Early career.

Born in Lindenfels, West Germany, Glock began his motorsport career in 1998 at the age of 15. He won several karting championships as well as the BMW ADAC Formula Junior Cup in 2000 and the Formula BMW ADAC Championship in 2001. In his first German Formula Three Championship season in 2002, he finished third in the standings en route to rookie of the year honours. In 2003, he competed in the Formula Three Euroseries, winning three races and scoring three other podium finishes, which were enough to place him in fifth position in the Championship.

Formula One.

Jordan (2004).

Glock was signed as Jordan Grand Prix's test driver for the 2004 Formula One season and made his Formula One debut at the Canadian Grand Prix replacing Giorgio Pantano, who had a contract dispute with Jordan. He finished 11th, but inherited 7th following the disqualification of the Williams and Toyota cars and thus scored two points on his debut.  He finished the season with Jordan, taking over from Pantano for the last three races. Glock's sponsorship with Deutsche Post helped bring back the colours of DHL to Jordan.

Champ Car.

2005.

In 2005, Glock shifted his career to the United States, racing in the Champ Car World Series with Paul Gentilozzi's Rocketsports team. His best finish was second place at the Circuit Gilles Villeneuve at the Molson Indy Montreal in Canada, where he was defeated by Oriol Servia. In the closing laps of the race Glock twice retained the lead over Servia by missing the track's final chicane. As the rules require drivers who gain or retain a position by driving off the racing surface to give way, Glock was asked to move over by Champ Car officials, and let Servia take the lead. Glock obliged midway through the final lap, giving him enough time to try to take the lead back, but to no avail. Glock finished 8th in the final season points standings and won the Champ Car World Series' Rookie of the Year award.

GP2.

2006–2007.

In 2006, Glock raced in Europe in the GP2 Series, the level immediately below Formula One. He started with the midfield BCN Competicion team, gaining average results. In mid-season, however, he moved to the front-running iSport team and after a string of improved results finished fourth in the drivers' standings, also winning an award for "most improved driver" in the series. In he tested an F1 car again for BMW Sauber, which led to him being signed in December as the team's second test driver for.  Glock was also re-signed for 2007 by iSport and won one feature race and four sprint races on his way to the championship. Following the serious crash of regular Formula One BMW driver Robert Kubica in Canada, it was speculated that Glock might take over the drive. However, the team instead chose its lead test driver Sebastian Vettel. Vettel's drive as a fill-in helped him get a full-time racing seat with the Toro Rosso team later in the season, starting at the Hungarian Grand Prix, and Glock was then promoted to the main test and reserve driver for BMW.

Return to Formula One.

Toyota (2008–2009).

After winning the GP2 Series in 2007, Glock was connected to several F1 teams. He signed a contract with Toyota F1, though still under a test driver contract with BMW, which led to the dispute being brought before the Contract Recognition Board. In November, the CRB ruled that Glock was free to race for Toyota in and shortly afterwards Glock signed a three-year contract to replace Ralf Schumacher at Toyota. He scored his first points of 2008 in the Canadian Grand Prix, finishing 4th ahead of Felipe Massa's Ferrari. Glock qualified a career-best fifth at the Hungarian Grand Prix, and finished the race in second place. At the Singapore Grand Prix, Glock finished 4th, one of his best of the season.  In the final race of the 2008 season, the Brazilian Grand Prix, Glock was seventh with a few laps to go and opted to remain on the track with dry-weather tyres, while most of the other drivers opted for wet tyres because of rain falling during the final laps of the race. Starting the final lap, Glock was fourth, but he was passed by Toro Rosso's Sebastian Vettel and McLaren's Lewis Hamilton in the final corners. Hamilton's pass on Glock was enough for him to win the 2008 Drivers' Championship. Glock finished the race in sixth and the championship in tenth position, with 25 points, behind teammate Jarno Trulli. 2009 started well enough for Glock. After being in the top 10 in all 3 practice sessions in Australia, he qualified 6th on the grid. However, the rear wing of his (and teammate Trulli's) Toyota was deemed to be too flexible and thus illegal, and his time was cleared and he started 19th. During the race, he worked his way through the pack, pulling off forceful manoeuvres, including one on Fernando Alonso and one on Sébastien Buemi to finish in 5th place. However, after the race, Lewis Hamilton was disqualified and stripped of his 4th-place finish, and Glock was promoted to 4th. A week later in Malaysia, he qualified 5th, but started 3rd after penalties to both Sebastian Vettel and Rubens Barrichello. At the start of the race, Glock slipped to 8th, but an inspired tyre choice as the rain started, coupled with precise driving, saw Glock finish in 3rd when the race was ended early on lap 32.  Consecutive seventh places for Glock in the rain in China, and in the dry in Bahrain had given him a total of 12 points for the season, although these finishes came in contrasting ways. In China he qualified a disappointing 14th, not making it out of Qualifying 2, whilst in Bahrain he qualified 2nd, led the race in the first stint, but he had a poor second stint on hard tyres which forced him to battle his way back to seventh by the end of the race. Glock earned his second podium of the season when he finished 2nd behind Lewis Hamilton at the Singapore Grand Prix after qualifying in 6th. The race began well when Glock passed Alonso and was given a place by Mark Webber who was forced to let Alonso overtake. Late in the race Glock seemed set for 3rd place until Nico Rosberg crossed the white line exiting the pits, earning him a drive through penalty and allowing Glock to easily take 2nd place.  In qualifying for the 2009 Japanese Grand Prix, Glock crashed heavily at the last corner and was airlifted to hospital with a leg injury. As he was not fit to race, Jarno Trulli was the only driver representing Toyota. On 11 October 2009, Toyota confirmed that its test driver Kamui Kobayashi would make his race debut in the Brazilian Grand Prix, as Glock had suffered further complications from his accident, resulting in a cracked vertebra and he would not be guaranteed to be fit in time to race in Brazil and Abu Dhabi. Toyota pulled out of F1 at the end of 2009, leaving an uncertain future for Glock.

Virgin (2010–2011).

Glock's future for a time appeared uncertain, but on 17 November new team Manor Grand Prix announced that he had signed for them and would be their lead driver for the 2010 and 2011 seasons. It seemed as though Glock would partner Polish driver Robert Kubica at Renault, but following Renault's decision to announce whether it will take part in Formula 1 for 2010, Glock chose an option where he will be guaranteed a drive although the car might be less competitive. Manor became Virgin Racing in November 2009 and that Glock's former GP2 rival Lucas di Grassi would become his teammate. Glock started the 2010 season with three successive retirements in Bahrain, Australia and Malaysia. In addition, he failed to start the Chinese Grand Prix due to engine failure; This was despite good qualifying performances which saw him out-qualify all of the new teams' drivers in Bahrain and regularly start higher than his teammate Di Grassi. The Spanish Grand Prix was where he recorded his first finish for the team, and his first finish of the season with 18th place. Glock's best result of the season saw him finish in 14th in Japan, the team's best result of the year.  In 2011, Jérôme d'Ambrosio joined Glock at the team, where he failed to start the.  On 24 July 2011, it was announced that Glock had signed a 3-year extension to his current contract, committing him to Virgin until 2014.

Marussia (2012).

The team was renamed as Marussia F1 for the 2012 season and he would partner his third teammate in his three years at the team, French rookie Charles Pic. Marussia were forced to pull out of pre-season testing after failing a crash test for rear impact but eventually they passed allowing Glock to compete in the opening race. Glock started the 2012 season strongly by finishing 14th in Australia which equaled his highest ever finish with the Virgin/Marussia team. Glock came 17th in Malaysia, and then scored two consecutive 19th-place finishes in China and Bahrain. Furthermore, he finished 18th in the, before he achieved 14th again in Monaco, and retired from the race with a brake malfunction. Glock withdrew from the after contracting a stomach bug. However, he was fit in time for the where he finished 18th, and he followed that up with 22nd at his home Grand Prix. It was reported at the Hungarian Grand Prix that a feud was brewing between Glock and his teammate after Pic blocked him during qualifying. Glock finished the race 21st after battling with Michael Schumacher and Pedro de la Rosa. Glock finished 15th at Spa after a collision with Pastor Maldonado. He suffered no damage and finished ahead of his teammate as they battled in the final stages of the race while also getting lapped by other cars. At Monza, he finished 17th after sustaining front wing damage after colliding with Vitaly Petrov in the second corner of lap 1.  However at Singapore, he produced his best result for Marussia, finishing in 12th place after a faultless performance. This crucially pushed Marussia into 10th place in the Constructors' Championship, due to a better non-points finishing record. In Japan Glock was up to 11th by the second lap after two first corner incidents, however he finished 16th. In Korea he finished 18th, and in India he came 20th after another battle with Michael Schumacher. He encountered Schumacher again in Abu Dhabi and let him pass to overtake Heikki Kovalainen who was in the crucial 12th place needed to demote Marussia to 11th in the Constructors' Championship. In São Paulo, he was running strongly and ahead of the Caterhams until he was hit by Jean-Éric Vergne. He claimed this 'destroyed his race' with Petrov ultimately passing Charles Pic to take 10th spot for Caterham in the championship. Glock finished the season 20th in the Drivers' Championship; his best yet for the Virgin/Marussia team.  For the 2013 season he was due to remain with Marussia and partner Max Chilton who would have been his fourth teammate in four years at the team, however on 21 January 2013 it was confirmed that Glock had left Marussia by mutual consent.

DTM (2013–).

Glock switched to the DTM in 2013, signing for BMW. In his third race he scored his first points and podium with third place. He would not score any more points until the final race of the season at Hockenheim, where he won his first DTM race of his career.

Personal life.

Glock lives in Switzerland with his wife, German model Isabell Reis. She travels the world with him during the season. Glock and Reis are neighbours and close friends with former Caterham F1 driver Heikki Kovalainen and his British girlfriend Catherine Hyde.

Racing record.

Career summary.

As Glock was a guest driver he was ineligible to score points.<br>

Complete Porsche Supercup results.

<nowiki>‡</nowiki> Not eligible for points.

Complete Formula One results.

Half points were awarded at the 2009 Malaysian Grand Prix as less than 75% of the race distance was completed.

Complete Deutsche Tourenwagen Masters results.

Driver retired, but was classified as they completed 75% of the winner's race distance.

Timo Glock (born 18 March 1982) is a German professional racing driver, and BMW Motorsport works driver.

提摩·格洛克(Timo Glock,1982年-3月18日),德国F1赛车手,曾效力于玛鲁西亚车队,2007年曾获得GP2世界冠军。2008年获得F1匈牙利站亚军。2012赛季结束后离开F1赛事,2013年开始他的德国房车赛(DTM)生涯。


Roman Rite.

