title: Redding, California

text: During the Gold Rush, 49ers found gold to the north on Rock, Middle and Salt creeks, near Shasta, California, and to the south along Oregon and Olney creeks but the area that is now Redding was poor placer gold ground and called Poverty Flats. In 1868 the first land agent for the Central Pacific Railroad, a former Sacramento politician named Benjamin B. Redding, bought property in Poverty Flats on behalf of the railroad for a northern terminus, which the tracks reached in 1872. In the process of building the terminus, the railroad also built the town of Redding which was officially incorporated on October 4, 1887. In 1888, Redding won the county seat from Shasta.


title: Redding, California

text: In the early twentieth century the town's economic growth was spurred by the significant copper and iron mineral extraction industry nearby. The mining industry eventually declined, causing the economy and population to falter by 1920. It recovered in the thirties as the economy boomed due to the construction of Shasta Dam to the northwest. The building of the dam, which was completed in 1945, caused Redding's population to nearly double, also spurring the growth and development of other towns in the area.


title: Redding, California

text: Redding continued to grow steadily in the 1950s due to the region's growing lumber industry and tourism brought about by the newly completed dam. The constructions of Whiskeytown and Keswick dams also helped boost the economy by bringing new workers to the area. Interstate 5 was built during the sixties and seventies, which added to development and tourism in the region.


title: Redding, California

text: Growth in Redding during the 1960s and 1970s was further spurred by the annexation of an area east of the Sacramento River that included the unincorporated community of Enterprise; the residents voted to support the annexation primarily to acquire less expensive electricity via Redding's municipal utility, which receives power from the dam.


title: Redding, California

text: During the 1970s, the lumber industry suffered from decline. In the early 1990's Lumber mills in the area closed down due to the preservation of the living habitat of the Spotted Owl. This heavily impacted the Redding area. The economy picked up, due to a retail and housing boom in the late 1980s that continued until the mid-1990s.


title: Redding, California

text: The 21st century has also seen a number of devastating wildfires near and in Redding. In 1999, the Jones Fire destroyed over 100 structures, followed by the Bear Fire in 2004. In late July 2018, the Carr Fire in Shasta County seriously impacted the Redding area with the destruction of at least 1,100 buildings, with several thousand more threatened, 38,000 people instructed to evacuate and 6 deaths. Most recently, the Fawn Fire in 2021 also resulted in the evacuation of over 4,000 people and the destruction of 185 buildings.


title: Redding, California

text: According to the United States Census Bureau, the city has a total area of . of it is land, and of it (2.50%) is beneath water.


title: Redding, California

text: Redding is located at the very northwestern end of the Central Valley, which transitions into the Cascade foothills. The city is surrounded by mountains to the north, east, and west and fertile farm land to the south. Outermost parts of the city are part of the Cascade foothills, whereas southern and central areas are in the Sacramento Valley.


title: Redding, California

text: The elevation in Redding is on average, whereas anywhere to the north, east, or west of downtown ranges between and feet. Southern portions range between and .


title: Redding, California

text: The Shasta Dam on the Sacramento River provides a considerable level of flood protection for Redding. The dam is capable of controlling flows up to 79,000 cubic feet (7,300 cubic meters) per second. The flow rate exceeded this threshold in both 1970 and 1974.


title: Redding, California

text: Soils in and around town are composed mostly of clay or gravelly loam texture, with red or brown mineral horizons. They are slightly or moderately acidic in their natural state.


title: Redding, California

text: There are several rare and endangered species in Redding and its immediate vicinity. The Redding Redevelopment Plan EIR notes the California State listed endangered species, slender Orcutt grass ("Orcuttia tenuis"), occurs in eastern Redding near the municipal airport, where vernal pools are known to exist. This endemic grass is a Federal Candidate for listing and is endangered throughout its range, confined to several populations, and seriously threatened by agriculture, overgrazing, and residential development. Vernal pools provide the preferred habitat for this plant, which the California Native Plant Society considers a rare and endangered species. These same vernal pools also support federally protected species such as the federally threatened vernal pool fairy shrimp (Branchinecta lynchi).


title: Redding, California

text: Redding has a hot-summer Mediterranean climate (Köppen: Csa), with very hot, dry summers and cool, wet winters. Redding is known for very high summer temperatures, despite being located just north of the 40th Parallel North. Winter (October–April) provides the most precipitation of any season in Redding—the weather tends to be either rainy or foggy and at times, snow occurs. While summers are mostly hot and dry, thunderstorms are not uncommon. The average daily maximum temperature in July stays near . The highest official recorded temperature in Redding was on July 20, 1988, recorded at the nearby Redding Regional Airport and the most recent of three occasions; however, some residents say they recall a high temperature of 121 in the summer of 1981 and even just recently, 126 in the summer of 2020. Redding has an average possible sunshine of 88%, the second-highest percentage (after Yuma, Arizona) of any US city.


title: Redding, California

text: Summer overnight lows are unusually warm by Sacramento Valley standards and average warmer than coastal towns' daytime highs. The warmest night annually averages . Since the station opened in 1986, the hottest night was in June 2004. Redding's warm summer days and nights compared to areas further south are a result of a greater distance to maritime influences than the lower end of the valley.


title: Redding, California

text: Redding occasionally receives snow, though it has received as much as of snow in a single storm, occurring on December 4–7, 1909 and December 22–24, 1968, including on December 23, 1968, the most in any calendar day on record. It rarely gets sleet or freezing rain. Frost occurs commonly in December through February, less often in March or November. In spring, rain is common. The city is located near the foothills of the Cascade and Klamath mountain ranges and it therefore gets much more rain than most places in the Sacramento Valley; temperature differentials between land and sea cause moist air from the latter to flow over the southern Sacramento valley during the summer months, producing intense heat in Redding. The direction of this winds switches from the north and east in the summer, as hot, high-pressure air flows from land to sea, making the area very dry. Tornadoes are extremely rare; flooding occurs only around the area near the Sacramento River. The coldest temperature recorded in Redding was on January 17, 2012, and December 9, 2009. The coldest daytime high of the year is averaging and the lowest on record is in 1990, which remains the latest year to record an ice day.


