Life cycle.

"Hydrangea" flowers are produced from early spring to late autumn; they grow in flowerheads (corymbs or panicles) most often at the ends of the stems. Typically the flowerheads contain two types of flowers: small non-showy flowers in the center or interior of the flowerhead, and large, showy flowers with large colorful sepals (tepals). These showy flowers are often extended in a ring, or to the exterior of the small flowers. Plants in wild populations typically have few to none of the showy flowers, while cultivated hydrangeas have been bred and selected to have more of the larger type flowers.  There are two flower arrangements in hydrangeas with corymb style inflorescences, which includes the commonly grown "bigleaf hydrangea"—"Hydrangea macrophylla". Mophead flowers are large round flowerheads resembling pom-poms or, as the name implies, the head of a mop. In contrast, lacecap flowers bear round, flat flowerheads with a center core of subdued, small flowers surrounded by outer rings of larger flowers having showy sepals or tepals. The flowers of some rhododendrons and viburnums can appear, at first glance, similar to those of some hydrangeas.  Hydrangea flowers, when cut, dehydrate easily and wilt very fast due to the large surface area of the petals. A wilted hydrangea may have its hydration restored by first having its stem immersed in boiling water; as the petals of the hydrangea can also absorb water, the petals may then be immersed, in room-temperature water, to restore the flower's hydration.

Colours and soil acidity.

In most species the flowers are white, but in some species (notably "H. macrophylla"), can be blue, red, pink, light purple, or dark purple. In these species, floral color change occurs due to the presence of aluminium ions which are available or tied up depending upon the soil pH. For "H. macrophylla" and "H. serrata" cultivars, the flower color can be determined by the relative acidity of the soil: an acidic soil (pH below 7), will have available aluminum ions and typically produce flowers that are blue to purple, whereas an alkaline soil (pH above 7) will tie up aluminum ions and result in pink or red flowers. This is caused by a color change of the flower pigments in the presence of aluminium ions which can be taken up into hyperaccumulating plants. Lowering the pH of potting soils or mixes usually does not change the flower color to blue, because these soils have no aluminum ions. The ability to blue or pink a hydrangea is also influenced by the cultivar. Some plants are selected for their ability to be blued, while others are bred and selected to be red, pink or white. The flower color of most other Hydrangea species is not affected by aluminum and cannot be changed or shifted. Hydrangeas are also nicknamed 'Change Rose'.

Fossil record.

"Hydrangea alaskana" is a fossil species recovered from paleogene strata in Jaw Mountain Alaska.  Four fossil seeds of "Hydrangea polonica" have been extracted from borehole samples of the Middle Miocene fresh water deposits in Nowy Sacz Basin, West Carpathians, Poland.

Cultivation and uses.

Hydrangeas are popular ornamental plants, grown for their large flowerheads, with "Hydrangea macrophylla" being by far the most widely grown with over 600 named cultivars, many selected to have only large sterile flowers in the flowerheads. Hydrangea macrophylla, also known as Bigleaf Hydrangea, can be broken up into two main categories; Mophead Hydrangea & Lacecap Hydrangea. Some are best pruned on an annual basis when the new leaf buds begin to appear. If not pruned regularly, the bush will become very 'leggy', growing upwards until the weight of the stems is greater than their strength, at which point the stems will sag down to the ground and possibly break. Other species only flower on 'old wood'. Thus new wood resulting from pruning will not produce flowers until the following season.  Hydrangea root and rhizome are indicated for treatment of conditions of the urinary tract in the PDR for Herbal Medicine and may have diuretic properties. Hydrangeas are moderately toxic if eaten, with all parts of the plant containing cyanogenic glycosides. "Hydrangea paniculata" is reportedly sometimes smoked as an intoxicant, despite the danger of illness and/or death due to the cyanide.  The flowers on a hydrangea shrub can change from blue to pink or from pink to blue from one season to the next depending on the acidity level of the soil. Adding organic materials such as coffee grounds, citrus peel or eggshells will increase acidity and turn hydrangea flowers blue, as described in an article on Gardenista. A popular pink hydrangea called Vanilla Strawberry has been named "Top Plant" by the "American Nursery and Landscape Association".  The hybrid "Runaway Bride Snow White", bred by Ushio Sakazaki from Japan, was named Plant of the Year at the 2018 RHS Chelsea Flower Show.

In culture.

In Japan, "ama-cha",甘茶 meaning sweet tea, is another herbal tea made from "Hydrangea serrata", whose leaves contain a substance that develops a sweet taste (phyllodulcin). For the fullest taste, fresh leaves are crumpled, steamed, and dried, yielding dark brown tea leaves. Ama-cha is mainly used for "kan-butsu-e" (the Buddha bathing ceremony) on April 8 every year—the day thought to be Buddha's birthday in Japan. During the ceremony, Ama-cha is poured over a statue of Buddha and served to people in attendance. A legend has it that on the day Buddha was born, nine dragons poured Amrita over him; ama-cha is substituted for Amrita in Japan.  In Korean tea, "Hydrangea serrata" (hangul:산수국 hanja:) is used for an herbal tea called "sugukcha" (수국차) or "ilsulcha" (이슬차).  The pink hydrangea has risen in popularity all over the world, but especially in Asia. Pink hydrangeas have many different meanings, but generally mean, "You are the beat of my heart," as described by the celebrated Asian florist Tan Jun Yong, where he was quoted saying, "The light delicate blush of the petals reminds me of a beating heart, while the size could only match the heart of the sender!"  Hydrangea quercifolia was declared the official state wildflower of Alabama in 1999.

Hydrangea (; common names hydrangea or hortensia) is a genus of 70–75 species of flowering plants native to Asia and the Americas. By far the greatest species diversity is in eastern Asia, notably Korea, China, and Japan. Most are shrubs 1 to 3 meters tall, but some are small trees, and others lianas reaching up to by climbing up trees. They can be either deciduous or evergreen, though the widely cultivated temperate species are all deciduous.


Techniques.

For either geolocating or positioning, the locating engine often uses radio frequency (RF) location methods, for example Time Difference Of Arrival (TDOA) for precision. TDOA systems often use mapping displays or other geographic information system. When satellite navigation (such as GPS) signals are unavailable, geolocation applications can use information from cell towers to triangulate the approximate position, a method that is not as accurate as GPS but has greatly improved in recent years. This is in contrast to earlier radiolocation technologies, for example Direction Finding where a line of bearing to a transmitter is achieved as part of the process.  Internet and computer geolocation can be performed by associating a geographic location with the Internet Protocol (IP) address, RFID, hardware embedded article/production number, embedded software number (such as UUID, Exif/IPTC/XMP or modern steganography), invoice, Wi-Fi positioning system, device fingerprint, canvas fingerprinting or device GPS coordinates, or other, perhaps self-disclosed information.  IP address location data can include information such as country, region, city, postal/zip code, latitude, longitude and time zone. Deeper data sets can determine other parameters such as domain name, connection speed, ISP, language, proxies, company name, US DMA/MSA, NAICS codes, and home/business.  At times geolocation can be more deductive, as with crowdsourcing efforts to determine the position of videos of training camps, combats, and beheadings in Syria by comparing features detected in the video with publicly available map databases such as Google Earth, as practiced by sites such as Bellingcat.

Standards.

Some standards and name servers include: ISO 3166, FIPS, INSEE, Geonames, IATA and ICAO. For geographic locations in the United States, the American National Standards Institute (ANSI) Codes are often used. ANSI INCITS 446-2008 is entitled "Identifying Attributes for Named Physical and Cultural Geographic Features (Except Roads and Highways) of the United States, Its Territories, Outlying Areas, and Freely Associated Areas, and the Waters of the Same to the Limit of the Twelve-Mile Statutory Zone A number of commercial solutions have been proposed:

Geolocation is the identification or estimation of the real-world geographic location of an object, such as a radar source, mobile phone, or Internet-connected computer terminal. In its simplest form, geolocation involves the generation of a set of geographic coordinates and is closely related to the use of positioning systems, but its usefulness is enhanced by the use of these coordinates to determine a meaningful location, such as a street address.


Background.

