everything that I would use to describe us."


title: Black Tie White Noise

text: "Black Tie White Noise" features an array of guest musicians, some of whom had not collaborated with Bowie for decades. Guitarist Mick Ronson, a member of the Spiders from Mars backing band from 1971 to 1973, appears on a cover of Cream's "I Feel Free" (1966). Ronson, whose last appearance was on 1973's "Pin Ups", reconnected with Bowie after the latter was impressed by the former's production work on Morrissey's "Your Arsenal" (1992). Bowie praised Ronson's contributions on "Black Tie" while the latter commented, "I hope David's album does well. He's put everything into it." Ronson died of cancer shortly after the album's release.


title: Black Tie White Noise

text: Pianist Mike Garson, whose last appearance on a Bowie record was 1975's "Young Americans", plays on "Looking for Lester". Bowie told "Record Collector" in 1993: "He really has a gift. He kind of plops those jewels on the track and they're quite extraordinary, eccentric pieces of piano playing." Trinidadian guitarist Tony Springer (credited as "Wild T" Springer) appears on a cover of Morrissey's "Your Arsenal" track "I Know It's Gonna Happen Someday". Bowie had met Springer in Canada during Tin Machine's It's My Life Tour and invited him to record. Bowie recalled that "he was an absolute delight", comparing his guitar style to Jimi Hendrix.


title: Black Tie White Noise

text: Gabrels plays lead guitar on "You've Been Around", although his contribution was placed low in the mix. The song was first attempted by Tin Machine during the sessions for their 1989 debut album, but Bowie was dissatisfied with the result so it was shelved, eventually rerecording it for "Black Tie". Singer Al B. Sure! duets with Bowie on the title track, of which the two worked on the arrangement extensively, leading Bowie to quip "I've never worked longer with any artist than with Al B".


title: Black Tie White Noise

text: "Black Tie" also features trumpet playing by Lester Bowie, whom David Bowie had wanted to work with throughout the 1980s. Lester, who played to tracks before he heard them, appears on six tracks; Pegg considers his contributions the album's "essential musical identity". A foil to Lester's trumpet was David's saxophone, which appears more prominently on "Black Tie" than any other David Bowie album. Rodgers found his saxophone playing challenging, telling "Rolling Stone": "I think David would be the first to admit that he's not a saxophonist in the traditional sense. [...] He uses his playing as an artistic tool. He's a painter. He hears an idea, and he goes with it. But he absolutely knows where he's going." The album's horn arrangements were composed by Afro-Cuban jazz player Chico O'Farrill. "Black Tie" also features several backing vocalists from "Let's Dance" and "Labyrinth" (1986), while pianist Philippe Saisse and producer David Richards returned from "Never Let Me Down".


title: Black Tie White Noise

text: "Black Tie White Noise" features a wide variety of musical influences and styles, including soul, hip-hop, disco, pop, avant-garde jazz and gospel. Author James E. Perone also found references to Bowie's plastic soul work of the 1970s. "Rolling Stone"s Jason Newman described the music as "a blend of Euro-disco, techno-rock, freestyle jazz, Middle Eastern riffs and hip-hop", while AllMusic's Stephen Thomas Erlewine considered "Black Tie" an "urban soul record" that balances styles of the "commercial dance rock" of "Let's Dance" with the art rock of the late 1970s Berlin Trilogy. A writer for "The Economist" later categorised the record as art rock and electronic. In 1993, Bowie told "Rolling Stone" that his intent for "Black Tie White Noise" was making a new type of house record that brought back the "strong melodic content" of the 1960s, finding "the new R&B [of today]" a mixture of "hip-hop and house". He commented: "I think this album comes from a very different emotional place. That's the passing of time, which has brought maturity and a willingness to relinquish full control over my emotions."


title: Black Tie White Noise

text: Lyrically, "Black Tie White Noise" is primarily separated into two major themes: racial harmony and Bowie's marriage to Iman. Perone finds the "Black Tie" signifies "a wedding" while "White Noise" epitomises the "instrumentally focused, slightly experimental jazz pieces". For his wedding ceremony, he had composed an instrumental intended to fuse him and Iman's English and Somalian cultures. Writing the piece triggered Bowie to make the album:


title: Black Tie White Noise

text: "Black Tie White Noise" opens with the instrumental "The Wedding", a funk adaptation of the instrumental Bowie composed for his wedding. It's a piece that, in Pegg's words, "fuses dance beats, distant backing vocals and Eastern-influenced saxophone cadences" that set the stage for the remaining tracklist. The "Black Tie" version of "You've Been Around" blends contemporary dance music with elements of jazz. Although Bowie and Gabrels wrote it together, O'Leary says the new version "effectively erased...Reeves Gabrels". Pegg states the lyrics foreshadow the "fractal images" Bowie used for his next studio album, "Outside" (1995). Bowie's cover of "I Feel Free" is musically different from Cream's original, being described by Pegg as "techno-funk" and likened by Perone to "1990s dance music".


title: Black Tie White Noise

text: Bowie's recorded the title track with a rougher edge to avoid ending up like "an 'Ebony and Ivory' for the Nineties". To evoke the racial theme, the lyrics reference "We Are the World" by the supergroup USA for Africa (1985) and Marvin Gaye's "What's Going On" (1971); Pegg says that the "black and white voices" of Al B Sure! assist in the theme's presentation. Musically, the track is funky, with prevalent saxophone and trumpet by David and Lester Bowie, respectively. "Jump They Say" discusses themes of mental illness, and is loosely based on David's step-brother Terry Burns, who committed suicide in 1985 after being hospitalised for schizophrenia. Bowie stated, "It's the first time I've felt capable of addressing it." Described by biographer David Buckley as "an eerie psychodrama", the song features prevalent backwards saxophone work from Bowie.


title: Black Tie White Noise

text: "Nite Flights" was written by singer-songwriter Scott Walker (as Scott Engel) and originally recorded by the Walker Brothers for their 1978 album of the same name. Bowie was a huge fan of the album, first hearing it while recording 1979's "Lodger", and decided to cover the song for "Black Tie White Noise". Musically, Pegg describes it as a "Euro-disco/jazz-funk fusion" evocative of the Berlin Trilogy, while it lyrically predates the content found on "Outside". Buckley considers "Pallas Athena", a mostly instrumental track reminiscent of the Berlin era, Bowie's most experimental work in a decade, combining "contemporary hip-hop dance rhythms" with the ambience of "Low" (1977). Bowie told "NME" in 1993 that he "[didn't] know what the fuck it's about".


title: Black Tie White Noise

text: Both "Miracle Goodnight" and "Don't Let Me Down & Down" support the wedding theme. The former is laden with synthesisers and mimics 1980s pop. The latter was originally recorded in Arabic by Mauritanian singer Tahra Mint Hembara (a friend of Iman's) in 1988 as "T Beyby"; her producer Martine Valmont wrote English lyrics and retitled it "Don't Let Me Down & Down". Bowie discovered it while browsing through Iman's CD collection and decided to cover it as a wedding gift. He stated, "[It was] one of those tracks that sort of in a diary-like way records the beginnings of a relationship." Comparing its arrangement to 1984's "Tonight", O'Leary calls it the "most obscure" cover of Bowie's entire career. On its lyrics, Pegg says it recalls the "romantic balladry" of "Win" and "Can You Hear Me?" from "Young Americans".


title: Black Tie White Noise

text: The jazz instrumental "Looking for Lester" features David and Lester Bowie soloing on saxophone and trumpet. The title is a play on John Coltrane's "Chasing the Train". The gospel cover of "I Know It's Gonna Happen Someday" is reminiscent of Bowie's early 1970s ballads, including a direct reference to the climax of "Rock 'n' Roll Suicide" (1972). Pegg describes the track as "Bowie covers Morrissey parodying "Ziggy Stardust" in the style of "Young Americans"". The album ends with "The Wedding Song", a vocal version of the opening track. Pegg considers the two tracks throwbacks to "It's No Game", which bookends "Scary Monsters (and Super Creeps)" (1980).


title: Black Tie White Noise

text: The cover artwork was taken by photographer Nick Knight. The inlay photography depicts Bowie in attire from the "Never Let Me Down" music video (1987): shirtsleeves with a Bogey hat holding a 1940s microphone. According to Buckley, the title was a comment on the racial mix of Bowie and Iman's marriage and the fusion of American and British musical styles Bowie was experimenting with. It was also in debt to the cut-up technique Bowie had discussed in an interview with writer William S. Burroughs in the mid-1970s. A working title for the album was "The Wedding Album". On the title, Bowie told "Record Collector" in 1993:


title: Black Tie White Noise

text: By the end of 1992, the rise of Britpop bands such as Blur, the Auteurs and Suede had influenced the UK music scene. These artists, particularly Suede, acknowledged Bowie's influence in interviews and their music, with Buckley describing Suede's debut single "The Drowners" as an homage to Bowie's glam rock work of the early 1970s. Shortly before the release of Suede's debut album and "Black Tie White Noise", "NME"s Steve Sutherland interviewed Bowie and Suede's lead singer Brett Anderson together, where the two discussed influences and exchanged compliments. The interview generated a large amount of publicity for the two artists' upcoming albums in the UK. Additionally, author Paul Trynka states that Ronson's guest appearance earned "Black Tie White Noise" more attention.