title: Redding, California

text: The 2010 United States Census reported that Redding had a population of 89,861. The population density was . The racial makeup of Redding was 77,117 (85.8%) White, 1,092 (1.2%) African American, 2,034 (2.3%) Native American, 3,034 (3.4%) Asian, 156 (0.2%) Pacific Islander, 2,307 (2.6%) from other races, and 4,121 (4.6%) from two or more races. There were 7,787 people of Hispanic or Latino origin, of any race (8.7%).


title: Redding, California

text: The Census reported that 87,841 people (97.8% of the population) lived in households, 1,138 (1.3%) lived in non-institutionalized group quarters, and 882 (1.0%) were institutionalized.


title: Redding, California

text: There were 36,130 households, out of which 11,012 (30.5%) had children under the age of 18 living in them, 16,001 (44.3%) were married couples living together, 4,806 (13.3%) had a female householder with no husband present, 1,984 (5.5%) had a male householder with no wife present. There were 2,570 (7.1%) unmarried opposite-sex partnerships, and 204 (0.6%) same-sex married couples or partnerships. 10,344 households (28.6%) were made up of individuals, and 4,622 (12.8%) had someone living alone who was 65 years of age or older. The average household size was 2.43. There were 22,791 families (63.1% of all households); the average family size was 2.94.


title: Redding, California

text: The population was spread out, with 20,518 people (22.8%) under the age of 18, 9,436 people (10.5%) aged 18 to 24, 21,725 people (24.2%) aged 25 to 44, 23,424 people (26.1%) aged 45 to 64, and 14,758 people (16.4%) who were 65 years of age or older. The median age was 38.5 years. For every 100 females, there were 93.8 males. For every 100 females age 18 and over, there were 90.4 males.


title: Redding, California

text: There were 38,679 housing units at an average density of , of which 19,968 (55.3%) were owner-occupied, and 16,162 (44.7%) were occupied by renters. The homeowner vacancy rate was 2.3%; the rental vacancy rate was 6.9%. 48,179 people (53.6% of the population) lived in owner-occupied housing units and 39,662 people (44.1%) lived in rental housing units.


title: Redding, California

text: The Redding Metropolitan Statistical Area (MSA) was recognized as the 29th Most Dynamic MSA in the United States in 2019 by the Walton Family Foundation. Redding was recognized for having a diversified economy with several large employers in different sectors.


title: Redding, California

text: According to the city's 2016 Comprehensive Annual Financial Report, the top employers in Redding are:


title: Redding, California

text: The city council is composed of Mayor Erin Resner, Vice Mayor Kristen Schreder, Julie Winter, Michael Dacquisto, and Mark Mezzano. The city manager is Barry Tippin.


title: Redding, California

text: Amtrak, the national passenger rail system, provides service to Redding station, operating its Coast Starlight daily in both directions between Seattle, Washington, and Los Angeles, California VA Portland, Oregon; Sacramento, California; Oakland, California; San Jose, California; Santa Barbara, California and all Intermediate station stops.


title: Redding, California

text: Amtrak California also provides Thruway Motorcoach service to Stockton or Sacramento for connections to the San Joaquins, which serve the San Francisco Bay Area, San Joaquin Valley and the Los Angeles area via bus connections.


title: Redding, California

text: Redding provides a city bus transportation system called RABA (Redding Area Bus Authority). RABA provides routes throughout the City of Redding and also provides transportation throughout Redding's suburbs. Transportation is also available by RABA to Burney, by Sage Stage to Alturas and by Trinity Transit to Weaverville. Redding is also served by the intercity bus companies Greyhound and Fronteras del Norte.


title: Redding, California

text: Shasta Regional Transportation Agency is developing a weekday commuter bus from Redding to the Sacramento Valley Station.


title: Redding, California

text: Air transportation for the Redding area is provided by two general aviation airports. Redding Regional Airport, located south of Redding, has scheduled flights from SkyWest (United Express) and Avelo Airlines. The smaller Benton Airpark is located on the western side of Redding.


title: Redding, California

text: This list includes notable persons who were born/raised/worked in, lived in, or whose identity was significantly influenced by Redding, as well as music groups that were founded in the area.


title: Russian submarine Belgorod (K-329)

text: K-329 "Belgorod" () is a modified design of the Oscar II class (NATO designation) Russian nuclear submarine. It was originally laid down in July 1992 as a Project 949A cruise missile submarine (NATO designation Oscar II class), but later was redesigned and the partly built hull was used to be reconfigured as a special operations vessel, able to operate unmanned underwater vehicles. The vessel was relaid in December 2012. Due to chronic underfunding, its construction was suspended then resumed at a low rate of progress before the ship was redesigned to become a unique vessel — the first Russian fifth-generation submarine, according to the Ministry of Defence.


title: Russian submarine Belgorod (K-329)

text: The K-329 Belgorod, along with the Status-6 Oceanic Multipurpose System, was one of the last weapons systems presented by Russian President Vladimir Putin during his annual speech on March 1, 2018. It tested at sea in 1H2022 and was commissioned by the Russian Navy in July 2022. The submarine was delivered to the Russian Navy on 8 July 2022.


title: Russian submarine Belgorod (K-329)

text: The "Belgorod" will reportedly be the first submarine to utilize the Status-6 Oceanic Multipurpose System.