The Great Exhibition of Products of French Industry organised in Paris, France, from 1798 to 1849 were precursors to the Great Exhibition of 1851 in London.  The Great Exhibition of the Works of Industry of All Nations was organised by Prince Albert, Henry Cole, Francis Henry, George Wallis, Charles Dilke and other members of the Royal Society for the Encouragement of Arts, Manufactures and Commerce as a celebration of modern industrial technology and design. It was arguably a response to the highly effective French Industrial Exposition of 1844: indeed, its prime motive was for Britain to make "clear to the world its role as industrial leader". Prince Albert, Queen Victoria's consort, was an enthusiastic promoter of the self-financing exhibition; the government was persuaded to form the Royal Commission for the Exhibition of 1851 to establish the viability of hosting such an exhibition. Queen Victoria and her family visited three times. Although the Great Exhibition was a platform on which countries from around the world could display their achievements, Britain sought to prove its own superiority. The British exhibits at the Great Exhibition "held the lead in almost every field where strength, durability, utility and quality were concerned, whether in iron and steel, machinery or textiles." Britain also sought to provide the world with the hope of a better future. Europe had just struggled through "two difficult decades of political and social upheaval," and now Britain hoped to show that technology, particularly its own, was the key to a better future.  Sophie Forgan says of the Exhibition that "Large, piled-up 'trophy' exhibits in the central avenue revealed the organisers' priorities; they generally put art or colonial raw materials in the most prestigious place. Technology and moving machinery were popular, especially working exhibits." She also notes that visitors "could watch the entire process of cotton production from spinning to finished cloth. Scientific instruments were found in class X, and included electric telegraphs, microscopes, air pumps and barometers, as well as musical, horological and surgical instruments."  A special building, nicknamed The Crystal Palace, or "The Great Shalimar", was built to house the show. It was designed by Joseph Paxton with support from structural engineer Charles Fox, the committee overseeing its construction including Isambard Kingdom Brunel, and went from its organisation to the grand opening in just nine months. The building was architecturally adventurous, drawing on Paxton's experience designing greenhouses for the sixth Duke of Devonshire. It took the form of a massive glass house, 1848 feet long by 454 feet wide (about 563 metres by 138 metres) and was constructed from cast iron-frame components and glass made almost exclusively in Birmingham and Smethwick. From the interior, the building's large size was emphasized with trees and statues; this served, not only to add beauty to the spectacle, but also to demonstrate man's triumph over nature. The Crystal Palace was an enormous success, considered an architectural marvel, but also an engineering triumph that showed the importance of the Exhibition itself. The building was later moved and re-erected in 1854 in enlarged form at Sydenham Hill in south London, an area that was renamed Crystal Palace. It was destroyed by fire on 30 November 1936.  Six million people—equivalent to a third of the entire population of Britain at the time—visited the Great Exhibition. The average daily attendance was 42,831 with a peak attendance of 109,915 on 7 October. The event made a surplus of £186,000 (£ in 2015), which was used to found the Victoria and Albert Museum, the Science Museum and the Natural History Museum. They were all built in the area to the south of the exhibition, nicknamed Albertopolis, alongside the Imperial Institute. The remaining surplus was used to set up an educational trust to provide grants and scholarships for industrial research; it continues to do so today.  The Exhibition caused controversy as its opening approached. Some conservatives feared that the mass of visitors might become a revolutionary mob. The English-born King Ernest Augustus I of Hanover, shortly before his death, wrote to Lord Strangford about it: The folly and absurdity of the Queen in allowing this trumpery must strike every sensible and well-thinking mind, and I am astonished the ministers themselves do not insist on her at least going to Osborne during the Exhibition, as no human being can possibly answer for what may occur on the occasion. The idea... must shock every honest and well-meaning Englishman. But it seems everything is conspiring to lower us in the eyes of Europe.  In modern times, the Great Exhibition is a symbol of the Victorian Age, and its thick catalogue, illustrated with steel engravings, is a primary source for High Victorian design. A memorial to the exhibition, crowned with a statue of Prince Albert, is located behind the Royal Albert Hall. It is inscribed with statistics from the exhibition, including the number of visitors and exhibitors (British and foreign), and the profit made.

Exhibits.

The official descriptive and illustrated catalogue of the event lists exhibitors not only from throughout Britain but also from its 'Colonies and Dependencies' and 44 'Foreign States' in Europe and the Americas. Numbering 13,000 in total, the exhibits included a Jacquard loom, an envelope machine, kitchen appliances, steel-making displays and a reaping machine that was sent from the United States.

Admission fees.

Admission prices to the Crystal Palace varied according to the date of visit, with ticket prices decreasing as the parliamentary season drew to an end and London traditionally emptied of wealthy individuals. Prices varied from three guineas (£ in 2015) (two guineas for a woman) for a season ticket, or £1 per day (for the first two days only), then reducing to five shillings per day (until May 22). The admission price was then further reduced to one shilling (£ in 2015), per day – except on Fridays, when it was set at two shillings and six pence and on Saturdays when it remained at five shillings. The one-shilling ticket proved most successful amongst the industrial classes, with four and a half million shillings (£ in 2015) being taken from attendees in this manner. Two thousand five hundred tickets were printed for the opening day, all of which were bought.  To attract future custom from the working classes, the newly expanding railways offered highly discounted tickets for people to travel from distant parts of the country and special rates were offered to parties, often led by the local vicar. Those too poor to travel lined up by the rail tracks to watch the long trains of open carriages steaming past.

Stereoscopic views.

The Great Exhibition of 1851 encouraged the production of souvenirs. Several manufacturers produced stereoscope cards which provided a three-dimensional view of the Exhibition. These paper souvenirs were printed lithographic cards which were hand-coloured and held together by cloth to give a three-dimensional view of the Great Exhibition. They offered a miniature view of the Crystal Palace Exhibition when one viewed the cards through the peep holes on the front cover. Visitors purchased these souvenirs so that they could relive the experience of going to the exhibition.

The Great Exhibition of the Works of Industry of All Nations or The Great Exhibition (sometimes referred to as the Crystal Palace Exhibition in reference to the temporary structure in which it was held), an international exhibition, took place in Hyde Park, London, from 1 May to 15 October 1851. It was the first in a series of World's Fairs, exhibitions of culture and industry that became popular in the 19th century. The Great Exhibition was organised by Henry Cole and by Prince Albert, husband of the reigning monarch of the United Kingdom, Queen Victoria. Famous people of the time attended, including Charles Darwin, Karl Marx, Samuel Colt, members of the Orléanist Royal Family and the writers Charlotte Brontë, Charles Dickens, Lewis Carroll, George Eliot, Alfred Tennyson and William Makepeace Thackeray. The opening music, under the superintendence of William Sterndale Bennett was directed by Sir George Smart.


History.

Historical antecedents come from ancient Roman times, with ancient Roman publicans (Latin: "publicanus", plural: "publicani") or ‘Roman contractors’ being engaged to erect or maintain public buildings, supply armies overseas, or collect certain taxes (such as tithes and customs). This system for letting contracts was well established by the 3rd century BC.  The modern practice of interim management started in the mid to late-1970s, when permanent employees in The Netherlands were protected by long notice periods and companies faced large costs for terminating employees. Hiring temporary managers seemed like an ideal solution.  Since the 1980s, the concept and use of interim managers as a resourcing tool for organisations has received attention from academic researchers and policy makers as well as practitioners. In 1984, Atkinson postulated the emergence of an organisation design comprising both a core and a peripheral workforce, using differing forms of contractual relationship (flexibility) on an international basis. Examples of further study include Kalleberg (2000), looking at temporary, contract and part-time work; and Bosch (2004) looking at Western European “employment” relationships.  A good example of interim management benefitting from a geo-political change was its use by the German privatization agency after reunification of East and West, post 1989. The demand was created for interim managers in Eastern Germany to apply the required management and leadership competencies necessary to re-structure the formerly state owned companies. Demand continued to grow in the 1990s in Germany as the economy struggled to deal with unification, recession and resultant ambitious economic forecasts for the ‘new’ economy. One prominent example, mentioned by Bruns (2006) was the appointment of Helmut Sihler as interim CEO of German Telekom AG in 2001.

The interim management value proposition.

There are several factors that make the interim management offering increasingly popular and cost-effective to client organisations. These factors are characterised as a ‘value proposition’ that interim managers offer to their clients.  Although there is some variation at the margins of interim management (with temporary workers, freelancers, contractors and consultants) the following factors are typical of the interim management value proposition:.

The interim management assignment lifecycle.

Interim assignments vary in scope and requirements, encompassing change management, ‘gap’ assignments, project management and turnaround management. The following stages of the ‘assignment lifecycle’ are typical of how interim managers enter into an assignment, reach and carry out the actual implementation, and finally exit the assignment. The assignment should include a plan for making resources available to meet the longer-term goals.  The early stages have much in common with consultancy, as do later stages with project management, but the accountability and responsibility that interim managers have for successful analysis and delivery of a fitting solution, is what makes these stages uniquely typical of the interim management approach.

Uses of interim management.

There are a number of different business situations that could result in the need for an interim manager. Typically these could be situations such as crisis management, sudden departure, illness, death, change management, managing change or transition, sabbaticals, MBOs and IPOs, mergers and acquisitions, and project management. The functions of an interim manager are almost endless, thus the scope of an interim manager's skill set is quite unique.  The interim management concept has taken root in the UK, Germany, and Belgium, and is spreading elsewhere, most notably in Australia, the US, France, and Ireland. In Spain recruitment increased by 68% in 2011, according to Michael Page Interim management, and since 2013 there is a first association called "Association Interim Management Spain". In Nigeria, the Institute Of Corporate and Interim Management has been approved by The Federal Ministry Of Education and established under Federal Government Decree No. 1 of 1990, to promote Corporate and Interim Management practice in Africa.

Interim management is the temporary provision of management resources and skills. Interim management can be seen as the short-term assignment of a proven heavyweight interim executive manager to manage a period of transition, crisis or change within an organization. In this situation, a permanent role may be unnecessary or impossible to find on short notice. Additionally, there may be nobody internally who is suitable for, or available to take up, the position in question.


Taxonomy.

The family the moor frog belongs to, Ranidae, is a broad group containing 605 species. The family is like a “catch-all” for ranoid frogs that do not belong to any other families. Since this is the case, the characteristics that define them are more general, and the frogs are found all throughout the world, on every continent but Antarctica.  The moor frog's genus, "Rana", is a little more specific. Frogs of this genus are found in Europe, Asia, South America, and North America. The moor frog is not found in either of the Americas, unlike the foothill yellow-legged frog, Cascades frog, and Columbia spotted frog, which are all found in North America.  The moor frog's scientific name, "Rana arvalis" means "frog of the fields". It is also called the Altai brown frog because frogs from the Altai Mountains in Asia have been included in the "R. arvalis" species. The Altai frogs have some different characteristics such as shorter shins, but currently there is no official distinction and all frogs are placed under "Rana arvalis". The taxonomy may be more defined in the future.

Description.

This is a small frog, characterized by an unspotted belly, a large, dark ear spot, and — often, not always — a pale stripe down the center of the back. They are generally described as a reddish-brown, but can also be yellow, gray, or light olive. Their bellies are white or yellow and they have a "bandit-like" black stripe going from their nose to their ears. They vary from 5.5 to 6.0 cm long, but can reach up to 7.0 cm in length, and their heads are more tapered than those of the Common frog ("Rana temporaria"). The skin on their flanks and thighs is smooth, and the posterior part of their tongues is forked and free. They have horizontal pupils, their feet are partially webbed, and their back legs are shorter than those of other species of frogs. The males are different from the females because of the nuptial pads on their first fingers and their paired guttural vocal sacs.

Distribution and habitat.