title: Black Tie White Noise

text: The lead single, "Jump They Say" backed by a remix of "Pallas Athena", was released on 15 March 1993. It came in numerous formats that contained various remixes of the track, a trend that continued in Bowie's work throughout the rest of the 1990s. The single became the artist's biggest hit since "Absolute Beginners" seven years earlier, peaking at number nine on the UK Singles Chart. It was supported by a Mark Romanek-directed music video featuring numerous references to Bowie's prior work. Pegg calls it one of his finest videos, praising its "non-linear" imagery.


title: Black Tie White Noise

text: "Black Tie White Noise" was issued shortly after on 5 April 1993 on different LP and CD formats, with the catalogue numbers 74321 13697 1 and 74321 13697 2, respectively. The LP release removed "The Wedding" and "Looking for Lester", while the CD edition featured a remix of "Jump They Say" and the outtake "Lucy Can't Dance". Meanwhile, the Japanese and Singaporean CDs contained a remix of "Pallas Athena" and "Don't Let Me Down & Down", respectively. Before its release, Bowie expressed love for the album, stating, "I don't think I've hit this peak before as a performer and a writer."


title: Black Tie White Noise

text: The album was a commercial success in the UK, entering the UK Albums Chart at number one and dethroning Suede's debut album; it was Bowie's final UK number one album until "The Next Day" in 2013. In America, it charted at number 39 on the "Billboard" 200, although its promotion was affected when Savage Records filed for bankruptcy shortly after its release. Although Bowie had signed a three-album deal, the label sued Bowie claiming substantial losses on "Black Tie". The case was dismissed and the label was dissolved; "Black Tie White Noise" became a rarity in record stores until reissues later in the 1990s.


title: Black Tie White Noise

text: The title track, backed by a remix of "You've Been Around", was released as the second single in June 1993, credited to David Bowie featuring Al B. Sure! Charting at number 36 in the UK, it was supported by a Romanek-directed music video, featuring both Bowie and Al B. Sure! and displaying, in Pegg's words, "a deft "bricolage" of images against the backdrop of an urban ghetto." "Miracle Goodnight", backed by "Looking for Lester", was issued as the third and final single in October 1993, charting at number 40 in the UK. Pegg argues it would have been a bigger hit had it been the lead single. "Nite Flights" was intended as the fourth single, but was cancelled by Arista Records following the performances of the two previous singles. Meanwhile, "Pallas Athena" was remixed by numerous DJs and anonymously became a popular club track in London and New York.


title: Black Tie White Noise

text: "Black Tie White Noise" received generally favourable reviews from music critics on release. Some reviewers considered it Bowie's finest since "Scary Monsters". Biographer Christopher Sandford states it was praised for its experimentation but criticised for an overall lack of cohesion. David Sinclair of "Q" magazine argued "Black Tie" "picks up where "Scary Monsters" left off" and "if any collection of songs could reinstate [Bowie's] godhead status, then this is it." He primarily criticised the lack of "obvious" hit singles, but felt the record was full of "imagination and charm" and deemed Bowie's saxophone performances some of his best to date. A reviewer for "Billboard" was also positive, describing it as a whole "trail-blazing and brilliant", further noting "inspired covers" and echoes of "Let's Dance", "Scary Monsters" and "Ziggy Stardust" (1972). Meanwhile, "Rolling Stone"s Paul Evans hailed it "one of the smartest records of a very smart career", finding references to the artist's previous works as well as new innovations that "point the way to future risk, to brave changes yet to come". Richard Cromelin of the "Los Angeles Times" considered it Bowie's "most committed-sounding music in years".


title: Black Tie White Noise

text: Other reviewers were more negative. A reviewer for "Vox" magazine found the radio-friendly singles calculated and Bowie's saxophone playing inferior to his musical contributions on ""Heroes"" (1977), but felt its "bent, ethnic-sounding notes create the album's most atmospheric moments". Dave Thompson found it lacked innovation in "The Rocket". Meanwhile, "Entertainment Weekly" Ken Tucker described "Black Tie" as a "stultifying yet annoying" record save for "Miracle Goodnight" and "I Know It's Gonna Happen Someday". Veteran critic Robert Christgau said in "The Village Voice" that the music was Bowie's "most arresting" because of its dance beats and electronic textures, but reacted negatively towards the lyrics.


title: Black Tie White Noise

text: Bowie did not tour in support of "Black Tie White Noise", telling "Record Collector" that it "takes up so much time". He also declined an invitation to perform on MTV's "Unplugged" programme. Instead, he made small appearances on American television and released a film to accompany the album. Directed by Bowie's long-time video director David Mallet, "" (1993) is a hybrid of interviews, footage shot during the recording sessions and mimed performances of six tracks shot by Mallet on 8 May 1993 at Hollywood Center Studios. Pegg calls it a "useful companion" to the album but finds Mallet's material uninspired. Sandford also considers the Mallet-directed material inferior to the two men's prior collaborations. The film was included as part of EMI's 2003 reissue campaign for the album, with a standalone DVD release following two years later. Although Bowie intended to resume the Tin Machine project following the release of "Black Tie", the idea never came to fruition. His next effort was the solo "The Buddha of Suburbia", released in November 1993.


title: Black Tie White Noise

text: "Black Tie White Noise" marked the beginning of Bowie's commercial revival and improved critical standing, with one reviewer later calling it a perfect way to begin the next chapter of his career. Despite its initial success—Pegg arguing it may have initially been "over-praised"—the album's critical standing in later decades has been mixed. Although several agreed it was his best since "Scary Monsters" at the time, critics remain divided on its cohesiveness, praising individual tracks but finding the album as a whole subpar. Pegg summarises: "It's a supremely confident, professional and commercial piece of work, and its best moments are exceptional." Some also felt the production aged poorly, with Trynka saying that its "overpolite, airbrushed sheen" meant that following the fall of Savage Records, "little bemoaned its passing". Others praised Lester Bowie's trumpet playing and David Bowie's vocal performances. In a positive review, BBC Music's David Quantick recognised "Black Tie White Noise" as a continuation of "Scary Monsters", wherein Bowie used aspects of his entire career in new, innovative ways. He credited the production and Bowie's "immense confidence" for an album that rose above its immediate predecessors. In AllMusic, Erlewine called it "an interesting first step in Bowie's creative revival", identifying ideas that Bowie further expanded with on later releases. In a 2016 retrospective ranking all of Bowie's 26 studio albums from worst to best, Bryan Wawzenek of "Ultimate Classic Rock" placed "Black Tie White Noise" at number 25 (above "Never Let Me Down"). In a 2018 list which included Bowie's two albums with Tin Machine, the writers of "Consequence of Sound" ranked "Black Tie White Noise" number 18 out of 28. David Sackllah wrote that the record holds up "fairly well" and, as the beginning of an experimental era, "Black Tie" "stood as one of his better works from the decade".


title: Black Tie White Noise

text: In 1994, an interactive CD-ROM based on "Black Tie White Noise" was developed by ION and released by MPC. The CD-ROM, which Bowie intended to be "fully interactive", gave users a chance to remake the "Jump They Say" video using pre-existing footage and view excerpts from the "Black Tie White Noise" film. It was not well received, although Perone considered it innovative for its time. Bowie initially expressed excitement in the project, but it ultimately did not live up to his expectations, stating in 1995 that he "absolutely loathed it".


title: Black Tie White Noise

text: In August 2003, "Black Tie White Noise" was reissued by EMI in a 3-CD deluxe edition to mark its tenth anniversary. It featured the original album, a CD of remixes and other tracks from the period (such as "Real Cool World"), and the original "Black Tie White Noise" film. In 2021, the album was remastered and included as part of the box set "Brilliant Adventure (1992–2001)".


title: Geography of Georgia (country)

text: Georgia is a country in the Caucasus region, on the coast of the Black Sea. Sometimes considered a transcontinental country, it is located at the intersection of Eastern Europe and Western Asia, and is today generally regarded as part of Europe. It is bordered to the north and northeast by Russia, to the south by Turkey and Armenia, and to the southeast by Azerbaijan.


title: Geography of Georgia (country)

text: Georgia is largely surrounded by the Greater Caucasus and Lesser Caucasus mountains, which form part of a natural boundary between Eastern Europe and Western Asia. Because the Europe–Asia boundary is essentially a “historical and cultural construct”, Georgia's continental placement has varied greatly. Anaximander placed the boundary between Europe and Asia along the Phasis River (the modern Rioni River), which effectively located northern parts of Georgia in Europe and the south in Asia, a convention also followed by Herodotus. According to one 18th century definition, which set the Kuma–Manych Depression as the continental boundary, Georgia and the entire Caucasus fell into Asia. However, yet other definition drew the line at Aras River, effectively placing all of Georgia in Europe.


title: Geography of Georgia (country)

text: Notwithstanding variations in geographic placement, Georgia’s proximity to the bulk of Europe, combined with various historical, cultural and political forces, has led increasingly to its inclusion in Europe. The country has joined European organizations, such as the Council of Europe and Eurocontrol, and has been deemed eligible to apply for membership of the European Union if it so wishes in the future.