title: Russian submarine Belgorod (K-329)

text: The submarine's construction was originally laid down on July 24, 1992 at the Severodvinsk Shipyard as pennant number 664 of the Oscar II class cruise missile submarines.


title: Russian submarine Belgorod (K-329)

text: On April 6, 1993, submarine 664 received the name "Belgorod" after the Russian city with that name and the tactical designation K-139. In 1995, crew training began at the Obninsk-based 510th Naval Training Center, named after L. G. Osipenko of the Russian Navy ("510-й учебный центр Военно-Морского Флота имени Л.Г. Осипенко"), but in 1997, construction was put on hold due to the severe economic crisis after the collapse of the Soviet Union (with the submarine three-quarters finished), mainly for financial reasons. On January 22, 1998, the crew was disbanded and the unfinished hull was mothballed. The loss of "Belgorod"s sister ship, the "Kursk", in 2000 led to the decision to resume construction of "Belgorod" to replace "Kursk," upgraded to Project 949AM specifications. By December 31, 2004 the hull was mostly complete, missing its powerplant, equipment and missile silos. The 100 million rubles provided by the Ministry of Defence was insufficient, and Sevmash was forced to use its own financial resources to make up for the deficit. Sevmash, on its own initiative, continued construction at a slow pace.


title: Russian submarine Belgorod (K-329)

text: The construction of the "Belgorod" was included in the 2006 investment plan of the Ministry of Defence, but during a visit at the shipyard by Minister of Defence Sergei Ivanov on July 20, 2006, came the news that the decision has been made not to commission the submarine in the Russian Navy. By that time, "Belgorod" was about 80% complete. The Ministry of Defence considered other options to finish the submarine, including selling it to the Indian Navy, which would have financed completion of the vessel.


title: Russian submarine Belgorod (K-329)

text: In 2009, re-designing the submarine and arming it with the cruise missiles originally developed for the Project 885 Yasen-class submarines was considered. In early 2012, the Commander-in-Chief of the Russian Navy, Admiral Vladimir Sergeyevich Vysotsky stated that "Belgorod" would be completed as a "special projects" vessel. On December 20, 2012, this specification received the official designation Project 09852. The submarine was planned for commissioning in the Navy in 2018, and a crew was formed once again in November of that same year.


title: Russian submarine Belgorod (K-329)

text: On April 23, 2019, the "Belgorod" was taken out of the covered dry dock and put afloat. The commander of the ship at that time was Captain 1st rank Anton Alyokhin. In the course of 2019, the sub was to complete its fitting out, nuclear reactor testing and sea worthiness trials. By June 2020, one source reported it "in service", though this appears to have been inaccurate. Others suggested it was still fitting out (possibly including sea trials). In January 2021, the director-general of the Russian Shipbuilder Sevmash, Mikhail Budnichenko, stated that tests on Belgorod were proceeding. The plans to commission the submarine in the Russian Navy in 2020 and to officially introduce the Poseidon system in 2021 did not materialize. A press report by the official Russia state-owned TASS agency from April 2021 indicates a new objective from the Russian Defense Ministry to send the K-329 into service in the Pacific zone. This information could confirm the problems encountered with the Losharik submarine and the shift to the background of the operations envisaged on the Arctic continental shelf. Also in April 2021, military analyst H. I. Sutton reported that the "Belgorod" was out of the water and had returned to the construction hall. On June 25, 2021, the "Belgorod" left the Severodvinsk shipyard for the first time on a trial regime by the builder Sevmash. The submarine was delivered to the Russian Navy on 8 July 2022.


title: Russian submarine Belgorod (K-329)

text: The "Belgorod" joined the . The division is a special formation, the operational arm of the (GUGI), which reports directly to the Russian Defence Ministry.


title: Russian submarine Belgorod (K-329)

text: In the construction process, the original 154-meter long hull was lengthened to 184 meters (which is almost 11 meter more than the Project 941 SSBNs - the world's largest submarines ever built) with a width of 18,2 meters.


title: Russian submarine Belgorod (K-329)

text: In June 2019, US military expert H.I. Sutton published satellite imagery of the Sevmash shipyard, which shows the K-329 ""Belgorod"" along with K-549 ""Knyaz Vladimir"" of the Borey project, with the Belgorod visibly longer and wider.


title: Russian submarine Belgorod (K-329)

text: On November 11, 2015, the Status-6 Oceanic Multipurpose System project was officially revealed to the public. The initial designation of Status-6 has since been changed to Poseidon (Russian weapon systems designation "2M39" and the NATO reporting name "Kanyon" has been assigned).


title: Russian submarine Belgorod (K-329)

text: The Poseidon type remotely operated underwater vehicle has a 10 000 km range, can dive to a depth of 1 000 meters and is designed to deliver nuclear warheads for the destruction of coastal infrastructure as a second nuclear strike option («оружия ответного удара»). The motherships for the Poseidon underwater drones are planned to be the 09852 ""Belgorod"" project submarines (like the ""Belgorod"") and the 09851 ""Khabarovsk"" project submarines. According to publications by the Russian state news agency TASS the submarines can carry up to six Poseidon vehicles at once and this view is shared by some military experts.


title: Russian submarine Belgorod (K-329)

text: Some sources state that in addition to the Poseidon AUVs, the Belgorod type can also operate as the mother ship for a single nuclear-powered mini-submarine of the 18511 project, otherwise known as Paltus type (Project 1851), used for the planting on the seabed of a self-contained mini-nuclear reactor of the ATGU 'Shelf' ("АТГУ Шельф", abbreviation stands for "Атомная турбогенераторная установка" - Nuclear Turbo-Generator Device) type. The ATGU Shelf is being developed for autonomous power generation of underwater sensor arrays and the submarine could piggy-back a single ATGU unit at a time, attached to its center deck section. The "Belgorod" is also planned to operate the Clavesin-2R-RM («"Клавесин-2Р-РМ"», clavesin is Russian for Harpsichord) unmanned underwater sensor vehicles.


