title: Chevrolet Tahoe

text: In Brazil the Tahoe GMT400 was sold under the name of "Grand Blazer", sourced from Argentina with rear-wheel drive only, regionally-sourced 6-cylinder engines (the late-type 4.1 M.P.F.I. Chevrolet straight-6 as the only gasoline-powered option and the 4.2L MWM Sprint 6.07T for those who preferred Diesel) and manual transmission. The GMT400 is used by Brazilian elite police units, such as the BOPE (Batalhão de Operações Policiais Especiais) in Rio de Janeiro and the ROTA (Rondas Ostensivas Tobias de Aguiar) and GATE (Grupo de Ações Taticas Especiais) in São Paulo. It is also used by the São Paulo State Police and the Rio Grande do Sul State Police. But as the cars grew old, the great majority of them were substituted, mainly by the smaller Chevrolet Blazer midsize SUV. The Tahoe name was not used in Brazil because it would be unfamiliar to most Brazilians since it refers to the Lake Tahoe on the border of Nevada and California.


title: Chevrolet Tahoe

text: Elsewhere in South America, Chile, has incorporated the Tahoe as a transport vehicle for the special operations unit (GOPE) of the Chilean Police (Carabineros de Chile) to carry communication equipment.


title: Chevrolet Tahoe

text: The Tahoe was also assembled in Venezuela from CKD kits for three generations, being phased out in 2014 along most of the local Chevrolet range due to unfavorable economic conditions and political circumstances. The fourth generation of the Tahoe has not been available in Venezuela.


title: Chevrolet Tahoe

text: In Ecuador, due to the tax benefits hybrid vehicles offer, the third generation of the Tahoe was offered only in the hybrid version until 2011. A review of the benefit to exclude hybrid vehicles with a displacement greater than 1.8L rendered the Tahoe Hybrid less cost-effective than the non-hybrid in Ecuador.


title: Chevrolet Tahoe

text: In North America, the Tahoe is used by many law enforcement agencies, fire departments, and EMS agencies. Prior to the announcement of the Z56 police package model the civilian base & LS models based on the GMT400 were used in police service. During the 1997 model year, the Tahoe was offered with the Z56 police option using suspension components from the discontinued 454SS truck – the first Tahoe Z56s were available only in 2WD until the GMT400 was phased out. The original prototype had rear disc brakes based on the B-body 9C1s whereas the production Z56s came with rear drum brakes. Plans for outfitting the Tahoe with the Z56 police package originated around the 1994 model year when GM broke news about phasing out its B-platform sedans (Caprice, Impala SS, Roadmaster) at the end of the 1996 model year where a replacement was imminent since GM ended production of its body-on-frame passenger sedans due to SUV sales. Since the introduction of the GMT900, Chevrolet currently offers two versions of the police package Tahoe; a four-wheel-drive version and a two-wheel-drive version. Just like the GMT400 based models civilian GMT800 Tahoe base & LS models were also used for police use until the Z56 police package option was reintroduced in 2004 late in the GMT800's life cycle by some agencies.


title: Chevrolet Tahoe

text: Chevrolet refers to the four-wheel drive (4WD) version as "Special Service Vehicle" (SSV) which has the 5W4 code. This version of the Tahoe can be used for all purposes except pursuits and high speed responses due to its high center of gravity just below the front window (height, not location), thus having a higher probability of rolling-over at high speeds. This version is preferred by agencies where snow, ice, flooding, rough terrain, and ground clearance are common issues.[34]


title: Chevrolet Tahoe

text: Chevrolet refers to the two-wheel drive (2WD) version—also known as the rear-wheel drive (RWD) version—as "Police Pursuit Vehicle" (PPV). This version be used for all purposes including pursuits and high speed responses. The center of gravity in this vehicle is lower than that of the four-wheel-drive version and the ground clearance is about 1 in (25 mm) less, with a standard rear bumper replacing the tow hitch on civilian Tahoes. Highway patrol agencies prefer the two-wheel-drive version, where pursuits and long distance responses are more common. As of the 2012 model year, the Tahoe was the last body-on-frame, rear-wheel drive police vehicle manufactured for the United States market since Ford phased out its aging Panther platform, the Volvo XC90-based Ford Police Interceptor (known as the Ford Explorer in civilian trim). Other SUVs like the Ford Expedition are used by many law enforcement and EMS agencies, but are not pursuit rated.[35]


title: Chevrolet Tahoe

text: Chevrolet built a 2015 Chevrolet Tahoe Police Patrol Vehicle that was previewed as a concept at the 2013 SEMA Show in Las Vegas. The vehicle became available in 2WD and 4WD drivetrains with orders coming in the first quarter of 2014 for special service models, followed by the orders for the police pursuit models afterwards.


title: Chevrolet Tahoe

text: The 2021 Tahoe PPV marks the most drastic change from the standard Tahoe. Rocker covers are borrowed from the GM LT4 engine found in high performance Corvettes, Camaros and Cadillacs. Engine and transmission coolers are PPV specific. Bridgestone co-developed "Firehawk Pursuit" tires with GM for the 20 inch steel wheels. 6 piston,16 inch rotor Brembo brakes are standard issue on the PPV. The suspension is lowered and further fortified. All wheel drive is standard and sent to the front as needed with a limited slip clutch in the transfer case. 160 MPH speedometer is standard and alternator almost doubles the amperage of the standard Tahoe. This version of the PPV uses the 9C1 code instead of the Z56 code.


title: Chevrolet Tahoe

text: When production of the CUCV II ended in 2000, GM redesigned it to coincide with civilian truck offerings. The CUCV nomenclature was changed to Light Service Support Vehicle in 2001. In 2005, LSSV production switched to AM General, a unit of MacAndrews and Forbes Holdings. The LSSV is a GM-built Chevrolet Silverado 1500, Chevrolet Silverado 2500 HD, Chevrolet Tahoe, or Chevrolet Suburban that is powered by 5.3 for the Tahoe, 6.0 for the Suburban, and a Duramax 6.6 liter turbo diesel engine for The pickup trucks. As GM has periodically redesigned its civilian trucks and SUVs from 2001 to the present, LSSVs have also been updated cosmetically.


title: Chevrolet Tahoe

text: The militarization of standard GM trucks/SUVs to become LSSVs includes exterior changes such as CARC paint (Forest Green, Desert Sand, or 3-color Camouflage), blackout lights, military bumpers, a brush guard, a NATO slave receptacle/NATO trailer receptacle, a pintle hook, tow shackles and a 24/12 volt electrical system. The dashboard has additional controls and dataplates. The truck also can be equipped with weapon supports in the cab, cargo tie down hooks, folding troop seats, pioneer tools, winches, and other military accessories. In the Canadian Army these vehicles are nicknamed "Milverado".


title: Chevrolet Tahoe

text: The Enhanced Mobility Package (EMP) option adds an uprated suspension, 4-wheel anti-lock brakes, a locking rear differential, beadlock tires, a tire pressure monitoring system and other upgrades. About 2,000 LSSV units have been sold to U.S. and international military and law enforcement organizations.


title: Chevrolet Tahoe

text: Effective 2018, sales of the GMC Yukon XL are reported together with the GMC Yukon. Sales figures for the Yukon XL prior to 2018 are listed with the Chevrolet Suburban.


title: Pica (disorder)

text: Pica is the eating or craving of things that are not food. It can be a disorder in itself or a sign of other cultural or medical phenomena. The ingested or craved substance may be biological, natural or manmade. The term was drawn directly from the medieval Latin word for magpie, a bird subject to much folklore regarding its opportunistic feeding behaviors.


title: Pica (disorder)

text: According to the "Diagnostic and Statistical Manual of Mental Disorders, 5th Edition" (DSM-5), pica as a standalone eating disorder must persist for more than one month at an age when eating such objects is considered developmentally inappropriate, not part of culturally sanctioned practice, and sufficiently severe to warrant clinical attention. Pica may lead to intoxication in children, which can result in an impairment of both physical and mental development. In addition, it can cause surgical emergencies to address intestinal obstructions, as well as more subtle symptoms such as nutritional deficiencies and parasitosis. Pica has been linked to other mental disorders. Stressors such as psychological trauma, maternal deprivation, family issues, parental neglect, pregnancy, and a disorganized family structure are risk factors for pica.


title: Pica (disorder)

text: Pica is most commonly seen in pregnant women, small children, and people who may have developmental disabilities such as autism. Children eating painted plaster containing lead may develop brain damage from lead poisoning. A similar risk exists from eating soil near roads that existed before the phase-out of tetraethyllead or that were sprayed with oil (to settle dust) contaminated by toxic PCBs or dioxin. In addition to poisoning, a much greater risk exists of gastrointestinal obstruction or tearing in the stomach. Another risk of eating soil is the ingestion of animal feces and accompanying parasites. Pica can also be found in animals such as dogs and cats.


title: Pica (disorder)

text: Pica is the consumption of substances with no significant nutritional value such as soap, drywall, or paint. Subtypes are characterized by the substance eaten:


title: Pica (disorder)

text: Complications may occur due to the substance consumed. For example, lead poisoning may result from the ingestion of paint or paint-soaked plaster, hairballs may cause intestinal obstruction and "Toxoplasma" or "Toxocara" infections may follow ingestion of feces or soil.


title: Pica (disorder)

text: Pica is currently recognized as a mental disorder by the "Diagnostic and Statistical Manual of Mental Disorders" (DSM-5). According to the DSM-5, mineral deficiencies are occasionally associated with pica, but biological abnormalities are rarely found. People practicing forms of pica, such as geophagy, pagophagy, and amylophagy, are more likely anemic or have low hemoglobin concentration in their blood, lower levels of red blood cells (hematocrit), or lower plasma zinc levels. Specifically, practicing geophagy is more likely to be associated with anemia or low hemoglobin. Practicing pagophagy and amylophagy is more highly associated with anemia. Additionally, children and pregnant women may be more likely to have anemia or low hemoglobin relative to the general population. Mental health conditions such as obsessive-compulsive disorder (OCD) and schizophrenia have been proposed as causes of pica. More recently, cases of pica have been tied to the obsessive–compulsive spectrum, and a move has arisen to consider OCD in the cause of pica. Sensory, physiological, cultural, and psychosocial perspectives have also been used to explain the causation of pica.