title: Geography of Georgia (country)

text: Despite its small area, Georgia has one of the most varied topographies of the former Soviet republics. It is one of the most mountainous countries in Europe, lying mostly in the Caucasus Mountains, with its northern boundary partly defined by the Greater Caucasus range. The Lesser Caucasus range, which runs parallel to the Turkish and Armenian borders, and the Surami Range, which connects the Greater Caucasus and the Lesser Caucasus, create natural barriers that are partly responsible for cultural and linguistic differences among regions. Because of their elevation and a poorly developed transportation infrastructure, many mountain villages are virtually isolated from the outside world during the winter. Earthquakes and landslides in mountainous areas present a significant threat to life and property. Among the most recent natural disasters were massive rock- and mudslides in Ajaria in 1989 that displaced thousands in southwestern Georgia, and two earthquakes in 1991 that destroyed several villages in Racha, upper Imereti and the Tskhinvali Region (South Ossetia).


title: Geography of Georgia (country)

text: Georgia has about 25,000 rivers, many of which power small hydroelectric stations. Drainage is into the Black Sea to the west and through Azerbaijan to the Caspian Sea to the east. The largest river is the Kura River, which flows 1,364 km from northeast Turkey across the plains of eastern Georgia, through the capital, Tbilisi, and into the Caspian Sea. The Rioni River, the largest river in western Georgia, rises in the Greater Caucasus and empties into the Black Sea at the port of Poti. Soviet engineers turned the river lowlands along the Black Sea coast into prime subtropical agricultural land, embanked and straightened many stretches of river, and built an extensive system of canals. Deep mountain gorges form topographical belts within the Greater Caucasus.


title: Geography of Georgia (country)

text: The coastline of Georgia is 310 km long. Out of the Georgian coastline, 57 km is the coastline of Ajaria (Ajara), and 200 km is the coastline of Abkhazia. The "Encyclopedia of the Nations" lists the total length of the coastline as 315 km long. Georgia has an Exclusive Economic Zone of in the Black Sea.


title: Geography of Georgia (country)

text: Georgia's climate is affected by temperate humid influences from the west and continental influences from the east. The Greater Caucasus range moderates local climate by serving as a barrier against cold air from the north. Warm, moist air from the Black Sea moves easily into the coastal lowlands from the west. Climatic zones are determined by distance from the Black Sea and by altitude. Along the Black Sea coast, from Abkhazia to the Turkish border, and in the region known as the Colchis Lowland inland from the coast, the dominant subtropical climate features high humidity and heavy precipitation ( per year; the Black Sea port of Batumi receives per year). Several varieties of palm trees grow in these regions, where the midwinter average temperature is and the midsummer average is .


title: Geography of Georgia (country)

text: The plains of eastern Georgia are shielded from the influence of the Black Sea by mountains that provide a more continental climate. Summer temperatures average to , winter temperatures to . Humidity is lower, and rainfall averages per year. Alpine and highland regions in the east and west, as well as a semi-arid region on the Iori Plateau to the southeast, have distinct microclimates.


title: Geography of Georgia (country)

text: At higher elevations, precipitation is sometimes twice as heavy as in the eastern plains. In the west, the climate is subtropical to about ; above that altitude (and to the north and east) is a band of moist and moderately warm weather, then a band of cool and wet conditions. Alpine conditions begin at about , and above snow and ice are present year-round.


title: Geography of Georgia (country)

text: Beginning in the 1980s, Black Sea pollution has greatly harmed Georgia's tourist industry. Inadequate sewage treatment is the main cause of that condition. In Batumi, for example, only 18 percent of wastewater was treated before release into the sea as of the early 1990s. As of the early 1990s, an estimated 70 percent of surface water contained health-endangering bacteria to which Georgia's high rate of intestinal disease was attributed.


title: Geography of Georgia (country)

text: The war in Abkhazia did substantial damage to the ecological habitats unique to that region. In other respects, experts considered Georgia's environmental problems less serious than those of more industrialized former Soviet republics. Solving Georgia's environmental problems was not a high priority of the national government in the post-Soviet years, however; in 1993 the minister for protection of the environment resigned to protest this inactivity. In January 1994, the Cabinet of Ministers announced a new, interdepartmental environmental monitoring system to centralize separate programs under the direction of the Ministry of Protection of the Environment. The system would include a central environmental and information and research agency. The Green Party used its small contingent in the parliament to press environmental issues in 1993.


title: Geography of Georgia (country)

text: Georgia participates in a number of international environmental agreements. It is a party to: Air Pollution, Biodiversity, Climate Change, Climate Change-Kyoto Protocol, Desertification, Endangered Species, Hazardous Wastes, Law of the Sea, Ozone Layer Protection, Ship Pollution, and Wetlands.


title: Rajgir

text: Rajgir, meaning "The City of Kings," is a historic town in the district of Nalanda in Bihar, India. As the ancient seat and capital of the Haryanka dynasty, the Pradyota dynasty, the Brihadratha dynasty and the Mauryan Empire, as well as the dwelling ground of such historical figures as The Buddha and The Mahavira, the city holds a place of prominence in Hindu, Buddhist and Jain scriptures. As of 2011, the population of the town was reported to be 71,459 while the population in the community development block was about 88,500.


title: Rajgir

text: Rajgir was the first capital of the ancient kingdom of Magadha, a state that would eventually evolve into the Mauryan Empire. It finds mention in India's renowned literary epic, the Mahabharata, through its king Jarasandha. The town's date of origin is unknown, although ceramics dating to about 1000 BC have been found in the city. The 2,500-year-old cyclopean wall is also located in the region.


title: Rajgir

text: The town is also notable in Jainism and Buddhism. It was the birthplace of the 20th Jain Tirthankar Munisuvrata, and is closely associated with the Mahavira and Gautama Buddha. Both Mahavira and Buddha taught their beliefs in Rajgir during the 6th and 5th century BC, and the Buddha was offered a forest monastery here by the king Bimbisara. As such, the city of Rajgir became one of the Buddha's most important preaching locations.


title: Rajgir

text: The ancient Nalanda university was located in the vicinity of Rajgir, and the contemporary Nalanda University named after it was founded in 2010 nearby. The town is also famed for its natural springs and towering hills that dominate the landscape.


title: Rajgir

text: The name Rajgir (Sanskrit "Rājagṛha", Pali: "Rājagaha"), literally meaning "royal mountain" comes from the historic Rājagṛiha, meaning "house of the king" or "royal house". It has also historically been known as Vasumati, Brahdrathapura, Grivraja/Girivraja and Kusagrapura. Girivraja means an enclosure of hills.


title: Rajgir

text: The epic Mahabharata calls it Girivraja and recounts the story of its king, Jarasandha, and his battle with the Pandava brothers and their allies Krishna. Mahabharata recounts a wrestling match between Bhima (one of the Pandavas) and Jarasandha, the then king of Magadha. Jarasandha was invincible as his body could rejoin any dismembered limbs. According to the legend, Bhim split Jarasandha into two and threw the two halves facing opposite to each other so that they could not join. There is a famous Jarasandha's Akhara (the place where martial arts are practised).


title: Rajgir

text: Rajgir was the capital of Haryanka dynasty kings Bimbisara (558–491 BC) and Ajatashatru (492–460 BC). Ajatashatru kept his father Bimbisara in captivity here. The sources do not agree on which of the Buddha's royal contemporaries, Bimbisara and Ajatashatru, was responsible for its construction. It was the ancient capital city of the Magadha kings until the 5th century BC when Udayin (460–440 BC), son of Ajatashatru, moved the capital to Pataliputra (modern Patna). Shishunaga (413-395 BC) founded Shishunaga dynasty in 413 BC with Rajgir as its initial capital before it was moved to Pataliputra.


title: Rajgir

text: It is associated with the founders of both the religions: Jainism and Buddhism, associated with both the historical Arihant Shraman Bhagawan Mahavira and Buddha.


title: Rajgir

text: It was here that Gautama Buddha spent several months meditating, and preaching at Gridhra-kuta, ('Hill of the Vultures'). He also delivered some of his famous sermons and initiated king Bimbisara of Magadha and others to Buddhism. It was here that Budhha delivered his famous Atanatiya Sutra. On one of the hills is the Saptaparni Cave where the First Buddhist Council was held under the leadership of Maha Kassapa.


title: Rajgir

text: Mahavira, the 24th Tirthankara spent fourteen years of his life at Rajgir and Nalanda, spending "Chaturmas" (i.e. 4 months of the rainy season) at a single place in Rajgir (Rajgruhi) and the rest in the places in the vicinity. It was the capital of one of his Shravaks (follower) King Shrenik. Thus Rajgir is also of religious importance to Jains. The twentieth Jain Tirthankara, Munisuvrata is supposed to have been born here. An ancient temple (about 1200 years old) dedicated to Munisuvrat Bhagwan is also present here along with many other Jain temples. This temple is also a place for four Kalyanakas of Bhagwan Munisuvratnath.It is also mentioned in Jain and Buddhist scriptures, which give a series of place-names, but without geographical context. The attempt to locate these places is based largely on reference to them and to other locations in the works of Chinese Buddhist pilgrims, particularly Faxian and Xuanzang. It is on the basis of Xuanzang in particular that the site is divided into Old and New Rajgir. The former lies within a valley and is surrounded by low-lying hills, Rajgir Hills. It is defined by an earthen embankment (the Inner Fortification), with which is associated the Outer Fortification, a complex of cyclopean walls that runs (with large breaks) along the crest of the hills. New Rajgir is defined by another, larger, embankment outside the northern entrance of the valley and next to the modern town.


title: Rajgir

text: The modern town is situated close to the Rajgir hills while the valley is surrounded by seven hills: Vaibhara, Ratna, Saila, Sona, Udaya, Chhatha, and Vipula. River Panchane flows through the outskirts of the town.