title: Russian submarine Belgorod (K-329)

text: The loss of the "Losharik" nuclear mini-submarine after a major fire in 2019 has caused a major setback for the "Belgorod" programme. At the same time, some sources suggest that the full entry into service of Poseidon may not occur on the submarine until around 2027.


title: Russian submarine Belgorod (K-329)

text: The "Belgorod" Project is aimed at the development of a multi-role submarine platform with wide range of intelligence capabilities, in addition to its combat role. Among the strategic aims, which have influenced the re-design of the K-329 "Belgorod" is the desire to set up and exploit the Arctic shelf is a major Geo-strategy objective for the Kremlin in the short to medium term, mostly for exploitation of energy resources in the High North, but also for control of the increasingly important sea trade route through the Arctic Ocean due to the melting of the Arctic ice. An example for this shift towards the Arctic region can be seen in a new project to modernize and deploy a network of sonar listening stations, positioned on the Arctic seabed (code name Harmony, Russian: "Гармония"). High-ranking officials at the Pentagon as well as officers from other NATO member states have expressed their concerns in the period between the end of 2015 and the end of 2017 about the Russian plans for undersea cables for telecommunications.


title: Russian submarine Belgorod (K-329)

text: The new objective, in April 2021, from the Russian Defense Ministry to send the K-329 into service in the Pacific zone comes with rising military tensions in the North Pacific. At the time of the submarine's commissioning in July 2022, it was reported that she would operate in an initial experimental role with the Northern Fleet before transferring to the Pacific.


title: Romain Saïss

text: Romain Ghanem Paul Saïss (; born 26 March 1990) is a professional footballer who plays as a centre-back for Süper Lig club Beşiktaş and captains the Morocco national team.


title: Romain Saïss

text: Saïss began his career with Valence, then played for Le Havre and Clermont of Ligue 2, and Angers of Ligue 1 before joining Wolverhampton Wanderers in 2016. He made 206 appearances and scored 15 goals, before moving to Beşiktaş in 2021.


title: Romain Saïss

text: Born in France to a Moroccan father and French mother, Saïss represents Morocco at international level. A full international since 2012, he has earned over 70 caps for Morocco, becoming the team's captain in 2019. He has represented the nation at three Africa Cup of Nations tournaments and two FIFA World Cups, helping the team come fourth at the 2022 edition of the latter.


title: Romain Saïss

text: Saïss began his senior career with Valence in the Championnat de France Amateur 2 (fifth-tier), and supplemented his €500 monthly salary with washing up at his parents' restaurant. At 21, he signed his first professional contract with Clermont in Ligue 2.


title: Romain Saïss

text: In June 2013, Saïss moved across Ligue 2 to Le Havre on a two year deal. When it ended, he joined Ligue 1 side Angers on a two-year contract.


title: Romain Saïss

text: On 30 August 2016, Saïss moved to England, joining EFL Championship club Wolverhampton Wanderers for an undisclosed fee on a four-year deal. He made his debut on 17 September in a 2–0 win at Newcastle United. In the game, he was subjected to racial abuse by opponent Jonjo Shelvey, who was given a five-match ban and £100,000 fine by The FA in December.


title: Romain Saïss

text: Following Wolves' promotion to the Premier League in 2018, Saïss made his debut Premier League appearance as a substitute in a 1–1 draw with Manchester United at Old Trafford on 22 September 2018. His first start in the Premier League came in a 2–1 defeat away to Cardiff City at the Cardiff City Stadium on 30 November. He scored his first Premier League goal in a 1–1 draw with Fulham at Craven Cottage on 26 December 2018. On 21 February 2019 he agreed a new contract until the summer of 2021.


title: Romain Saïss

text: On 25 July 2019 Saïss made his debut appearance in UEFA European club football competition as a late substitute in Wolves's 2–0 home win against Crusaders in the 2019–20 UEFA Europa League Second Qualifying Round and on 24 October he scored his first goal in such a competition when he scored the opening goal of a 2–1 away win at Slovan Bratislava in the 2019–20 UEFA Europa League group stage.


title: Romain Saïss

text: Saïss triggered an automatic one-year extension to his contract on 18 March 2021, by making 20 starts in the Premier League during the 2020–21 season, tying him to the club until June 2022. He was described as the Moroccan Maldini by head coach Bruno Lage on 15 December that year, after his display in the away Premier League tie at Brighton & Hove Albion, where he scored the only goal in a much longed-for win (Wolves's first-ever win at Brighton in the top-flight in seven attempts dating back to 1979). He made his 100th appearance in the Premier League in 2–0 win away to Tottenham Hotspur on 13 February 2022. His 200th competitive appearance in all competitions for Wolves was on 5 March 2022 in a home fixture against Crystal Palace.


title: Romain Saïss

text: On 31 May 2022, Saïss announced that he would leave Wolves at the end of his contract on 1 July, having played 206 games for the club over six seasons, and scoring 15 goals, nine of them in the Premier League.


title: Romain Saïss

text: On 14 June 2022, Saïss moved to Turkey, joining Süper Lig club Beşiktaş. He made his debut on 6 August as the season began with a 1–0 home win over Kayserispor.


title: Romain Saïss

text: Saïss, who was born and raised in France to a Moroccan father and a French mother, chose to represent the Morocco national team. He made his debut in a 1–0 friendly loss to Togo in November 2012.