title: Pica (disorder)

text: Pica may be a cultural practice not associated with a deficiency or disorder. Ingestion of kaolin (white clay) among African-American women in the US state of Georgia shows the practice there to be a DSM-4 "culture-bound syndrome" and "not selectively associated with other psychopathology". Similar kaolin ingestion is also widespread in parts of Africa. Such practices may stem from health benefits such as the ability of clay to absorb plant toxins and protect against toxic alkaloids and tannic acids.


title: Pica (disorder)

text: No single test confirms pica, but because pica can occur in people who have lower than normal nutrient levels and poor nutrition (malnutrition), the health care provider should test blood levels of iron and zinc.


title: Pica (disorder)

text: Hemoglobin can also be checked to test for anemia. Lead levels should always be checked in children who may have eaten paint or objects covered in lead-paint dust. The healthcare provider should test for infection if the patient has been eating contaminated soil or animal waste.


title: Pica (disorder)

text: In individuals with autism, schizophrenia, and certain physical disorders (such as Kleine-Levin syndrome), non-nutritive substances may be eaten. In such instances, pica should not be noted as an additional diagnosis.


title: Pica (disorder)

text: Treatment for pica may vary by patient and suspected cause (e.g., child, developmentally disabled, pregnant, or psychogenic) and may emphasize psychosocial, environmental and family-guidance approaches; iron deficiency may be treatable through iron supplements or through dietary changes. An initial approach often involves screening for, and if necessary, treating any mineral deficiencies or other comorbid conditions. For pica that appears to be of psychogenic cause, therapy and medication such as SSRIs have been used successfully. However, previous reports have cautioned against the use of medication until all non-psychogenic causes have been ruled out.


title: Pica (disorder)

text: Looking back at the different causes of pica related to assessment, the clinician tries to develop a treatment. First, there is pica as a result of social attention. A strategy might be used of ignoring the person's behavior or giving them the least possible attention. If their pica is a result of obtaining a favorite item, a strategy may be used where the person is able to receive the item or activity without eating inedible items. The individual's communication skills should increase so that they can relate what they want to another person without engaging in this behavior. If pica is a way for a person to escape an activity or situation, the reason why the person wants to escape the activity should be examined and the person should be moved to a new situation. If pica is motivated by sensory feedback, an alternative method of feeling that sensation should be provided. Other nonmedication techniques might include other ways for oral stimulation such as gum. Foods such as popcorn have also been found helpful. These things can be placed in a "pica box" that should be easily accessible to the individual when they feel like engaging in pica.


title: Pica (disorder)

text: Behavior-based treatment options for pica can be useful for individuals who have a developmental disability or mental illness. Behavioral treatments have been shown to reduce pica severity by 80% in people with intellectual disabilities. These treatments may involve using positive reinforcement normal behavior. Many use aversion therapy, where the patient learns through positive reinforcement which foods are good and which ones they should not eat. Often, treatment is similar to the treatment of obsessive-compulsive or addictive disorders (such as exposure therapy). In some cases, treatment is as simple as addressing the fact they have this disorder and why they may have it. A recent study classified nine such classes of behavioral intervention: Success with treatment is generally high and generally fades with age, but it varies depending on the cause of the disorder. Developmental causes tend to have a lower success rate.


title: Pica (disorder)

text: The prevalence of pica is difficult to establish because of differences in definition and the reluctance of patients to admit to abnormal cravings and ingestion, thus leading to the prevalence recordings of pica among at-risk groups being in the range of 8% to 65% depending on the study. Based on compiled self-report and interview data of pregnant and postpartum women, pica is most prevalent geographically in Africa, with an estimated prevalence of 44.8%, followed by North and South America (23.0%) and Eurasia (17.5%). Factors associated with Pica in this population were determined to be anemia and low levels of education, both of which are associated with low socioeconomic backgrounds. Two studies of adults with intellectual disabilities living in institutions found that 21.8% and 25.8% of these groups had pica.


title: Pica (disorder)

text: Prevalence rates for children are unknown. Young children commonly place non-nutritious material into their mouths. This activity occurs in 75% of 12-month-old infants, and 15% of two- to three-year-old children.


title: Pica (disorder)

text: The term pica originates in the Latin word for magpie, "pīca", a bird famed for its unusual eating behaviors and believed to eat almost anything. The Latin may have been a translation of a Greek word meaning both 'magpie, jay' and 'pregnancy craving, craving for strange food'. In 13th-century Latin work, pica was referenced by the Greeks and Romans; however, it was not addressed in medical texts until 1563.


title: Pica (disorder)

text: In the southern United States in the 1800s, geophagia was a common practice among the slave population. Geophagia is a form of pica in which the person consumes earthly substances such as clay, and is particularly prevalent to augment a mineral-deficient diet. Noteworthy is the fact that kaolin was consumed by West Africans enslaved in the Southeastern United States, particularly the Georgia belt, due to the antidiarrheal qualities in the treatment of dysentery and other abdominal ailments. The practice of consuming kaolin rocks was thereafter studied scientifically, the results of which led to the subsequent pharmaceutical commercialization of kaolinite, the clay mineral contained in kaolin. Kaolinite became the active ingredient in drugs such as Kaopectate and Pepto-Bismol, although the formulations have since found additional active ingredients to replace kaolinite.


title: Pica (disorder)

text: Research on eating disorders from the 16th to the 20th centuries suggests that during that time in history, pica was regarded more as a symptom of other disorders rather than its own specific disorder. Even today, what could be classified as pica behavior is a normative practice in some cultures as part of their beliefs, healing methods, or religious ceremonies.


title: Pica (disorder)

text: Prior to the elimination of the category of "feeding disorders in infancy and early childhood", which is where pica was classified, from the DSM-5, pica was primarily diagnosed in children. However, since the removal of the category, psychiatrists have started to diagnose pica in people of all ages.


title: Pica (disorder)

text: Unlike in humans, pica in dogs or cats may be a sign of immune-mediated hemolytic anemia, especially when it involves eating substances such as tile grout, concrete dust, and sand. Dogs exhibiting this form of pica should be tested for anemia with a complete blood count or at least hematocrit levels. Although several theories have been proposed by experts to explain pica in animals, insufficient evidence exists to prove or disprove any of them.


title: Michael Ballack

text: Michael Ballack (; born 26 September 1976) is a German former professional footballer. He is among the top goal scorers in the history of the German national team. Ballack wore the number 13 shirt for every team he has played for, except 1. FC Kaiserslautern. He was selected by Pelé as one of FIFA's 100 Greatest Living Players, and as the UEFA Club Midfielder of the Year in 2002. He won the German Footballer of the Year award three times – in 2002, 2003 and 2005. Ballack was known for his passing range, powerful shot, physical strength and commanding presence in midfield.


title: Michael Ballack

text: Ballack began his career as a youth at enterprise sports community BSG Motor "Fritz Heckert" Karl-Marx-Stadt in 1983. He then joined the youth department of football club FC Karl-Marx-Stadt. Ballack made his debut for Germany's under-21 side on 26 March 1996. Although the team were relegated in his first season, his performances in the Regionalliga the following season led to a transfer to 1. FC Kaiserslautern in 1997. He won the Bundesliga in his first season at the club, his first major honour. He became a first team regular in 1998–99 season and also earned his first senior national cap for Germany. He moved to Bayer Leverkusen for €4.1 million in 1999. The 2001–02 season saw him win a slew of runners-up medals: Bayer Leverkusen finished second in the Bundesliga, DFB-Pokal, UEFA Champions League and Germany lost to Brazil in the 2002 World Cup Final.


title: Michael Ballack

text: A €12.9 million move to Bayern Munich led to further honours: the team won the Bundesliga and DFB-Pokal double in 2003, 2005 and 2006. Ballack had become a prolific goalscorer from midfield, scoring 58 goals for Bayern between 2002 and 2006. He joined Premier League club Chelsea in mid-2006 and won English honours in his first season at the club. Injury ruled him out of much of 2007, but he returned the following season to help Chelsea reach their first ever Champions League final. He also went on to win the FA Cup again in 2009 and then once more as part of a league and cup double in 2010.


title: Michael Ballack

text: Internationally, Ballack has played in the UEFA European Football Championship in 2000, 2004 and 2008, and the FIFA World Cup in 2002 and 2006. Jürgen Klinsmann appointed him captain of the national team in 2004. Ballack scored consecutive game-winning goals in the quarter-final and semi-final to help his country to the 2002 World Cup final and led his team to the semi-finals of the 2006 World Cup and the Euro 2008 final.


title: Michael Ballack

text: Ballack was born on 26 September 1976 in Görlitz, a town in Bezirk Dresden, East Germany (now Saxony, Germany). He is the only child of Stephan Ballack, an engineer, and his wife Karin, a secretary. The family moved to Chemnitz (then called Karl-Marx-Stadt) when Ballack was very young and it was there that he started to play football. He first began playing football for sports community.


title: Michael Ballack

text: Ballack's parents sent him to train with sports community BSG Motor "Fritz Heckert" Karl-Marx-Stadt at the age of seven. Ballack was praised by coach Steffen Hänisch. Hänisch was particularly impressed by the well-developed technique for Ballack's age and his ability to shoot with both feet. Ballack was then allowed to attend the elite Children and Youth Sports School (KSJ) "Emil Wallner" in Karl-Marx-Stadt. He then joined the larger and more promoted football club FC Karl-Marx-Stadt (renamed Chemnitzer FC in 1990) in 1988. The father of Ballack had played second-division football himself in Germany.


title: Michael Ballack

text: In 1995, Ballack earned his first professional contract, thanks to his performances in the role of central midfielder. He was dubbed the "Little Kaiser", in reference to Franz Beckenbauer, who was nicknamed ""Der Kaiser"". His professional debut came on 4 August 1995, on the first day of the new 2. Bundesliga season. Chemnitz lost the game 2–1, against VfB Leipzig. At the end of the season, during which Ballack made 15 appearances, Chemnitz were relegated to the multi-tiered, regional third division. The following season, Ballack became a regular first-team player as Chemnitz missed out on an immediate return to the Bundesliga. He did not miss a game and scored ten goals for the "Sky Blues". It was not enough for Chemnitz to be promoted, but in the summer of 1997, coach Otto Rehhagel of just-promoted 1. FC Kaiserslautern signed Ballack at their return to top flight football.