"Vigil".

The every-night monastic canonical hour that later became known as matins was at first called a "vigil", from Latin "vigilia". For soldiers, this word meant a three-hour period of being on the watch during the night. Even for civilians, night was commonly spoken of as divided into four such watches: the Gospels use the term when recounting how, at about "the fourth watch of the night", Jesus came to his disciples who in their boat were struggling to make headway against the wind, and one of the Psalms says to the Lord: "A thousand years in your sight are but as yesterday when it is past, or as a watch in the night."  The sixth-century "Rule of Saint Benedict" uses the term "vigiliae" ("vigils") fifteen times to speak of these celebrations, accompanying it four times with the adjective "nocturnae" ("nocturnal") and once with the words "septem noctium" ("of the seven nights", i.e., the nights of the week).  English versions of this document often obscure its use of the term "vigil", translating it as "Night Hour" or "Night Office". Thus Leonard J. Doyle's English version uses "Night Office" to represent indifferently the unaccompanied noun "vigilia" ("vigil"), the phrase "nocturna vigilia" ("night vigil"), and the phrases "nocturna hora" ("night hour) and "nocturna laus" ("nocturnal praise").  The practice of rising for prayer in the middle of the night is as old as the Church. Tertullian (c. 155 – c. 240) speaks of the "nocturnal convocations" ("nocturnae convocationes") of Christians and their "absence all the night long at the paschal solemnities" ("sollemnibus Paschae abnoctantes") Cyprian (c. 200 – 258) also speaks of praying at night, but not of doing so as a group: "Let there be no failure of prayers in the hours of night — no idle and reckless waste of the occasions of prayer" ("nulla sint horis nocturnis precum damna, nulla orationum pigra et ignava dispendia"). The "Apostolic Tradition" speaks of prayer at midnight and again at cockcrow, but seemingly as private, not communal, prayer. At an earlier date, Pliny the Younger reported in about 112 that Christians gathered on a certain day before light, sang hymns to Christ as to a god and shared a meal. The solemn celebration of vigils in the churches of Jerusalem in the early 380s is described in the "Peregrinatio Aetheriae".  Prayer at midnight and at cockcrow was associated with passages in the Gospel of Matthew and the Gospel of Mark. On the basis of the Gospel of Luke, too, prayer at any time of the night was seen as having eschatological significance.  The quotation from Tertullian above refers to the all-night vigil service held at Easter. A similar service came to be held in the night that led to any Sunday. By the fourth century this Sunday vigil had become a daily observance, but no longer lasted throughout the night. What had been an all-night vigil became a service only from cockcrow to before dawn. Saint Benedict wrote about it as beginning at about 2 in the morning ("the eighth hour of the night") and ending in winter well before dawn (leaving an interval in which the monks were to devote themselves to study or meditation), but having to be curtailed in summer in order to celebrate lauds at daybreak.

"Matins".

The word "matins" is derived from Latin adjective "matutinus", meaning "of or belonging to the morning". It was at first applied to the psalms recited at dawn, but later became attached to the prayer originally offered, according to the fourth-century "Apostolic Constitutions", at cockcrow and, according to the sixth-century "Rule of Saint Benedict", at could be calculated to be the eighth hour of the night (the hour that began at about 2 a.m.).  Between the vigil office and the dawn office there was in the long winter nights there was an interval, which "should be spent in study by those [monks] who need a better knowledge of the Psalter or the lessons"; in the summer nights the interval was short, only enough for the monks to "go out for the necessities of nature". The vigil office was also shortened in the summer months by replacing readings with a passage of scripture recited by heart, but keeping the same number of psalms. Both in summer and in winter the vigil office was longer than on other days, with more reading and the recitation of canticles in addition to the psalms.  Outside of monasteries few rose at night to pray. The canonical hour of the vigil was said in the morning, followed immediately by lauds, and the name of "matins" became attached to the lengthier part of what was recited at that time of the day, while the name of "lauds", a name originally describing only the three Psalms 148−150 recited every day at the end of the dawn office (until excised in the 1911 reform of the Roman Breviary by Pope Pius X; see Lauds), was applied to the whole of that office, substituting for the lost name of "matins" or variants such as "laudes matutinae" (morning praises) and "matutini hymni" (morning hymns). An early instance of the application of the named "matins" to the vigil office is that of the Council of Tours in 567, which spoke of "ad matutinum sex antiphonae".  The "Rule of Saint Benedict" clearly distinguished this one nighttime hour, to which he applied Psalm 118/119:62, "At midnight I rise to praise you, because of your righteous rules", from the seven daytime hours, including "matutini" (matins, the hour of the morning psalms at dawn), which he associated with Psalm 118/119:164, "Seven times a day I praise you for your righteous rules".  The word "vigil" also took on a different meaning: no longer a prayerful "watch at night" before a religious feast, but the "day" before a feast.

Monastic matins.

The canonical hour began with the versicles, "O God, come to my assistance; O Lord, make haste to help me" and "O Lord, Thou wilt open my lips, and my mouth shall declare Thy praise" (the latter said three times) followed by Psalm 3 and Psalm 94/95 (the Invitatory). The Invitatory was to be recited slowly out of consideration for any late-arriving monk, since anyone appearing after its conclusion was punished by having to stand in a place apart. After this a hymn was sung.  Next came two sets of six psalms followed by readings. (Such sets would later be called nocturns.) The first set was of six psalms followed by three readings from the Old or New Testaments or from Church Fathers. Each reading was followed by a responsory. The second set of six psalms was followed by a passage from the Apostle Paul recited by heart and by some prayers. The Night Office then concluded with a versicle and a litany that began with Kyrie eleison.  Since summer nights are shorter, from Easter to October a single passage from the Old Testament, recited by heart, took the place of the three readings used during the rest of the year.  On Sundays, the office was longer, and therefore began a little earlier. Each set of six psalms was followed by four readings instead of three after the first set and a single recitation by heart after the second set. Then three canticles taken from Old Testament books other than the Psalms were recited, followed by four readings from the New Testament, the singing of the Te Deum, and a reading by the abbot from the Gospels, after which another hymn was sung.

"Roman Breviary" matins.

In the "Roman Breviary", use of which was made obligatory throughout the Latin Church (with exceptions for forms of the Liturgy of the Hours that could show they had been in continuous use for at least two hundred years) by Pope Pius V in 1568, matins and lauds were seen as a single canonical hour, with lauds as an appendage to matins.  Its matins began, as in the monastic matins, with versicles and the invitatory Psalm 94 (Psalm 95 in the Masoretic text) chanted or recited in the responsorial form, that is to say, by one or more cantors singing one verse, which the choir repeated as a response to the successive verses sung by the cantors. A hymn was then sung.  After that introduction, Sunday matins had three sections ("nocturns"), the first with 12 psalms and 3 very short scriptural readings; the second with 3 psalms and 3 equally short patristic readings; and the third with 3 psalms and 3 short extracts from a homily. Matins of feasts of double or semidouble rank had 3 nocturns, each with 3 psalms and 3 readings. On a feast of simple rank, a "feria" or a vigil day, matins had 12 psalms and 3 readings with no division into nocturns.  The psalms used at matins in the Roman Breviary from Sunday to Saturday were Psalms 1−108/109 in consecutive order, omitting a few that were reserved for other canonical hours: Psalms 4, 5, 21/22−25/26, 41/42, 50/51, 53/54, 62/63, 66/67, 89/90−92/93. The consecutive order was not observed for the invitatory psalms, recited every day, and in the matins of feasts.  Each reading was followed by a responsory, except the last one, when this was followed by the "Te Deum".

20th-century changes.

Matins underwent profound changes in the 20th century. The first of these changes was the reform of the Roman Breviary by Pope Pius X in 1911, resulting in what Pope Paul VI called "a new Breviary". The reservation of Psalms 1-108/109 to matins and the consecutive order within that group were abandoned, and, apart from the invitatory psalm, which continued in its place at matins every day, no psalm was ordinarily repeated within the same week. To facilitate an even distribution among the days of the week, the longer psalms were divided into shorter portions, as only the very long Psalm 118/119 had been previously. Matins no longer had 18 psalms on Sundays, 12 on ordinary days and 9 on the more important feasts: on every day it had 9 psalms, either distributed among three nocturns or recited all together, maintaining the distinction between celebrations as three nocturns with nine readings (including Sundays) and those arranged as a single nocturn with only three readings.  In 1947, Pope Pius XII entrusted examination of the whole question of the Breviary to a commission which conducted a worldwide consultation of the Catholic bishops. He authorized recitation of the psalms in a new Latin translation and in 1955 ordered a simplification of the rubrics.  In 1960, Pope John XXIII issued his "Code of Rubrics", which assigned nine-readings matins only to first-class and second-class feasts and therefore reduced the readings of Sunday matins to three.  In 1970, Pope Paul VI published a revised form of the Liturgy of the Hours, in which the psalms were arranged in a four-week instead of a one-week cycle, but the variety of other texts was greatly increased, in particular the scriptural and patristic readings, while the hagiographical readings were purged of non-historical legendary content.  What had previously been called matins was given the name of "office of readings" ("officium lectionis") and was declared appropriate for celebrating at any hour, while preserving its nocturnal character for those who wished to celebrate a vigil. For that purpose alternative hymns are provided and an appendix contains material, in particular canticles and readings from the Gospels, to facilitate celebration of a vigil. The Catholic Church has thus restored to the word "vigil" the meaning it had in early Christianity. Pope John XIII's "Code of Rubrics" still used the word "vigil" to mean the "day before" a feast, but recognized the quite different character of the Easter Vigil, which, "since it is not a liturgical day, is celebrated in its own way, as a night watch". The Roman liturgy now uses the term "vigil" either in this sense of "a night watch" or with regard to a Mass celebrated in the evening before a feast, not before the hour of First Vespers.  The psalmody of the office of readings consists of three psalms or portions of psalms, each with its own antiphon. These are followed by two extended readings with their responsories, the first from the Bible (but not from the Gospels), and the second being patristic, hagiographical, or magisterial. As already mentioned, a Gospel reading may optionally be added, preceded by vigil canticles, in order to celebrate a vigil. These are given in an appendix of the book of the Liturgy of the Hours.  To those who find it seriously difficult, because of their advanced age or for reasons peculiar to them, to observe the revised Liturgy of the Hours Pope Paul VI gave permission to keep using the previous Roman Breviary either in whole or in part. In 2007 Pope Benedict XVI allowed all clergy of the Latin Church to fulfil their canonical obligations by using the 1961 "Roman Breviary" issued under Pope John XXIII (but not earlier editions such as that of Pius X or Pius V). Traditionalist Catholic communities, such as the Priestly Fraternity of St. Peter and the Institute of Christ the King Sovereign Priest, avail of this authorization.