title: Romain Saïss

text: Saïss was in the Moroccan squad that reached the quarter-finals of the 2017 Africa Cup of Nations in Gabon. He scored his first international goal in their 3–1 group win over Togo. In June 2018, he was named in Morocco's 23-man squad for the 2018 FIFA World Cup in Russia, and featured in group games against Iran and Spain. After the 2019 Africa Cup of Nations, in which Morocco made the last 16, Saïss became the captain of the "Atlas Lions".


title: Romain Saïss

text: On 10 November 2022, Saïss was named in Morocco's 26-man squad for the 2022 FIFA World Cup in Qatar. He scored the opening goal of a 2–0 group stage victory over Belgium on 27 November, Morocco's first goal of the tournament. The goal had previously been awarded to Abdelhamid Sabiri, but Saïss was later credited for the goal by FIFA. In the semi-final against France – the first ever played by an African nation – he was substituted after 21 minutes due to injury as Morocco lost 2–0.


title: Romain Saïss

text: Saïss's father is Moroccan and his mother is French, both restaurant owners. He is a Muslim and observes fasting in the month of Ramadan.


title: Eigendecomposition of a matrix

text: In linear algebra, eigendecomposition is the factorization of a matrix into a canonical form, whereby the matrix is represented in terms of its eigenvalues and eigenvectors. Only diagonalizable matrices can be factorized in this way. When the matrix being factorized is a normal or real symmetric matrix, the decomposition is called "spectral decomposition", derived from the spectral theorem.


title: Eigendecomposition of a matrix

text: A (nonzero) vector of dimension is an eigenvector of a square matrix if it satisfies a linear equation of the form


title: Eigendecomposition of a matrix

text: for some scalar . Then is called the eigenvalue corresponding to . Geometrically speaking, the eigenvectors of are the vectors that merely elongates or shrinks, and the amount that they elongate/shrink by is the eigenvalue. The above equation is called the eigenvalue equation or the eigenvalue problem.


title: Eigendecomposition of a matrix

text: We call the characteristic polynomial, and the equation, called the characteristic equation, is an th order polynomial equation in the unknown . This equation will have distinct solutions, where . The set of solutions, that is, the eigenvalues, is called the spectrum of .


title: Eigendecomposition of a matrix

text: The integer is termed the algebraic multiplicity of eigenvalue . The algebraic multiplicities sum to : formula_4


title: Eigendecomposition of a matrix

text: There will be linearly independent solutions to each eigenvalue equation. The linear combinations of the solutions (except the one which gives the zero vector) are the eigenvectors associated with the eigenvalue . The integer is termed the geometric multiplicity of . It is important to keep in mind that the algebraic multiplicity and geometric multiplicity may or may not be equal, but we always have . The simplest case is of course when . The total number of linearly independent eigenvectors, , can be calculated by summing the geometric multiplicities


title: Eigendecomposition of a matrix

text: The eigenvectors can be indexed by eigenvalues, using a double index, with being the th eigenvector for the th eigenvalue. The eigenvectors can also be indexed using the simpler notation of a single index , with .


title: Eigendecomposition of a matrix

text: where is the square matrix whose th column is the eigenvector of , and is the diagonal matrix whose diagonal elements are the corresponding eigenvalues, . Note that only diagonalizable matrices can be factorized in this way. For example, the defective matrix formula_8 (which is a shear matrix) cannot be diagonalized.


title: Eigendecomposition of a matrix

text: The eigenvectors are usually normalized, but they need not be. A non-normalized set of eigenvectors, can also be used as the columns of . That can be understood by noting that the magnitude of the eigenvectors in gets canceled in the decomposition by the presence of . If one of the eigenvalues has more than one linearly independent eigenvectors (that is, the geometric multiplicity of is greater than 1), then these eigenvectors for this eigenvalue can be chosen to be mutually orthogonal; however, if two eigenvectors belong to two different eigenvalues, it may be impossible for them to be orthogonal to each other (see Example below). One special case is that if is a normal matrix, then by the spectral theorem, it's always possible to diagonalize in an orthonormal basis .


title: Eigendecomposition of a matrix

text: The linearly independent eigenvectors with nonzero eigenvalues form an orthogonal basis (not necessarily orthonormal) for all possible products , for , which is the same as the image (or range) of the corresponding matrix transformation, and also the column space of the matrix . The number of linearly independent eigenvectors with nonzero eigenvalues is equal to the rank of the matrix , and also the dimension of the image (or range) of the corresponding matrix transformation, as well as its column space.


title: Eigendecomposition of a matrix

text: The linearly independent eigenvectors with an eigenvalue of zero form a basis (which can be chosen to be orthonormal) for the null space (also known as the kernel) of the matrix transformation .


title: Eigendecomposition of a matrix

text: giving us the solutions of the eigenvalues for the matrix as or , and the resulting diagonal matrix from the eigendecomposition of is thus formula_23.


title: Eigendecomposition of a matrix

text: If a matrix can be eigendecomposed and if none of its eigenvalues are zero, then is invertible and its inverse is given by


title: Eigendecomposition of a matrix

text: If formula_29 is a symmetric matrix, since formula_30 is formed from the eigenvectors of formula_29, formula_30 is guaranteed to be an orthogonal matrix, therefore formula_33. Furthermore, because is a diagonal matrix, its inverse is easy to calculate:


title: Eigendecomposition of a matrix

text: When eigendecomposition is used on a matrix of measured, real data, the inverse may be less valid when all eigenvalues are used unmodified in the form above. This is because as eigenvalues become relatively small, their contribution to the inversion is large. Those near zero or at the "noise" of the measurement system will have undue influence and could hamper solutions (detection) using the inverse.