title: Rajgir

text: The landscape of Rajgir or Pant WLS is uneven terrain enclosed by five hills; Ratnagiri, Vipulgiri, Vaibhagiri, Songiri and Udaygiri. It is situated in Nalanda Forest Division covering an area of 35.84 km under the Nalanda district administration. This wildlife sanctuary, notified in 1978, represents a remnant patch of forests nestled in the Rajgir hills within the south Gangetic Plain.


title: Rajgir

text: It is home to a number of wild animals viz. Mammals; Blue bull (Boselaphus tragocamelus), Chital or Spotted deer (Axis axis), Indian crested porcupine (Hystrix indica), Small Indian civet (Viverricula indica) Jungle cat (Felis chaus), Birds; Painted spurfowl (Galloperdix lunulata), Eurasian thick knee (Burhinus oedicnemus) and Painted sandgrouse (Pterocles indicus) Reptiles; Bengal monitor (Varanus bengalensis) and amphibians can be seen in this region; Indian Bullfrog (Hoplobatrachus tigerinus), Jerdon's bullfrog (Hoplobatrachus crassus), Ornate narrow-mouthed frog (Microhyla ornata), Indian tree frog (Polypedates maculatus).


title: Rajgir

text: According to 2011 Indian Census, Rajgir had a total population of 41,587, of which 21,869 were males and 19,718 were females. The population within the age group of 0 to 6 years was 6,922. The total number of literates in Rajgir was 24,121, which constituted 58.0% of the population with male literacy of 65.4% and female literacy of 49.8%. The effective literacy rate of the 7+ population of Rajgir was 69.6%, of which the male literacy rate was 78.1% and the female literacy rate was 60.1%. The Scheduled Castes and Scheduled Tribes population was 11,724 and 42 respectively. Rajgir had 7030 households in 2011.


title: Rajgir

text: The main tourist attractions include the ancient city walls from Ajatashatru's period, Bimbisar's Jail, Jarasandh's Akhara, Gridhra-kuta, ('Hill of the Vultures'), Son Bhandar Caves and the Jain temples on the five peaks.


title: Rajgir

text: Another major attraction is the peace pagoda, "Vishwa Shanti Stupa", built-in 1969, one of the 80 peace pagodas in the world, to spread the message of peace and non-violence. It is the oldest peace pagoda in India. The rope-way that leads to it is another attraction, which was gifted by Japanese spiritual leader Fuji Guruji in the 1960s.


title: Rajgir

text: Rajgir has hot water springs, locally known as "Brahmakund", a sacred place for Hindus where water from seven different springs ("Saptarshi") merge and is notable for its healing effects.


title: Rajgir

text: There is a Japanese temple beside the Venu Vana, an artificial forest with historical associations to Buddha and the kings of the region. Other places of interest include the Rajgir Heritage Museum, the Sariputta Stupa, Ghora Katora Lake, and the Rajgir glass bridge.


title: Rajgir

text: The Son Bhandar caves are situated in Rajgir. The caves are concerned with Jainism and are considered to belong to 3–4 century AD. After Cunningham's inspection, several scholars visited this place and some had opinions to concern with Buddhism. After some time all Buddhism connections were refused because of an inscription found on the southern wall of a cave. According to this inscription these caves were built by inspiration of a Jain Muni Vair for Jain ascetics. Sculptures of Teerthankaras were also carved in these caves. From an architectural aspect; these caves are analogous to Nagarjuni cave and Barabar Caves caves of Mauryan era. Therefore, it can be concluded that construction time should not differ much from the above-mentioned caves.


title: Rajgir

text: These caves should be related to Digambar sect of Jainism as Xuanzang wrote in his book about Vaibhar Hill of Rajgir that the place was occupied by Digambar Jain monks for meditation purposes. After some centuries these caves were converted by Hindus as Vishnu sculpture was also found from the mound of a cave.


title: Rajgir

text: Bihar State Tourism Development Corporation provides travel facility from state capital Patna to visit Bodh circuit (Bodhgaya, Rajgir, Nalanda, Vaishali, Kesaria, Lumbini, Kushinagar, Sarnath), Jain Circuit (Rajgir, Pawapuri) and Sikh Circuit in Bihar.


title: Rajgir

text: Located in Patna division, this Nagar Panchayat type of municipal council mainly depends upon tourism and is supplemented by agriculture. A number of resorts and hotels are located in Rajgir to serve the tourists. In addition, Rajgir is located near the tourist spots like Nalanda, Pawapuri and Kundalpur.


title: Rajgir

text: Nalanda International Cricket Stadium is a proposed cricket stadium in the city. In 2013, it was announced by the Chief Minister of Bihar Nitish Kumar that an international cricket stadium will be constructed at Rajgir in Bihar's Nalanda district.


title: Rajgir

text: Nalanda University, a modern university that is based on the famous university and Buddhist monastery of ancient India, has been established with its campus in Rajgir. It began its first academic session on 1 September 2014.


title: Andrey Kolmogorov

text: Andrey Nikolaevich Kolmogorov (, 25 April 1903 – 20 October 1987) was a Soviet mathematician who contributed to the mathematics of probability theory, topology, intuitionistic logic, turbulence, classical mechanics, algorithmic information theory and computational complexity.


title: Andrey Kolmogorov

text: Andrey Kolmogorov was born in Tambov, about 500 kilometers south-southeast of Moscow, in 1903. His unmarried mother, Maria Y. Kolmogorova, died giving birth to him. Andrey was raised by two of his aunts in Tunoshna (near Yaroslavl) at the estate of his grandfather, a well-to-do nobleman.


title: Andrey Kolmogorov

text: Little is known about Andrey's father. He was supposedly named Nikolai Matveevich Kataev and had been an agronomist. Kataev had been exiled from St. Petersburg to the Yaroslavl province after his participation in the revolutionary movement against the tsars. He disappeared in 1919 and was presumed to have been killed in the Russian Civil War.


title: Andrey Kolmogorov

text: Andrey Kolmogorov was educated in his aunt Vera's village school, and his earliest literary efforts and mathematical papers were printed in the school journal "The Swallow of Spring". Andrey (at the age of five) was the "editor" of the mathematical section of this journal. Kolmogorov's first mathematical discovery was published in this journal: at the age of five he noticed the regularity in the sum of the series of odd numbers: formula_1 etc.


title: Andrey Kolmogorov

text: In 1910, his aunt adopted him, and they moved to Moscow, where he graduated from high school in 1920. Later that same year, Kolmogorov began to study at Moscow State University and at the same time Mendeleev Moscow Institute of Chemistry and Technology. Kolmogorov writes about this time: "I arrived at Moscow University with a fair knowledge of mathematics. I knew in particular the beginning of set theory. I studied many questions in articles in the Encyclopedia of Brockhaus and Efron, filling out for myself what was presented too concisely in these articles."


title: Andrey Kolmogorov

text: Kolmogorov gained a reputation for his wide-ranging erudition. While an undergraduate student in college, he attended the seminars of the Russian historian S. V. Bakhrushin, and he published his first research paper on the fifteenth and sixteenth centuries' landholding practices in the Novgorod Republic. During the same period (1921–22), Kolmogorov worked out and proved several results in set theory and in the theory of Fourier series.


title: Andrey Kolmogorov

text: In 1922, Kolmogorov gained international recognition for constructing a Fourier series that diverges almost everywhere. Around this time, he decided to devote his life to mathematics.


title: Andrey Kolmogorov

text: In 1925, Kolmogorov graduated from Moscow State University and began to study under the supervision of Nikolai Luzin. He formed a lifelong close friendship with Pavel Alexandrov, a fellow student of Luzin; indeed, several researchers have concluded that the two friends were involved in a homosexual relationship, although neither acknowledged this openly during their lifetimes. Kolmogorov (together with Aleksandr Khinchin) became interested in probability theory. Also in 1925, he published his work in intuitionistic logic, "On the principle of the excluded middle", in which he proved that under a certain interpretation, all statements of classical formal logic can be formulated as those of intuitionistic logic. In 1929, Kolmogorov earned his Doctor of Philosophy (Ph.D.) degree, from Moscow State University.


title: Andrey Kolmogorov

text: In 1930, Kolmogorov went on his first long trip abroad, traveling to Göttingen and Munich, and then to Paris. He had various scientific contacts in Göttingen, first with Richard Courant and his students working on limit theorems, where diffusion processes turned out to be the limits of discrete random processes, then with Hermann Weyl in intuitionistic logic, and lastly with Edmund Landau in function theory. His pioneering work, "About the Analytical Methods of Probability Theory," was published (in German) in 1931. Also in 1931, he became a professor at Moscow State University.


title: Andrey Kolmogorov

text: In 1933, Kolmogorov published his book, "Foundations of the Theory of Probability", laying the modern axiomatic foundations of probability theory and establishing his reputation as the world's leading expert in this field. In 1935, Kolmogorov became the first chairman of the department of probability theory at Moscow State University. Around the same years (1936) Kolmogorov contributed to the field of ecology and generalized the Lotka–Volterra model of predator–prey systems.