Non-Roman Western Rites.

In the office of the Church of Jerusalem, of which the pilgrim Ætheria gives us a description, the vigils on Sundays terminated with the solemn reading of the Gospel, in the Church of the Holy Sepulchre. This practice of reading the Gospel has been preserved in the Benedictine liturgy. In the Tridentine Roman Liturgy this custom, so ancient and so solemn, was no longer represented but by the Homily; but after the Second Vatican Council it has been restored for the celebration of vigils.  The Ambrosian Liturgy, better perhaps than any other, preserved traces of the great vigils or "pannychides", with their complex and varied display of processions, psalmodies, etc. The same liturgy also preserved vigils of long psalmody. This nocturnal office adapted itself at a later period to a more modern form, approaching more and more closely to the Roman liturgy. Here too were found the three nocturns, with Antiphon, psalms, lessons, and responses, the ordinary elements of the Roman matins, and with a few special features quite Ambrosian.  As revised after the Second Vatican Council, the Ambrosian liturgy of the hours uses for what once called matins either the designation "the part of matins that precedes lLauds in the strict sense" or simply "office of readings". Its structure is similar to that of the Roman Liturgy of the Hours, with variations such as having on Sundays three canticles, on Saturdays a canticle and two psalms, in place of the three psalms of the other days in the Ambrosian Rite and of every day in the Roman Rite.  In the Mozarabic liturgy, on the contrary, Matins is a system of antiphons, collects, and versicles which make them quite a departure from the Roman system.

Eastern Christianity.

Armenian Rite.

In the Armenian liturgy of the hours, Matins is known as the Midnight Office (Armenian: ի մեջ գիշերի ""i mej gisheri""). The Armenian Book of Hours, or Zhamagirk` (Armenian: Ժամագիրք) states that the Midnight Office is celebrated in commemoration of God the Father.  Much of the service consists of the kanon (Armenian: Կանոնագլուխ ""kanonagloukh""), consisting of a sequence of psalms, hymns, prayers, and in some instances readings from the Gospels, varying according to tone of the day, feast, or liturgical season. The Armenian kanon is quite different in form from the canon of the Byzantine matins service, though both likely share a common ancestor in the pre-dawn worship of the Jerusalem liturgy.

Basic Outline of Matins in the Armenian Church.

Introduction (common to all liturgical hours): "Blessed is our Lord Jesus Christ. Amen. Our father...Amen."  Fixed Preface  “Lord, if you open my lips, my mouth shall declare your praise.” (twice)  Acclamation: “Blessed is the consubstantial and unitary Holy Trinity...Amen.  Psalms: 3, 88, 102, 142  “Glory to the Father...now and always...Amen”  Hymn of the Night Liturgy by Nerses Shnorhali: “Let us remember your name in the night, Lord...”  Proclamation by John Mandakuni “Having all been awakened in the night from the repose of sleep...”  “Lord, have mercy” (variable number of times: thrice for Sundays and feasts of Christ, 50 times for the feasts of saints, 100 times on days of fasting)  Hymn of Nerses Shnorhali: “All the world... (Ashkharh amenayn)”  “Lord, have mercy” (thrice). “Through the intercession of the Birthgiver of God: Remember, Lord, and have mercy.”  Hymn of Nerses Shnorhali: “The rising of the sun... (Aṛawowt lowsoy)”  Prayer: “We thank you...”  Blessed is our Lord Jesus Christ. Amen. Alleluia, alleluia.  At this point a section of the Psalter is read, followed by a canticle from the Old or New Testament. See Armenian Liturgy. Following the Psalms and the Canticle is the Canon, a complex sequence of psalms, hymns, and prayers which varies in part according to the liturgical calendar.  Conclusion: "Our father...Amen."  The Armenian Matins or Midnight Office bears some resemblance with the Midnight Office of the Byzantine Rite, such as the recitation of a movable set of hymns depending on the feast. However, the Armenian Midnight Office is generally more elaborate than the Byzantine Midnight Office, in that the Armenian counterpart includes readings from the Gospel, as well as cycles of psalms and prayers reflecting the liturgical season or feast. Other material in the Byzantine office of Matins which has a counterpart in the Armenian daily office, such as the recitation of large sections of the Psalter and the recitation of biblical canticles, occurs in the Armenian liturgy at the Sunrise Hour which follows Matins, corresponding to Lauds.

Byzantine Rite.

In the Eastern Churches, matins is called "orthros" in Greek (, meaning "early dawn" or "daybreak") and "Oútrenya" in Slavonic (Оўтреня). It is the last of the four night offices, which also include vespers, compline, and midnight office. In traditional monasteries it is celebrated daily so as to end at sunrise. In parishes it is normally served only on Sundays and feast days.  Matins is the longest and most complex of the daily cycle of services. The "akolouth" (fixed portion of the service) is composed primarily of psalms and litanies. The sequences (variable parts) of matins are composed primarily of hymns and canons from the Octoechos (an eight-tone cycle of hymns for each day of the week, covering eight weeks), and from the Menaion (hymns for each calendar day of the year).  Matins opens with what is called the "Royal Beginning", so called because the psalms (19 and 20) are attributed to King David and speak of the Messiah, the "king of kings"; in former times, the ektenia (litany) also mentioned the emperor by name. The Sunday orthros is the longest of the regular orthros services. If celebrated in its entirety it can last up to three hours.

Matins is a canonical hour of Christian liturgy.

黎明颂或称凌晨祈祷、晨祷,是一天中的第一场祈祷,属于日课经部分。修士们要在子夜时分诵唱。 神父们也应该做黎明颂,但在时间上没有严格的规定,可以根据教区的工作自由选定。


Family and early career.

Leo VI was born into a Roman family, and his father was Christophorus, who had been "primicerius" under Pope John VIII around the year 876. Tradition has it that he was a member of the Sanguini family. Before his pontificate, Leo served as the cardinal-priest of Santa Susanna.

Pontificate.

Leo was elected pope around June 928, during a period of anarchy. He was chosen by the "senatrix" Marozia, who had gained control of Rome via the domination of her husband Guy, Margrave of Tuscany, and who had ordered the imprisonment and death of Leo’s predecessor, John X.  During his brief pontificate, Leo confirmed the decisions of the Synod of Spalato. He completed his predecessor’s investigations into the ecclesiastical situation in Dalmatia, and proceeded to give the pallium to Archbishop John of Salona, and ordered all the bishops of Dalmatia to obey him. He also ordered the bishop of Nona and others to limit themselves to the extent of their dioceses. Leo then banned castrati from marrying. He also issued an appeal for help against the Arab raiders who were threatening Rome, stating that: ”Whoever died faithful in this struggle will not see himself refused entry into the heavenly kingdom.”  The chronicler Flodoard said of him: ”Through the virtue of Peter, Leo the sixth was taken and received, he was preserved for seven months and five days, and like his predecessors, he joined the company of the prophets.”  Leo died in February 929, and was succeeded by Stephen VII. He was buried at St. Peter’s Basilica.

Pope Leo VI (880 – 12 February 929) was the bishop of Rome and nominal ruler of the Papal States for just over seven months, from June 928 to his death. His pontificate occurred during the period known as the "Saeculum obscurum".

教宗良六世(;)是一位罗马人,928年5月或6月接替教宗若望十世(914年3月或4月-928年5月或6月在位)岀任教宗。他于928年5月或6月-928年12月或929年1月在位教宗,由教宗德范七世(929年1月至931年2月在位)接替。他是PrimiceriusChristopher的儿子,并在被选为教宗之前拥有圣苏撒纳堂区领衔司铎头衔。


History.

The effect is named after the German physicist Johannes Stark, who discovered it in 1913. It was independently discovered in the same year by the Italian physicist Antonino Lo Surdo, and in Italy it is thus sometimes called the Stark–Lo Surdo effect. The discovery of this effect contributed importantly to the development of quantum theory and was rewarded with the Nobel Prize in Physics for Johannes Stark in the year 1919.  Inspired by the magnetic Zeeman effect, and especially by Lorentz's explanation of it, Woldemar Voigt performed classical mechanical calculations of quasi-elastically bound electrons in an electric field. By using experimental indices of refraction he gave an estimate of the Stark splittings. This estimate was a few orders of magnitude too low. Not deterred by this prediction, Stark undertook measurements on excited states of the hydrogen atom and succeeded in observing splittings.  By the use of the Bohr–Sommerfeld ("old") quantum theory, Paul Epstein and Karl Schwarzschild were independently able to derive equations for the linear and quadratic Stark effect in hydrogen. Four years later, Hendrik Kramers derived formulas for intensities of spectral transitions. Kramers also included the effect of fine structure, which includes corrections for relativistic kinetic energy and coupling between electron spin and orbital motion. The first quantum mechanical treatment (in the framework of Heisenberg's matrix mechanics) was by Wolfgang Pauli. Erwin Schrödinger discussed at length the Stark effect in his third paper on quantum theory (in which he introduced his perturbation theory), once in the manner of the 1916 work of Epstein (but generalized from the old to the new quantum theory) and once by his (first-order) perturbation approach. Finally, Epstein reconsidered the linear and quadratic Stark effect from the point of view of the new quantum theory. He derived equations for the line intensities which were a decided improvement over Kramers' results obtained by the old quantum theory.  While first-order perturbation effects for the Stark effect in hydrogen are in agreement for the Bohr–Sommerfeld model and the quantum-mechanical theory of the atom, higher-order effects are not. Measurements of the Stark effect under high field strengths confirmed the correctness of the quantum theory over the Bohr model.

Mechanism.

Overview.

An electric field pointing from left to right, for example, tends to pull nuclei to the right and electrons to the left. In another way of viewing it, if an electronic state has its electron disproportionately to the left, its energy is lowered, while if it has the electron disproportionately to the right, its energy is raised.  Other things being equal, the effect of the electric field is greater for outer electron shells, because the electron is more distant from the nucleus, so it travels farther left and farther right.  The Stark effect can lead to splitting of degenerate energy levels. For example, in the Bohr model, an electron has the same energy whether it is in the 2s state or any of the 2p states. However, in an electric field, there will be hybrid orbitals (also called quantum superpositions) of the 2s and 2p states where the electron tends to be to the left, which will acquire a lower energy, and other hybrid orbitals where the electron tends to be to the right, which will acquire a higher energy. Therefore, the formerly degenerate energy levels will split into slightly lower and slightly higher energy levels.

Classical electrostatics.