The species has an extensive distribution across Europe. It can be found inhabiting an area stretching from the lowlands of Central and Southern Europe to Siberia, in Austria, Belarus, Belgium, Czech Republic, Denmark, Estonia, Finland, France, Germany, Hungary, Latvia, Lithuania, Moldova, Netherlands, Norway, Poland, Romania, Russian Federation, Slovakia, Slovenia, Sweden, Switzerland, and Ukraine. However, they are believed to be extirpated in Switzerland and possibly in Siberia as well; the records of frogs being in Siberia at all may have been in error. Alsace, France, constitutes the western boundary of their territory. Moor frogs were also confirmed to have been present in East Anglia in the UK, after archaeological remains were found.  The types of land they can inhabit are greatly varied. They live in tundra, forest tundra, forest, forest steppe, and steppe, forest edges and glades, semideserts, swamps, meadows, fields, bush lands, and gardens. They prefer areas untouched by humans, such as damp meadows and bogs, but they still may be able to live in agricultural and urban areas.  Moor frogs provide a good model for studying local adaptation as they experience a wide range of environments and are relatively limited in their movements. Their restriction in movements implies limited gene flow and facilitates evolution through adaptive genetic differentiation among populations.

Ecology.

Hibernation.

Moor frogs will hibernate sometime between September and June, depending on the latitude of the location. Frogs in southwestern, plains areas will disappear later (around November or December) and return earlier (February). Frogs in cold, polar areas, though, will disappear sooner (in September) and return later (in June).

Breeding.

The mating season takes place between March and June right after the end of hibernation. Males form breeding choruses, and their songs sound similar to those of the agile frog, ("Rana dalmatina"). Their calls can "sound like air escaping from a submerged empty bottle: 'waug...waug...waug'. Males can also develop bright-blue coloration for a few days during the season.  The spawning happens very quickly and is completed in three to 28 days. The spawn of each frog is laid in one or two clusters of 500-3000 eggs in warm, shallow waters like in ponds.

Metamorphosis.

Metamorphosis happens between June and October. Larvae are about 45 mm long and colored dark with small metallic dots. When they become tadpoles, they eat algae and small invertebrates. The adult frogs' feeding is halted during the breeding season, but their diets consist of insects and various invertebrates.

Effects of acidification on population.

Environmental plasticity.

Increased acidity levels in breeding areas may be problematic for moor frog populations, as it reduces survival and growth of the aquatic embryos and larvae. When exposed to acidity, moor frogs were however shown to be able to adapt relatively rapidly (within 16–40 generations). Local adaptation to acidity is also possible in survival during the embryonic stage, during which frogs are most sensitive to severe acidity. Moreover, compared to those from neutral sites, acid origin populations have higher embryonic and larval acid tolerance (survival and larval period were less negatively affected by low pH), higher larval growth but slower larval development rates, and larger metamorphosing size. Divergence in embryonic acid tolerance and metamorphic size correlates most strongly with breeding pond pH, whereas divergence in larval period and larval growth correlates most strongly with latitude and predator density, respectively.

Maternal effects.

For female moor frogs, in order to optimize their maternal investments, they need to balance between their own fitness and the fitness of their offspring. Additionally, under the great pressure exerted by acidification, female moor frogs also need to do a trade-off between quality and quantity of the offspring.  Environmental stress, like acidity, may either select for or select against certain phenotypes and hence may increase variation in fitness. The adaptive optima for the population would shift greatly compared to those living in less acidic and more benign environments, thereby making the allocation of resources even more important. As a result of the increasing variation in fitness, frogs from acidic environments may also favor different reproductive strategies than those more benign environments. Compared to neutral origin females, acid origin females tend to invest relatively more in fecundity than in egg size, invest more in their offspring than in self-maintenance, and increase their reproductive effort as their residual reproductive value decreases. Consequently, acid origin females increase the clutch size and total reproductive output with age, while neutral origin females only increase egg size but not clutch size or total reproductive output with age.  In conclusion, environmental acidification lowers maternal investment, selects for investment in larger eggs at a cost to fecundity, imposes negative effects on reproductive output, and alters the relationship between female phenotype and maternal investment, as well as strengthens the egg-size-fecundity trade-off.

Population threats.

This species is generally common and often abundant. It faces few major threats and is currently classified as Least Concern by the IUCN. The moor frog may be impacted by the destruction and pollution of breeding sites and adjacent habitats, mostly through urbanization, recreational use of waterside areas, and intensive agriculture. The species does not appear to be notably susceptible to chytridiomycosis, although the fungus has been detected in frogs in Germany.

The moor frog ("Rana arvalis") is a slim, reddish-brown, semiaquatic amphibian native to Europe and Asia. It is a member of the family Ranidae, or true frogs.


Early life.

Nathaniel Dwayne Hale was born on August 19, 1969, in Clarksdale, Mississippi. At the Life Line Baptist Church—where his father Daniel Lee Hale was pastor and his mother Ruth Holmes led the choir—Nate began singing in childhood.  At age 14, following his parents' divorce, he moved to Long Beach, California, where he continued singing at the New Hope Baptist Church. While friends with Warren G and RBX, he was a cousin of Snoop Dogg, Daz Dillinger, Butch Cassidy, and Lil' 1⁄2 Dead.

Military career.

At age 17, Hale dropped out of high school, left home, and 30 days later enlisted in the Marines. He was stationed at Camp Schwab, in Okinawa, Japan, in the Material Readiness Battalion of the 3rd Force Service Support Group, which supplied ammunition to most of the Pacific. After three years as an ammunition specialist, he was discharged in 1989. Hale would recall that he had joined the military since he had "wanted to see if he was a man."

Entertainment career.

213 trio.

In 1990, Nate Dogg, Snoop Dogg, and Warren G, formed a rap trio called 213. They recorded their first demo tape in the back of the famed V.I.P. record store in Long Beach. The demo was later heard by Dr. Dre at a bachelor party.

Solo career.

Nate Dogg debuted on Dr. Dre's first solo album, "The Chronic", in 1992. Nate's trademark singing, complementing the new gangsta rap sound G-funk, was well received by fans and critics alike, and he signed to Dre's label, Death Row Records, in 1993. Nate Dogg also featured on Snoop Dogg's debut solo album, "Doggystyle", in 1993, his singing prominent on the track "Ain't No Fun (If the Homies Can't Have None)."  In 1994, Nate Dogg cowrote his duo with Warren G, the single "Regulate." Nate was also featured on 2Pac releases, including his group's, also released in 1994. In July 1998, amid his departure from Death Row Records, the label released his double album, delayed about two years, "G-Funk Classics Vol. 1 & 2". In 2001, his Elektra Records followup, "Music & Me", peaked at #3 on the "Billboard" hip-hop chart. He also had an eponymous album that saw unauthorized release in 2003.

Collaborations.

Nate Dogg was often sought to sing on other artists' tracks, usually to sing the hook. As a featured artist, he charted 16 times on the "Billboard" Hot 100, and in 2003 reached #1 via 50 Cent's "21 Questions."  Otherwise, his successful collaborations are numerous, including 2Pac's "All Bout U," Dr. Dre's "The Next Episode," Westside Connection's "Gangsta Nation," Mos Def's "Oh No,", Fabolous' "Can't Deny It," Ludacris's "Area Codes," Kurupt's "Behind the Walls," Mark Ronson's "Ooh Wee," Houston's "I Like That," Eminem's "'Till I Collapse," his "Never Enough", his "Shake That," and Mobb Deep's "Have a Party."  Further, in 2002, appearing on television, Nate Dogg was on a celebrity episode of "The Weakest Link", where, finally eliminated by Xzibit and Young MC, he was among the final three.

Legal troubles.

Nate Hale was charged for a 1991 robbery of a Check Changers shop and for a 1994 robbery of Taco Bell in San Pedro, but was acquitted. Yet in 1996, he was convicted of a drug offense in Los Angeles County.  On June 17, 2000, for allegedly assaulting his former girlfriend and setting her mother's car afire in Lakewood, Hale was charged with kidnapping, domestic violence, terrorist threats, and arson. Andre "Dr. Dre" Young posted $1 million bond. The charges were dismissed while he pleaded no contest to illegal gun possession by a felon, and received a $1,000 fine and three years probation.  On April 12, 2002, a tour bus carrying Hale, while outside of Kingman, Arizona, was found with two pistols and four ounces of cannabis, whereby he was booked and then released on $3,500 bond. The next month, the weapon charges were dropped for his guilty plea on a drug charge, and he was sentenced to probation, community service, and drug counseling.  In July 2006, Hale was charged with misdemeanor aggravated trespassing, telephone harassment, battery assault, dissuading a witness from reporting a crime, and breaking a restraining order. In March 20, 2008, pleading guilty to trespassing and battery, he lost gun-ownership rights for 10 years, received three years probation, and was ordered to a domestic-violence intervention program.  On June 23, 2008, after allegedly threatening his estranged wife by emails and chasing her on Interstate 405, Hale was charged with two felony counts of criminal threats and one count of stalking. He pleaded not guilty. In April 2009, as the alleged victim had failed to contact prosecutors, the charges were dropped. Incidentally, he was also convicted of driving under the influence of drugs.

Health problems and death.

On December 19, 2007, Hale suffered a stroke. After a week in Pomona Valley Hospital Medical Center, he entered a rehabilitation facility. Although his body's left side was weakened, neither his cognition nor voice were affected and a full recovery was expected.  Hale sustained another stroke on September 12, 2008. On March 15, 2011, in Long Beach, California, at age 41, by complications of multiple strokes, or by congestive heart failure, he died. Hale was interred in Long Beach at Forest Lawn Memorial Park.  In 2013, Nate Dogg's son Naijiel Hale committed to play football at the University of Arizona. A couple of years later, in 2015, Nate's other son, Nathaniel Jr., having adopted the stage name Lil Nate Dogg, released his own album, "Son of a G".

Awards and nominations.

Nate Dogg was nominated for four Grammy Awards.

Nathaniel Dwayne Hale (August 19, 1969 – March 15, 2011), known professionally as Nate Dogg, was an American singer, rapper and songwriter. His smooth vocals made the hooks of numerous artists' rap songs, especially in the West Coast's G-funk era in the 1990s.


History.