title: Eigendecomposition of a matrix

text: Two mitigations have been proposed: truncating small or zero eigenvalues, and extending the lowest reliable eigenvalue to those below it.


title: Eigendecomposition of a matrix

text: The first mitigation method is similar to a sparse sample of the original matrix, removing components that are not considered valuable. However, if the solution or detection process is near the noise level, truncating may remove components that influence the desired solution.


title: Eigendecomposition of a matrix

text: The second mitigation extends the eigenvalue so that lower values have much less influence over inversion, but do still contribute, such that solutions near the noise will still be found.


title: Eigendecomposition of a matrix

text: The reliable eigenvalue can be found by assuming that eigenvalues of extremely similar and low value are a good representation of measurement noise (which is assumed low for most systems).


title: Eigendecomposition of a matrix

text: If the eigenvalues are rank-sorted by value, then the reliable eigenvalue can be found by minimization of the Laplacian of the sorted eigenvalues:


title: Eigendecomposition of a matrix

text: where the eigenvalues are subscripted with an to denote being sorted. The position of the minimization is the lowest reliable eigenvalue. In measurement systems, the square root of this reliable eigenvalue is the average noise over the components of the system.


title: Eigendecomposition of a matrix

text: The eigendecomposition allows for much easier computation of power series of matrices. If is given by


title: Eigendecomposition of a matrix

text: The off-diagonal elements of are zero; that is, is also a diagonal matrix. Therefore, calculating reduces to just calculating the function on each of the eigenvalues.


title: Eigendecomposition of a matrix

text: When is normal or real symmetric matrix, the decomposition is called "spectral decomposition", derived from the spectral theorem.


title: Eigendecomposition of a matrix

text: A complex-valued square matrix is normal (meaning , where is the conjugate transpose) if and only if it can be decomposed as


title: Eigendecomposition of a matrix

text: where is a unitary matrix (meaning ) and is a diagonal matrix. The columns u, ..., u of form an orthonormal basis and are eigenvectors of with corresponding eigenvalues "λ", ..., "λ".


title: Eigendecomposition of a matrix

text: If is restricted to be a Hermitian matrix (), then has only real valued entries. If is restricted to a unitary matrix, then takes all its values on the complex unit circle, that is, .


title: Eigendecomposition of a matrix

text: As a special case, for every real symmetric matrix, the eigenvalues are real and the eigenvectors can be chosen real and orthonormal. Thus a real symmetric matrix can be decomposed as


title: Eigendecomposition of a matrix

text: where is an orthogonal matrix whose columns are (the above chosen, real and orthonormal) eigenvectors of , and is a diagonal matrix whose entries are the eigenvalues of .


title: Eigendecomposition of a matrix

text: This sequence will almost always converge to an eigenvector corresponding to the eigenvalue of greatest magnitude, provided that has a nonzero component of this eigenvector in the eigenvector basis (and also provided that there is only one eigenvalue of greatest magnitude). This simple algorithm is useful in some practical applications; for example, Google uses it to calculate the page rank of documents in their search engine. Also, the power method is the starting point for many more sophisticated algorithms. For instance, by keeping not just the last vector in the sequence, but instead looking at the span of "all" the vectors in the sequence, one can get a better (faster converging) approximation for the eigenvector, and this idea is the basis of Arnoldi iteration. Alternatively, the important QR algorithm is also based on a subtle transformation of a power method.


title: Eigendecomposition of a matrix

text: However, in practical large-scale eigenvalue methods, the eigenvectors are usually computed in other ways, as a byproduct of the eigenvalue computation. In power iteration, for example, the eigenvector is actually computed before the eigenvalue (which is typically computed by the Rayleigh quotient of the eigenvector). In the QR algorithm for a Hermitian matrix (or any normal matrix), the orthonormal eigenvectors are obtained as a product of the matrices from the steps in the algorithm. (For more general matrices, the QR algorithm yields the Schur decomposition first, from which the eigenvectors can be obtained by a backsubstitution procedure.) For Hermitian matrices, the Divide-and-conquer eigenvalue algorithm is more efficient than the QR algorithm if both eigenvectors and eigenvalues are desired.


title: Eigendecomposition of a matrix

text: Recall that the "geometric" multiplicity of an eigenvalue can be described as the dimension of the associated eigenspace, the nullspace of . The algebraic multiplicity can also be thought of as a dimension: it is the dimension of the associated generalized eigenspace (1st sense), which is the nullspace of the matrix for "any sufficiently large ". That is, it is the space of "generalized eigenvectors" (first sense), where a generalized eigenvector is any vector which "eventually" becomes 0 if is applied to it enough times successively. Any eigenvector is a generalized eigenvector, and so each eigenspace is contained in the associated generalized eigenspace. This provides an easy proof that the geometric multiplicity is always less than or equal to the algebraic multiplicity.


title: Eigendecomposition of a matrix

text: A conjugate eigenvector or coneigenvector is a vector sent after transformation to a scalar multiple of its conjugate, where the scalar is called the conjugate eigenvalue or coneigenvalue of the linear transformation. The coneigenvectors and coneigenvalues represent essentially the same information and meaning as the regular eigenvectors and eigenvalues, but arise when an alternative coordinate system is used. The corresponding equation is


title: Eigendecomposition of a matrix

text: For example, in coherent electromagnetic scattering theory, the linear transformation represents the action performed by the scattering object, and the eigenvectors represent polarization states of the electromagnetic wave. In optics, the coordinate system is defined from the wave's viewpoint, known as the Forward Scattering Alignment (FSA), and gives rise to a regular eigenvalue equation, whereas in radar, the coordinate system is defined from the radar's viewpoint, known as the Back Scattering Alignment (BSA), and gives rise to a coneigenvalue equation.