The Stark effect originates from the interaction between a charge distribution (atom or molecule) and an external electric field. Before turning to quantum mechanics we describe the interaction classically and consider a continuous charge distribution ρ(r). If this charge distribution is non-polarizable its interaction energy with an external electrostatic potential "V"(r) is If the electric field is of macroscopic origin and the charge distribution is microscopic, it is reasonable to assume that the electric field is uniform over the charge distribution. That is, "V" is given by a two-term Taylor expansion, where we took the origin 0 somewhere within ρ. Setting "V"(0) as the zero energy, the interaction becomes Here we have introduced the dipole moment μ of ρ as an integral over the charge distribution. In case ρ consists of "N" point charges "q" this definition becomes a sum

Perturbation theory.

Electric-field perturbation applied to a classical hydrogen atom produces a distortion of the electron orbit in a direction perpendicular to the applied field. This effect can be shown without perturbation theory using the relation between the angular momentum and the Laplace–Runge–Lenz vector. Using the Laplace-Runge-Lenz approach, one can see both the transverse distortion and the usual Stark effect. The transverse distortion is not mentioned in most textbooks. This approach can also lead to an "exactly solvable" approximate model Hamiltonian for an atom in a strong oscillatory field. “There are few exactly-solvable problems in quantum mechanics, and even fewer with a time-dependent Hamiltonian.”  Turning now to quantum mechanics an atom or a molecule can be thought of as a collection of point charges (electrons and nuclei), so that the second definition of the dipole applies. The interaction of atom or molecule with a uniform external field is described by the operator This operator is used as a perturbation in first- and second-order perturbation theory to account for the first- and second-order Stark effect.

First order.

Let the unperturbed atom or molecule be in a "g"-fold degenerate state with orthonormal zeroth-order state functions formula_7. (Non-degeneracy is the special case "g" = 1). According to perturbation theory the first-order energies are the eigenvalues of the "g" x "g" matrix with general element If "g" = 1 (as is often the case for electronic states of molecules) the first-order energy becomes proportional to the expectation (average) value of the dipole operator formula_9,  Because a dipole moment is a polar vector, the diagonal elements of the perturbation matrix V vanish for systems with an inversion center (such as atoms). Molecules with an inversion center in a non-degenerate electronic state do not have a (permanent) dipole and hence do not show a linear Stark effect.  In order to obtain a non-zero matrix V for systems with an inversion center it is necessary that some of the unperturbed functions formula_11 have opposite parity (obtain plus and minus under inversion), because only functions of opposite parity give non-vanishing matrix elements. Degenerate zeroth-order states of opposite parity occur for excited hydrogen-like (one-electron) atoms or Rydberg states. Neglecting fine-structure effects, such a state with the principal quantum number "n" is "n"-fold degenerate and where formula_13 is the azimuthal (angular momentum) quantum number. For instance, the excited "n" = 4 state contains the following formula_14 states, The one-electron states with even formula_14 are even under parity, while those with odd formula_14 are odd under parity. Hence hydrogen-like atoms with "n">1 show first-order Stark effect.  The first-order Stark effect occurs in rotational transitions of symmetric top molecules (but not for linear and asymmetric molecules). In first approximation a molecule may be seen as a rigid rotor. A symmetric top rigid rotor has the unperturbed eigenstates with 2(2"J"+1)-fold degenerate energy for |K| > 0 and (2"J"+1)-fold degenerate energy for K=0. Here "D" is an element of the Wigner D-matrix. The first-order perturbation matrix on basis of the unperturbed rigid rotor function is non-zero and can be diagonalized. This gives shifts and splittings in the rotational spectrum. Quantitative analysis of these Stark shift yields the permanent electric dipole moment of the symmetric top molecule.

Second order.

As stated, the quadratic Stark effect is described by second-order perturbation theory. The zeroth-order eigenproblem is assumed to be solved. The perturbation theory gives with the components of the polarizability tensor α defined by The energy "E" gives the quadratic Stark effect.  Neglecting the hyperfine structure (which is often justified — unless extremely weak electric fields are considered), the polarizability tensor of atoms is isotropic, For some molecules this expression is a reasonable approximation, too.  It is important to note that for the ground state formula_23 is "always" positive, i.e., the quadratic Stark shift is always negative.

Problems.

The perturbative treatment of the Stark effect has some problems. In the presence of an electric field, states of atoms and molecules that were previously bound (square-integrable), become formally (non-square-integrable) resonances of finite width. These resonances may decay in finite time via field ionization. For low lying states and not too strong fields the decay times are so long, however, that for all practical purposes the system can be regarded as bound. For highly excited states and/or very strong fields ionization may have to be accounted for. (See also the article on the Rydberg atom).

Quantum-confined Stark effect.

In a semiconductor heterostructure, where a small bandgap material is sandwiched between two layers of a larger bandgap material, the Stark effect can be dramatically enhanced by bound excitons. This is because the electron and hole which form the exciton are pulled in opposite directions by the applied electric field, but they remain confined in the smaller bandgap material, so the exciton is not merely pulled apart by the field. The quantum-confined Stark effect is widely used for semiconductor-based optical modulators, particularly for optical fiber communications.

Applications.

The Stark effect is at the basis of the spectral shift measured for voltage-sensitive dyes used for imaging of the firing activity of neurons.

The Stark effect is the shifting and splitting of spectral lines of atoms and molecules due to the presence of an external electric field. It is the electric-field analogue of the Zeeman effect, where a spectral line is split into several components due to the presence of the magnetic field. Although initially coined for the static case, it is also used in the wider context to describe the effect of time-dependent electric fields. In particular, the Stark effect is responsible for the pressure broadening (Stark broadening) of spectral lines by charged particles in plasmas. For most spectral lines, the Stark effect is either linear (proportional to the applied electric field) or quadratic with a high accuracy.

斯塔克效应(英语:Stark effect)是原子和分子光谱谱线在外加电场中发生位移和分裂的现象。分裂和位移量称为斯塔克分裂或斯塔克位移。斯塔克效应又可分为一阶和二阶斯塔克效应。一阶的情况下光谱分裂或位移是与电场强度呈线性关系,二阶则是和电场强度呈二次方关系。


Etymology.

The term "minivan" originated in North America in order to differentiate the smaller passenger vehicles from full-size vans (such as the Ford E-Series, Dodge Ram Van and Chevrolet Van), which were then simply called 'vans'.  The first known use of the term minivan was in 1959, however it was not until the 1980s that the term became commonly used.

Predecessors.

The 1936 Stout Scarab is often regarded as the first minivan. The passenger seats in the Scarab were moveable and could be configured for the passengers to sit around a table in the rear of the cabin. Passengers entered and exited the Scarab via a centrally-mounted door.  The DKW Schnellaster— manufactured from 1949 to 1962— featured front-wheel drive, a transverse engine, flat floor and multi-configurable seating, all of which would later become characteristics of minivans.  In 1950, the Volkswagen Type 2 adapted a bus-shaped body to chassis of a small passenger car (the Volkswagen Beetle). When Volkswagen introduced a sliding side door to the Type 2 in 1968, it then had the prominent features that would later come to define a minivan: compact length, three rows of forward-facing seats, station wagon-style top-hinged tailgate/liftgate, sliding side door, passenger car base.  The 1956-1969 Fiat Multipla also had many features in common with modern minivans. The Multipla was based on the chassis of the Fiat 600 and had a rear engine and cab forward layout.

North America.

1970s to 1990s.

In the late 1970s, Chrysler began a development program to design "a small affordable van that looked and handled more like a car." The result of this program was the first American minivan, the 1984 Plymouth Voyager. The Voyager debuted the minivan design features of front-wheel drive, a flat floor and a sliding door for rear passengers. The badge-engineered Dodge Caravan was also released in for the 1984 model year, and was sold alongside the Voyager.  The term minivan came into use largely in comparison to size to full-size vans; at six feet tall or lower, 1980s minivans were intended to fit inside a typical garage door opening. In 1984, "The New York Times" described minivans "the hot cars coming out of Detroit," noting that "analysts say the mini-van has created an entirely new market, one that may well overshadow the... station wagon."  In response to the popularity of the Voyager/Caravan, General Motors released the 1985 Chevrolet Astro and GMC Safari badge-engineered twins, and Ford released the 1986 Ford Aerostar. These vehicles used a traditional rear-wheel drive layout, unlike the Voyager/Caravan. By the end of the 1980s, demand for minivans as family vehicles had largely superseded full-size station wagons in the United States.  During the 1990s, the minivan segment underwent several major changes. Many models switched to the front-wheel drive layout used by the Voyager/Caravan minivans, for example Ford replaced the Aerostar with the front-wheel drive Mercury Villager (a rebadged Nissan Quest) for 1993 and the Ford Windstar for 1995. The models also increased in size, as a result of the extended-wheelbase ("Grand") versions of the Voyager and Caravan which were in 1987. An increase in luxury features and interior equipment was seen in the Eddie Bauer version of the 1988 Ford Aerostar, the 1990 Chrysler Town & Country and the 1990 Oldsmobile Silhouette. The third-generation Plymouth Voyager, Dodge Caravan and Chrysler Town & Country — released for the 1996 model year — were available with an additional sliding door on the drivers side.

2000 to present.

The highest selling year for minivans was in 2000, when 1.4 million units were sold. However, in the following years, the increasing popularity of sport utility vehicles (SUVs) began to erode sales of minivans. North American sales of the Volkswagen Transporter (sold as the 'Volkswagen Eurovan') ceased in 2003. Ford exited the segment in 2006, when the Ford Freestar was cancelled, Chrysler discontinued its short-wheelbase minivans in 2007 (although long-wheelbase minivans remained in production in the form of the Chrysler RT-platform minivans) and General Motors exited the segment in 2009 with the cancellation of the Chevrolet Uplander. It has been suggested that the lesser popularity of minivans is due to the minivan's image as a vehicle for older, domestically-oriented drivers.  In 2013, sales of the segment reached approximately 500,000 (one-third of its 2000 peak). Despite the declining sales for the segment in the late 2000s, several European brands launched minivans in the North American market. The Volkswagen Routan (a rebadged Dodge Grand Caravan) was sold from 2009-2013. In 2010, Ford began North American sales of the European-built Ford Transit Connect Wagon. North American sales of the Mercedes-Benz Vito (sold as the 'Mercedes-Benz Metris') began in 2016. However, the Nissan Quest and Mazda MPV were both discontinued in 2016.  The five highest selling models in the United States in 2018 were the Dodge Grand Caravan, Chrysler Pacifica, Honda Odyssey, Toyota Sienna and Kia Sedona.

Europe.