title: Michael Ballack

text: It was during the seventh match of the 1997–98 Bundesliga season, away to Karlsruhe, that Rehhagel decided to give Ballack his first Bundesliga appearance, substituting him onto the field for the final five minutes of the encounter. On 28 March 1998, Ballack made his first-team debut-start against Bayer Leverkusen.


title: Michael Ballack

text: Ballack made 16 appearances for his new team during the season as the club became the first-ever newly promoted team to lift the Bundesliga title. In the following season, Ballack became both a regular member of the team (he made 30 appearances, scoring 4 goals in the league) and one of the side's leading players. Kaiserslautern reached the quarter finals of the Champions League, but were eliminated by Bayern Munich.


title: Michael Ballack

text: It was at Bayer Leverkusen that Ballack made his breakthrough. Coaches Christoph Daum and Klaus Toppmöller granted him an attacking role in the midfield. Ballack was instrumental to the success of Leverkusen, scoring 27 goals in the league and nine in Europe over the course of his three seasons at the BayArena.


title: Michael Ballack

text: In 2000, Bayer Leverkusen needed only a draw against minnows SpVgg Unterhaching to win the Bundesliga title, but an own goal by Ballack helped send the team to a crushing 0–2 defeat, while Bayern Munich clinched the title with a 3–1 victory over Werder Bremen. The 2001–02 season was a disappointing one for Bayer Leverkusen. In the Bundesliga, the team surrendered a five-point lead at the top of the table over the last three games of the season to finish second behind Borussia Dortmund; lost the UEFA Champions League final 2–1 to Real Madrid; and lost the DFB-Pokal final 4–2 to Schalke 04. These three runner-up finishes were dubbed a "Treble Horror": Bayer Leverkusen was dubbed "Bayer Neverkusen" in English, while the German nickname became "Vizekusen". Ballack and Leverkusen teammates Bernd Schneider, Carsten Ramelow and Oliver Neuville were also beaten finalists with Germany in the 2002 FIFA World Cup, although Ballack was suspended for the final itself. Ballack finished with 17 league goals and his performance over the season led to him being voted into the UEFA.com users' Team of 2002 as well as being named German Footballer of the Year.


title: Michael Ballack

text: In spite of Real Madrid's interest, Ballack decided to sign with Bayern Munich in a €12.9 million deal in 2002 after his impressive performances in the World Cup. In his first season with the club, Bayern won the Bundesliga with 75 points as well as the DFB-Pokal, with Ballack scoring twice and defeating former club 1. FC Kaiserslautern in the latter's final. In his second season, however, Bayern lost both their Bundesliga and DFB-Pokal crowns to Werder Bremen.


title: Michael Ballack

text: In his third season with the Bavarians, Ballack enjoyed success in the 2004–05 season as Bayern Munich completed another double. New coach Felix Magath stated he was the only automatic starter in their midfield. In four seasons at Bayern, Ballack won three Bundesliga and DFB-Pokal doubles, scoring 44 goals in 107 Bundesliga matches. Between 1998 and 2005, Ballack scored 61 goals in total in the domestic league.


title: Michael Ballack

text: Ballack's critics, however, noted his frequent "choking" in important Champions League matches. This resulted in open public criticism from club general manager Uli Hoeneß, communications director Karl-Heinz Rummenigge and club president Franz Beckenbauer, all former Bayern players. Beckenbauer later went as far as to accuse Ballack of "saving his strength" for prospective employers after Ballack turned in an average performance in the 2006 DFB-Pokal final against Eintracht Frankfurt.


title: Michael Ballack

text: Ballack agreed to join English Premier League club Chelsea on a free transfer on 15 May 2006. During his last season with Bayern, there were rumours of interest from Manchester United, Real Madrid, Internazionale and Milan, but Ballack instead chose to go to Stamford Bridge. Shortly after arriving at Chelsea, Ballack stated that he hoped to end his career at Chelsea.


title: Michael Ballack

text: Ballack's debut for Chelsea came on 31 July 2006, during a practice match at UCLA's intramural football pitch. Chelsea presented him to the media the following day where the club also gave him his favoured number 13 shirt, worn throughout his career. Upon doing so, William Gallas, who previously wore the number 13 shirt for Chelsea, was given the number 3 shirt. This move created animosity between Gallas and the club as Gallas felt that he was underappreciated. On 27 August 2006, Ballack made his Premier League debut for Chelsea against Blackburn Rovers. On 12 September, he scored his first goal for the club on his Champions League debut against Werder Bremen.


title: Michael Ballack

text: He received the first straight red card of his career in Chelsea's 1–0 win over Liverpool on 17 September 2006, after being judged to have stamped on Mohamed Sissoko's leg. Ballack scored his first Premier League goal on 21 October 2006 against Portsmouth at Stamford Bridge with a header. His first FA Cup goal came in the 109th minute in the semi-final against Blackburn on 15 April 2007. This goal resulted in Chelsea progressing into the FA Cup final. He scored eight goals in all competitions for the club in the 2006–07 season, including a free-kick against Everton at Goodison Park, as well as a half-volley against Porto which sent Chelsea through to the quarter-finals of the Champions League. Throughout his first season at Chelsea, Ballack was criticised for his lethargic performances – for playing as though he had "a huge cigar in his mouth".


title: Michael Ballack

text: On 29 April 2007, Chelsea released a statement on their official website, informing fans that Ballack had undergone ankle surgery in Munich. As a result, Ballack did not play in the FA Cup final against Manchester United, which Chelsea won 1–0 through Didier Drogba's extra time goal. This was Ballack's second trophy this season, his first being the League Cup, the final of which he started.


title: Michael Ballack

text: Despite persistent rumours in the summer 2007 transfer window, Ballack denied that he wanted to leave and no such move materialised. Chelsea left Ballack out of their Champions League squad for the 2007–08 group stage as they realised that his injury would prevent him from playing any useful part and preferred to select the fully fit Steve Sidwell. The German international had an ankle operation in the summer and Chelsea could not take the risk of him not regaining full fitness before the end of the group stage. Thus, Ballack could not play in the Champions League before the knockout stages began in February. The club was only able to select 23 out of a possible 25 players for their Champions League squad due to the new UEFA regulations on "association-trained players" and "club-trained players". Due to this regulation, Chelsea were also unable to select young player Scott Sinclair and could only pick 23 players as their only "club-trained player" was John Terry. For this reason, it was deemed unwise to gamble on Ballack being fit at some point.


title: Michael Ballack

text: Ballack made his return to the side in Chelsea's 2–0 League Cup win over Liverpool on 19 December 2007. Ballack tallied an assist late in the game to striker Andriy Shevchenko. On 26 December 2007, Ballack made his Premier League return in a thrilling game against Aston Villa which ended 4–4. He came on for Frank Lampard in the 26th minute after the latter had picked up a thigh injury. In first-half stoppage time, he won a penalty after being brought down in the box by Zat Knight, which Andriy Shevchenko converted. In the 88th minute, with the score tied at 3–3, Ballack stepped up to take a free-kick, which he buried into the bottom left corner of the goal, but the match ended in a 4–4 draw.


title: Michael Ballack

text: Ballack captained the Chelsea team in the absence of captain John Terry and vice-captain Frank Lampard in a 2–1 win over Newcastle United on 29 December 2007. Ballack then played his 50th game in a Chelsea shirt in a 2–1 win against Fulham in which he scored the winning goal for Chelsea. He also scored the only goal that won the match for Chelsea against Reading to extend the blues' winning streak to a record of nine. And, on 5 March 2007, he scored again, this time against Olympiacos in the Champions League round of 16 in a 3–0 win. He scored the winning goal in the 2–0 win in the second leg of the quarter-finals against Fenerbahçe, a victory that secured Chelsea a place in the semi-finals.


title: Michael Ballack

text: Ballack continued to score vital goals and, on 26 April 2008, he scored a header and a penalty to give Chelsea a 2–1 win over Manchester United. He was named Man of The Match for his performance. It brought the two teams level in the race for the Premier League title only two matchdays before the end of the season.


title: Michael Ballack

text: The season ended on a low note for Ballack as Chelsea finished runners-up in the League Cup, Premier League and Champions League. This completed another treble horror for Ballack and his club. On 29 June 2008, Germany, captained by Ballack, lost to Spain 1–0 in the final of UEFA Euro 2008. This became the second season in Ballack's career after 2002 that he was runner-up for four major trophies.


title: Michael Ballack

text: The 2008–09 season started well for Ballack, as he set up Joe Cole to score the first goal in a 4–0 win over Portsmouth in the first game of the season. Ballack was injured shortly after missing the games against Manchester United, Liverpool and Arsenal. Ballack's return from injury has been a lift for Chelsea as he set up Deco to score a scissor kick in a 2–0 win against Bolton Wanderers. Ballack's first goal of the '09 season came against Southend United in their FA Cup replay, a match which Chelsea went on to win 4–1. Ballack's first Premier League goal of the 2008–09 season came on 11 April 2009 in a match against Bolton, ending 4–3 for Chelsea. He came on as a second-half substitute as Chelsea won the 2009 FA Cup final. On 2 June 2009, Ballack signed a one-year contract extension with Chelsea.


title: Michael Ballack

text: In Chelsea's second game of the season, away at Sunderland, Ballack scored his first goal of the 2009–10 campaign in their 3–1 win. Ballack also scored against Burnley in a 3–0 win. Ballack made his first Champions League appearance for the season against Porto. On 20 September 2009, he scored his third league goal, against Tottenham. On 17 January 2010, he scored his fourth league goal and third assist in a 7–2 win against Sunderland. In Chelsea's fifth round FA Cup tie against Cardiff City, Ballack scored the goal which put "the Blues" back in front; Chelsea ultimately won 4–1.


title: Michael Ballack

text: Ballack was sent off in Chelsea's 4–2 defeat against Manchester City on 27 February 2010. Chelsea went on to win the 2009–10 Premier League, Ballack's first league title in England. He also started as Chelsea were victorious against Portsmouth in the 2010 FA Cup final, however he would come off injured shortly before half-time after a tackle by Kevin-Prince Boateng. As a result of the injury, Ballack was not able to participate in the 2010 World Cup.


title: Michael Ballack

text: On 9 June 2010, it was announced that Ballack, along with teammates Joe Cole and Juliano Belletti, would leave Chelsea on a free transfer after his contract was not renewed. It was reported that while manager Carlo Ancelotti wanted to retain Ballack, club owner Roman Abramovich was only willing to offer a one-year deal due to Ballack's age. As of December 2012, Ballack had the lowest loss record of any player with more than 100 appearances in the Premier League, losing just 10 of his 105 appearances.