title: Eigendecomposition of a matrix

text: A generalized eigenvalue problem (second sense) is the problem of finding a (nonzero) vector that obeys


title: Eigendecomposition of a matrix

text: where and are matrices. If obeys this equation, with some , then we call the "generalized eigenvector" of and (in the second sense), and is called the "generalized eigenvalue" of and (in the second sense) which corresponds to the generalized eigenvector . The possible values of must obey the following equation


title: Eigendecomposition of a matrix

text: If linearly independent vectors can be found, such that for every , , then we define the matrices and such that


title: Eigendecomposition of a matrix

text: And since is invertible, we multiply the equation from the right by its inverse, finishing the proof.


title: Eigendecomposition of a matrix

text: The set of matrices of the form , where is a complex number, is called a "pencil"; the term "matrix pencil" can also refer to the pair of matrices.


title: Eigendecomposition of a matrix

text: which is a standard eigenvalue problem. However, in most situations it is preferable not to perform the inversion, but rather to solve the generalized eigenvalue problem as stated originally. This is especially important if and are Hermitian matrices, since in this case is not generally Hermitian and important properties of the solution are no longer apparent.


title: Eigendecomposition of a matrix

text: If and are both symmetric or Hermitian, and is also a positive-definite matrix, the eigenvalues are real and eigenvectors and with distinct eigenvalues are -orthogonal (). In this case, eigenvectors can be chosen so that the matrix defined above satisfies


title: Eigendecomposition of a matrix

text: and there exists a basis of generalized eigenvectors (it is not a defective problem). This case is sometimes called a "Hermitian definite pencil" or "definite pencil".


title: Sky

text: The sky is an unobstructed view upward from the surface of the Earth. It includes the atmosphere and outer space. It may also be considered a place between the ground and outer space, thus distinct from outer space.


title: Sky

text: In the field of astronomy, the sky is also called the celestial sphere. This is an abstract sphere, concentric to the Earth, on which the Sun, Moon, planets, and stars appear to be drifting. The celestial sphere is conventionally divided into designated areas called constellations.


title: Sky

text: Usually, the term "sky" informally refers to a perspective from the Earth's surface; however, the meaning and usage can vary. An observer on the surface of the Earth can see a small part of the sky, which resembles a dome (sometimes called the "sky bowl") appearing flatter during the day than at night. In some cases, such as in discussing the weather, the sky refers to only the lower, denser layers of the atmosphere.


title: Sky

text: The daytime sky appears blue because air molecules scatter shorter wavelengths of sunlight more than longer ones (redder light). The night sky appears to be a mostly dark surface or region spangled with stars. The Sun and sometimes the Moon are visible in the daytime sky unless obscured by clouds. At night, the Moon, planets, and stars are similarly visible in the sky.


title: Sky

text: Some of the natural phenomena seen in the sky are clouds, rainbows, and aurorae. Lightning and precipitation are also visible in the sky. Certain birds and insects, as well as human inventions like aircraft and kites, can fly in the sky. Due to human activities, smog during the day and light pollution during the night are often seen above large cities.


title: Sky

text: The word "sky" comes from the Old Norse , meaning 'cloud, abode of God'. The Norse term is also the source of the Old English , which shares the same Indo-European base as the classical Latin , meaning 'obscure'.


title: Sky

text: In Old English, the term "heaven" was used to describe the observable expanse above the earth. Throughout mentions in Middle English, it was gradually restricted to its current, religious meaning.


title: Sky

text: Except for direct sunlight, most of the light in the daytime sky is caused by scattering, which is dominated by a small-particle limit called Rayleigh scattering. The scattering due to molecule-sized particles (as in air) is greater in the directions both toward and away from the source of light than it is in directions perpendicular to the incident path. Scattering is significant for light at all visible wavelengths, but is stronger at the shorter (bluer) end of the visible spectrum, meaning that the scattered light is bluer than its source: the Sun. The remaining direct sunlight, having lost some of its shorter-wavelength components, appears slightly less blue.


title: Sky

text: Scattering also occurs even more strongly in clouds. Individual water droplets refract white light into a set of colored rings. If a cloud is thick enough, scattering from multiple water droplets will wash out the set of colored rings and create a washed-out white color.


title: Sky

text: The sky can turn a multitude of colors such as red, orange, purple, and yellow (especially near sunset or sunrise) when the light must travel a much longer path (or optical depth) through the atmosphere. Scattering effects also partially polarize light from the sky and are most pronounced at an angle 90° from the Sun. Scattered light from the horizon travels through as much as 38 times the air mass as does light from the zenith, causing a blue gradient looking vivid at the zenith and pale near the horizon. Red light is also scattered if there is enough air between the source and the observer, causing parts of the sky to change color as the Sun rises or sets. As the air mass nears infinity, scattered daylight appears whiter and whiter.


title: Sky

text: Apart from the Sun, distant clouds or snowy mountaintops may appear yellow. The effect is not very obvious on clear days, but is very pronounced when clouds cover the line of sight, reducing the blue hue from scattered sunlight. At higher altitudes, the sky tends toward darker colors since scattering is reduced due to lower air density. An extreme example is the Moon, where no atmospheric scattering occurs, making the lunar sky black even when the Sun is visible.


title: Sky

text: Sky luminance distribution models have been recommended by the International Commission on Illumination (CIE) for the design of daylighting schemes. Recent developments relate to "all sky models" for modelling sky luminance under weather conditions ranging from clear to overcast.


title: Sky

text: The brightness and color of the sky vary greatly over the course of a day, and the primary cause of these properties differs as well. When the Sun is well above the horizon, direct scattering of sunlight (Rayleigh scattering) is the overwhelmingly dominant source of light. However, during twilight, the period between sunset and night or between night and sunrise, the situation is more complex.