The third Cistercian monastery on German territory was founded by Adelheid of Lare (Lohra), wife of Count Volkmar of Klettenberg, under the first abbot Henry I (1127–28); the foundation was backed by King Lothair III and confirmed in 1137 by Pope Innocent II. The constituent convent arrived in 1129 from Kamp Abbey in the Rhineland, where Adelheid had stayed on a pilgrimage. The premises were conveniently situated on the Wieda creek and the southern slopes of the Harz mountains. Shortly afterwards construction work of a Romanesque basilica began, which was dedicated in 1137. Two Cistercian daughter houses were founded: Pforta ("Sancta Maria ad Portam", 1137) near Naumburg and Sittichenbach Abbey (1141) near Eisleben in the County of Mansfeld.  Walkenried grew rich and acquired lands as far away as the Rhineland and Pomerania. The monks gave much attention to land clearance and development, especially mining, smelting and charcoal works, and also the construction of fishponds. They used the Upper Harz water management system to cultivate the surrounding estates along the Helme river down to Thuringia, which are today called Goldene Aue. The abbey also held a library, where the 14th-century flagellant and millenarian Konrad Schmid, though a layman, educated himself. In the 13th century, about 100 monks and more than 200 lay brothers lived in the abbey, which became one of the most affluent and significant Cistercian monasteries in Germany. In 1209 the erection of a new basilica modelled on Morimond Abbey began, supported by Emperor Otto IV. The church, then one of the largest in Northern Germany, and the adjacent cloister were finished in a Gothic style and consecrated by Bishop Siegfried II of Hildesheim in 1290. The Counts of Klettenberg held the office of a "Vogt" (reeve), which upon their extinction about 1260 passed to the Counts of Hohnstein.  When in the mid 14th century plague epidemics depopulated the Harz region, both the mining in the Upper Harz and the agricultural business stagnated and the abbey began to decline. In the early 16th century, the premises were settled by only 12 monks and the abbot. The German Peasants' War brought the monastery to the verge of destruction, when on Easter 1525, a mob of about 800 peasants from the southern Harz region marched against Walkenried. Abbot Paulus (1520–36) and the monks fled, taking the archives with them. The abbey was plundered and the church spire torn down, severely damaging the underlying crossing vault.  In view of the Protestant Reformation the abbey was finally declared an immediate "Reichsstift" (Imperial abbey) by Emperor Charles V in 1542. Nevertheless, the next abbot, John VIII (1530–59), was very worldly and extravagant; in 1546 he and his monks turned Lutheran. Thereupon Count Ernst of Hohnstein, as patron of the abbey, laid a complaint before the Habsburg emperor, who in 1548 ordered that everything in the abbey should be restored to its former condition, but his command was unheeded. After the count's death the entire County of Hohnstein became Protestant, and in 1556, a Latin school was opened at Walkenried. Four Lutheran abbots directed the abbey until 1578 when the Count of Hohnstein appointed his son as administrator, after whose death in 1593 the Halberstadt cathedral chapter left the administration of Hohnstein and Walkenried Abbey to the Princes of Brunswick-Wolfenbüttel.  During the Thirty Years' War the abbey was for a short time (1629–31) restored to the Cistercians. The 1648 Peace of Westphalia put an end to the existence of the Protestant monastery and the abbey was secularised. In 1668, the Latin school was closed. The Wolfenbüttel dukes ruled the former abbey's estates within an incorporated "Amt" also comprising the neighbouring villages of Zorge and Hohegeiß.  From that time the abbey was systematically quarried as a source of building stone. The Gothic church was greatly damaged since the destruction of the roof tower by the peasants in 1525; today only a few picturesque remains are still in existence. The library was also destroyed by the peasants, but the archives are preserved at the Herzog August Library in Wolfenbüttel. Otherwise, however the claustral buildings are generally well preserved. The chapter hall has served since 1570 as a Lutheran church. The demolition of the buildings was stopped in 1817, first comprehensive works to renovate the cloister started in 1876. Since 1977 the premises are managed by the Osterode district authorities; a museum opened in 2006.

Walkenried Abbey () was a Cistercian abbey located in the village of Walkenried in Lower Saxony, Germany. Founded in 1127 on the southern rim of the Harz mountain range, the remnants of the monastic complex since 2010 are part of the Upper Harz Water Regale World Heritage Site.


Biography.

Born at Le Havre, Normandy, in northern France, she was without fortune, but she was exceedingly well-educated. Her father, captain of the port in Le Havre, died in 1613 with her mother following shortly after. Madeleine and her brother Georges de Scudéry were placed in the care of an uncle who cared for them very well. He gave Madeleine an abnormally well-rounded education: she studied writing, spelling, drawing, dancing, painting, and needlework. In addition, on her own, Madeleine studied agriculture, medicine, cooking, Spanish, and Italian.

Works.

Her lengthy novels, such as "Artamène, ou le Grand Cyrus" (10 vols., 1648–53), "Clélie" (10 vols., 1654–61), "Ibrahim, ou l'illustre Bassa" (4 vols., 1641), "Almahide, ou l'esclave reine" (8 vols., 1661–63) were the delight of Europe, commended by other literary figures such as Madame de Sévigné. "Artamène", which contains about 2.1 million words, ranks as the longest novel ever published. Her novels derive their length from endless conversations and, as far as incidents go, successive abductions of the heroines, conceived and told decorously. Contemporary readers also enjoyed these novels because they gave a glimpse into the life of important society figures. These figures were often disguised as Persian, Greek, and Roman warriors and maidens. In fact, Scudéry created the roman à clef to provide a forum for her thinly veiled fiction featuring political and public figures.  "Les Femmes Illustres" (1642) addresses itself to women and defends education, rather than the beauty or cosmetic, as a means of social mobility for women. This text was a means to justify women's participation in rhetoric and literary culture. It uses women speakers as models for the speeches, including Cleopatra of Egypt. In "Les Femmes Illustres" (1642), "Conversations Sur Divers Sujets" (1680), and "Conversations Nouvelles sur Divers Sujets, Dediees Au Roy" (1684), Madeleine de Scudéry adapted classical rhetorical theory from Cicero, Quintilian, Aristotle, and the sophists to a theory of salon conversation and letter writing. Scudéry's Conversations Sur Divers Sujets, included dialogues covering "Conversation," "The Art of Speaking," "Raillery," "Invention," and "The Manner of Writing Letters." This text offers the rhetoric of salon conversation and model scenarios where women take intellectual control of the conversation. Other works devoted to conversations, pertaining to the education of women include: "The Slave Queen" (1660), "Mathilda of Aguilar, a Spanish Tale," (1667), and "The Versailles Promenade, or the Tale of Celanire" (1669). These covered the art of speaking, invention, the manner of writing letters, and scenarios where women had control of the intellectual conversation.  Scudéry's novels are usually set in the classical world or "the Orient", but their language and action reflect fashionable ideas of the 17th century, and the characters can be identified with Mademoiselle de Scudéry's contemporaries. In "Clélie", Herminius represents Paul Pellisson; Scaurus and Lyriane were Paul Scarron and his wife (who became Mme de Maintenon); and in the description of Sapho in vol. 10 of "Le Grand Cyrus" the author paints herself.  In "Clélie", Scudéry invented the famous "Carte de Tendre", a map of an Arcadia where the geography is all based around the theme of love: the river of Inclination flows past the villages of "Billet Doux" (love letter), "Petits Soins" (Little Trinkets) and so forth. Scudéry was a skilled conversationalist; several volumes purporting to report her conversations upon various topics were published during her lifetime. She had a distinct vocation as a pedagogue.

Later years.

Madeleine survived her brother by more than thirty years, and in her later days published numerous volumes of conversations, to a great extent extracted from her novels, thus forming a kind of anthology of her work. Scudéry was deaf for the last 40 years of her life. She outlived her vogue to some extent, but retained a circle of friends, like Marie Dupré, to whom she was always the "incomparable Sapho."  Her "Life and Correspondence" was published at Paris by MM. Rathery and Boutron in 1873.

Legacy.

Madeleine de Scudéry was part of a movement in the late Renaissance in England and France where women used classical rhetorical theory for their own. She revised discourse to be modeled on conversation rather than public speaking, favoring that as a means of rhetoric, the speaker in the salon built on the ideas of the speaker before them, opting for consensus rather than argument. She is one of the central figures associated with the "salon" conversation and letter writing.

Cultural references.

Controversial in her own era, Mademoiselle de Scudéry was satirized by Molière in his plays "Les Précieuses ridicules" (1659) and "Les Femmes savantes" (1672) and by Antoine Furetière in his "Roman Bourgeois" (1666).  The 19th century German writer E.T.A. Hoffmann wrote what is usually referred to as the first German-language detective story, featuring Scudéry as the central figure. "Das Fräulein von Scuderi" (Mademoiselle de Scudery) is still widely read today, and is the origin of the "Cardillac syndrome" in psychology. Mademoiselle de Scudéry is also featured prominently in "Madeleine: One of Love's Jansenists", a novel published in 1919 by modernist writer Hope Mirrlees. The novel is set in and around the literary circles of the 17th Century Précieuses. The protagonist, a young woman named Madeleine Troqueville, becomes enamored of Mademoiselle de Scudéry, who snubs young Madeleine. It has been suggested that the novel is a roman à clef with Natalie Clifford Barney portrayed as Mademoiselle de Scudéry.

Literature.

Summaries of the stories and keys to the characters may be found in Heinrich Körting, "Geschichte des französischen Romans im 17ten Jahrhundert" (second edition, Oppeln, 1891).

Madeleine de Scudéry (15 November 1607 – 2 June 1701), often known simply as Mademoiselle de Scudéry, was a French writer.


History.

The concept of diminishing returns can be traced back to the concerns of early economists such as Johann Heinrich von Thünen, Jacques Turgot, Adam Smith, James Steuart, Thomas Robert Malthus, and David Ricardo. However, classical economists such as Malthus and Ricardo attributed the successive diminishment of output to the decreasing quality of the inputs. Neoclassical economists assume that each "unit" of labor is identical. Diminishing returns are due to the disruption of the entire productive process as additional units of labor are added to a fixed amount of capital. The law of diminishing returns remains an important consideration in farming.

Example.