title: Michael Ballack

text: On 25 June 2010, Ballack signed a two-year contract with former club Bayer Leverkusen. On 19 August 2010, he scored the first goal for Leverkusen in a 3–0 win against Tavriya Simferopol in the UEFA Europa League qualifiers. On 6 October 2010, it was announced that Ballack would not play again in 2010 at the club or international level due to a shin injury sustained 11 September 2010 in a Bundesliga match against Hannover 96.


title: Michael Ballack

text: On 20 February 2011, Ballack made his return from injury, coming on as a substitute for Simon Rolfes against VfB Stuttgart; Leverkusen won the match 4–2. Ballack scored his second Europa League goal against Metalist Kharkiv, a match Leverkusen won 2–0 and the two-legged tie 6–0 on aggregate to progress to the round of 16. Ballack played the full 90 minutes against Schalke 04, assisting Eren Derdiyok's goal in an eventual 2–0 victory.


title: Michael Ballack

text: Ballack announced his retirement on 2 October 2012. He had been in talks with Major League Soccer's Montreal Impact and A-League club Western Sydney Wanderers.


title: Michael Ballack

text: On 5 June 2013, Ballack played a farewell match at Leipzig's Red Bull Arena. The match was won by a World XI 4–3 against the "Friends of Ballack", with Ballack scoring his second hat-trick in his career. First he scored two goals with "Friends of Ballack" in the first half and scored his third goal and the winner in the second half for the World XI. Participants in the match included former teammates and friends Lothar Matthäus, Didier Drogba, Miroslav Klose, Andriy Shevchenko, Phillip Lahm, Hasan Salihamidžić, Dimitar Berbatov, Michael Essien, André Schürrle, Ricardo Carvalho, Dietmar Hamann, Florent Malouda, Carsten Jancker, Torsten Frings, Jens Lehmann, Christian Wörns, Mehdi Mahdavikia and Per Mertesacker, as well as Formula 1 racing driver Michael Schumacher. The teams were coached by Ballack's former Chelsea coach José Mourinho and his former national team coach Rudi Völler.


title: Michael Ballack

text: On 26 March 1996, Ballack debuted for the Germany national under-21 team against Denmark, shortly after signing for Chemnitzer FC. In all, he played 19 matches for this side, scoring four goals. Then, following his move to 1. FC Kaiserslautern, senior team head coach Berti Vogts called him up to the squad.


title: Michael Ballack

text: Ballack's first senior Germany appearance, however, did not come until 28 April 1999, when he came on as a substitute for Dietmar Hamann in a match against Scotland.


title: Michael Ballack

text: Ballack only played 63 minutes at UEFA Euro 2000. In the 2002 FIFA World Cup, he scored in matches against the United States and South Korea during the knockout rounds as Germany reached the final. However, he was booked for a tactical foul during the semi-final match against South Korea and was suspended for the final, which Germany went on to lose 2–0 to Brazil. He was included in the World Cup All Star Team. Ballack missing the final ultimately led to a lasting revision of the yellow card amnesty rule in order "to give the best players a chance to play in the final". Following Euro 2004, Jürgen Klinsmann replaced Rudi Völler at the helm of the national team and Ballack took over from Oliver Kahn as captain. He scored three goals — all penalties — in the 2005 Confederations Cup, in which Germany were eliminated by Brazil in the semifinals.


title: Michael Ballack

text: In the 2006 World Cup, he was unable to start in Germany's first game against Costa Rica due to a calf strain, but appeared in the following five matches. Germany were eliminated in the semi-finals, but they managed to clinch third place in a match against Portugal. He was named Man of the Match in the games against Ecuador and Argentina, and was included in FIFA's World Cup All Star Team for a second consecutive time. After the tournmanent, Klinsmann stood down as national team head coach and was succeeded by assistant Joachim Löw.


title: Michael Ballack

text: Ballack started and captained Germany in their first game of Euro 2008 against Poland. He proved to be an influential figure in the midfield as Germany came back from a shock defeat to Croatia to make it to the final, scoring a free kick against Austria to secure Germany a 1–0 win and a place in the quarter-finals. In the quarter-finals, he scored a header against Portugal to make the score 3–1 in their 3–2 win after an assist by Bastian Schweinsteiger's 60th minute free-kick, helping Germany to advance to the semi-finals. Germany went on to beat Turkey 3–2 in the semifinals. Prior to the final, Ballack sustained a calf injury but eventually overcame it in time. Germany, however, ended up losing 1–0 to Spain. Nevertheless, he was named in the Squad of the Tournament.


title: Michael Ballack

text: Ballack scored four goals in the 2010 World Cup qualifiers, but missed the 2010 World Cup after suffering an ankle injury from a foul by Portsmouth's Kevin-Prince Boateng in the 2009-10 FA Cup final. Ballack did travel to South Africa to provide moral support for the national team but he departed after Philipp Lahm, who was appointed team captain due to Ballack's injury, commented after the quarter-finals that he would not relinquish the captaincy back to Ballack. Team manager Oliver Bierhoff criticized Lahm's comments and clarified the situation, saying, "Philipp Lahm is the World Cup captain and Michael Ballack is still the captain."


title: Michael Ballack

text: Germany played strongly in the tournament despite Ballack's absence, including a 4–1 win over England and a 4–0 win over Argentina en route to finishing third, thanks to emerging midfield talents such as Sami Khedira, Thomas Müller, and Mesut Özil. Former German captain Lothar Matthäus suggested that Ballack's absence had allowed these young players to blossom.


title: Michael Ballack

text: Since the 2010 World Cup qualifiers, Ballack had not been called up for any international matches. It was reported that Germany coach Joachim Löw was waiting for Ballack to retire from international football after the 2010 World Cup, however Ballack refused to give up despite a rash of injuries suffered in 2010–11 with Bayer Leverkusen. On 16 June 2011, it was announced that Ballack would no longer be a part of the national team. The German Football Association (DFB) offered him two friendlies to reach 100 matches for Germany, which he refused, accusing Löw of disrespecting him ever since his injury dating back to March 2010 and calling the invitation to compete in another two games for Germany a "farce".


title: Michael Ballack

text: Ballack organized a farewell game by himself and invited Jogi Löw and Philipp Lahm. The teams on the pit were named Worldplayers vs. Ballack and Friends. Lahm played for 90 minutes. In attendance were Boris Becker, Michael Schumacher, Lothar Matthäus and Rudi Völler.


title: Michael Ballack

text: Ballack is considered to be one of the best and versatile midfielders of his generation; he played in several midfield positions during his career, and was noted for his powerful shot with both feet. Due to his tall frame, he was also known for his ability in the air, which made him a goal threat on set pieces.


title: Michael Ballack

text: On a technical level, he was a commanding, physically strong and aggressive player, with excellent passing range, who moved the ball efficiently. The technicality and intelligence of his game was extremely high. He started his football career as a sweeper, but when he moved to Leverkusen in 1999, then-coach Christoph Daum moved him to midfield. He adapted to a deeper role during his spell at Chelsea.


title: Michael Ballack

text: In 2011, Ballack's international coach at the time, Joachim Löw, praised him, describing him as a player who "exudes authority and calm on the pitch".


title: Michael Ballack

text: Ballack's surname is of Sorbian origin. He was the only child of father Stephan, an engineer who played third-division football, and mother Karin, a secretary and swimmer.


title: Michael Ballack

text: On 14 July 2008, Ballack married his long-time girlfriend Simone Lambe. The couple had three children together: Louis (born 2001), Emilio (2002–2021), and Jordi (born 2005). The couple divorced in 2012. He dated Natacha Tannous from 2015 to 2019.


title: Michael Ballack

text: During Euro 2012, the 2014 World Cup, and Euro 2016, Ballack worked as a studio analyst for ESPN, often alongside Alexi Lalas.


title: Iron maiden

text: The iron maiden is a torture device, consisting of a solid iron cabinet with a hinged front and spike-covered interior, sufficiently tall to enclose a human being. The first stories citing the iron maiden were composed in the 18th century. The function of iron maidens closing by themselves is considered to be a myth, heightened by the belief that people of the Middle Ages were uncivilized; evidence of their actual use is difficult to find. They have become a very popular image in media involving the Middle Ages.


title: Iron maiden

text: Despite its reputation as a medieval instrument of torture, there is no evidence of the existence of iron maidens before the 18th century. There are, however, ancient reports of the Spartan tyrant Nabis using a similar device around 200 B.C. for extortion and murder. The Abbasid vizier Ibn al-Zayyat is said to have created a "wooden oven-like chest that had iron spikes" for torture, which would ironically be used during his own imprisonment and execution in 847.


title: Iron maiden

text: Wolfgang Schilds, a professor of criminal law, criminal law history, and philosophy of law at the Bielefeld University, has argued that putative iron maidens were pieced together from artifacts found in museums to create spectacular objects intended for (commercial) exhibition. Several 19th-century iron maidens are on display in museums around the world, including the San Diego Museum of Man, the Meiji University Museum, and several torture museums in Europe.


title: Iron maiden

text: The 19th-century iron maidens may have been constructed as probable misinterpretation of a medieval Schandmantel, which was made of wood and metal but without spikes. Inspiration for the iron maiden may also have come from the Carthaginian execution of Marcus Atilius Regulus as recorded in Tertullian's "To the Martyrs" (Chapter 4) and Augustine of Hippo's "The City of God" (I.15), in which the Carthaginians "shut him into a tight wooden box, where he was forced to stand, spiked with the sharpest nails on all sides so that he could not lean in any direction without being pierced," or from Polybius' account of Nabis of Sparta's deadly statue of his wife, the Iron Apega (earliest form of the device).


title: Iron maiden

text: The most famous iron maiden that popularized the design was that of Nuremberg, first displayed possibly as far back as 1802. The original was lost in the Allied bombing of Nuremberg in 1945. A copy "from the Royal Castle of Nuremberg", crafted for public display, was sold through J. Ichenhauser of London to the Earl of Shrewsbury in 1890 along with other torture devices, and, after being displayed at the World's Columbian Exposition, Chicago, 1893, was taken on an American tour. This copy was auctioned in the early 1960s and is now on display at the Medieval Crime Museum, Rothenburg ob der Tauber.