title: Andrey Kolmogorov

text: During the Great Purge in 1936, Kolmogorov's doctoral advisor Nikolai Luzin became a high-profile target of Stalin's regime, in what is now called the "Luzin Affair". Kolmogorov and several other students of Luzin testified against Luzin, accusing him of plagiarism, nepotism, and other forms of misconduct; the hearings eventually concluded that he was a servant to "fascistoid science" and thus an enemy of the Soviet people. Luzin lost his academic positions, but curiously, he was not arrested nor expelled from the Academy of Sciences of the Soviet Union. The question of whether Kolmogorov and others were coerced into testifying against their teacher remains a topic of considerable speculation among historians; all parties involved refused to publicly discuss the case for the rest of their lives. Soviet-Russian mathematician Semën Samsonovich Kutateladze concluded in 2013, after reviewing archival documents made available during the 1990s and other surviving testimonies, that the students of Luzin had initiated the accusations against Luzin out of personal acrimony; there was no evidence that the students were coerced by the state, nor was there any evidence to support their allegations of academic misconduct. Soviet historian of mathematics A.P. Yushkevich surmised that, unlike many of the other high-profile persecutions of the era, Stalin did not personally initiate the persecution of Luzin, and eventually concluded that he was not a threat to the regime, which would explain the unusually mild punishment relative to other contemporaries.


title: Andrey Kolmogorov

text: In a 1938 paper, Kolmogorov "established the basic theorems for smoothing and predicting stationary stochastic processes"—a paper that had major military applications during the Cold War. In 1939, he was elected a full member (academician) of the USSR Academy of Sciences.


title: Andrey Kolmogorov

text: During World War II Kolmogorov contributed to the Russian war effort by applying statistical theory to artillery fire, developing a scheme of stochastic distribution of barrage balloons intended to help protect Moscow from German bombers.


title: Andrey Kolmogorov

text: In his study of stochastic processes, especially Markov processes, Kolmogorov and the British mathematician Sydney Chapman independently developed the pivotal set of equations in the field, which have been given the name of the Chapman–Kolmogorov equations.


title: Andrey Kolmogorov

text: Later, Kolmogorov focused his research on turbulence, where his publications (beginning in 1941) influenced the field. In classical mechanics, he is best known for the Kolmogorov–Arnold–Moser theorem, first presented in 1954 at the International Congress of Mathematicians. In 1957, working jointly with his student Vladimir Arnold, he solved a particular interpretation of Hilbert's thirteenth problem. Around this time he also began to develop, and was considered a founder of, algorithmic complexity theory – often referred to as Kolmogorov complexity theory.


title: Andrey Kolmogorov

text: Kolmogorov married Anna Dmitrievna Egorova in 1942. He pursued a vigorous teaching routine throughout his life, not only at the university level but also with younger children, as he was actively involved in developing a pedagogy for gifted children (in literature, music, and mathematics). At Moscow State University, Kolmogorov occupied different positions, including the heads of several departments: probability, statistics, and random processes; mathematical logic. He also served as the Dean of the Moscow State University Department of Mechanics and Mathematics.


title: Andrey Kolmogorov

text: In 1971, Kolmogorov joined an oceanographic expedition aboard the research vessel "Dmitri Mendeleev". He wrote a number of articles for the "Great Soviet Encyclopedia." In his later years, he devoted much of his effort to the mathematical and philosophical relationship between probability theory in abstract and applied areas.


title: Andrey Kolmogorov

text: A quotation attributed to Kolmogorov is [translated into English]: "Every mathematician believes that he is ahead of the others. The reason none state this belief in public is because they are intelligent people."


title: Andrey Kolmogorov

text: Vladimir Arnold once said: "Kolmogorov – Poincaré – Gauss – Euler – Newton, are only five lives separating us from the source of our science".


title: Andrey Kolmogorov

text: Kolmogorov, Andrey Nikolaevich; Fomin, Sergei Vasilyevich (1975) [1970]. Introductory real analysis. New York: Dover Publications. ..


title: Fort Polk

text: Fort Polk is a United States Army installation located in Vernon Parish, Louisiana, about 10 miles (15 km) east of Leesville and 30 miles (50 km) north of DeRidder in Beauregard Parish.


title: Fort Polk

text: It was named to honor Leonidas Polk, the first Episcopal Bishop of the Diocese of Louisiana, a leader of the breakaway Protestant Episcopal Church in the Confederate States of America, and a Confederate general in the American Civil War. It is one of the U.S. Army installations named for Confederate soldiers recommended for renaming by the Congressional Naming Commission; its recommendation is that the post be renamed Fort Johnson.


title: Fort Polk

text: The post encompasses about . Some are owned by the Department of the Army and by the U.S. Forest Service, mostly in the Kisatchie National Forest. In 2013, there were 10,877 troops stationed at Fort Polk, which generated an annual payroll of $980 million. Louisiana officials lobbied the Army and the United States Congress to keep troop strength at full capacity despite looming defense cuts.


title: Fort Polk

text: Fort Polk began as a base for the Louisiana Maneuvers in the 1940s. It served the 1st Armored Division in the 1950s, and became a basic training post during Vietnam War years of the 1960s and '70s. It hosted the 5th Infantry Division (Mechanized) in the 1970s-1980s, and the 2nd Armored Cavalry Regiment in the 1990s and the 1st Maneuver Enhancement Brigade, and the 162nd Infantry Brigade in the 2000s. Fort Polk is now home to the Joint Readiness Training Center (JRTC), the 3rd Brigade Combat Team, 10th Mountain Division, 115th Combat Support Hospital, U.S. Army Garrison and Bayne-Jones Army Community Hospital.


title: Fort Polk

text: The land that is now Fort Polk is part of a region of cultural resources, including archaeological sites, historic houses and structures, and other sites of historical value. The U.S. Army has spent considerable time, effort, and money to find and inventory thousands of archaeological sites on Fort Polk and the property owned by the U.S. Forest Service where the Army trains.


title: Fort Polk

text: Construction of Camp Polk began in 1941. Thousands of wooden barracks sprang up quickly to support an Army preparing to do battle on the North African, European and Pacific fronts. Soldiers at Polk participated in the Louisiana Maneuvers, which were designed to test U.S. troops preparing for World War II.


title: Fort Polk

text: Until 1939, the Army had mostly been an infantry force with supporting artillery, engineer, and cavalry units. Few units had been motorized or mechanized. As U.S. involvement in World War II became more likely, the Army recognized the need to modernize the service. But it also needed large-scale maneuvers to test a fast-growing, inexperienced force. That is where Fort Polk and the Louisiana Maneuvers came in.


title: Fort Polk

text: The Maneuvers involved half a million soldiers in 19 Army divisions, and took place over in August and September 1941. The troops were divided into equal armies of two notional countries: Kotmk (Kansas, Oklahoma, Texas, Missouri, Kentucky) and Almat (Arkansas, Louisiana, Mississippi, Alabama, Tennessee). These countries were fighting over navigation rights in the Mississippi River. The Maneuvers gave Army leadership the chance to test a new doctrine that stressed the need for both mass and mobility. Sixteen armored divisions sprang up during World War II after the lessons learned during the Louisiana Maneuvers were considered. These divisions specialized in moving huge combined-arms mechanized units long distances in combat.


title: Fort Polk

text: On the defensive front, U.S. doctrine was based on two needs: the ability to defeat Blitzkrieg tactics; and how to deal with large numbers of German tanks attacking relatively narrow areas. As such, the Maneuvers also tested the concept of the tank destroyer. In this concept, highly mobile guns were held in reserve until friendly forces were attacked by enemy tanks. Then, the tank destroyers would be rapidly deployed to the flanks of the penetration. Tank destroyers employed aggressive, high-speed hit-and-run tactics. The conclusion drawn was that tank destroyer battalions should be raised. Immediately after the war, the battalions were disbanded and the anti-tank role was taken over by the Infantry, Engineer, and Armor branches.


title: Fort Polk

text: While primarily a training facility, Camp Polk also served as a military prison for Germans captured during World War II. The first prisoners of war (POWs), who began arriving in Louisiana in July 1943, were from the Afrika Korps, Field Marshal Erwin Rommel's troops who fought in North Africa. They were housed in a large fenced-in compound in the area now encompassing Honor Field, Fort Polk's parade ground. Finding themselves captured, transported across the ocean, and imprisoned in the middle of summer was made to hurt their spirits. In his book "Up Front", author Bill Mauldin noted that it was more practical to ship prisoners to camps in the U.S. on otherwise empty troop ships returning from the ETO, housing and feeding them in the U.S. where escape was far less likely, rather than further burdening outbound cargo ships with provisions for prisoners in camps based in Europe. He added that American GIs resented the fact that German POWs were allowed to breathe the air in the U.S. while GIs were on the battlegrounds of a devastated Europe through the duration of the war, but they understood the logic of keeping the POWs in the U.S. rather than in Europe.


title: Fort Polk

text: The POWs picked cotton, cut rice, and cut lumber. They also helped sandbag the raging Red River in the summer of 1944. Prisoners were not forced to work, and some refused. Those who worked earned scrip for their labor, with which they could buy such necessities as toothpaste or snacks at their own Post Exchange.


title: Fort Polk

text: From the end of World War II until the early 1960s, the post was closed and reopened numerous times. During much of this time, it was open only in the summers to support reserve component training. Soldiers were stationed there temporarily during the Korean War and the Berlin Crisis.


title: Fort Polk

text: In August 1950, the 45th Infantry Division of the Oklahoma Army National Guard became the first unit to train at Fort Polk in preparation for the Korean War. During the Korean War the 45th Infantry Division suffered 4,004 casualties; 834 killed in action and 3,170 wounded in action The division was awarded four campaign streamers and one Presidential Unit Citation.