An example is a factory that has a fixed stock of capital, or tools and machines, and a variable supply of labor. As the firm increases the number of workers, the total output of the firm grows but at an ever-decreasing rate. This is because after a certain point, the factory becomes overcrowded and workers begin to form lines to use the machines. The long-run solution to this problem is to increase the stock of capital, that is, to buy more machines and to build more factories.

Returns and costs.

There is an inverse relationship between returns of inputs and the cost of production, although other features such as input market conditions can also affect production costs. Suppose that a kilogram of seed costs one dollar, and this price does not change. Assume for simplicity that there are no fixed costs. One kilogram of seeds yields one ton of crop, so the first ton of the crop costs one dollar to produce. That is, for the first ton of output, the marginal cost as well as the average cost of the output is $1 per ton. If there are no other changes, then if the second kilogram of seeds applied to land produces only half the output of the first (showing diminishing returns), the marginal cost would equal $1 per half ton of output, or $2 per ton, and the average cost is $2 per 3/2 tons of output, or $4/3 per ton of output. Similarly, if the third kilogram of seeds yields only a quarter ton, then the marginal cost equals $1 per quarter ton or $4 per ton, and the average cost is $3 per 7/4 tons, or $12/7 per ton of output. Thus, diminishing marginal returns imply increasing marginal costs and increasing average costs.  Cost is measured in terms of opportunity cost. In this case the law also applies to societies – the opportunity cost of producing a single unit of a good generally increases as a society attempts to produce more of that good. This explains the bowed-out shape of the production possibilities frontier.

In economics, diminishing returns is the decrease in the marginal (incremental) output of a production process as the amount of a single factor of production is incrementally increased, while the amounts of all other factors of production stay constant.


Location and functions.

Some chaperone systems work as foldases: they support the folding of proteins in an ATP-dependent manner (for example, the GroEL/GroES or the DnaK/DnaJ/GrpE system). Although most newly synthesized proteins can fold in absence of chaperones, a minority strictly requires them for the same. Other chaperones work as holdases: they bind folding intermediates to prevent their aggregation, for example DnaJ or Hsp33. Chaperones can also work as disaggregases, i.e. they can interact with aberrant protein assemblies and revent them to monomers. Some chaperones can assist in protein degradation, leading proteins to protease systems, such as the ubiquitin-proteasome system in eukaryotes.  Many chaperones are heat shock proteins, that is, proteins expressed in response to elevated temperatures or other cellular stresses. The reason for this behaviour is that protein folding is severely affected by heat and, therefore, some chaperones act to prevent or correct damage caused by misfolding.  Macromolecular crowding may be important in chaperone function. The crowded environment of the cytosol can accelerate the folding process, since a compact folded protein will occupy less volume than an unfolded protein chain. However, crowding can reduce the yield of correctly folded protein by increasing protein aggregation. Crowding may also increase the effectiveness of the chaperone proteins such as GroEL, which could counteract this reduction in folding efficiency.  More information on the various types and mechanisms of a subset of chaperones that encapsulate their folding substrates (e.g. GroES) can be found in the article for chaperonins. Chaperonins are characterized by a stacked double-ring structure and are found in prokaryotes, in the cytosol of eukaryotes, and in mitochondria.  Other types of chaperones are involved in transport across membranes, for example membranes of the mitochondria and endoplasmic reticulum (ER) in eukaryotes. A bacterial translocation—specific chaperone maintains newly synthesized precursor polypeptide chains in a translocation-competent (generally unfolded) state and guides them to the translocon.  New functions for chaperones continue to be discovered, such as bacterial adhesin activity, induction of aggregation towards non-amyloid aggregates, suppression of toxic protein oligomers via their clustering, and in responding to diseases linked to protein aggregation (e.g. see prion) and cancer maintenance.

Human chaperone proteins.

Chaperones are found in, for example, the endoplasmic reticulum (ER), since protein synthesis often occurs in this area.

Endoplasmic reticulum.

In the endoplasmic reticulum (ER) there are general, lectin- and non-classical molecular chaperones helping to fold proteins.

Nomenclature and examples of bacterial and archaeal chaperones.

There are many different families of chaperones; each family acts to aid protein folding in a different way. In bacteria like "E. coli", many of these proteins are highly expressed under conditions of high stress, for example, when the bacterium is placed in high temperatures. For this reason, the term "heat shock protein" has historically been used to name these chaperones. The prefix "Hsp" designates that the protein is a heat shock protein.

Hsp60.

Hsp60 (GroEL/GroES complex in "E. coli") is the best characterized large (~ 1 MDa) chaperone complex. GroEL is a double-ring 14mer with a hydrophobic patch at its opening; it is so large it can accommodate native folding of 54-kDa GFP in its lumen. GroES is a single-ring heptamer that binds to GroEL in the presence of ATP or ADP. GroEL/GroES may not be able to undo previous aggregation, but it does compete in the pathway of misfolding and aggregation. Also acts in mitochondrial matrix as molecular chaperone.

Hsp70.

Hsp70 (DnaK in "E. coli") is perhaps the best characterized small (~ 70 kDa) chaperone.  The Hsp70 proteins are aided by Hsp40 proteins (DnaJ in "E. coli"), which increase the ATP consumption rate and activity of the Hsp70s.  It has been noted that increased expression of Hsp70 proteins in the cell results in a decreased tendency toward apoptosis.  Although a precise mechanistic understanding has yet to be determined, it is known that Hsp70s have a high-affinity bound state to unfolded proteins when bound to ADP, and a low-affinity state when bound to ATP.  It is thought that many Hsp70s crowd around an unfolded substrate, stabilizing it and preventing aggregation until the unfolded molecule folds properly, at which time the Hsp70s lose affinity for the molecule and diffuse away. Hsp70 also acts as a mitochondrial and chloroplastic molecular chaperone in eukaryotes.

Hsp90.

Hsp90 (HtpG in "E. coli") may be the least understood chaperone. Its molecular weight is about 90 kDa, and it is necessary for viability in eukaryotes (possibly for prokaryotes as well).  Heat shock protein 90 (Hsp90) is a molecular chaperone essential for activating many signaling proteins in the eukaryotic cell.  Each Hsp90 has an ATP-binding domain, a middle domain, and a dimerization domain. Originally thought to clamp onto their substrate protein (also known as a client protein) upon binding ATP, the recently published structures by Vaughan "et al." and Ali "et al." indicate that client proteins may bind externally to both the N-terminal and middle domains of Hsp90.  Hsp90 may also require co-chaperones-like immunophilins, Sti1, p50 (Cdc37), and Aha1, and also cooperates with the Hsp70 chaperone system.

Hsp100.

Hsp100 (Clp family in "E. coli") proteins have been studied "in vivo" and "in vitro" for their ability to target and unfold tagged and misfolded proteins.  Proteins in the Hsp100/Clp family form large hexameric structures with unfoldase activity in the presence of ATP. These proteins are thought to function as chaperones by processively threading client proteins through a small 20 Å (2 nm) pore, thereby giving each client protein a second chance to fold.  Some of these Hsp100 chaperones, like ClpA and ClpX, associate with the double-ringed tetradecameric serine protease ClpP; instead of catalyzing the refolding of client proteins, these complexes are responsible for the targeted destruction of tagged and misfolded proteins.  Hsp104, the Hsp100 of Saccharomyces cerevisiae, is essential for the propagation of many yeast prions. Deletion of the HSP104 gene results in cells that are unable to propagate certain prions.

History.

The investigation of chaperones has a long history. The term "molecular chaperone" appeared first in the literature in 1978, and was invented by Ron Laskey to describe the ability of a nuclear protein called nucleoplasmin to prevent the aggregation of folded histone proteins with DNA during the assembly of nucleosomes. The term was later extended by R. John Ellis in 1987 to describe proteins that mediated the post-translational assembly of protein complexes. In 1988, it was realised that similar proteins mediated this process in both prokaryotes and eukaryotes. The details of this process were determined in 1989, when the ATP-dependent protein folding was demonstrated "in vitro".

Clinical significance.

There are many disorders associated with mutations in genes encoding chaperones (i.e. multisystem proteinopathy) that can affect muscle, bone and/or the central nervous system.

In molecular biology, molecular chaperones are proteins that assist the conformational folding or unfolding and the assembly or disassembly of other macromolecular structures. Chaperones are present when the macromolecules perform their normal biological functions and have correctly completed the processes of folding and/or assembly. The chaperones are concerned primarily with protein folding. The first protein to be called a chaperone assists the assembly of nucleosomes from folded histones and DNA and such assembly chaperones, especially in the nucleus, are concerned with the assembly of folded subunits into oligomeric structures.


History.

In 1916, the first edition of the "Campeonato Sudamericano de Fútbol" (South-American Football Championship), now known as the "Copa América", was contested in Argentina to commemorate the centenary of the Argentine Declaration of Independence. The four participating associations of that tournament gathered together in Buenos Aires in order to officially create a governing body to facilitate the organization of the tournament. Thus, CONMEBOL was founded on 9 July 1916 under the initiative of Uruguayan Héctor Rivadavia Gómez, but approved by the football associations of Argentina, Brazil, Chile, and Uruguay. The first Constitutional Congress on 15 December of that same year, which took place in Montevideo, ratified the decision.  Over the years, the other football associations in South America joined, with the last being Venezuela in 1952. Guyana, Suriname, and the French overseas department of French Guiana, while geographically in South America, are not part of CONMEBOL. Consisting of a French territory, a former British territory, and a former Dutch territory, they are part of the Confederation of North, Central American and Caribbean Association Football (CONCACAF), mainly due to historical, cultural, and sporting reasons. With ten member nations, CONMEBOL is the smallest and the only fully continental land-based FIFA confederation (no insular countries or associates from different continents).

Competitions.

CONMEBOL competitions.

National teams:  Clubs:  Inter Continental:

International.

The main competition for men's national teams is the Copa América, started in 1916. CONMEBOL also runs national competitions at Under-20, Under-17 and Under-15 levels. For women's national teams, CONMEBOL operates the Copa América Femenina for senior national sides, as well as Under-20 and Under-17 championships.  In futsal, there is the Copa América de Futsal and Campeonato Sudamericano de Futsal Sub-20. The Campeonato Sudamericano Femenino de Futsal is the women's equivalent to the man's tournament.