title: Iron maiden

text: Some historians have argued that Johann Philipp Siebenkees made up the history of the device. According to Siebenkees' colportage, it was first used on August 14, 1515, to execute a coin forger.


title: Blue Ridge Mountains

text: The Blue Ridge Mountains are a physiographic province of the larger Appalachian Mountains range. The mountain range is located in the Eastern United States, and extends 550 miles southwest from southern Pennsylvania through Maryland, West Virginia, Virginia, North Carolina, South Carolina, Tennessee, and Georgia. This province consists of northern and southern physiographic regions, which divide near the Roanoke River gap. To the west of the Blue Ridge, between it and the bulk of the Appalachians, lies the Great Appalachian Valley, bordered on the west by the Ridge and Valley province of the Appalachian range.


title: Blue Ridge Mountains

text: The Blue Ridge Mountains are known for having a bluish color when seen from a distance. Trees put the "blue" in Blue Ridge, from the isoprene released into the atmosphere. This contributes to the characteristic haze on the mountains and their perceived color.


title: Blue Ridge Mountains

text: Within the Blue Ridge province are two major national parks – the Shenandoah National Park in the northern section, and the Great Smoky Mountains National Park in the southern section. The eight national forests include George Washington and Jefferson, Cherokee, Pisgah, Nantahala and Chattahoochee. The Blue Ridge Parkway, a long scenic highway, connects the two parks and runs along the ridge crest-lines, as does the Appalachian Trail.


title: Blue Ridge Mountains

text: Although the term "Blue Ridge" is sometimes applied exclusively to the eastern edge or front range of the Appalachian Mountains, the geological definition of the Blue Ridge province extends westward to the Ridge and Valley area, encompassing the Great Smoky Mountains, the Great Balsams, the Roans, the Blacks, the Brushy Mountains (a "spur" of the Blue Ridge) and other mountain ranges.


title: Blue Ridge Mountains

text: The Blue Ridge extends as far south as Mount Oglethorpe in Georgia and as far north into Pennsylvania as South Mountain. While South Mountain dwindles to hills between Gettysburg and Harrisburg, the band of ancient rocks that form the core of the Blue Ridge continues northeast through the New Jersey and Hudson River highlands, eventually reaching The Berkshires of Massachusetts and the Green Mountains of Vermont.


title: Blue Ridge Mountains

text: The Blue Ridge contains the highest mountains in eastern North America south of Baffin Island. About 125 peaks exceed in elevation. The highest peak in the Blue Ridge (and in the entire Appalachian chain) is Mt. Mitchell in North Carolina at . There are 39 peaks in North Carolina and Tennessee higher than ; by comparison, in the northern portion of the Appalachian chain only New Hampshire's Mt. Washington rises above . Southern Sixers is a term used by peak baggers for this group of mountains.


title: Blue Ridge Mountains

text: The Blue Ridge Parkway runs along crests of the Southern Appalachians and links two national parks: Shenandoah and Great Smoky Mountains. In many places along the parkway, there are metamorphic rocks (gneiss) with folded bands of light-and dark-colored minerals, which sometimes look like the folds and swirls in a marble cake.


title: Blue Ridge Mountains

text: Most of the rocks that form the Blue Ridge Mountains are ancient granitic charnockites, metamorphosed volcanic formations, and sedimentary limestone. Recent studies completed by Richard Tollo, a professor and geologist at George Washington University, provide greater insight into the petrologic and geochronologic history of the Blue Ridge basement suites. Modern studies have found that the basement geology of the Blue Ridge is made of compositionally unique gneisses and granitoids, including orthopyroxene-bearing charnockites. Analysis of zircon minerals in the granite completed by John Aleinikoff at the U.S. Geological Survey has provided more detailed emplacement ages.


title: Blue Ridge Mountains

text: Many of the features found in the Blue Ridge and documented by Tollo and others have confirmed that the rocks exhibit many similar features in other North American Grenville-age terranes. The lack of a calc-alkaline affinity and zircon ages less than 1.2 billion years old suggest that the Blue Ridge is distinct from the Adirondacks, Green Mountains, and possibly the New York-New Jersey Highlands. The petrologic and geochronologic data suggest that the Blue Ridge basement is a composite orogenic crust that was emplaced during several episodes from a crustal magma source. Field relationships further illustrate that rocks emplaced prior to 1.078–1.064 billion years ago preserve deformational features. Those emplaced post-1.064 billion years ago generally have a massive texture and missed the main episode of Mesoproterozoic compression.


title: Blue Ridge Mountains

text: The Blue Ridge Mountains began forming during the Silurian Period over 400 million years ago. Approximately 320 million years ago, North America and Europe collided, pushing up the Blue Ridge. At the time of their emergence, the Blue Ridge were among the highest mountains in the world and reached heights comparable to the much younger Alps. Today, due to weathering and erosion over hundreds of millions of years, the highest peak in the range, Mount Mitchell in North Carolina, is only high – still the highest peak east of the Mississippi River in the US.


title: Blue Ridge Mountains

text: The English who settled colonial Virginia in the early 17th century recorded that the native Powhatan name for the Blue Ridge was "Quirank". At the foot of the Blue Ridge, various tribes including the Siouan Manahoacs, the Iroquois, and the Shawnee hunted and fished. A German physician-explorer, John Lederer, first reached the crest of the Blue Ridge in 1669 and again the following year; he also recorded the Virginia Siouan name for the Blue Ridge ("Ahkonshuck").


title: Blue Ridge Mountains

text: At the Treaty of Albany negotiated by Lieutenant Governor Alexander Spotswood (1676–1740), of Virginia with the Iroquois between 1718 and 1722, the Iroquois ceded lands they had conquered south of the Potomac River and east of the Blue Ridge to the Virginia Colony. This treaty made the Blue Ridge the new demarcation point between the areas and tribes subject to the Six Nations, and those tributaries to the Colony. When colonists began to disregard this by crossing the Blue Ridge and settling in the Shenandoah Valley in the 1730s, the Iroquois began to object, finally selling their rights to the Valley, on the west side of the Blue Ridge, at the Treaty of Lancaster in 1744.


title: Blue Ridge Mountains

text: The Blue Ridge Mountains have stunted oak and oak-hickory forest habitats, which comprise most of the Appalachian slope forests. Flora also includes grass, shrubs, hemlock and mixed-oak pine forests.


title: Blue Ridge Mountains

text: While the Blue Ridge range includes the highest summits in the eastern United States, the climate is nevertheless too warm to support an alpine zone, and thus the range lacks the tree line found at lower elevations in the northern half of the Appalachian range. Statistical modelling predicts that the alpine treeline would exist at above 7,985 feet (2434 m) in the climate zone and latitude of the southern Appalachians. The highest parts of the Blue Ridge are generally vegetated in dense Southern Appalachian spruce-fir forests.


title: Blue Ridge Mountains

text: The largest city located in the Blue Ridge Mountains is Roanoke, located in Southwest Virginia, while the largest Metropolitan Area is the Asheville metropolitan area in Western North Carolina. Other notable cities in the Blue Ridge Mountains include Charlottesville, Frederick, Hagerstown, Chambersburg, Greenville, Johnson City, and Lynchburg.


title: Higher education

text: Higher education is tertiary education leading to award of an academic degree. Higher education, also called post-secondary education, third-level or tertiary education, is an optional final stage of formal learning that occurs after completion of secondary education. It represents levels 6, 7 and 8 of the 2011 version of the International Standard Classification of Education structure. Tertiary education at a non-degree level is sometimes referred to as further education or continuing education as distinct from higher education.


title: Higher education

text: The right of access to higher education is mentioned in a number of international human rights instruments. The UN International Covenant on Economic, Social and Cultural Rights of 1966 declares, in Article 13, that "higher education shall be made equally accessible to all, on the basis of capacity, by every appropriate means, and in particular by the progressive introduction of free education". In Europe, Article 2 of the First Protocol to the European Convention on Human Rights, adopted in 1950, obliges all signatory parties to guarantee the right to education.


title: Higher education

text: Higher education, also called post-secondary education, third-level or tertiary education, is an optional final stage of formal learning that occurs after completion of secondary education. This consists of Universities, Colleges and Polytechnics that offer formal degrees beyond high school or secondary school education.


title: Higher education

text: The International Standard Classification of Education in 1997 initially classified all tertiary education together in 1997 version of its schema. They were referred to as level 5 and doctoral studies at level 6. In 2011, this was refined and expanded 2011 version of the structure. Higher education at undergraduate level, masters and doctoral level became levels 6, 7 and 8. Non-degree level Tertiary education, sometimes referred to as further education or continuing education was reordered ISCED 2011 level 4, with level 5 for some higher courses.


title: Higher education

text: In the days when few pupils progressed beyond primary education or basic education, the term "higher education" was often used to refer to secondary education, which can create some confusion. This is the origin of the term "high school" for various schools for children between the ages of 14 and 18 (United States) or 11 and 18 (UK and Australia).


title: Higher education

text: In the US, higher education is provided by universities, academies, colleges, seminaries, conservatories, and institutes of technology, and certain college-level institutions, including vocational schools, universities of applied sciences, trade schools, and other career-based colleges that award degrees. Tertiary education at non-degree level is sometimes referred to as further education or continuing education as distinct from higher education.


title: Higher education

text: Higher education includes teaching, research, exacting applied work (e.g. in medical schools and dental schools), and social services activities of universities.


title: Higher education

text: Within the realm of teaching, it includes both the "undergraduate" level, and beyond that, "graduate-level" (or "postgraduate" level). The latter level of education is often referred to as graduate school, especially in North America. In addition to the skills that are specific to any particular degree, potential employers in any profession are looking for evidence of critical thinking and analytical reasoning skills, teamworking skills, information literacy, ethical judgment, decision-making skills, fluency in speaking and writing, problem solving skills, and a wide knowledge of liberal arts and sciences.


title: Higher education

text: The oldest known institutions of higher education are credited to Dynastic Egypt, with Pr-Anx (houses of life) built as libraries and scriptorium, containing works on law, architecture, mathematics, and medicine, and involved in the training of "swnw" and "swnwt" (male and female Doctors); extant Egyptian papyri from the 3rd millennia BC, are in several collections.


title: Higher education

text: In the Greek world, Plato's Academy (c. 387 - 86 BC), Aristotle's Lycaeum (c. 334 - 86 BC) and other philosophical-mathematical schools became models for other establishments, particularly in Alexandria of Egypt, under the Ptolemies.