Introduced several months after the Chrysler minivans, the 1984 Renault Espace was the first European-developed minivan developed primarily for passenger use (as the Volkswagen Caravelle/Vanagon was a derivative of a commercial van). Beginning development in the 1970s under the European subsidiaries of Chrysler, the Espace was intended as a successor for the Matra Rancho (a primitive CUV), leading to its use of front-hinged doors. While slow-selling at the time of its release, the Espace would go on to become the most successful European-brand minivans.  Initially intending to sell the Espace in the United States, the 1987 sale of AMC to Chrysler cancelled plans of Renault doing so. At the end of the 1980s, Chrysler and Ford commenced sales of American-brand minivans in Europe, selling the Chrysler Voyager and Ford Aerostar (with varying degrees of success). Deriving its minivans from American designs, General Motors imported the Oldsmobile Silhouette (branded as the Pontiac Trans Sport), later marketing the American-produced Opel/Vauxhall Sintra.  In the 1990s, several joint ventures produced long-running minivan designs. In 1994, the Sevel Nord-produced Eurovans were introduced, marketed by Citroën, Fiat, Lancia, and Peugeot; two generations were produced through 2014. In contrast to the Espace, the Eurovans were produced with two sliding doors; to increase interior space, the gearshift was relocated to the dashboard and the handbrake was moved. In 1995, Ford of Europe and Volkswagen entered a joint venture, producing the Ford Galaxy, SEAT Alhambra, and Volkswagen Sharan. Adopting a similar configuration as the Espace, the three model lines were launched with front-hinged doors; for 2010, SEAT and Volkswagen introduced a second generation, adopting sliding doors. Despite high expectations during the 1990s, the full-size MPV market fell short, and some consumers thought of MPVs as being large like vans. Other MPVs on the market at the time include Mitsubishi Space Wagon and Honda Shuttle. Renault set a new "compact MPV" standard with the Renault Scenic in 1996 which became a hit. The five highest selling minivans in Europe in 2018 were the Ford S-Max, SEAT Alhambra, Volkswagen Sharan, Renault Espace and Ford Galaxy.

Asia.

Contrasting with compact passenger vans developed from commercial vehicles, Japanese manufacturers commenced development of minivans starting from compact MPVs in the 1980s. In 1982, the Nissan Prairie became one of the first compact minivans. Derived closely from a compact sedan, the Prairie was configured with sliding doors, folding rear seats, and a lifting rear hatch. The Mitsubishi Chariot (exported to North America as the Colt Vista) adopted nearly the same form factor, using wagon-style front-hinged doors.  In 1989, the Mazda MPV was introduced as the first full-size minivan (derived from the Mazda 929 sedan). Developed primarily for American sales, the MPV exceeded Japanese compact size regulations; it was also sold in Japan and other markets. In line with American minivans, a passenger-side door was used; a hinged door was used (a driver-side door was introduced for 1996).  For 1990, the Toyota Previa mid-engine minivan was introduced (sold as the "Estima" in Japan). While largely retaining the configuration of its TownAce predecessor, the Previa was designed solely as a passenger vehicle, with nearly panoramic window glass (excluding the B and D-pillars). Replaced in North America by the locally produced Sienna, the Previa remains in production for Japanese and Australian markets; the larger Alphard is produced as a luxury vehicle.  Following the introduction of the Nissan Quest (co-developed with Ford for North America), Nissan introduced the Nissan Elgrand in 1997 for worldwide markets; the Nissan Serena has grown into the large MPV segment as well.  Honda has produced its Honda Odyssey line of minivans since 1994; since 1999, a separate (larger) version has been produced for the United States and Canada. Until 2013, the Japan-produced version of the Odyssey was designed with front-hinged doors. In a design feature that was adopted by other manufacturers, the first generation of the Odyssey featured a rear seat that folded flat into the floor.  Expanding beyond compact MPVs, Mitsubishi entered the minivan segment in 2003 with the Mitsubishi Grandis, using front-hinged doors. Sold outside of North America, the Grandis was marketed through 2011.  Adapting a similar layout to the Chrysler minivans, the Kia Carnival (also sold the Kia Sedona) was introduced in 1998 with dual sliding doors. Sharing its configuration with the Honda Odyssey, the Hyundai Trajet was sold from 1999 to 2008 in markets outside of North America; the Hyundai Entourage was a rebadged Kia Sedona.  Introduced in 2004, the SsangYong Rodius is the highest-capacity minivan, seating up to 11 passengers.  In 1999, Shanghai GM commenced production of the Buick GL8 minivan, derived from a minivan platform designed by GM in the United States. After two generations of production, the GL8 is the final minivan produced by General Motors or its joint ventures today.

Related vehicle categories.

Compact MPV.

Compact MPV— an abbreviation for Compact Multi-Purpose Vehicle— is a vehicle size class for the middle size of MPVs/minivans. The Compact MPV size class sits between the mini MPV and minivan size classes.  Compact MPVs remain predominantly a European phenomenon, although they are also built and sold in many Latin American and Asian markets. As of 2016, the only compact MPV sold widely in the United States is the Ford C-Max.

Mini MPV.

Mini MPV — an abbreviation for Mini Multi-Purpose Vehicle — is a vehicle size class for the smallest size of minivans (MPVs). The Mini MPV size class sits below the compact MPV size class and the vehicles are often built on the platforms of B-segment hatchback models.  Several PSA Peugeot Citroën minivans based on B-segment platforms have been marketed as 'leisure activity vehicles' in Europe. These include the Citroën Berlingo (1996–present).

Leisure activity vehicle.

A leisure activity vehicle (abbreviated LAV) is a small van or minivan; the segment is popularized primarily in Europe. One of the first LAVs was the 1977 Matra Rancho (among the first crossover SUVs and a precursor to the Renault Espace), with European manufacturers expanding the segment in the late 1990s, following the introduction of the Citroen Berlingo and Renault Kangoo.  Leisure activity vehicles are typically derived from supermini or subcompact car platforms, differing from mini MPVs in body design. To maximize interior space, LAVs are taller in height with a vertically-oriented liftgate (or the side-hinged doors of a cargo van); the body typically features a more vertically-oriented windshield and longer hood/bonnet. Marketed as an alternative to sedan-derived small family cars, LAVs have seating with a lower H-point than MPVs or minivans, offering two (or three) rows of seating.  Though sharing underpinnings with superminis, subcompacts, and mini MPVs, the use of an extended wheelbase can make leisure activity vehicles longer than the vehicles they are derived from. For example, the Fiat Doblò is one of the longest LAVs with a total length of, versus the of the Opel Meriva (a mini MPV) and the of the Peugeot 206 SW (a supermini).  List of leisure activity vehicles (similar vehicles are grouped together):

Minivan is a van for vehicles designed to transport passengers in the rear seating row(s), with reconfigurable seats in two or three rows. The equivalent terms in British English are multi-purpose vehicle (MPV), people carrier and people mover. Minivans often have a 'one-box' or 'two-box' body configuration, a higher roof, a flat floor, a sliding door for rear passengers, and high H-point seating.

多功能休旅车(Multi-Purpose Vehicle,缩写成「MPV」;Multi-Utility Vehicle,缩写成「MUV」),美国称之为「Minivan」,是一种由厢型车、休旅车多型态混合体的车辆,搭乘人数可达7至8人左右。


Overview.

A logical connective is truth-functional if the truth-value of a compound sentence is a function of the truth-value of its sub-sentences. A class of connectives is truth-functional if each of its members is. For example, the connective ""and"" is truth-functional since a sentence like ""Apples are fruits and carrots are vegetables"" is true "if, and only if" each of its sub-sentences ""apples are fruits"" and ""carrots are vegetables"" is true, and it is false otherwise. Some connectives of a natural language, such as English, are not truth-functional.  Connectives of the form "x "believes that"..." are typical examples of connectives that are not truth-functional. If e.g. Mary mistakenly believes that Al Gore was President of the USA on April 20, 2000, but she does not believe that the moon is made of green cheese, then the sentence  is true while  is false. In both cases, each component sentence (i.e. ""Al Gore was president of the USA on April 20, 2000"" and ""the moon is made of green cheese"") is false, but each compound sentence formed by prefixing the phrase ""Mary believes that"" differs in truth-value. That is, the truth-value of a sentence of the form ""Mary believes that..."" is not determined solely by the truth-value of its component sentence, and hence the (unary) connective (or simply "operator" since it is unary) is non-truth-functional.  The class of classical logic connectives (e.g. &, →) used in the construction of formulas is truth-functional. Their values for various truth-values as argument are usually given by truth tables. Truth-functional propositional calculus is a formal system whose formulae may be interpreted as either true or false.

Table of binary truth functions.

In two-valued logic, there are sixteen possible truth functions, also called Boolean functions, of two inputs "P" and "Q". Any of these functions corresponds to a truth table of a certain logical connective in classical logic, including several degenerate cases such as a function not depending on one or both of its arguments. Truth and falsehood is denoted as 1 and 0 in the following truth tables, respectively, for sake of brevity.

Functional completeness.

Because a function may be expressed as a composition, a truth-functional logical calculus does not need to have dedicated symbols for all of the above-mentioned functions to be functionally complete. This is expressed in a propositional calculus as logical equivalence of certain compound statements. For example, classical logic has equivalent to. The conditional operator "→" is therefore not necessary for a classical-based logical system if "¬" (not) and "∨" (or) are already in use.  A minimal set of operators that can express every statement expressible in the propositional calculus is called a "minimal functionally complete set". A minimally complete set of operators is achieved by NAND alone {↑} and NOR alone {↓}.  The following are the minimal functionally complete sets of operators whose arities do not exceed 2:

Algebraic properties.

Some truth functions possess properties which may be expressed in the theorems containing the corresponding connective. Some of those properties that a binary truth function (or a corresponding logical connective) may have are:  A set of truth functions is functionally complete if and only if for each of the following five properties it contains at least one member lacking it:

Arity.

A concrete function may be also referred to as an "operator". In two-valued logic there are 2 nullary operators (constants), 4 unary operators, 16 binary operators, 256 ternary operators, and formula_33 "n"-ary operators. In three-valued logic there are 3 nullary operators (constants), 27 unary operators, 19683 binary operators, 7625597484987 ternary operators, and formula_34 "n"-ary operators. In "k"-valued logic, there are "k" nullary operators, formula_35 unary operators, formula_36 binary operators, formula_37 ternary operators, and formula_38 "n"-ary operators. An "n"-ary operator in "k"-valued logic is a function from formula_39. Therefore, the number of such operators is formula_40, which is how the above numbers were derived.  However, some of the operators of a particular arity are actually degenerate forms that perform a lower-arity operation on some of the inputs and ignores the rest of the inputs. Out of the 256 ternary boolean operators cited above, formula_41 of them are such degenerate forms of binary or lower-arity operators, using the inclusion–exclusion principle. The ternary operator formula_42 is one such operator which is actually a unary operator applied to one input, and ignoring the other two inputs.  "Not" is a unary operator, it takes a single term (¬"P"). The rest are binary operators, taking two terms to make a compound statement ("P" ∧ "Q", "P" ∨ "Q", "P" → "Q", "P" ↔ "Q").  The set of logical operators may be partitioned into disjoint subsets as follows:  In this partition, formula_44 is the set of operator symbols of "arity".  In the more familiar propositional calculi, formula_45 is typically partitioned as follows:

Principle of compositionality.