title: Fort Polk

text: Most of the units who rotated through Camp Polk during 1952-54 were trained for combat by the 37th Infantry Division of the Ohio Army National Guard. Although the 37th Division itself was not sent to Korea as a unit, nearly every soldier was sent as an individual replacement.


title: Fort Polk

text: In 1955, the U.S. military conducted another large training exercise that covered a substantial portion of Louisiana. Named Operation Sagebrush, the focus of this exercise was to evaluate the effectiveness of military operations in a nuclear environment. The exercise lasted for 15 days with 85,000 troops participating. A provisional army, meant to represent U.S. forces, was built around the 1st Armored Division and an opposing force was built around the 82nd Airborne Division. U.S. Air Force bombers and fighter planes also participated in this exercise with powerful aircraft operating in the sky, stirring great interest among the citizens of the region. Also participating as part of the provisional army was the 15th Infantry Regiment (actually designated as 15th Infantry Combat Command) of the 3rd Infantry Division from Fort Benning.


title: Fort Polk

text: Upon completion of Operation Sagebrush, Camp Polk was declared a permanent installation and the 1st Armored Division was reassigned from Fort Hood to the newly renamed Fort Polk to continue to test mobility and combat strategies for the nuclear age. The 1st Armored Division, with its modern M-48 Patton Tanks and new helicopters, remained at Fort Polk until June 1959, before returning to Fort Hood.


title: Fort Polk

text: In 1962, Fort Polk began converting to both basic training and an advanced individual training (AIT) center. A small portion of Fort Polk is filled with dense, jungle-like vegetation, so this, along with Louisiana's heat, humidity and precipitation (similar to southeast Asia) helped commanders acclimatize new infantry soldiers in preparation for combat in Vietnam. This training area became known as Tigerland. For the next 12 years, more soldiers were shipped to Vietnam from Fort Polk than from any other American training base. For many, Fort Polk was the only stateside Army post they saw before assignment overseas. Many soldiers reported to basic training at Fort Polk and stayed on post for infantry training at Tigerland before being assigned to infantry line companies in Vietnam.


title: Fort Polk

text: In October 1974, Fort Polk became the new home of the 5th Infantry Division (Mechanized), and basic training and AIT started being phased out. Fort Polk changed from a Continental Army Command (CONARC) post in July 1975 and became a Forces Command (FORSCOM) member. In the spring of 1976, the Infantry Training Center at Fort Polk closed its doors and ceased operations. The final chapter of the Vietnam War ended for Fort Polk. The Combat Engineer Battalion of the 588th lived on North Fort Polk, Louisiana.


title: Fort Polk

text: With the end of the Vietnam War, Fort Polk experienced a transition from an installation focused on basic and advanced individual training to that of the home of the reactivated 5th Infantry Division (Mechanized). Activated in September 1975, the division called Fort Polk home until it was inactivated in November 1992. The date of this inactivation, November 24, 1992, was exactly 75 years from the date of the original activation of the division on November 24, 1917. The division was organized with two active duty brigades and a brigade from the Louisiana National Guard. From 1972 until 1987, Fort Polk hosted the 1st Battalion, 40th Armor Regiment. During that time 1/40th Armor participated in training exercises with the Louisiana Army National Guard and 5th Infantry Division units. It was part of the Rapid Deployment Force for the operations in Grenada, but was not deployed, instead it was reassigned to the hills nol (German Defense Plan). In 1983, the 1/40 Armor took part in the Reforger 1984 exercises in Bavaria and two deployments to the National Training Center in 1984 and 1985. The 1/40 Armor was deactivated at Fort Polk in 1987. It was reactivated as the 1st Squadron, 40th Cavalry at Fort Richardson in Alaska in 2005. While at Fort Polk, the 5th Infantry Division participated in the NATO Reforger 78 and 84 Exercise in Europe and the 1989 Invasion of Panama, known as Operation Just Cause. From June to August 1987 the 95th Division (Tng) conducted basic training exercises of approximately 600 recruits. During the stay of the 5th Infantry Division (Mechanized), Fort Polk experienced a major building program that included new barracks, motor pools, 1000 family housing units, chapels, and dental clinics. The Bayne-Jones Army Community Hospital, named after Stanhope Bayne-Jones, a modern Post Exchange, commissary, warehouses, classrooms, athletic complexes and improved gunnery ranges.


title: Fort Polk

text: Effective 21 March 1976, the 1st Battalion 61st Infantry was reactivated and once again assigned to the 5th Division at Fort Polk.


title: Fort Polk

text: In 1993, the Joint Readiness Training Center moved from Fort Chaffee, Arkansas, to Fort Polk, and once again, the post was called on to prepare soldiers for conflict. Each year, JRTC typically conducts several rotations for units about to deploy. During the 1990s, Fort Polk-based soldiers deployed to Haiti, Southwest Asia, Suriname, Panama, Bosnia, and other locations. Weather support for the exercise is completed by the units participating in the exercise in conjunction with the 26th Operational Weather Squadron.


title: Fort Polk

text: The 2nd Armored Cavalry Regiment arrived at Fort Polk in 1993 as the armored cavalry regiment of the XVIII Airborne Corps. Elements of the regiment deployed to Haiti in 1995 in support of Operation Uphold Democracy and to Bosnia in 1996 in support of Operation Joint Endeavor. The 2nd ACR deployed to Kuwait, Qatar, Jordan and Djibouti in 2002 to in support of Operation Enduring Freedom, and then deployed in Iraq in 2003 in support of Operation Iraqi Freedom (now known as Operation New Dawn).


title: Fort Polk

text: The Army announced on 14 May 2004, that the 2nd Armored Cavalry Regiment would be transformed into an Infantry-based Stryker Brigade and move to Fort Lewis, Washington. The transfer of the 2nd Armored Cavalry Regiment from Fort Polk to Fort Lewis was completed in 2006. The 2nd Stryker Cavalry Regiment was later moved to Vilseck, Germany.


title: Fort Polk

text: The Joint Readiness Training Center is focused on improving unit readiness by providing highly realistic, stressful, joint and combined arms training across the full spectrum of conflict. The JRTC is one of the Army's three "Dirt" Combat Training Centers resourced to train infantry brigade task forces and their subordinate elements in the Joint Contemporary Operational Environment.


title: Fort Polk

text: With great emphasis on realism, the JRTC Operations Group provides rotational units with the opportunity to conduct joint operations which emphasize contingency force missions. The JRTC training scenario is based on each participating organization's mission essential tasks list and many of exercises are mission rehearsals for actual operations the organization is scheduled to conduct.


title: Fort Polk

text: JRTC scenarios allow complete integration of Air Force and other military services as well as host-nation and civilian role players. The exercise scenarios replicate many of the unique situations and challenges a unit may face to include host national officials and citizens, insurgents and terrorists, news media coverage and non-governmental organizations.


title: Fort Polk

text: The mission of the Opposing Force is handled by the 1st Battalion, 509th Infantry Regiment (1-509th IR). It is the job of the 1-509th IR to conduct combat operations as a dedicated, capabilities-based Opposing Force (OPFOR) to provide realistic, stressful, and challenging combat conditions for JRTC rotational units.


title: Fort Polk

text: The 3rd Brigade Combat Team, 36th Infantry Division was officially activated at Fort Polk in February 2014 as 3rd Brigade Combat Team, 10th Mountain Division, utilizing the assets of the 4th Brigade Combat Team, 10th Mountain Division, which was inactivated. As part of the Army's transformation initiative, this organization was designed to create a highly mobile, lethal, and flexible combat unit to support the rapid buildup of combat power wherever needed across the globe. The structure of the brigade is modular and provides for organic infantry, cavalry, field artillery, maintenance, logistic and support capabilities. While stilled flagged as 4th Brigade, it deployed in support of Operation Enduring Freedom from 2006 to 2007 then again for Operation Iraqi Freedom from December 2007 to January 2009. The brigade deployed to Afghanistan in fall 2010 and returned to the U.S. in fall 2011. From 2016 to 2019, the "Patriot Brigade," as they are known, became part of the 36th Infantry Division (Army National Guard) as part of the Army's Associated Unit Pilot. The "Patriot Brigade" was the only Regular Army unit assigned to the 36th ID but returned to the 10th Mountain Division when the Army's Associated Unit Pilot ended.


title: Fort Polk

text: The 115th Combat Support Hospital traces its origin to Evacuation Hospital #15, originally organized at Fort Riley, Kansas on 21 March 1918. At the onset of hostilities during World War I, the unit sailed aboard the "S.S. Mataika," departing the United States on 22 August 1918, and arriving in France 3 September 1918. Evacuation Hospital #15 earned a battle streamer for its participation in the Meuse-Argonne Forest offensive from 26 September 1918 through 11 November 1918. The hospital, having served honorably and proud during World War I, returned to the United States aboard the "S.S. America" and was demobilized at Camp Lewis, Washington on 28 June 1919. Evacuation Hospital #15 was reconstituted as the 15th Evacuation Hospital in 1936, after having been organized as an inactive unit of the Regular Army on 1 October 1933.


title: Fort Polk

text: 115th Combat Support Hospital is a deployable medical unit that provides medical specialities to the battlefield. Medical specialties provided by the 115th Combat Support Hospital include: general surgery, orthopaedics, podiatry, and physical therapy. Additional support for clinical operations is provided through a pharmacy, X-ray services, clinical laboratories, anaesthesia, and operative services. The 115th Combat Support Hospital is also staffed to provide medical command management and administrative support through an organic medical headquarters.