title: Higher education

text: In South Asia, the city of Takṣaśilā, later the great Buddhist monastery of Nālandā (c. 427 - 1197 CE), attracted students and professors even from distant regions.


title: Higher education

text: In China, the Han dynasty established chairs to teach the Five Confucean Classics, in the Grand School, Taixue (c. 3 - 1905 CE), to train cadres for the imperial administration. All these higher-learning institutions became models for other schools within their sphere of cultural influence.


title: Higher education

text: In 425 CE, the Byzantine emperor Theodosius II innovated as he established the Pandidakterion, with a faculty of 31 professors, to train public servants. In the 7th and 8th centuries, "cathedral schools" were created in Western Europe. Meanwhile, the first Medresahs were founded in the Moslem empire – initially mere primary schools in the premises of major mosques, which gradually evolved toward secondary, later higher education. However high the intellectual level of these schools could be, it would be anachronistic to call them "universities". Their organization and purposes were markedly different from the corporations of students and teachers, independent from both the Church and the State, which established themselves from the 12th century in Western Europe as "Universitas Studiorum".


title: Higher education

text: According to UNESCO and Guinness World Records, the University of al-Qarawiyyin in Fez, Morocco is the oldest existing continually operating higher educational institution in the world. and is occasionally referred to as the oldest university by scholars. Undoubtedly, there are older institutions of higher education, for example, the University of Ez-Zitouna in Montfleury, Tunis, was first established in 737.


title: Higher education

text: Since World War II, developed and many developing countries have increased the participation of the age group who mostly studies higher education from the elite rate, of up to 15 per cent, to the mass rate of 16 to 50 per cent. In many developed countries, participation in higher education has continued to increase towards universal or, what Trow later called, open access, where over half of the relevant age group participate in higher education. Higher education is important to national economies, both as an industry, in its own right, and as a source of trained and educated personnel for the rest of the economy. College educated workers have commanded a measurable wage premium and are much less likely to become unemployed than less educated workers.


title: Higher education

text: In recent years, universities have been criticized for permitting or actively encouraging grade inflation. Also, the supply of graduates in many fields of study is exceeding the demand for their skills, aggravating graduate unemployment, underemployment, overqualification, credentialism and educational inflation. Some commentators have suggested that the impact of the COVID-19 pandemic on education is rapidly making certain aspects of the traditional higher education system obsolete.


title: Higher education

text: The general higher education and training that takes place in a university, college, or Institute of technology usually includes significant theoretical and abstract elements, as well as applied aspects (although limited offerings of internships or SURF programs attempt to provide practical applications). In contrast, the vocational higher education and training that takes place at vocational universities and schools usually concentrates on practical applications, with very little theory.


title: Higher education

text: In addition, professional-level education is always included within Higher Education, and usually in graduate schools since many postgraduate academic disciplines are both vocationally, professionally, and theoretically/research oriented, such as in the law, medicine, pharmacy, dentistry, and veterinary medicine. A basic requirement for entry into these graduate-level programs is almost always a bachelor's degree, although alternative means of obtaining entry into such programs may be available at some universities. Requirements for admission to such high-level graduate programs is extremely competitive, and admitted students are expected to perform well.


title: Higher education

text: When employers in any profession consider hiring a college graduate, they are looking for evidence of critical thinking, analytical reasoning skills, teamworking skills, information literacy, ethical judgment, decision-making skills, communication skills (using both text and speech), problem solving skills, and a wide knowledge of liberal arts and sciences. However, most employers consider the average graduate to be more or less deficient in all of these areas.


title: Higher education

text: In the United States, there are large differences in wages and employment associated with different degrees. Medical doctors and lawyers are generally the highest paid workers, and have among the lowest unemployment rates. Among undergraduate fields of study, science, technology, engineering, math, and business generally offer the highest wages and best chances of employment, while education, communication, and liberal arts degrees generally offer lower wages and a lower likelihood of employment.


title: Higher education

text: Academic areas that are included within the liberal arts include great books, history, languages including English, linguistics, literature, mathematics, music, philosophy, political science, psychology, religious studies, science, environmental science, sociology and theater.


title: Higher education

text: Teaching engineering is teaching the application of scientific, economic, social, and practical knowledge in order to design, build, maintain, and improve structures, machines, devices, systems, materials and processes. It may encompass using insights to conceive, model and scale an appropriate solution to a problem or objective. The discipline of engineering is extremely broad, and encompasses a range of more specialized fields of engineering, each with a more specific emphasis on particular areas of technology and types of application. Engineering disciplines include aerospace, biological, civil, chemical, computer, electrical, industrial and mechanical.


title: Higher education

text: The performing arts differ from the plastic arts or visual arts, insofar as the former uses the artist's own body, face and presence as a medium; the latter uses materials such as clay, metal or paint, which can be molded or transformed to create a work of art.


title: Higher education

text: The plastic arts or visual arts are a class of art forms, that involve the use of materials, that can be moulded or modulated in some way, often in three dimensions. Examples are painting, sculpture, and drawing.


title: Higher education

text: Higher vocational education and training takes place at the non-university tertiary level. Such education combines teaching of both practical skills and theoretical expertise. Higher education differs from other forms of post-secondary education such as that offered by institutions of vocational education, which are more colloquially known as trade schools. Higher vocational education might be contrasted with education in a usually broader scientific field, which might concentrate on theory and abstract conceptual knowledge.


title: Higher education

text: This describes a distinct form of higher education that offers a particularly intense integration with the world of work in all its aspects (including teaching, learning, research and governance) and at all levels of the overarching Qualifications Framework of the European Higher Education Area. Its function is to diversify learning opportunities, enhance employability, offer qualifications and stimulate innovation, for the benefit of learners and society.


title: Higher education

text: The intensity of integration with the world of work (which includes enterprise, civil society and the public sector) is manifested by a strong focus on application of learning. This approach involves combining phases of work and study, a concern for employability, cooperation with employers, the use of practice-relevant knowledge and use-inspired research.


title: Higher education

text: Examples of providers of professional higher education may include graduate colleges of architecture, business, journalism, law, library science, optometry, pharmacy, public policy, human medicine, professional engineering, podiatric medicine, scientific dentistry, K-12 education, and veterinary medicine.


title: Higher education

text: A 2014 report by the Organisation for Economic Co-operation and Development states that by 2014, 84 percent of young people were completing upper secondary education over their lifetimes, in high-income countries. Tertiary-educated individuals were earning twice as much as median workers. In contrast to historical trends in education, young women were more likely to complete upper secondary education than young men. Additionally, access to education was expanding and growth in the number of people receiving university education was rising sharply. By 2014, close to 40 percent of people aged 25–34 (and around 25 percent of those aged 55–64), were being educated at university.


title: Higher education

text: The Lisbon Recognition Convention stipulates that degrees and periods of study must be recognised in all of the Signatory Parties of the convention.


title: Joey Lauren Adams

text: Joey Lauren Adams (born January 9, 1968) is an American actress and director. Adams starred in "Chasing Amy", for which she was nominated for the Golden Globe Award for Best Actress – Motion Picture Musical or Comedy, and played smaller roles in other Kevin Smith View Askewniverse films.


title: Joey Lauren Adams

text: Adams began her film career in 1977 with a small role in "". From there she began to find larger roles. In 1991, Adams appeared in "Top of the Heap", the 100th episode of "Married... with Children", and subsequently starred in its short-lived spinoff. In 1993, Adams landed her first major film role as Simone in Richard Linklater's "Dazed and Confused". The same year, she appeared in the "Saturday Night Live" spinoff film "Coneheads" as one of Connie Conehead's friends.


title: Joey Lauren Adams

text: Two years later, Adams appeared in "Mallrats", written and directed by Kevin Smith. The two started dating during the film's post-production, and their relationship provided the inspiration for Smith's next film, "Chasing Amy". The relationship did not last long, but ended on friendly terms. Meanwhile, in 1996, while Smith was finalizing the script for "Chasing Amy", Adams was cast in the slapstick comedy "Bio-Dome", which was directed by Jason Bloom. Adams played Monique, Bud Macintosh's (Pauly Shore) girlfriend.


title: Joey Lauren Adams

text: Adams played a leading role in 1997's "Chasing Amy", portraying Alyssa Jones, a lesbian who falls in love with a man, played by Ben Affleck. Later, Smith would describe "Chasing Amy" as a "sort of penance/valentine" and a "thank-you homage" to Adams. In addition to her acting work on the film, Adams wrote and performed the song "Alive" for the film's soundtrack.


title: Joey Lauren Adams

text: Adams' performance in "Chasing Amy" earned her both the 1997 Chicago Film Critics Award and Las Vegas Film Critics Society Award for Most Promising Actress, and a Golden Globe nomination for Best Actress-Motion Picture Musical or Comedy. From there, Adams was originally slated to play the female lead in Smith's next film, 1999's "Dogma", but Linda Fiorentino ultimately won the role. However, she would later make brief appearances in two other Smith projects: the 2001 film "Jay and Silent Bob Strike Back", and the 2004 animated short "", featured on the "Clerks X" DVD. In both of these appearances, Adams reprises the role of Alyssa Jones.


title: Joey Lauren Adams

text: Her post-Smith projects included playing a spunky veterinarian's assistant who falls in love with a single father (Vince Vaughn) in 1998's "A Cool, Dry Place". The following year, Adams appeared in her first big-budget Hollywood release, playing Adam Sandler's love interest in the successful comedy "Big Daddy". She then went on to appear in many smaller films, including "Beautiful" and "In the Shadows". In 2005, she had a guest role in an episode of the TV series "Veronica Mars".


title: Joey Lauren Adams

text: Also in 2006, Adams released her directorial debut film, "Come Early Morning", starring Ashley Judd, Jeffrey Donovan, Diane Ladd, Tim Blake Nelson and Laura Prepon. The film, shot on location in Little Rock, Arkansas, was selected for the 2006 Sundance Film Festival.


title: Joey Lauren Adams

text: In 2006, she, along with Lian Lunson and Nicole Holofcener, was awarded the Women in Film Dorothy Arzner Directors Award. On November 24, 2009, Interscope Records released Adams' directorial debut for a music video entitled "Belle of the Boulevard" by Dashboard Confessional.


title: Joey Lauren Adams

text: Adams returned to TV in March 2010, on the Showtime series "The United States of Tara". She appeared in six episodes as Pammy, a barmaid who falls for Buck, one of the title character's alternate personalities.