Instead of using truth tables, logical connective symbols can be interpreted by means of an interpretation function and a functionally complete set of truth-functions (Gamut 1991), as detailed by the principle of compositionality of meaning. Let "I" be an interpretation function, let "Φ", "Ψ" be any two sentences and let the truth function "f" be defined as:  Then, for convenience, "f", "f" "f" and so on are defined by means of "f":  or, alternatively "f", "f" "f" and so on are defined directly:  Then  etc.  Thus if "S" is a sentence that is a string of symbols consisting of logical symbols "v"..."v" representing logical connectives, and non-logical symbols "c"..."c", then if and only if have been provided interpreting "v" to "v" by means of "f" (or any other set of functional complete truth-functions) then the truth-value of is determined entirely by the truth-values of "c"..."c", i.e. of. In other words, as expected and required, "S" is true or false only under an interpretation of all its non-logical symbols.

Computer science.

Logical operators are implemented as logic gates in digital circuits. Practically all digital circuits (the major exception is DRAM) are built up from NAND, NOR, NOT, and transmission gates. NAND and NOR gates with 3 or more inputs rather than the usual 2 inputs are fairly common, although they are logically equivalent to a cascade of 2-input gates. All other operators are implemented by breaking them down into a logically equivalent combination of 2 or more of the above logic gates.  The "logical equivalence" of "NAND alone", "NOR alone", and "NOT and AND" is similar to Turing equivalence.  The fact that all truth functions can be expressed with NOR alone is demonstrated by the Apollo guidance computer.

In logic, a truth function is a function that accepts truth values as input and produces a truth value as output, i.e., the input and output are all truth values. The typical example is in propositional logic, wherein a compound statement is constructed by one or two statements connected by a logical connective; if the truth value of the compound statement is determined by the truth value(s) of the constituent statement(s), the compound statement is called a truth function, and the logical connective is said to be truth functional.

在逻辑中,真值函数是从语言的句子生成的函数。它采用来自 {T,F} (就是真实和虚假)的真值。例如句子 A → B 生成真值函数 h(A,B),它的真值是 F,当且仅当 A 的值是 T 而 B 的值是 F。n 个变量的命题句子生成 2^{2^n} 个真值函数。比如,如果有像 A → (B → A) 这样的 2 个变量的命题则有 16 个生成的真值函数。


Overview.

The Visitor  design pattern is one of the twenty-three well-known "GoF design patterns" that describe how to solve recurring design problems to design flexible and reusable object-oriented software, that is, objects that are easier to implement, change, test, and reuse.  What problems can the Visitor design pattern solve?  When new operations are needed frequently and the object structure consists of many unrelated classes, it's inflexible to add new subclasses each time a new operation is required because "[..] distributing all these operations across the various node classes leads to a system that's hard to understand, maintain, and change."  What solution does the Visitor design pattern describe?  This makes it possible to create new operations independently from the classes of an object structure by adding new visitor objects.  See also the UML class and sequence diagram below.

Definition.

The Gang of Four defines the Visitor as: The nature of the Visitor makes it an ideal pattern to plug into public APIs thus allowing its clients to perform operations on a class using a "visiting" class without having to modify the source.

Uses.

Moving operations into visitor classes is beneficial when  A drawback to this pattern, however, is that it makes extensions to the class hierarchy more difficult, as new classes typically require a new codice_1 method to be added to each visitor.

Use case example.

Consider the design of a 2D computer-aided design (CAD) system. At its core there are several types to represent basic geometric shapes like circles, lines, and arcs. The entities are ordered into layers, and at the top of the type hierarchy is the drawing, which is simply a list of layers, plus some added properties.  A fundamental operation on this type hierarchy is saving a drawing to the system's native file format. At first glance it may seem acceptable to add local save methods to all types in the hierarchy. But it is also useful to be able to save drawings to other file formats. Adding ever more methods for saving into many different file formats soon clutters the relatively pure original geometric data structure.  A naive way to solve this would be to maintain separate functions for each file format. Such a save function would take a drawing as input, traverse it, and encode into that specific file format. As this is done for each added different format, duplication between the functions accumulates. For example, saving a circle shape in a raster format requires very similar code no matter what specific raster form is used, and is different from other primitive shapes. The case for other primitive shapes like lines and polygons is similar. Thus, the code becomes a large outer loop traversing through the objects, with a large decision tree inside the loop querying the type of the object. Another problem with this approach is that it is very easy to miss a shape in one or more savers, or a new primitive shape is introduced, but the save routine is implemented only for one file type and not others, leading to code extension and maintenance problems.  Instead, the visitor pattern can be applied. It encodes a logical operation on the whole hierarchy into one class containing one method per type. In the CAD example, each save function would be implemented as a separate Visitor subclass. This would remove all duplication of type checks and traversal steps. It would also make the compiler complain if a shape is omitted.  Another motive is to reuse iteration code. For example, iterating over a directory structure could be implemented with a visitor pattern. This would allow creating file searches, file backups, directory removal, etc., by implementing a visitor for each function while reusing the iteration code.

Structure.

UML class and sequence diagram.

In the above UML class diagram, the codice_2 class doesn't implement a new operation directly. Instead, codice_2 implements a "dispatching operation" codice_4 that "dispatches" (delegates) a request to the "accepted visitor object" (codice_5). The codice_6 class implements the operation (codice_7).
 codice_8 then implements codice_4 by dispatching to codice_10. The codice_6 class implements the operation (codice_12).  The UML sequence diagram shows the run-time interactions: The codice_13 object traverses the elements of an object structure (codice_14) and calls codice_4 on each element.
 First, the codice_13 calls codice_4 on codice_2, which calls codice_19 on the accepted codice_20 object. The element itself (codice_21) is passed to the codice_20 so that it can "visit" codice_2 (call codice_24).
 Thereafter, the codice_13 calls codice_4 on codice_8, which calls codice_28 on the codice_20 that "visits" codice_8 (calls codice_31).

Details.

The visitor pattern requires a programming language that supports single dispatch, as common object-oriented languages (such as C++, Java, Smalltalk, Objective-C, Swift, JavaScript, Python and C#) do. Under this condition, consider two objects, each of some class type; one is termed the "element", and the other is "visitor".  The "visitor" declares a codice_1 method, which takes the element as an argument, for each class of element. "Concrete visitors" are derived from the visitor class and implement these codice_1 methods, each of which implements part of the algorithm operating on the object structure. The state of the algorithm is maintained locally by the concrete visitor class.  The "element" declares an codice_34 method to accept a visitor, taking the visitor as an argument. "Concrete elements", derived from the element class, implement the codice_34 method. In its simplest form, this is no more than a call to the visitor's codice_1 method. Composite elements, which maintain a list of child objects, typically iterate over these, calling each child's codice_34 method.  The "client" creates the object structure, directly or indirectly, and instantiates the concrete visitors. When an operation is to be performed which is implemented using the Visitor pattern, it calls the codice_34 method of the top-level element(s).  When the codice_34 method is called in the program, its implementation is chosen based on both the dynamic type of the element and the static type of the visitor. When the associated codice_1 method is called, its implementation is chosen based on both the dynamic type of the visitor and the static type of the element, as known from within the implementation of the codice_34 method, which is the same as the dynamic type of the element. (As a bonus, if the visitor can't handle an argument of the given element's type, then the compiler will catch the error.)  Thus, the implementation of the codice_1 method is chosen based on both the dynamic type of the element and the dynamic type of the visitor. This effectively implements double dispatch. For languages whose object systems support multiple dispatch, not only single dispatch, such as Common Lisp or C# via the Dynamic Language Runtime (DLR), implementation of the visitor pattern is greatly simplified (a.k.a. Dynamic Visitor) by allowing use of simple function overloading to cover all the cases being visited. A dynamic visitor, provided it operates on public data only, conforms to the open/closed principle (since it does not modify extant structures) and to the single responsibility principle (since it implements the Visitor pattern in a separate component).  In this way, one algorithm can be written to traverse a graph of elements, and many different kinds of operations can be performed during that traversal by supplying different kinds of visitors to interact with the elements based on the dynamic types of both the elements and the visitors.

C# example.

This example shows how to print a tree representing a numeric expression involving literals and their addition. The same example is presented using both classic and Dynamic Language Runtime implementations.

Classic visitor.

A classic visitor where the Print operations for each type are implemented in one ExpressionPrinter class as a number of overloads of the Visit method. using System; using System.Text;  namespace Wikipedia

Dynamic Visitor.

This example declares a separate codice_43 class that takes care of the printing. The expression classes must expose their members to make this possible.  using System; using System.Text;  namespace Wikipedia

Smalltalk example.

In this case, it is the object's responsibility to know how to print itself on a stream. The visitor here is then the object, not the stream. "There's no syntax for creating a class. Classes are created by sending messages to other classes." WriteStream subclass: #ExpressionPrinter  ExpressionPrinter»write: anObject  Object subclass: #Expression  Expression subclass: #Literal  Literal class»with: aValue  Literal»value: aValue  Literal»putOn: aStream  Expression subclass: #Addition  Addition class»left: a right: b  Addition»left: anExpression  Addition»right: anExpression  Addition»putOn: aStream  Object subclass: #Program  Program»main

C++ example.

Sources.

class AbstractDispatcher; // Forward declare AbstractDispatcher  class File { // Parent class for the elements (ArchivedFile, SplitFile and  // Forward declare specific elements (files) to be dispatched class ArchivedFile; class SplitFile; class ExtractedFile;  class AbstractDispatcher { // Declares the interface for the dispatcher  class ArchivedFile : public File { // Specific element class #1 };  class SplitFile : public File { // Specific element class #2 };  class ExtractedFile : public File { // Specific element class #3 };  class Dispatcher : public AbstractDispatcher { // Implements dispatching of all  };  int main() {

Go example.

Go does not support overloading, so the visit methods need different names.