title: Fort Polk

text: During peacetime operations the 115th Field Hospital trains at the JRTC and Fort Polk. As a deployable medical systems hospital with the most modern equipment available, the unit is capable of being deployed in an area of operations during a contingency, war or national emergency.


title: Fort Polk

text: U.S. Army Garrison provides installation support for all tenant units as well as JRTC rotational units.


title: Fort Polk

text: The Fort Polk medical facility comprises the Bayne-Jones Army Community Hospital, the Wellness and Readiness Center, the Department of Behavioural Health and the United States Army Air Ambulance Detachment. The hospital is named in honour of Brigadier General Stanhope Bayne-Jones, a native of New Orleans, Louisiana. A bacteriologist and preventive medicine specialist, he achieved worldwide acclaim as the individual responsible for the control of typhus in Europe at the conclusion of World War II.


title: Fort Polk

text: The Louisiana Army National Guard maintains a maintenance facility on Fort Polk which services its major units such as the 256th Infantry Brigade Combat Team and 225th Engineer Brigade.


title: Fort Polk

text: In 2008 Fort Polk began a land expansion plan. The plan calls for the acquisition of 100,000 acres for large JRTC maneuvers and live fire operations. This will be the largest land expansion since World War II, located south and southeast of Peason Ridge, and the first parcel was purchased in 2012. Eminent domain is an option if needed. Fort Polk issued a press release on May 5, 2014, that 32,500 acres of the targeted 47,500, out of the 100,000 approved, has been acquired. Fifty-four landowners are involved, twenty-nine residences, with the U.S. Army Corps of Engineers being the Army's real estate agent.


title: Fort Polk

text: There have been several times when Fort Polk was at risk of closing. In 2002 the Army stated a position of ""No acquisition of land through purchase or withdrawal of public domain lands is proposed"", but in 2005 there were concerns of the post being "at risk", with a proposal to look at land expansion. In 2008 the Army started seeking new land for expansion, or there would be a risk of closure to seek a larger training area, and this led to the current land purchases.


title: Fort Polk

text: An area covering 105,545 acres within the post has been designated Fort Polk Wildlife Management Area. An estimated 700 to 750 horses roam training lands on and around Fort Polk. The fate of the horses has been the subject of debate since the Army started removing them in 2017. Army officials say the animals represent a safety hazard, while advocates have argued they should be left alone.


title: Tomas Arana

text: Tomas Clifford Arana (born April 3, 1955) is an American actor. He is best known for his roles in the films "The Hunt for Red October" (1990), "The Bodyguard" (1992), "L.A. Confidential" (1997), "Gladiator" (2000), "The Bourne Supremacy" (2004), "Limitless" (2011) and "The Dark Knight Rises" (2012).


title: Tomas Arana

text: Arana has played leading and supporting roles in over 30 European productions including films by directors Lina Wertmüller, Liliana Cavani, Carlo Verdone and Michele Soavi, and with the Japanese director Koreyoshi Kurahara in the Toho production "See You". He appeared as Quintus in Ridley Scott's "Gladiator", Michael Bruening in Curtis Hanson's "L.A. Confidential" and in the second film of the Bourne series, "The Bourne Supremacy". In theatre, Arana was the producer and a leading actor in the theatre company Falso Movimento, based in Naples, Italy. Under Arana and artistic director Mario Martone (now an Italian film director), Falso Movimento won many awards including Best Play of the Year and Best Set Design, as well as the Mondello Prize.


title: Tomas Arana

text: Arana also played the GRU sleeper agent Loginov in the 1990 film adaptation of Tom Clancy's novel "The Hunt for Red October", the would-be killer in 1992's "The Bodyguard" starring Kevin Costner and Whitney Houston, a Belarusian resistance leader in Edward Zwick's 2008 film "Defiance", and The Man In The Tan Coat in 2011's "Limitless" alongside Bradley Cooper and Robert De Niro. He appeared in the third installment of Christopher Nolan's Batman trilogy, "The Dark Knight Rises", as Bruce Wayne's lawyer. In 2013 Arana appeared in the miniseries "Crimes" of the German television broadcaster "ZDF". In 2014, Arana appeared as a Kree ambassador in "Guardians of the Galaxy".


title: Tomas Arana

text: Arana divides his time between Italy and Hollywood and has three sons. He is fluent in Italian as well as English, and speaks conversational French and Spanish. He is a kendo practitioner.


title: Tap and die

text: Taps and dies are tools used to create screw threads, which is called threading. Many are cutting tools; others are forming tools. A tap is used to cut or form the female portion of the mating pair (e.g. a nut). A die is used to cut or form the male portion of the mating pair (e.g. a bolt). The process of cutting or forming threads using a tap is called "tapping", whereas the process using a die is called "threading".


title: Tap and die

text: Both tools can be used to clean up a thread, which is called "chasing". However, using an ordinary tap or die to clean threads generally removes some material, which results in looser, weaker threads. Because of this, machinists generally clean threads with special taps and dies—called "chasers"—made for that purpose. Chasers are made of softer materials and don't cut new threads. However they still fit tighter than actual fasteners, and are fluted like regular taps and dies so debris can escape. Car mechanics, for example, use chasers on spark plug threads, to remove corrosion and carbon build-up.


title: Tap and die

text: While modern nuts and bolts are routinely made of metal, this was not the case in earlier ages, when woodworking tools were employed to fashion very large wooden bolts and nuts for use in winches, windmills, watermills, and flour mills of the Middle Ages; the ease of cutting and replacing wooden parts was balanced by the need to resist large amounts of torque, and bear up against ever heavier loads of weight. As the loads grew ever heavier, bigger and stronger bolts were needed to resist breakage. Some nuts and bolts were measured by the foot or yard. This development eventually led to a complete replacement of wood parts with metal parts of an identical measure. When a wooden part broke, it usually snapped, ripped, or tore. With the splinters having been sanded off, the remaining parts were reassembled, encased in a makeshift mold of clay, and molten metal poured into the mold, so that an identical replacement could be made on the spot.


title: Tap and die

text: Metalworking taps and dies were often made by their users during the 18th and 19th centuries (especially if the user was skilled in tool making), using such tools as lathes and files for the shaping, and the smithy for hardening and tempering. Thus builders of, for example, locomotives, firearms, or textile machinery were likely to make their own taps and dies. During the 19th century the machining industries evolved greatly, and the practice of buying taps and dies from suppliers specializing in them gradually supplanted most such in-house work. Joseph Clement was one such early vendor of taps and dies, starting in 1828. With the introduction of more advanced milling practice in the 1860s and 1870s, tasks such as cutting a tap's flutes with a hand file became a thing of the past. In the early 20th century, thread-grinding practice went through significant evolution, further advancing the state of the art (and applied science) of cutting screw threads, including those of taps and dies.


title: Tap and die

text: During the 19th and 20th centuries, thread standardization was evolving simultaneously with the techniques of thread generation, including taps and dies.


title: Tap and die

text: The largest tap and die company to exist in the United States was Greenfield Tap & Die (GTD) of Greenfield, Massachusetts. GTD was so vital to the Allied war effort from 1940–1945 that anti-aircraft guns were placed around its campus in anticipation of possible Axis air attack. The GTD brand is now a part of Widia Products Group.


title: Tap and die

text: A "tap" cuts or forms a thread on the inside surface of a hole, creating a female surface that functions like a nut. The three taps in the image illustrate the basic types commonly used by most machinists:


title: Tap and die

text: Whether manual or automatic, the processing of tapping begins with forming (usually by drilling) and slightly countersinking a hole to a diameter somewhat smaller than the tap's major diameter. The correct hole diameter is listed on a drill and tap size chart, a standard reference in many machine shops. The proper diameter for the drill is called the "tap drill size". Without a tap drill chart, you can compute the correct tap drill diameter with:


title: Tap and die

text: where formula_2 is the tap drill size, formula_3 is the major diameter of the tap (e.g., ⅜ inch for a ⅜"-16 tap), and formula_4 is the thread pitch (16 in the case of a ⅜"-16 tap). For a ⅜"-16 tap, the above formula would produce as a result, which is the correct tap drill diameter for a ⅜"-16 tap. The above formula ultimately results in an approximate 75 percent thread.


title: Tap and die

text: where formula_2 is the tap drill size, formula_3 is the major diameter of the tap (e.g., 10 mm for a M10×1.5 tap), and pitch is the pitch of the thread (1.5 mm in the case of a standard M10 tap) and so the correct drill size is 8.5 mm. This works for both fine and coarse pitches, and also produces an approximate 75 percent thread.


title: Tap and die

text: With soft or average hardness materials, such as plastic, aluminum or mild steel, common practice is to use an intermediate (plug) tap to cut the threads. If the threads must extend to the bottom of a blind hole, the machinist uses an intermediate (plug) tap to cut threads until the point of the tap reaches bottom, and then switches to a bottoming tap to finish. The machinist must frequently eject chips to avoid jamming or breaking the tap. With hard materials, the machinist may start with a taper tap, whose less severe diameter transition reduces the torque required to cut threads. To threads to the bottom of a blind hole, the machinist follows the taper tap with an intermediate (plug) tap, and then a bottoming tap to finish.