title: Joey Lauren Adams

text: Adams is also known for her distinctive voice which one film critic referred to as that of a "sex-kitten-on-helium". Regarding her voice, Adams commented: "It's not a normal voice. It doesn't fit into people's preconceptions about what a woman's voice should sound like. My mom doesn't think I have an unusual voice, though. I'm sure it's helped me get some roles. But "Chasing Amy" I almost didn't get. There was concern the voice would grate on some people, which some critics said it did." Another film critic said that whether viewers loved it or hated it, her voice had "the potential to hypnotize."


title: Joey Lauren Adams

text: Adams was born in North Little Rock, Arkansas, the youngest of three children. Her father was a lumber yard owner. Adams grew up in the Overbrook neighborhood of North Little Rock and graduated from North Little Rock Northeast High School in 1986. She announced her intention to pursue acting after one year as an exchange student in Australia. In a May 7, 1997, appearance on "The Tonight Show with Jay Leno" to promote "Chasing Amy", Adams revealed she was a niece to "Hee-Haw" cast member and ordained minister Grady Nutt.


title: Bitwise operation

text: In computer programming, a bitwise operation operates on a bit string, a bit array or a binary numeral (considered as a bit string) at the level of its individual bits. It is a fast and simple action, basic to the higher-level arithmetic operations and directly supported by the processor. Most bitwise operations are presented as two-operand instructions where the result replaces one of the input operands.


title: Bitwise operation

text: On simple low-cost processors, typically, bitwise operations are substantially faster than division, several times faster than multiplication, and sometimes significantly faster than addition. While modern processors usually perform addition and multiplication just as fast as bitwise operations due to their longer instruction pipelines and other architectural design choices, bitwise operations do commonly use less power because of the reduced use of resources.


title: Bitwise operation

text: In the explanations below, any indication of a bit's position is counted from the right (least significant) side, advancing left. For example, the binary value 0001 (decimal 1) has zeroes at every position but the first (i.e., the rightmost) one.


title: Bitwise operation

text: The bitwise NOT, or bitwise complement, is a unary operation that performs logical negation on each bit, forming the ones' complement of the given binary value. Bits that are 0 become 1, and those that are 1 become 0. For example:


title: Bitwise operation

text: The result is equal to the two's complement of the value minus one. If two's complement arithmetic is used, then codice_1.


title: Bitwise operation

text: For unsigned integers, the bitwise complement of a number is the "mirror reflection" of the number across the half-way point of the unsigned integer's range. For example, for 8-bit unsigned integers, codice_2, which can be visualized on a graph as a downward line that effectively "flips" an increasing range from 0 to 255, to a decreasing range from 255 to 0. A simple but illustrative example use is to invert a grayscale image where each pixel is stored as an unsigned integer.


title: Bitwise operation

text: A bitwise AND is a binary operation that takes two equal-length binary representations and performs the logical AND operation on each pair of the corresponding bits. Thus, if both bits in the compared position are 1, the bit in the resulting binary representation is 1 (1 × 1 = 1); otherwise, the result is 0 (1 × 0 = 0 and 0 × 0 = 0). For example:


title: Bitwise operation

text: The operation may be used to determine whether a particular bit is "set" (1) or "clear" (0). For example, given a bit pattern 0011 (decimal 3), to determine whether the second bit is set we use a bitwise AND with a bit pattern containing 1 only in the second bit:


title: Bitwise operation

text: Because the result 0010 is non-zero, we know the second bit in the original pattern was set. This is often called "bit masking". (By analogy, the use of masking tape covers, or "masks", portions that should not be altered or portions that are not of interest. In this case, the 0 values mask the bits that are not of interest.)


title: Bitwise operation

text: The bitwise AND may be used to clear selected bits (or flags) of a register in which each bit represents an individual Boolean state. This technique is an efficient way to store a number of Boolean values using as little memory as possible.


title: Bitwise operation

text: For example, 0110 (decimal 6) can be considered a set of four flags, where the first and fourth flags are clear (0), and the second and third flags are set (1). The third flag may be cleared by using a bitwise AND with the pattern that has a zero only in the third bit:


title: Bitwise operation

text: Because of this property, it becomes easy to check the parity of a binary number by checking the value of the lowest valued bit. Using the example above:


title: Bitwise operation

text: A bitwise OR is a binary operation that takes two bit patterns of equal length and performs the logical inclusive OR operation on each pair of corresponding bits. The result in each position is 0 if both bits are 0, while otherwise the result is 1. For example:


title: Bitwise operation

text: The bitwise OR may be used to set to 1 the selected bits of the register described above. For example, the fourth bit of 0010 (decimal 2) may be set by performing a bitwise OR with the pattern with only the fourth bit set:


title: Bitwise operation

text: A bitwise XOR is a binary operation that takes two bit patterns of equal length and performs the logical exclusive OR operation on each pair of corresponding bits. The result in each position is 1 if only one of the bits is 1, but will be 0 if both are 0 or both are 1. In this we perform the comparison of two bits, being 1 if the two bits are different, and 0 if they are the same. For example:


title: Bitwise operation

text: The bitwise XOR may be used to invert selected bits in a register (also called toggle or flip). Any bit may be toggled by XORing it with 1. For example, given the bit pattern 0010 (decimal 2) the second and fourth bits may be toggled by a bitwise XOR with a bit pattern containing 1 in the second and fourth positions:


title: Bitwise operation

text: Assembly language programmers and optimizing compilers sometimes use XOR as a short-cut to setting the value of a register to zero. Performing XOR on a value against itself always yields zero, and on many architectures this operation requires fewer clock cycles and memory than loading a zero value and saving it to the register.


title: Bitwise operation

text: If the set of bit strings of fixed length "n" (i.e. machine words) is thought of as an "n"-dimensional vector space formula_1 over the field formula_2, then vector addition corresponds to the bitwise XOR.


title: Bitwise operation

text: The bit shifts are sometimes considered bitwise operations, because they treat a value as a series of bits rather than as a numerical quantity. In these operations, the digits are moved, or "shifted", to the left or right. Registers in a computer processor have a fixed width, so some bits will be "shifted out" of the register at one end, while the same number of bits are "shifted in" from the other end; the differences between bit shift operators lie in how they determine the values of the shifted-in bits.


title: Bitwise operation

text: If the width of the register (frequently 32 or even 64) is larger than the number of bits (usually 8) of the smallest addressable unit, frequently called byte, the shift operations induce an addressing scheme from the bytes to the bits.


title: Bitwise operation

text: Thereby the orientations "left" and "right" are taken from the standard writing of numbers in a place-value notation, such that a left shift increases and a right shift decreases the value of the number ― if the left digits are read first, this makes up a big-endian orientation.


title: Bitwise operation

text: Disregarding the boundary effects at both ends of the register, arithmetic and logical shift operations behave the same, and a shift by 8 bit positions transports the bit pattern by 1 byte position in the following way:


title: Bitwise operation

text: In an "arithmetic shift", the bits that are shifted out of either end are discarded. In a left arithmetic shift, zeros are shifted in on the right; in a right arithmetic shift, the sign bit (the MSB in two's complement) is shifted in on the left, thus preserving the sign of the operand.


title: Bitwise operation

text: In the first case, the leftmost digit was shifted past the end of the register, and a new 0 was shifted into the rightmost position. In the second case, the rightmost 1 was shifted out (perhaps into the carry flag), and a new 1 was copied into the leftmost position, preserving the sign of the number. Multiple shifts are sometimes shortened to a single shift by some number of digits. For example:


title: Bitwise operation

text: A left arithmetic shift by "n" is equivalent to multiplying by 2 (provided the value does not overflow), while a right arithmetic shift by "n" of a two's complement value is equivalent to taking the floor of division by 2. If the binary number is treated as ones' complement, then the same right-shift operation results in division by 2 and rounding toward zero.


title: Bitwise operation

text: In a "logical shift", zeros are shifted in to replace the discarded bits. Therefore, the logical and arithmetic left-shifts are exactly the same.


title: Bitwise operation

text: However, as the logical right-shift inserts value 0 bits into the most significant bit, instead of copying the sign bit, it is ideal for unsigned binary numbers, while the arithmetic right-shift is ideal for signed two's complement binary numbers.


title: Bitwise operation

text: In this operation, sometimes called "rotate no carry", the bits are "rotated" as if the left and right ends of the register were joined. The value that is shifted into the right during a left-shift is whatever value was shifted out on the left, and vice versa for a right-shift operation. This is useful if it is necessary to retain all the existing bits, and is frequently used in digital cryptography.


title: Bitwise operation

text: "Rotate through carry" is a variant of the rotate operation, where the bit that is shifted in (on either end) is the old value of the carry flag, and the bit that is shifted out (on the other end) becomes the new value of the carry flag.


title: Bitwise operation

text: A single "rotate through carry" can simulate a logical or arithmetic shift of one position by setting up the carry flag beforehand. For example, if the carry flag contains 0, then codice_3 is a logical right-shift, and if the carry flag contains a copy of the sign bit, then codice_3 is an arithmetic right-shift. For this reason, some microcontrollers such as low end PICs just have "rotate" and "rotate through carry", and don't bother with arithmetic or logical shift instructions.


title: Bitwise operation

text: Rotate through carry is especially useful when performing shifts on numbers larger than the processor's native word size, because if a large number is stored in two registers, the bit that is shifted off one end of the first register must come in at the other end of the second. With rotate-through-carry, that bit is "saved" in the carry flag during the first shift, ready to shift in during the second shift without any extra preparation.


title: Bitwise operation

text: In C-family languages, the logical shift operators are "codice_5" for left shift and "codice_6" for right shift. The number of places to shift is given as the second argument to the operator. For example,


title: Bitwise operation

text: assigns codice_7 the result of shifting codice_8 to the left by two bits, which is equivalent to a multiplication by four.


title: Bitwise operation

text: Shifts can result in implementation-defined behavior or undefined behavior, so care must be taken when using them. The result of shifting by a bit count greater than or equal to the word's size is undefined behavior in C and C++. Right-shifting a negative value is implementation-defined and not recommended by good coding practice; the result of left-shifting a signed value is undefined if the result cannot be represented in the result type.


title: Bitwise operation

text: In C#, the right-shift is an arithmetic shift when the first operand is an int or long. If the first operand is of type uint or ulong, the right-shift is a logical shift.