Club.

CONMEBOL also runs the two main club competitions in South America: the Copa Libertadores was first held in 1960 and the Copa Sudamericana was launched by CONMEBOL in 2002 as an indirect successor to the Supercopa Libertadores (begun in 1988). A third competition, the Copa CONMEBOL, started in 1992 and was abolished in 1999. In women's football, CONMEBOL also conducts the Copa Libertadores Femenina for club teams. The competition was first held in 2009.  The Recopa Sudamericana pits the past year's winners of the Copa Libertadores against the winners of the Copa Sudamericana (previously the winners of the Supercopa Libertadores) and came into being in 1989.  The Intercontinental Cup was jointly organised with UEFA between the Copa Libertadores and the UEFA Champions League winners.

Rankings.

National teams.

<nowiki>*</nowiki> Inactive for more than 18 months and therefore not ranked Men's update: 20 February 2020 Women's update: 27 March 2020

Clubs.

Football Database rankings.

Last updated: 5 April 2020

Beach soccer national teams.

Men's update: 23 September 2018

Major tournaments.

For each tournament, the flag of the host country and the number of teams in each finals tournament (in brackets) are shown.

Corruption.

On 27 May 2015, several CONMEBOL leaders were arrested in Zürich, Switzerland by Swiss police and indicted by the U.S. Department of Justice on charges of corruption, money laundering, and racketeering. Those swept up in the operation include former CONMEBOL presidents Eugenio Figueredo and Nicolás Léoz and several football federations presidents such as Carlos Chávez and Sergio Jadue. On 3 December 2015, the CONMEBOL President Juan Ángel Napout was also arrested.

The South American Football Confederation (CONMEBOL, ; ; or CSF) is the continental governing body of football in South America (apart from Guyana, Suriname, and French Guiana), and it is one of FIFA's six continental confederations. The oldest continental confederation in the world, its headquarters are located in Luque, Paraguay, near Asunción. CONMEBOL is responsible for the organization and governance of South American football's major international tournaments. With 10 member football associations, it has the fewest members of all the confederations in FIFA.


History.

The company originates from a merger of two companies—Lux AB and Svenska Elektron AB, the former an established manufacturer and the latter a younger company founded by a former vacuum salesman who had also been an employee of the former firm. The origins of Electrolux are closely tied to the vacuum, but today it also makes major appliances.

Sales company to major manufacturer.

In 1919, a Svenska Elektron AB acquisition, Elektromekaniska AB, became Elektrolux (the spelling was changed to Electrolux in 1957). It initially sold Lux branded vacuum cleaners in several European countries.  In 1923, the company acquired AB Arctic and subsequently added absorption refrigerators to its product line. Other appliances soon followed, including washing machines in 1951, dishwashers in 1959, and food service equipment in 1962.

Mergers and acquisitions.

The company has often and regularly expanded through mergers and acquisitions.  While Electrolux had bought several companies before the 1960s, that decade saw the beginnings of a new wave of M&A activity. The company bought ElektroHelios, Norwegian Elektra, Danish Atlas, Finnish Slev, and Flymo, et al., in the nine years from 1960 to 1969. This style of growth continued through the 1990s, seeing Electrolux purchase scores of companies including, for a time, Husqvarna.

Hans Werthen.

Hans Werthen, President and later Chairman of the Board, led the strategic core of an increasingly decentralized Electrolux—and was instrumental to its rapid growth.

Restructuring.

While attempts to cut costs, centralise administration, and wring out economies of scale from Electrolux's operations were made in the 1960s and 1970s with the focus so firmly on growth, further company-wide restructuring efforts only began in the late 1990s.

A public company.

Electrolux made an initial public offering on the London Stock Exchange in 1928 (it was delisted in 2010) and another on the Stockholm Stock Exchange in 1930.  Currently, its shares trade on the NASDAQ OMX Nordic Market and over-the-counter. Electrolux is an OMX Nordic 40 constituent stock.

2000 to present.

In North America, the Electrolux name was long used by vacuum cleaner manufacturer Aerus LLC, originally established to sell Swedish Electrolux products. In 2000, Aerus transferred trademark rights back to the Electrolux Group, and ceased using the Electrolux name in 2004.  Conversely, Electrolux-made vacuums carried the Eureka brand name, which Electrolux continued to use while also selling Electrolux branded vacuums after 2000. Electrolux USA customer service maintains a database of Electrolux made vacuums and provides a link to Aerus's website for the convenience of owners of Electrolux branded Aerus vacuums.  Keith McLoughlin took over as President and CEO on January 1, 2011, and became the company's first non Swedish chief executive.  In August 2011, Electrolux acquired from Sigdo Koppers the Chilean appliance manufacturer CTI obtaining several brands with the purchase including: Fensa, Gafa, Mademsa and Somela.  On February 6, 2017, Electrolux announced that it had agreed to acquire Anova Applied Electronics, Inc. (company), the U.S.-based provider of the Anova Precision Cooker.

Brands.

Electrolux sells under a wide variety of brand names worldwide. Most of them were acquired through mergers and acquisitions and only do business in a single country or geographic area. The following is an incomplete list.  Note: This list does not include brands such as Kenmore and John Lewis, which may sell Electrolux produced appliances but are not owned by or affiliated with Electrolux, as Electrolux acts as an OEM for these brands.

Slogan.

The company's current international slogan is "Shape living for the Better". In the past it used to be "Thinking of you". In the 1960s the company successfully marketed vacuums in the United Kingdom with the slogan "Nothing sucks like an Electrolux".  In the United States, it was frequently assumed that using this slogan was a brand blunder. In fact, the informal American meaning of the word sucks was already well known at the time in the United Kingdom, and the company hoped the slogan, with its possible double entendre, would gain attention. In Indonesia, the Electrolux previous slogans as "Kalau saja semua seawet Electrolux" (English: If Only All Durable as Electrolux).

Electrolux AB (commonly known as Electrolux, ) is a Swedish multinational home appliance manufacturer, headquartered in Stockholm. It is consistently ranked the world's second largest appliance maker by units sold after Whirlpool.


Early life.

Higuita was born in Medellín, Antioquia to a single mother, Maria Dioselina. His mother died when he was very young, so his grandma had to take care of him. He was very poor as a child, so he had to work as newspaper mailman and many other jobs in order to survive.

Club career.

Higuita started his playing career with Millonarios and transferred to Atlético Nacional in 1986. He played the majority of his club career with the Colombian side where he helped the team win the Colombian League on numerous occasions as well as the Copa Libertadores and Copa Interamericana, both in 1989. After leaving them, he moved to Spain to play with Real Valladolid for one season, before coming back to Atletico Nacional for four years. He then left for Mexico to play for Veracruz before coming back to the Colombian league to play for Atletico's city rivals, Independiente Medellín.  He briefly retired in 2005 after failing a drug test while playing for Aucas.  He came out of retirement on 21 July 2007 to sign for Venezuelan club Guaros FC. In January 2008, aged 41, he signed for the Colombian second division team Deportivo Rionegro. In June 2008 he signed for another Colombia team, Deportivo Pereira, and finally retired on 25 January 2010.

International career.

Higuita's first major tournament was the 1989 Copa América, where the team was knocked out in the first round. In the 1990 FIFA World Cup, he played an important part to lead the country into the round of 16 for the first time ever. However, Higuita's unorthodox playing style caused a mistake by him that knocked Colombia out of the World Cup, when he tried to feint Cameroon striker Roger Milla but failed, and Milla dispossessed him and scored, which put Cameroon through to the quarter-finals. Higuita described it as "a mistake as big as a house". As a result of such behaviour, Higuita was nicknamed "El Loco" ("The Madman").  He played in the 1991 Copa América where the team finished fourth. His last call up for the national team was for the 1999 Copa América.  Higuita often took set-pieces for the Colombian national team, in all, he scored three goals in his 68 international appearances.

Style of play.

On the pitch, Higuita was known for his dramatic flair, composure under pressure, and eccentric playing style, often taking unnecessary risks and actively coming out of his area to anticipate opponents, play the ball out to defenders, undertake individual dribbling runs, and attempt to score goals, which led him to be described as a'sweeper-keeper'; he was therefore a pioneer in influencing other goalkeepers to take more responsibility for situations further away from the goal. Although he was a goalkeeper, Higuita also became known for scoring directly from free-kicks, as well as penalties.  His style of play led to the creation of the Back-pass rule, which is also known as the "Higuita Law."  IFFHS ranked Higuita the 8th best keeper in South American history.  Higuita's style of play, which was first shown to a global audience during the 1990 FIFA World Cup, was pioneering in influencing goalkeepers to take more responsibility for situations further from the goal.

Scorpion Kick.

Furthermore, Higuita reportedly invented the scorpion kick, a movement which involves the player jumping forward, positioning their legs over their head, and in doing so, kicks the ball away with their heels; one of Higuita's most notable uses of the scorpion was when he performed it while clearing a cross from Jamie Redknapp during a friendly against England at Wembley Stadium on 6 September 1995, earning him considerable media attention. It ranked 94th in Channel 4's "100 Greatest Sporting Moments" in 2002.

Coaching career.

Higuita has expressed the wish to coach the Colombian national team and in December 2008 he got the job of goalkeeper coach for his former club Real Valladolid.  He joined Al Nassr FC in Saudi Arabia in 2011, and was the club goalkeeper coach for about 5 years, until 2016.  He rejoined Atletico Nacional on 28 June 2017 after receiving a coaching job as the goalkeeping coach. Upon rejoining, he said "the dream of my life was to return to Atletico Nacional".

Personal life.