title: Tap and die

text: Tapping may either be achieved by a hand tapping by using a set of taps (first tap, second tap & final (finish) tap) or using a machine to do the tapping, such as a lathe, radial drilling machine, bench type drill machine, pillar type drill machine, vertical milling machines, HMCs, VMCs. Machine tapping is faster, and generally more accurate because human error is eliminated. Final tapping is achieved with single tap.


title: Tap and die

text: Although in general machine tapping is more accurate, tapping operations have traditionally been very tricky to execute due to frequent tap breakage and inconsistent quality of tapping.


title: Tap and die

text: To overcome these problems, special tool holders are required to minimize the chances of tap breakage during tapping. These are usually classified as conventional tool holders and CNC tool holders.


title: Tap and die

text: The biggest problem with simple hand-tapping is accurately aligning the tap with the hole so that they are coaxial—in other words, going in straight instead of on an angle. The operator must get this alignment close to ideal to produce good threads and not break the tap. The deeper the thread depth, the more pronounced the effect of the angular error. With a depth of 1 or 2 diameters, it matters little. With depths beyond 2 diameters, the error becomes too pronounced to ignore. Another fact about alignment is that the first thread cut or two establishes the direction that the rest of the threads will follow. You can't correct the angle after the first thread or two.


title: Tap and die

text: To help with this alignment task, several kinds of jigs and fixtures can be used to provide the correct geometry (i.e., accurate coaxiality with the hole) without having to use freehand skill to approximate it:


title: Tap and die

text: Tapping case studies with typical examples of tapping operations in various environments are shown on source machinetoolaid.com


title: Tap and die

text: Double-lead taps and insert taps need different speeds and feeds, and different starting hole diameters than other taps.


title: Tap and die

text: A "die" cuts an external thread on cylindrical material, such as a rod, which creates a male threaded piece that functions like a bolt. Dies are generally made in two styles: solid and adjustable.


title: Tap and die

text: An adjustable die may be adjusted either by an integrated screw or by a set of screws set in to the die holder (termed a "die stock").


title: Tap and die

text: Integral adjusting screws may be arranged to work axially, where the movement of the adjusting screw into a threaded hole in the die forces the slit section of the die open, or tangentially where a screw threaded in to one side of the slit bears against the opposite side of the slit.


title: Tap and die

text: Dies without integrated screws are adjusted inside the die stock by radially-arranged screws. Two screws in the stock bear in to indentations on either side of the slit, tending to squeeze the slit closed, whilst a third screw with a tapered tip screws in to the slit forcing it open. Working these three screws against each other adjusts the die.


title: Tap and die

text: Solid dies cut a nominal thread form and depth, whose accuracy is subject to the precision the die was made with, and the effects of wear. Adjustable dies can be slightly compressed or expanded to provide some compensation for wear, or to achieve different classes of thread fit (class A, B and more rarely, C). Adjustable taps also exist but are not common. These have a tip that is split through the flutes and an axial screw which forces the cutting edges slightly apart.


title: Tap and die

text: The work piece (blank) to be threaded, which is usually slightly smaller in diameter than the die's major diameter, is given a slight taper (chamfer) at the end that is to be threaded. This chamfer helps center the die on the blank and reduces the force required to start the thread cutting. Once the die has started, it self-feeds. Periodic reversal of the die is often required to break the chip and prevent crowding.


title: Tap and die

text: "s", also known as "rethreading dies", are dies made for cleaning up damaged threads, have no split for resizing and are made from a hexagonal bar so that a wrench may be used to turn them. The process of repairing damaged threads is referred to as "chasing." Rethreading dies cannot be used to cut new threads as they lack chip forming teeth. However the external profile of a die does not strictly map to its function. Manufacturers of dies have produced models in a hex form which are intended for the creation of new threads. These appear identical to solid dies in all aspects besides the external shape. Hexagonal thread cutting dies are used with a die stock with hexagonal holding features.


title: Tap and die

text: The use of a suitable lubricant is essential with most tapping and threading operations. Recommended lubricants for some common materials are as follows:


title: Longest common subsequence problem

text: The longest common subsequence (LCS) problem is the problem of finding the longest subsequence common to all sequences in a set of sequences (often just two sequences). It differs from the longest common substring problem: unlike substrings, subsequences are not required to occupy consecutive positions within the original sequences. The longest common subsequence problem is a classic computer science problem, the basis of data comparison programs such as the codice_1 utility, and has applications in computational linguistics and bioinformatics. It is also widely used by revision control systems such as Git for reconciling multiple changes made to a revision-controlled collection of files.


title: Longest common subsequence problem

text: For example, consider the sequences (ABCD) and (ACBAD). They have 5 length-2 common subsequences: (AB), (AC), (AD), (BD), and (CD); 2 length-3 common subsequences: (ABD) and (ACD); and no longer common subsequences. So (ABD) and (ACD) are their longest common subsequences.


title: Longest common subsequence problem

text: For the general case of an arbitrary number of input sequences, the problem is NP-hard. When the number of sequences is constant, the problem is solvable in polynomial time by dynamic programming.


title: Longest common subsequence problem

text: Given formula_1 sequences of lengths formula_2, a naive search would test each of the formula_3 subsequences of the first sequence to determine whether they are also subsequences of the remaining sequences; each subsequence may be tested in time linear in the lengths of the remaining sequences, so the time for this algorithm would be


title: Longest common subsequence problem

text: For the case of two sequences of "n" and "m" elements, the running time of the dynamic programming approach is O("n" × "m"). For an arbitrary number of input sequences, the dynamic programming approach gives a solution in


title: Longest common subsequence problem

text: The LCS is not necessarily unique; in the worst case, the number of common subsequences is exponential in the lengths of the inputs, so the algorithmic complexity must be at least exponential.


title: Longest common subsequence problem

text: The LCS problem has an optimal substructure: the problem can be broken down into smaller, simpler subproblems, which can, in turn, be broken down into simpler subproblems, and so on, until, finally, the solution becomes trivial. LCS in particular has overlapping subproblems: the solutions to high-level subproblems often reuse solutions to lower level subproblems. Problems with these two properties are amenable to dynamic programming approaches, in which subproblem solutions are memoized, that is, the solutions of subproblems are saved for reuse.


title: Longest common subsequence problem

text: The prefix "S" of "S" is defined as the first "n" characters of "S". For example, the prefixes of "S" = (AGCA) are


title: Longest common subsequence problem

text: Let "LCS"("X", "Y") be a function that computes a longest subsequence common to "X" and "Y". Such a function has two interesting properties.


title: Longest common subsequence problem

text: "LCS"("X"^"A","Y"^"A") = "LCS"("X","Y")^"A", for all strings "X", "Y" and all symbols "A", where ^ denotes string concatenation. This allows one to simplify the "LCS" computation for two sequences ending in the same symbol.


title: Longest common subsequence problem

text: For example, "LCS"("BANANA","ATANA") = "LCS"("BANAN","ATAN")^"A", Continuing for the remaining common symbols, "LCS"("BANANA","ATANA") = "LCS"("BAN","AT")^"ANA".


title: Longest common subsequence problem

text: If "A" and "B" are distinct symbols ("A"≠"B"), then "LCS"(X^A,Y^B) is one of the maximal-length strings in the set { "LCS"("X"^"A","Y"), "LCS"("X","Y"^"B") }, for all strings "X", "Y".


title: Longest common subsequence problem

text: "LCS"("ABCDEFG","BCDGK") is the longest string among "LCS"("ABCDEFG","BCDG") and "LCS"("ABCDEF","BCDGK"); if both happened to be of equal length, one of them could be chosen arbitrarily.


title: Longest common subsequence problem

text: Let two sequences be defined as follows: formula_6 and formula_7. The prefixes of formula_8 are formula_9; the prefixes of formula_10 are formula_11. Let formula_12 represent the set of longest common subsequence of prefixes formula_13 and formula_14. This set of sequences is given by the following.


title: Longest common subsequence problem

text: To find the LCS of formula_13 and formula_14, compare formula_18 and formula_19. If they are equal, then the sequence formula_20 is extended by that element, formula_18. If they are not equal, then the longest among the two sequences, formula_22, and formula_23, is retained. (If they are the same length, but not identical, then both are retained.)


title: Longest common subsequence problem

text: The longest subsequence common to "R" = (GAC), and "C" = (AGCAT) will be found. Because the "LCS" function uses a "zeroth" element, it is convenient to define zero prefixes that are empty for these sequences: "R" = Ø; and "C" = Ø. All the prefixes are placed in a table with "C" in the first row (making it a column header) and "R" in the first column (making it a row header).


title: Longest common subsequence problem

text: This table is used to store the LCS sequence for each step of the calculation. The second column and second row have been filled in with Ø, because when an empty sequence is compared with a non-empty sequence, the longest common subsequence is always an empty sequence.


title: Longest common subsequence problem

text: "LCS"("R", "C") is determined by comparing the first elements in each sequence. G and A are not the same, so this LCS gets (using the "second property") the longest of the two sequences, "LCS"("R", "C") and "LCS"("R", "C"). According to the table, both of these are empty, so "LCS"("R", "C") is also empty, as shown in the table below. The arrows indicate that the sequence comes from both the cell above, "LCS"("R", "C") and the cell on the left, "LCS"("R", "C").


title: Longest common subsequence problem

text: "LCS"("R", "C") is determined by comparing G and G. They match, so G is appended to the upper left sequence, "LCS"("R", "C"), which is (Ø), giving (ØG), which is (G).