title: Bitwise operation

text: The C-family of languages lack a rotate operator (although C++20 provides codice_9 and codice_10), but one can be synthesized from the shift operators. Care must be taken to ensure the statement is well formed to avoid undefined behavior and timing attacks in software with security requirements. For example, a naive implementation that left-rotates a 32-bit unsigned value codice_7 by codice_12 positions is simply


title: Bitwise operation

text: However, a shift by codice_13 bits results in undefined behavior in the right-hand expression codice_14 because codice_15 is codice_16, and codice_16 is outside the range 0–31 inclusive. A second try might result in


title: Bitwise operation

text: where the shift amount is tested to ensure that it does not introduce undefined behavior. However, the branch adds an additional code path and presents an opportunity for timing analysis and attack, which is often not acceptable in high-integrity software. In addition, the code compiles to multiple machine instructions, which is often less efficient than the processor's native instruction.


title: Bitwise operation

text: To avoid the undefined behavior and branches under GCC and Clang, the following is recommended. The pattern is recognized by many compilers, and the compiler will emit a single rotate instruction:


title: Bitwise operation

text: There are also compiler-specific intrinsics implementing circular shifts, like _rotl8, _rotl16, _rotr8, _rotr16 in Microsoft Visual C++. Clang provides some rotate intrinsics for Microsoft compatibility that suffers the problems above. GCC does not offer rotate intrinsics. Intel also provides x86 intrinsics.


title: Bitwise operation

text: In Java, all integer types are signed, so the "codice_5" and "codice_6" operators perform arithmetic shifts. Java adds the operator "codice_20" to perform logical right shifts, but since the logical and arithmetic left-shift operations are identical for signed integer, there is no "codice_21" operator in Java.


title: Bitwise operation

text: In Pascal, as well as in all its dialects (such as Object Pascal and Standard Pascal), the logical left and right shift operators are "codice_28" and "codice_29", respectively. Even for signed integers, codice_29 behaves like a logical shift, and does not copy the sign bit. The number of places to shift is given as the second argument. For example, the following assigns "x" the result of shifting "y" to the left by two bits:


title: Bitwise operation

text: Bitwise operations are necessary particularly in lower-level programming such as device drivers, low-level graphics, communications protocol packet assembly, and decoding.


title: Bitwise operation

text: Although machines often have efficient built-in instructions for performing arithmetic and logical operations, all these operations can be performed by combining the bitwise operators and zero-testing in various ways. For example, here is a pseudocode implementation of ancient Egyptian multiplication showing how to multiply two arbitrary integers codice_31 and codice_32 (codice_31 greater than codice_32) using only bitshifts and addition:


title: Bitwise operation

text: Another example is a pseudocode implementation of addition, showing how to calculate a sum of two integers codice_31 and codice_32 using bitwise operators and zero-testing:


title: Bitwise operation

text: Sometimes it is useful to simplify complex expressions made up of bitwise operations, for example when writing compilers. The goal of a compiler is to translate a high level programming language into the most efficient machine code possible. Boolean algebra is used to simplify complex bitwise expressions.


title: Bitwise operation

text: It can be hard to solve for variables in boolean algebra, because unlike regular algebra, several operations do not have inverses. Operations without inverses lose some of the original data bits when they are performed, and it is not possible to recover this missing information.


title: Bitwise operation

text: Operations at the top of this list are executed first. See the main article for a more complete list.


title: Escape velocity

text: In celestial mechanics, escape velocity or escape speed is the minimum speed needed for a free, non-propelled object to escape from the gravitational influence of a primary body, thus reaching an infinite distance from it. It is typically stated as an ideal speed, ignoring atmospheric friction. Although the term "escape velocity" is common, it is more accurately described as a speed than a velocity because it is independent of direction; the escape speed increases with the mass of the primary body and decreases with the distance from the primary body. The escape speed thus depends on how far the object has already traveled, and its calculation at a given distance takes into account that without new acceleration it will slow down as it travels—due to the massive body's gravity—but it will never quite slow to a stop.


title: Escape velocity

text: A rocket, continuously accelerated by its exhaust, can escape without ever reaching escape speed, since it continues to add kinetic energy from its engines. It can achieve escape at any speed, given sufficient propellant to provide new acceleration to the rocket to counter gravity's deceleration and thus maintain its speed.


title: Escape velocity

text: More generally, escape velocity is the speed at which the sum of an object's kinetic energy and its gravitational potential energy is equal to zero; an object which has achieved escape velocity is neither on the surface, nor in a closed orbit (of any radius). With escape velocity in a direction pointing away from the ground of a massive body, the object will move away from the body, slowing forever and approaching, but never reaching, zero speed. Once escape velocity is achieved, no further impulse need be applied for it to continue in its escape. In other words, if given escape velocity, the object will move away from the other body, continually slowing, and will asymptotically approach zero speed as the object's distance approaches infinity, never to come back. Speeds higher than escape velocity retain a positive speed at infinite distance. Note that the minimum escape velocity assumes that there is no friction (e.g., atmospheric drag), which would increase the required instantaneous velocity to escape the gravitational influence, and that there will be no future acceleration or extraneous deceleration (for example from thrust or from gravity of other bodies), which would change the required instantaneous velocity.


title: Escape velocity

text: Escape speed at a distance "d" from the center of a spherically symmetric primary body (such as a star or a planet) with mass "M" is given by the formula


title: Escape velocity

text: where "G" is the universal gravitational constant () and "g" is the local gravitational acceleration (or the surface gravity, when "d" = "r"). The escape speed is independent of the mass of the escaping object. For example, the escape speed from Earth's surface is about and the surface gravity is about 9.8 m/s (9.8 N/kg, 32 ft/s).


title: Escape velocity

text: When given an initial speed formula_2 greater than the escape speed formula_3 the object will asymptotically approach the "hyperbolic excess speed" formula_4 satisfying the equation:


title: Escape velocity

text: The existence of escape velocity is a consequence of conservation of energy and an energy field of finite depth. For an object with a given total energy, which is moving subject to conservative forces (such as a static gravity field) it is only possible for the object to reach combinations of locations and speeds which have that total energy; and places which have a higher potential energy than this cannot be reached at all. By adding speed (kinetic energy) to the object it expands the possible locations that can be reached, until, with enough energy, they become infinite.


title: Escape velocity

text: For a given gravitational potential energy at a given position, the escape velocity is the minimum speed an object without propulsion needs to be able to "escape" from the gravity (i.e. so that gravity will never manage to pull it back). Escape velocity is actually a speed (not a velocity) because it does not specify a direction: no matter what the direction of travel is, the object can escape the gravitational field (provided its path does not intersect the planet).


title: Escape velocity

text: An elegant way to derive the formula for escape velocity is to use the principle of conservation of energy (for another way, based on work, see below). For the sake of simplicity, unless stated otherwise, we assume that an object will escape the gravitational field of a uniform spherical planet by moving away from it and that the only significant force acting on the moving object is the planet's gravity. Imagine that a spaceship of mass "m" is initially at a distance "r" from the center of mass of the planet, whose mass is "M", and its initial speed is equal to its escape velocity, formula_6. At its final state, it will be an infinite distance away from the planet, and its speed will be negligibly small. Kinetic energy "K" and gravitational potential energy "U" are the only types of energy that we will deal with (we will ignore the drag of the atmosphere), so by the conservation of energy,


title: Escape velocity

text: We can set "K" = 0 because final velocity is arbitrarily small, and "U" = 0 because final distance is infinity, so


title: Escape velocity

text: The same result is obtained by a relativistic calculation, in which case the variable "r" represents the "radial coordinate" or "reduced circumference" of the Schwarzschild metric.


title: Escape velocity

text: Defined a little more formally, "escape velocity" is the initial speed required to go from an initial point in a gravitational potential field to infinity and end at infinity with a residual speed of zero, without any additional acceleration. All speeds and velocities are measured with respect to the field. Additionally, the escape velocity at a point in space is equal to the speed that an object would have if it started at rest from an infinite distance and was pulled by gravity to that point.


title: Escape velocity

text: In common usage, the initial point is on the surface of a planet or moon. On the surface of the Earth, the escape velocity is about 11.2 km/s, which is approximately 33 times the speed of sound (Mach 33) and several times the muzzle velocity of a rifle bullet (up to 1.7 km/s). However, at 9,000 km altitude in "space", it is slightly less than 7.1 km/s. Note that this escape velocity is relative to a non-rotating frame of reference, not relative to the moving surface of the planet or moon (see below).


title: Escape velocity

text: The escape velocity is independent of the mass of the escaping object. It does not matter if the mass is 1 kg or 1,000 kg; what differs is the amount of energy required. For an object of mass formula_9 the energy required to escape the Earth's gravitational field is "GMm / r", a function of the object's mass (where "r" is radius of the Earth, nominally 6,371 kilometres (3,959 mi), "G" is the gravitational constant, and "M" is the mass of the Earth, ). A related quantity is the specific orbital energy which is essentially the sum of the kinetic and potential energy divided by the mass. An object has reached escape velocity when the specific orbital energy is greater than or equal to zero.


title: Escape velocity

text: An alternative expression for the escape velocity formula_6 particularly useful at the surface on the body is:


title: Escape velocity

text: where "r" is the distance between the center of the body and the point at which escape velocity is being calculated and "g" is the gravitational acceleration at that distance (i.e., the surface gravity).


title: Escape velocity

text: For a body with a spherically-symmetric distribution of mass, the escape velocity formula_6 from the surface is proportional to the radius assuming constant density, and proportional to the square root of the average density ρ.


title: Escape velocity

text: Note that this escape velocity is relative to a non-rotating frame of reference, not relative to the moving surface of the planet or moon, as explained below.


title: Escape velocity

text: The escape velocity "relative to the surface" of a rotating body depends on direction in which the escaping body travels. For example, as the Earth's rotational velocity is 465 m/s at the equator, a rocket launched tangentially from the Earth's equator to the east requires an initial velocity of about 10.735 km/s "relative to the moving surface at the point of launch" to escape whereas a rocket launched tangentially from the Earth's equator to the west requires an initial velocity of about 11.665 km/s "relative to that moving surface". The surface velocity decreases with the cosine of the geographic latitude, so space launch facilities are often located as close to the equator as feasible, e.g. the American Cape Canaveral (latitude 28°28′ N) and the French Guiana Space Centre (latitude 5°14′ N).