Higuita is married to Magnolia, with whom he has three children, Andrés, Pamela and Wilfred. He also has a daughter, Cindy Carolina, from a previous marriage.  He is friends with Diego Maradona and played in the Argentine's farewell match in 2001.  Higuita was imprisoned in 1993 after getting involved in a kidnapping. Acting as a go-between for the drug barons Pablo Escobar and Carlos Molina, he was largely responsible for securing the release of Molina's daughter by delivering the ransom money. He received $64,000 for his services, which breaks Colombian law as it is an offence to profit from a kidnapping. He was incarcerated for seven months before being released without charge. Commenting on the case, he has stated that "I'm a footballer, I didn't know anything about kidnapping laws."  In the ESPN documentary "The Two Escobars", Higuita claimed that he was arrested for visiting Pablo during his time in prison with the desire to thank him for turning himself in thus stabilizing Colombia for a short period. He supported this theory claiming that all he was asked during questioning was solely about Pablo Escobar himself and no kidnapping.  Because of the term in prison Higuita was not fit for the 1994 FIFA World Cup. In another scandal, he tested positive for cocaine on 23 November 2004 while playing for Aucas, an Ecuadorian football club.  In 2005, Higuita participated in the reality TV program "La isla de los famosos: Una aventura pirata" ("The Island of the Famous: A Pirate Adventure"), a show similar to "Survivor". Also in 2005, he underwent plastic surgery to completely change his appearance.  Higuita has expressed the wish to become more politically active.

Career statistics.

International goals.

"Scores and results lists Colombia's goal tally first."

Honours.

Club.

Atlético Nacional

International.

Colombia

José René Higuita Zapata (; born 27 August 1966) is a Colombian former professional footballer who played as a goalkeeper. He was nicknamed "El Loco" ("The Madman") for his high-risk'sweeper-keeper' playing style and his flair for the dramatic.


History.

Planning began in the late 1970s and the final project was submitted in 1985. Construction of four operating units began in 1987. The project was expected to be completed in 1991 with estimated building costs of 35 billion Kčs. Six villages were demolished by the then-Communist government to make way for the power station.  After the Velvet revolution in 1990 the Czechoslovakian government decided to cease construction of the third and fourth reactors. Work continued on the first two reactors; in the 1990s alterations to the original design were made by Westinghouse in conjunction with SUJB and the IAEA to bring reliability and safety levels into conformance with Western European standards. The standards audit was carried out by Halliburton NUS. As part of the alterations information and control systems were added, electrical modifications carried out, and cabling, reactor core and fuel elements were replaced. In 1993 the Czech government decided to complete the plant in the face of delays and cost overruns, with expected completion at the time estimated for 1997. In 1994 an opinion poll reported that 68% of Czech citizens were in favor of nuclear power development.  In 1998 construction still was not completed and costs reached 71 CZK billion. The Czech government again reconsidered completion of the plant. In 1999 the decision was made to continue, hoping for an expected completion in 2000 with a maximum cost of 98.6 CZK billion. The project was controversial; national and international (mainly Austrian) opposition was stronger than in the early 1990s. In a 1999 opinion poll 47% of Czech citizens were in favor and 53% against nuclear power development, a fall from 1994. In subsequent years the same poll showed change to 63% in favor and 37% against in 2000 with 58% in favor and 42% against in 2001, indicating fluctuation of opinion. As early as 1993 there were local and international protests against the plant's construction. Large grassroots civil disobedience actions took place in 1996 and 1997. These were organized by the so-called Clean Energy Brigades. In September and October 2000, Austrian anti-nuclear protesters demonstrated against the Temelin Nuclear Power Plant and at one stage temporarily blocked all 26 border crossings between Austria and the Czech Republic. The first reactor was finally commissioned in 2000 and the second in 2002.

Technical data.

Most information was taken from ČEZ website Others from leaflet "Energy from South Bohemia" by ČEZ Group and the IAEA PRIS database. In 2013 the reactors were updated from 3000 MW thermal output to 3120 MW output, bringing the total output to 1003 MWe net and 1056 MWe gross. In 2015 turbomachinery was updated, bringing the total output to the current 1026 MWe net and 1080 MWe gross.

The reactor vessel (active zone).

The reactor contains 163 fuel assemblies. A single assembly has the shape of ~4.5m long hexagonal and inside are 312 fuel rods and 61 control rods. The fuel rods contain stacked cylindrical fuel pellets. Fuel enrichment: max. 4% (average 3.5%) of U (fissile isotope) Fuel load UO: 92t (The reactor splits about 3 kg of uranium every day) Fuel Replacement cycle: 4 years (every year 1/4 is changed) vessel height: ~11m, outside diameter: ~4.5m, wall thickness: 193mm The vessel is designed for up to 17.6MPa at 350 °C The vessel is made of high quality, low-alloy chrome-nickel-molybdenum-vanadium steel  For the reactor to produce thermal output 1W, 30 billion fissions of uranium-235 must take place every second. For a coal power station to produce the same output 1,500,000,000 billion carbon atoms must be burned.

Reactor cooling system.

Number of cooling loops: 4 Quantity of primary circuit coolant: 337 m Operating pressure: 15.7MPa Coolant inlet temperature: approx. 290 °C (554F) Coolant outlet temperature: approx. 320 °C (608F) Coolant flow through reactor: 23.5 m/s

Steam generator.

Number per reactor block: 4 Steam delivered per one generator: 1470 t/hour Steam outlet pressure: 6.3MPa Steam outlet temperature: 278.5 °C (533.3F)

Cooling circuit.

The plant has 4 cooling towers (each reactor has 2 towers). Each tower has a height of, a diameter of, and an external wall surface area of. Pure water is evaporated in cooling tower (~0.3m/s). The water needs to be constantly refilled.

Protective Envelope (containment).

Height of cylindrical section: 38m Inside diameter of cylindrical section: 45m Wall thickness: 1.2m Thickness of steel lining: 8mm

Turbine generator set.

Number per production block: 1 Number of steam turbine sections: 1 high pressure + 3 low pressure Speed: 3000 rpm Voltage on alternator's terminal: 24kV Alternator cooling: hydrogen – water

Reliability.

The International Atomic Energy Agency data show that Reactor 1 reaches a cumulative operating factor of about 63%, and Reactor 2 an operating factor of about 76%. The cumulative operating factor figures for Temelín NPP reactors are lower than the figures of similar reactors operated in Russia, where the cumulative operating factor is around 80-87%. ČEZ had increased operating factor and production in recent years and the plant reached 84% in 2012 with a total record production of 15 TWh.

New reactors.

Plans to build all four original reactors were reopened in 2005. However, in 2014 the prospective plans were cancelled.  In 2007 planning was suspended because a new government agreed not to promote nuclear energy; a Green Party was a member of the coalition government. However, in July 2008 ČEZ requested the Ministry of the Environment conduct an environmental impact assessment for two additional reactors. In 2009 regional approval was granted for the new build. In August 2009, ČEZ sought bids for two pressurized water reactors (PWRs). Shortly after the Fukushima nuclear accidents, Prime Minister Petr Nečas announced that the construction of new reactors will continue according to the original plans, but with the tender selection delayed to 2013.  In July 2012 ČEZ opened bids for the public contract for completing the Temelín Nuclear Power Plant in the presence of the bidders - Areva, a consortium of the Westinghouse Electric Company, LLC and WESTINGHOUSE ELECTRIC ČR, and a consortium of ŠKODA JS, Atomstroyexport, and Gidropress. In October 2012 ČEZ informed Areva that they have in their bid failed to meet statutory requirements. Moreover, Areva has not fulfilled some other crucial criteria defined in the tender. Since the award procedure has been conducted in accordance with the Public Procurement Act, Areva's bid had to be excluded from further evaluation.  In March 2013, a Russian led consortium, comprising Atomstroyexport, Gidropress and Skoda, signed contracts with the three Czech companies ZAT, HOCHTIEF CZ and UJV Rez, for the construction of the two new nuclear reactor units for Temelín-3 and Temelín-4. The reactors proposed are the MIR-1200 (Modernised International Reactor). ZAT would supply automated systems for the plant, HOCHTIEF CZ would be responsible for construction of the nuclear island, and UJV Rez would help compile project documentation for the nuclear and turbine islands, and also create working documentation for construction of the plant. A statement said the consortium is aiming for a “localisation level” of 75 percent. The other running project for the contract was Westinghouse with its AP1000 reactor. The winner of the contract was scheduled to be announced at the end of 2013.  In April 2014, ČEZ cancelled the project after the Czech government stated it does not plan to provide guarantees or other mechanisms to support the construction of low-emission power plants following discussions in the EU. The ČEZ CEO stated:

Temelín Nuclear Power Station (, abbreviation "JETE") is located near Temelín, a small village in the Czech Republic. Temelín NPP is owned by ČEZ Group, which employs 1000 workers at this site. The adjacent castle Vysoký Hrádek serves as an information centre.


Plant characteristics.

The plant has four reactors. As of December 31, 2011 CEZ reported turbine generator output (gross capacity) as listed below. Net capacity is a baseline estimate only. In 2005, Unit 3 was upgraded to 456 MWe gross capacity, and the same upgrade was made to Unit 1 and Unit 4 in 2007. Unit 3 was further upgraded in 2009 to 500MWe. In total an extra 240 MWe of capacity has been or will be added before 2013 in a comprehensive program of improvements including steam plant replacement, addition of instrumentation and fuel changes.  The reactors are fuelled by uranium dioxide UO2. Fuel is placed in the reactor in 312 fuel assemblies. Each assembly consists of 126 fuel rods with a hermetically sealed fuel.  Dukovany Nuclear Power Station has 8 cooling towers, each 125 metres tall.  West of the facility there is a 136 metre tall guyed tower for monitoring air radioactivity.  In 1994, a visitor information centre was opened at the site.

Power distribution.

The power lines leaving Dukovany Nuclear Power Station are mainly installed on delta type pylons. They run to Slavetice substation situated at 49°6'15" N and 16°7'10" E. At this substation the powerline to Dürnrohr in Austria starts.  Plant owner CEZ plans to install a district heating circuit to supply heat to homes and businesses in Brno. A pipeline over 40 kilometres in length could be installed after regional officials have considered CEZ's environmental impact statement for the project, submitted in July 2010.

Replacement.

In 2019 the Czech government gave preliminary approval for at least one new nuclear power unit for about 2035 to replace the four units expected to shut down between 2035 and 2037. The financial model proposed is a state guarantee so finance can be obtained at government interest rates, but no subsidy on operating costs or above market-price electricity rates.