Sources.

package main  import "fmt"  type Visitor interface {  type element interface {  type Wheel struct {  func (self *Wheel) Accept(visitor Visitor) string {  func (self *Wheel) getName() string {  func (self *Engine) Accept(visitor Visitor) string {  func (self *Body) Accept(visitor Visitor) string {  type Car struct {  func (self *Car) Accept(visitor Visitor) string {  func (self *PrintVisitor) visitWheel(wheel Wheel) string { func (self *PrintVisitor) visitEngine(engine Engine) string { func (self *PrintVisitor) visitBody(body Body) string { func (self *PrintVisitor) visitCar(car Car) string {  /* output: visiting car visiting engine visiting body visiting front left wheel visiting front right wheel visiting back left wheel visiting back right wheel func main() {

Java example.

The following example is in the language Java, and shows how the contents of a tree of nodes (in this case describing the components of a car) can be printed. Instead of creating codice_44 methods for each node subclass (codice_45, codice_46, codice_47, and codice_48), one visitor class (codice_49) performs the required printing action. Because different node subclasses require slightly different actions to print properly, codice_49 dispatches actions based on the class of the argument passed to its codice_1 method. codice_52, which is analogous to a save operation for a different file format, does likewise.

Sources.

import java.util.List;  interface CarElement {  interface CarElementVisitor {  class Wheel implements CarElement {  class Body implements CarElement {  class Engine implements CarElement {  class Car implements CarElement {  class CarElementDoVisitor implements CarElementVisitor {  class CarElementPrintVisitor implements CarElementVisitor {  public class VisitorDemo {  A more flexible approach to this pattern is to create a wrapper class implementing the interface defining the accept method. The wrapper contains a reference pointing to the codice_53 that could be initialized through the constructor. This approach avoids having to implement an interface on each element. "See article Java Tip 98 article below"

Common Lisp example.

Sources.

((elements :initarg :elements)))  (defmethod do-something (object other-object)  (defmethod do-something ((object wheel) (other-object integer))  (defmethod do-something ((object wheel) (other-object symbol))  (let ((a (make-instance 'auto

Notes.

The codice_54 parameter is superfluous in codice_55. The reason is that it is possible to use an anonymous function that calls the desired target method with a lexically captured object:  (defmethod traverse (function (a auto)) ;; other-object removed  Now, the multiple dispatch occurs in the call issued from the body of the anonymous function, and so codice_55 is just a mapping function that distributes a function application over the elements of an object. Thus all traces of the Visitor Pattern disappear, except for the mapping function, in which there is no evidence of two objects being involved. All knowledge of there being two objects and a dispatch on their types is in the lambda function.

Python example.

Python does not support method overloading in classical sense (polymorphic behavior according to type of passed parameters), so the "visit" methods for the different model types need to have different names.

Sources.

Visitor pattern example.  from abc import ABCMeta, abstractmethod  NOT_IMPLEMENTED = "You should implement this."  class CarElement:  class Body(CarElement):  class Engine(CarElement):  class Wheel(CarElement):  class Car(CarElement):  class CarElementVisitor:  class CarElementDoVisitor(CarElementVisitor):  class CarElementPrintVisitor(CarElementVisitor):  car = Car() car.accept(CarElementPrintVisitor()) car.accept(CarElementDoVisitor())

Output.

Visiting front left wheel. Visiting front right wheel. Visiting back left wheel. Visiting back right wheel. Visiting body. Visiting engine. Visiting car. Kicking my front left wheel. Kicking my front right wheel. Kicking my back left wheel. Kicking my back right wheel. Moving my body. Starting my engine. Starting my car.

Abstraction.

If one is using Python 3 or above, they can make a general implementation of the accept method: class Visitable: One could extend this to iterate over the class's method resolution order if they would like to fall back on already-implemented classes. They could also use the subclass hook feature to define the lookup in advance.

In object-oriented programming and software engineering, the visitor design pattern is a way of separating an algorithm from an object structure on which it operates. A practical result of this separation is the ability to add new operations to existing object structures without modifying the structures. It is one way to follow the open/closed principle.

访问者模式是一种将算法与对象结构分离的软件设计模式。


Wolstenholme primes.

A prime "p" is called a Wolstenholme prime iff the following condition holds:  If "p" is a Wolstenholme prime, then Glaisher's theorem holds modulo "p". The only known Wolstenholme primes so far are 16843 and 2124679 ; any other Wolstenholme prime must be greater than 10. This result is consistent with the heuristic argument that the residue modulo "p" is a pseudo-random multiple of "p". This heuristic predicts that the number of Wolstenholme primes between "K" and "N" is roughly "ln ln N − ln ln K". The Wolstenholme condition has been checked up to 10, and the heuristic says that there should be roughly one Wolstenholme prime between 10 and 10. A similar heuristic predicts that there are no "doubly Wolstenholme" primes, for which the congruence would hold modulo "p".

A proof of the theorem.

There is more than one way to prove Wolstenholme's theorem. Here is a proof that directly establishes Glaisher's version using both combinatorics and algebra.  For the moment let "p" be any prime, and let "a" and "b" be any non-negative integers. Then a set "A" with "ap" elements can be divided into "a" rings of length "p", and the rings can be rotated separately. Thus, the "a"-fold direct sum of the cyclic group of order "p" acts on the set "A", and by extension it acts on the set of subsets of size "bp". Every orbit of this group action has "p" elements, where "k" is the number of incomplete rings, i.e., if there are "k" rings that only partly intersect a subset "B" in the orbit. There are formula_10 orbits of size 1 and there are no orbits of size "p". Thus we first obtain Babbage's theorem Examining the orbits of size "p", we also obtain Among other consequences, this equation tells us that the case "a=2" and "b=1" implies the general case of the second form of Wolstenholme's theorem.  Switching from combinatorics to algebra, both sides of this congruence are polynomials in "a" for each fixed value of "b". The congruence therefore holds when "a" is any integer, positive or negative, provided that "b" is a fixed positive integer. In particular, if "a=-1" and "b=1", the congruence becomes This congruence becomes an equation for formula_14 using the relation When "p" is odd, the relation is When "p"≠3, we can divide both sides by 3 to complete the argument.  A similar derivation modulo "p" establishes that for all positive "a" and "b" if and only if it holds when "a=2" and "b=1", i.e., if and only if "p" is a Wolstenholme prime.

The converse as a conjecture.

It is conjectured that if  when "k=3", then "n" is prime. The conjecture can be understood by considering "k" = 1 and 2 as well as 3. When "k" = 1, Babbage's theorem implies that it holds for "n" = "p" for "p" an odd prime, while Wolstenholme's theorem implies that it holds for "n" = "p" for "p" > 3, and it holds for "n" = "p" if "p" is a Wolstenholme prime. When "k" = 2, it holds for "n" = "p" if "p" is a Wolstenholme prime. These three numbers, 4 = 2, 8 = 2, and 27 = 3 are not held for () with "k" = 1, but all other prime square and prime cube are held for () with "k" = 1. Only 5 other composite values (neither prime square nor prime cube) of "n" are known to hold for () with "k" = 1, they are called Wolstenholme pseudoprimes, they are  The first three are not prime powers, the last two are 16843 and 2124679, 16843 and 2124679 are Wolstenholme primes. Besides, with an exception of 16843 and 2124679, no composites are known to hold for () with "k" = 2, much less "k" = 3. Thus the conjecture is considered likely because Wolstenholme's congruence seems over-constrained and artificial for composite numbers. Moreover, if the congruence does hold for any particular "n" other than a prime or prime power, and any particular "k", it does not imply that

Generalizations.

Leudesdorf has proved that for a positive integer "n" coprime to 6, the following congruence holds:

In mathematics, Wolstenholme's theorem states that for a prime number formula_1, the congruence holds, where the parentheses denote a binomial coefficient. For example, with "p" = 7, this says that 1716 is one more than a multiple of 343. The theorem was first proved by Joseph Wolstenholme in 1862. In 1819, Charles Babbage showed the same congruence modulo "p", which holds for formula_3. An equivalent formulation is the congruence for formula_1, which is due to Wilhelm Ljunggren (and, in the special case formula_6, to J. W. L. Glaisher) and is inspired by Lucas' theorem.

在数论上,沃尔斯滕霍尔姆定理说明,对于大于或等于5的质数,有


Description.

Bromeliads are plants that are adapted to various climates. Foliage takes different shapes, from needle-thin to broad and flat, symmetrical to irregular, spiky to soft. The foliage, which usually grows in a rosette, is widely patterned and colored. Leaf colors range from maroon, through shades of green, to gold. Varieties may have leaves with red, yellow, white and cream variations. Others may be spotted with purple, red, or cream, while others have different colors on the tops and botecies "Tillandsia cyanea" have a fragrance resembling that of clove spice.  One study found 175,000 bromeliads per hectare (2.5 acres) in one forest; that many bromeliads can sequester 50,000 liters (more than 13,000 gallons) of water.  Various organisms take advantage of the pools of water trapped by bromeliads. A study of 209 plants from the Ecuadorian lowlands identified 11,219 animals, representing more than 300 distinct species, many of which are found only on bromeliads. Examples include some species of ostracods, small salamanders about in length, and tree frogs. Jamaican bromeliads are home to "Metopaulias depressus", a reddish-brown crab across, which has evolved social behavior to protect its young from predation by "Diceratobasis macrogaster", a species of damselfly whose larvae live in bromeliads. Some bromeliads even form homes for other species of bromeliads.

Distribution.

Plants in the Bromeliaceae are widely represented in their natural climates across the Americas. One species can be found in Africa. They can be found at altitudes from sea level to 4200 meters, from rainforests to deserts. 1814 species are epiphytes, some are lithophytes, and some are terrestrial. Accordingly, these plants can be found in the Andean highlands, from northern Chile to Colombia, in the Sechura Desert of coastal Peru, in the cloud forests of Central and South America, in southern United States from southern Virginia to Florida to Texas, and in far southern Arizona.

Ecology.

Bromeliads often serve as phytotelmata, accumulating water between their leaves. The aquatic habitat created as a result is host to a diverse array of invertebrates, especially aquatic insect larvae. These bromeliad invertebrates benefit their hosts by increasing nitrogen uptake into the plant.  Trees or branches that have a higher incidence of sunlight tend to have more bromeliads. In contrast, the sectors facing west receive less sunlight and therefore fewer bromeliads. In addition, thicker trees have more bromeliads, possibly because they are older and have greater structural complexity.

Evolution.