Popular culture.

The Dukovany reactor complex appears in the video game "Tom Clancy's EndWar" as a potential battlefield.

The Dukovany Nuclear Power Station is a nuclear power plant near Dukovany, a village in the Czech Republic. It was the second nuclear power plant in Czechoslovakia (the Bohunice Nuclear Power Plant in what is now Slovakia was constructed in 1958), and the first one in what is now the Czech Republic. It is situated from the city of Třebíč, near the Dalešice Reservoir, where the plant sources its water supply. In 1970 Czechoslovakia and the Soviet Union ratified a contract for construction of two nuclear power plants. Actual construction work began four years later. From 1985 to 1987, four power units with pressurized water reactors were commissioned. All four are still in operation.


"Bona fides".

"Bona fides" is a Latin phrase meaning "good faith". Its ablative case is "bona fide", meaning "in good faith", which is often used as an adjective to mean "genuine". While today "fides" is concomitant to faith, a more technical translation of the Latin concept would be something like "reliability", in the sense of a trust between two parties for the potentiality of a relationship. In ancient Rome "bona fides" was always assumed by both sides, had implied responsibilities, and both legal and religious consequences if broken. Fides was one of the original virtues to be considered a religious "divinity" in Roman paganism. Modern interpretation is that it is a return of favor for the completion of a favor.

Law.

In law, "bona fides" denotes the mental and moral states of honesty and conviction regarding either the truth or the falsity of a proposition, or of a body of opinion; likewise regarding either the rectitude or the depravity of a line of conduct. As a legal concept "bona fides" is especially important in matters of equity. The concept of "bona fide" is also proclaimed by the original version of "Magna Carta". In contract law, the implied covenant of good faith is a general presumption that the parties to a contract will deal with each other honestly and fairly, so as not to destroy the right of the other party or parties to receive the benefits of the contract. In insurance law, the insurer's breach of the implied covenant may give rise to a legal liability known as insurance bad faith.  Most US jurisdictions view breaches of implied covenants of good faith and fair dealing solely as a variant of breach of contract. Linguistically, in the US, American English usage of "bona fides" applies it as synonymous with credentials, professional background, and documents attesting a person's identity, which is not synonymous with "bona fide" occupational qualifications. More recently, other common law countries have begun to adopt good faith as a general principle. In the UK, the High Court in "Yam Seng Pte Ltd v Int Trade Corp Ltd" expressed this preference. In Canada, the Supreme Court declared in "Bhasin v. Hrynew" that good faith was a general organizing principle.

Employment efforts.

"Bona fide" occupational qualifications (employer's good faith effort) are qualities or attributes that employers are allowed to consider when making decisions on the hiring and retaining of employees. An employer's good faith effort is used as an evaluation tool by the jurisdiction during the annual program review process to determine an employer's level of commitment to the reduction goals of the Washington State's Commute Trip Reduction (CTR) Law. United States federal and state governments are required by affirmative action (and other such laws) to look for disabled, minority, female, and veteran business enterprises when bidding public jobs. Good faith effort law varies from state to state and even within states depending on the awarding department of the government. Most good faith effort requires advertising in state certified publications, usually a trade and a focus publication. Other countries such as Canada have similar programs.

In wikis.

Public wikis depend on implicitly or explicitly assuming that its users are acting in good faith. Wikipedia's principle "Assume Good Faith" (often abbreviated AGF) has been a stated guideline since 2005. It has been described as "the first principle in the Wikipedia etiquette". According to one study of users' motives for contributing to Wikipedia, "while participants have both individualistic and collaborative motives, collaborative (altruistic) motives dominate."

Good faith (), in human interactions, is a sincere intention to be fair, open, and honest, regardless of the outcome of the interaction. While some Latin phrases have lost their literal meaning over centuries, this is not the case with "bona fides"; it is still widely used and interchangeable with its generally accepted modern-day English translation of "good faith". It is an important concept within law and business. The opposed concepts are bad faith, "mala fides" (duplicity) and perfidy (pretense). In contemporary English, the usage of "bona fides" is synonymous with credentials and identity. The phrase is sometimes used in job advertisements, and should not be confused with the "bona fide" occupational qualifications or the employer's good faith effort, as described below.


General definition in the context of error analysis.

Given a problem formula_4 and an algorithm formula_5 with an input "x", the "absolute" error is formula_6 and the "relative" error is formula_7.  In this context, the "absolute" condition number of a problem "f" is  and the "relative" condition number is

Matrices.

For example, the condition number associated with the linear equation "Ax" = "b" gives a bound on how inaccurate the solution "x" will be after approximation. Note that this is before the effects of round-off error are taken into account; conditioning is a property of the matrix, not the algorithm or floating-point accuracy of the computer used to solve the corresponding system. In particular, one should think of the condition number as being (very roughly) the rate at which the solution "x" will change with respect to a change in "b". Thus, if the condition number is large, even a small error in "b" may cause a large error in "x". On the other hand, if the condition number is small, then the error in "x" will not be much bigger than the error in "b".  The condition number is defined more precisely to be the maximum ratio of the relative error in "x" to the relative error in "b".  Let "e" be the error in "b". Assuming that "A" is a nonsingular matrix, the error in the solution "A""b" is "A""e". The ratio of the relative error in the solution to the relative error in "b" is  This is easily transformed to  The maximum value (for nonzero "b" and "e") is then seen to be the product of the two operator norms as follows:  The same definition is used for any consistent norm, i.e. one that satisfies  When the condition number is exactly one (which can only happen if "A" is a scalar multiple of a linear isometry), then a solution algorithm can find (in principle, meaning if the algorithm introduces no errors of its own) an approximation of the solution whose precision is no worse than that of the data.  However, it does not mean that the algorithm will converge rapidly to this solution, just that it will not diverge arbitrarily because of inaccuracy on the source data (backward error), provided that the forward error introduced by the algorithm does not diverge as well because of accumulating intermediate rounding errors.  The condition number may also be infinite, but this implies that the problem is ill-posed (does not possess a unique, well-defined solution for each choice of data; that is, the matrix is not invertible), and no algorithm can be expected to reliably find a solution.  The definition of the condition number depends on the choice of norm, as can be illustrated by two examples.  If formula_14 is the norm defined in the square-summable sequence space l (which matches the usual distance in a standard Euclidean space and is usually noted as formula_15), then  where formula_17 and formula_18 are maximal and minimal singular values of formula_19 respectively. Hence:  The condition number with respect to "L" arises so often in numerical linear algebra that it is given a name, the condition number of a matrix.  If formula_14 is the norm defined in the sequence space l of all bounded sequences (which matches the maximum of distances measured on projections into the base subspaces and is usually denoted by formula_28), and formula_19 is lower triangular non-singular (i.e., formula_30), then  The condition number computed with this norm is generally larger than the condition number computed with square-summable sequences, but it can be evaluated more easily (and this is often the only practicably computable condition number, when the problem to solve involves a "non-linear algebra", for example when approximating irrational and transcendental functions or numbers with numerical methods).  If the condition number is not too much larger than one, the matrix is well-conditioned, which means that its inverse can be computed with good accuracy. If the condition number is very large, then the matrix is said to be ill-conditioned. Practically, such a matrix is almost singular, and the computation of its inverse, or solution of a linear system of equations is prone to large numerical errors. A matrix that is not invertible has condition number equal to infinity.

Nonlinear.

Condition numbers can also be defined for nonlinear functions, and can be computed using calculus. The condition number varies with the point; in some cases one can use the maximum (or supremum) condition number over the domain of the function or domain of the question as an overall condition number, while in other cases the condition number at a particular point is of more interest.

One variable.

The condition number of a differentiable function formula_4 in one variable as a function is formula_33. Evaluated at a point formula_34, this is  Most elegantly, this can be understood as (the absolute value of) the ratio of the logarithmic derivative of formula_4, which is formula_37, and the logarithmic derivative of formula_34, which is formula_39, yielding a ratio of formula_40. This is because the logarithmic derivative is the infinitesimal rate of relative change in a function: it is the derivative formula_41 scaled by the value of formula_4. Note that if a function has a zero at a point, its condition number at the point is infinite, as infinitesimal changes in the input can change the output from zero to positive or negative, yielding a ratio with zero in the denominator, hence infinite relative change.  More directly, given a small change formula_43 in formula_34, the relative change in formula_34 is formula_46, while the relative change in formula_47 is formula_48. Taking the ratio yields  The last term is the difference quotient (the slope of the secant line), and taking the limit yields the derivative.  Condition numbers of common elementary functions are particularly important in computing significant figures and can be computed immediately from the derivative; see significance arithmetic of transcendental functions. A few important ones are given below:

Several variables.

Condition numbers can be defined for any function formula_4 mapping its data from some domain (e.g. an formula_51-tuple of real numbers formula_34) into some codomain (e.g. an formula_53-tuple of real numbers formula_47), where both the domain and codomain are Banach spaces. They express how sensitive that function is to small changes (or small errors) in its arguments. This is crucial in assessing the sensitivity and potential accuracy difficulties of numerous computational problems, for example, polynomial root finding or computing eigenvalues.  The condition number of formula_4 at a point formula_34 (specifically, its relative condition number) is then defined to be the maximum ratio of the fractional change in formula_47 to any fractional change in formula_34, in the limit where the change formula_59 in formula_34 becomes infinitesimally small:  where formula_14 is a norm on the domain/codomain of formula_4.  If formula_4 is differentiable, this is equivalent to:  where denotes the Jacobian matrix of partial derivatives of formula_4 at formula_34, and formula_68 is the induced norm on the matrix.

In the field of numerical analysis, the condition number of a function measures how much the output value of the function can change for a small change in the input argument. This is used to measure how sensitive a function is to changes or errors in the input, and how much error in the output results from an error in the input. Very frequently, one is solving the inverse problem: given formula_1 one is solving for "x," and thus the condition number of the (local) inverse must be used. In linear regression the condition number of the moment matrix can be used as a diagnostic for multicollinearity.