Bromeliads are among the more recent plant groups to have emerged. The greatest number of primitive species resides in the Andean highlands of South America, where they originated in the tepuis of the Guiana Shield approximately 100 million years ago. However, the family did not diverge into its extant subfamilies until 19 million years ago. The long period between the origin and diversification of bromeliads, during which no extant species evolved, suggests that there was much speciation and extinction during that time, which would explain the genetic distance of the Bromeliaceae from other families within the Poales. The most basal genus, "Brocchinia", is endemic to the Guiana Shield, and is placed as the sister group to the remaining genera in the family. The subfamilies Navioideae and Lindmanioideae are endemic to the Guiana Shield as well.  The West African species "Pitcairnia feliciana" is the only bromeliad not endemic to the Americas, and is thought to have reached Africa via long-distance dispersal about 12 million years ago.

Radiation of "Hechtia" and Tillandsioideae.

The first groups to leave the Guiana Shield were the genus "Hechtia", which spread to Central America via long-distance dispersal, and the subfamily Tillandsioideae, which spread gradually into northern South America. Both of these movements occurred approximately 15.4 million years ago. When it reached the Andes mountains, the speciation of Tillandsioideae occurred quite rapidly, largely due to the Andean uplift, which was also occurring rapidly from 14.2 to 8.7 million years ago. The uplift created a new mountainous environment for the epiphytic Tillandsioides to colonize, and greatly altered the region's geological and climatic conditions. These new conditions directly drove the speciation of the Tillandsioides, and also drove the speciation of their animal pollinators, such as hummingbirds.

Evolution of the Bromelioideae.

Around 5.5 million years ago, a clade of epiphytic Bromelioids arose in Serra do Mar, a lush mountainous region on the coast of Southeastern Brazil. This is thought to have been caused not only by the uplift of Serra do Mar itself at that time, but also because of the continued uplift of the distant Andes mountains, which impacted the circulation of air and created a cooler, wetter climate in Serra do Mar. These epiphytes thrived in this humid environment, since their trichomes rely on water in the air rather than from the ground like terrestrial plants. Many epiphytic bromeliads with the tank habit also speciated here.  Even before this, a few other bromeliads had already dispersed to the Brazilian shield while the climate was still arid, likely through a gradual process of short-distance dispersal. These make up the terrestrial members of the Bromelioideae, which have highly xeromorphic characters.

Adaptations.

Bromeliads are able to live in a vast array of environmental conditions due to their many adaptations. Trichomes, in the form of scales or hairs, allow bromeliads to capture water in cloud forests and help to reflect sunlight in desert environments. Some bromeliads have also developed an adaptation known as the tank habit, which involves them forming a tightly bound structure with their leaves that helps to capture water and nutrients in the absence of a well-developed root system. Bromeliads also use crassulacean acid metabolism (CAM) photosynthesis to create sugars. This adaptation allows bromeliads in hot or dry climates to open their stomates at night rather than during the very day, which reduces water loss.  Both CAM and epiphytism have evolved multiple times within the family, with some taxa even reverting to C3 photosynthesis as they radiated into less arid climates.

Classification.

The family Bromeliaceae is currently placed in the order Poales.

Subfamilies.

The family Bromeliaceae is organized into eight subfamilies:  Bromeliaceae were originally split into three subfamilies based on morphological seed characters: Bromelioideae (seeds in baccate fruits), Tillandsioideae (plumose seeds), and Pitcairnioideae (seeds with wing-like appendages). However, molecular evidence has revealed that while Bromelioideae and Tillandsioideae are monophyletic, Pitcairnioideae is, in fact, paraphyletic and should be split into six subfamilies: Brocchinioideae, Lindmanioideae, Hechtioideae, Navioideae, Pitcairnioideae, and Puyoideae.  Brocchinioideae is defined as the most basal branch of Bromeliaceae based on both morphological and molecular evidence, namely genes in chloroplast DNA.  Lindmanioideae is the next most basal branch distinguished from the other subfamilies by convolute sepals and chloroplast DNA.  Hechtioideae is also defined based on analyses of chloroplast DNA; similar morphological adaptations to arid environments also found in other groups (namely the genus "Puya)" are attributed to convergent evolution.  Navioideae is split from Pitcairnioideae based on its cochlear sepals and chloroplast DNA.  Puyoideae has been re-classified multiple times and its monophyly remains controversial according to analyses of chloroplast DNA.

Cultivation and uses.

Humans have been using bromeliads for thousands of years. The Incas, Aztecs, Maya and others used them for food, protection, fiber and ceremony, just as they are still used today. European interest began when Spanish conquistadors returned with pineapple, which became so popular as an exotic food that the image of the pineapple was adapted into European art and sculpture. In 1776, the species "Guzmania lingulata" was introduced to Europe, causing a sensation among gardeners unfamiliar with such a plant. In 1828, "Aechmea fasciata" was brought to Europe, followed by "Vriesea splendens" in 1840. These transplants were so successful, they are still among the most widely grown bromeliad varieties.  In the 19th century, breeders in Belgium, France and the Netherlands started hybridizing plants for wholesale trade. Many exotic varieties were produced until World War I, which halted breeding programs and led to the loss of some species. The plants experienced a resurgence of popularity after World War II. Since then, Dutch, Belgian and North American nurseries have greatly expanded bromeliad production.  Only one bromeliad, the pineapple ("Ananas comosus"), is a commercially important food crop. Bromelain, a common ingredient in meat tenderizer, is extracted from pineapple stems. Many other bromeliads are popular ornamental plants, grown as both garden and houseplants.  Bromeliads are important food plants for many peoples. For example, the Pima of Mexico occasionally consume flowers of "Tillandsia erubescens" and "T. recurvata" due to their high sugar content; in Argentina and Bolivia, the shoot apices of "T. rubella" and "T. maxima" are consumed; in Venezuela, indigenous coastal tribes eat a sour-tasting but sweet-smelling berry, known as 'Maya', of "Bromelia chrysantha" as a fruit or in fermented beverages.

Collectors.

Édouard André was a French collector/explorer whose many discoveries of bromeliads in the Cordilleras of South America would be influential on horticulturists to follow. He served as a source of inspiration to 20th-century collectors, in particular Mulford B. Foster and Lyman Smith of the United States and Werner Rauh of Germany and Michelle Jenkins of Australia.

The Bromeliaceae (the bromeliads) is a family of monocot flowering plants of 75 genera and around 3590 known species native mainly to the tropical Americas, with a few species found in the American subtropics and one in tropical west Africa, "Pitcairnia feliciana".

凤梨科(学名:)为单子叶植物禾本目的一科,多于地面生长或附生,有者可高达10米以上,部分作为观赏花卉,也有用于生产水果(-{zh-cn:菠萝; zh-tw:凤梨; zh-hk:菠萝; zh-sg:黄梨;}-;"")或纤维的。在自然环境下,观赏凤梨绝大多数都是「着生」而非「寄生」于大型树之上方,并且和许多植物如兰科植物等混合生长。根系看似不发达,却具有强大的附着力,可以轻易将植物体固着在树干上方。


Design.

The external iSight's 1⁄4-inch color CCD sensor has 640×480-pixel VGA resolution, with a custom-designed three-part F/2.8 lens with two aspherical elements. It features autoexposure, autofocusing from 50 mm to infinity, and video capture at 30 frames per second in 24-bit color with a variety of shutter speeds. However, the iSight has an image delay of approximately 120 ms.  The iSight incorporates internal microphones with dual-element noise suppression. The actual camera only takes up one-quarter of the unit; the remaining space is primarily occupied by its two microphones and mounting socket.  The iSight camera weighs 2.3 ounces (63.8 grams). It uses a single FireWire 400 (IEEE 1394a) cable (included) for audio, video and power. Four camera mounts, a plastic tube carrying case and a FireWire camera mount adapter are also included. The user can select the mounting bracket most appropriate for their monitor or other mounting surface. It is fully compatible with its native macOS, as well as partially compatible with the Microsoft Windows and Linux operating systems.  The iSight has a small green LED that illuminates when the camera is in use. It also has an iris that closes by twisting the front of the camera.

Built-in iSight.

Although external and internal iSights have significant differences, Apple has used the "iSight" name to brand its built-in video camera found in their MacBook (Includes Redesigned MacBook), MacBook Air and MacBook Pro notebook computers, iMac desktop computers produced since late 2005 and the LED Cinema Display. While the external iSight is similar to the built-in iSight, the built-in iSight uses an internal USB 2.0 interface and not the FireWire 400 (IEEE 1394a) interface used by the external iSight camera. Further, the built-in iSight has a plastic lens, is fixed-focus, and uses a CMOS active pixel sensor, rather than the CCD used in the external iSight. With the LED-Backlit MacBook Pros, Apple has moved to using a sensor capable of 1280x1024 pixels. The built-in iSight can also be used in the Photo Booth application on macOS and iOS.  In 2011, the iSight branding on cameras built-in to displays on the MacBook Pro and iMac was renamed to FaceTime camera. The FaceTime HD cameras included with the 2011 and later models of the MacBook Pro and iMac can output 720p high-definition video. The iMac Pro, released in December 2017, introduced a newer generation FaceTime HD camera which now outputs 1080p video.

Security concerns.

Some MacBooks are affected by the iSeeYou vulnerability, potentially allowing their iSight cameras to record the user without the user's knowledge.

iSight on Linux.

Linux kernel 3.0+ internally contains the driver for the iSight camera.  For previous versions of the kernel, one has to manually take out the firmware from Apple's driver through a specific program. This is because the Apple driver cannot be deployed inside a Linux distribution, the cause being legal issues. This lack of native support in the kernel for iSight persists on MacBook 2.1.

iSight Camera vs. FaceTime Camera.

The June 2010 release of the iPhone 4, where Apple introduced the FaceTime communication platform, also involved them naming the integrated front-facing camera on the device a "FaceTime Camera". All subsequent devices and models, including smartphones and personal computers, released after this announcement had the camera branded as FaceTime cameras.  In March 2012, with the release of the third generation iPad, Apple re-introduced the iSight camera branding for the "rear" camera on iPhone and iPod Touch releases (retroactively, in the cases of older models still being sold at the time). Apple would once again discontinue use of the iSight branding in 2014, starting with the release of the iPhone 6.  In general usage the iSight rear camera is used to take higher-resolution photos in scenarios where better quality is usually desired, whereas the front-facing camera is used for lower-resolution casual video conversations using the FaceTime communication platform.

iSight is a brand name used by Apple Inc. to refer to cameras on various devices. The name was originally used for the external iSight webcam, which retailed for US$149, connected to a computer via a FireWire cable, and came with a set of mounts to place it atop any then current Apple display, laptop computer, all-in-one desktop computer, or flat surface.

iSight是一种由苹果公司所制造的摄像头。iSight分为内置式和外接式两种,外接式iSight通过FireWire连接,可以挂载在目前苹果公司的笔记型电脑、整合式台式电脑,以及显示器上。