title: Sky

text: Green flashes and green rays are optical phenomena that occur shortly after sunset or before sunrise, when a green spot is visible above the Sun, usually for no more than a second or two, or it may resemble a green ray shooting up from the sunset point. Green flashes are a group of phenomena that stem from different causes, most of which occur when there is a temperature inversion (when the temperature increases with altitude rather than the normal decrease in temperature with altitude). Green flashes may be observed from any altitude (even from an aircraft). They are usually seen above an unobstructed horizon, such as over the ocean, but are also seen above clouds and mountains. Green flashes may also be observed at the horizon in association with the Moon and bright planets, including Venus and Jupiter.


title: Sky

text: Earth's shadow is the shadow that the planet casts through its atmosphere and into outer space. This atmospheric phenomenon is visible during civil twilight (after sunset and before sunrise). When the weather conditions and the observing site permit a clear view of the horizon, the shadow's fringe appears as a dark or dull bluish band just above the horizon, in the low part of the sky opposite of the (setting or rising) Sun's direction. A related phenomenon is the Belt of Venus (or antitwilight arch), a pinkish band that is visible above the bluish band of Earth's shadow in the same part of the sky. No defined line divides Earth's shadow and the Belt of Venus; one colored band fades into the other in the sky.


title: Sky

text: Twilight is divided into three stages according to the Sun's depth below the horizon, measured in segments of 6°. After sunset, the civil twilight sets in; it ends when the Sun drops more than 6° below the horizon. This is followed by the nautical twilight, when the Sun is between 6° and 12° below the horizon (depth between −6° and −12°), after which comes the astronomical twilight, defined as the period between −12° and −18°. When the Sun drops more than 18° below the horizon, the sky generally attains its minimum brightness.


title: Sky

text: Several sources can be identified as the source of the intrinsic brightness of the sky, namely airglow, indirect scattering of sunlight, scattering of starlight, and artificial light pollution.


title: Sky

text: The term night sky refers to the sky as seen at night. The term is usually associated with skygazing and astronomy, with reference to views of celestial bodies such as stars, the Moon, and planets that become visible on a clear night after the Sun has set. Natural light sources in a night sky include moonlight, starlight, and airglow, depending on location and timing. The fact that the sky is not completely dark at night can be easily observed. Were the sky (in the absence of moon and city lights) absolutely dark, one would not be able to see the silhouette of an object against the sky.


title: Sky

text: The night sky and studies of it have a historical place in both ancient and modern cultures. In the past, for instance, farmers have used the state of the night sky as a calendar to determine when to plant crops. The ancient belief in astrology is generally based on the belief that relationships between heavenly bodies influence or convey information about events on Earth. The "scientific" study of the night sky and bodies observed within it, meanwhile, takes place in the science of astronomy.


title: Sky

text: Within visible-light astronomy, the visibility of celestial objects in the night sky is affected by light pollution. The presence of the Moon in the night sky has historically hindered astronomical observation by increasing the amount of ambient lighting. With the advent of artificial light sources, however, light pollution has been a growing problem for viewing the night sky. Special filters and modifications to light fixtures can help to alleviate this problem, but for the best views, both professional and amateur optical astronomers seek viewing sites located far from major urban areas.


title: Sky

text: Along with pressure tendency, the condition of the sky is one of the more important parameters used to forecast weather in mountainous areas. Thickening of cloud cover or the invasion of a higher cloud deck is indicative of rain in the near future. At night, high thin cirrostratus clouds can lead to halos around the Moon, which indicate the approach of a warm front and its associated rain. Morning fog portends fair conditions and can be associated with a marine layer, an indication of a stable atmosphere. Rainy conditions are preceded by wind or clouds which prevent fog formation. The approach of a line of thunderstorms could indicate the approach of a cold front. Cloud-free skies are indicative of fair weather for the near future. The use of sky cover in weather prediction has led to various weather lore over the centuries.


title: Sky

text: Within 36 hours of the passage of a tropical cyclone's center, the pressure begins to fall and a veil of white cirrus clouds approaches from the cyclone's direction. Within 24 hours of the closest approach to the center, low clouds begin to move in, also known as the bar of a tropical cyclone, as the barometric pressure begins to fall more rapidly and the winds begin to increase. Within 18 hours of the center's approach, squally weather is common, with sudden increases in wind accompanied by rain showers or thunderstorms. Within six hours of the center's arrival, rain becomes continuous. Within an hour of the center, the rain becomes very heavy and the highest winds within the tropical cyclone are experienced. When the center arrives with a strong tropical cyclone, weather conditions improve and the sun becomes visible as the eye moves overhead. Once the system departs, winds reverse and, along with the rain, suddenly increase. One day after the center's passage, the low overcast is replaced with a higher overcast, and the rain becomes intermittent. By 36 hours after the center's passage, the high overcast breaks and the pressure begins to level off.


title: Sky

text: Flight is the process by which an object moves through or beyond the sky (as in the case of spaceflight), whether by generating aerodynamic lift, propulsive thrust, aerostatically using buoyancy, or by ballistic movement, without any direct mechanical support from the ground. The engineering aspects of flight are studied in aerospace engineering which is subdivided into aeronautics, which is the study of vehicles that travel through the air, and astronautics, the study of vehicles that travel through space, and in ballistics, the study of the flight of projectiles. While human beings have been capable of flight via hot air balloons since 1783, other species have used flight for significantly longer. Animals, such as birds, bats, and insects are capable of flight. Spores and seeds from plants use flight, via use of the wind, as a method of propagating their species.


title: Sky

text: Many mythologies have deities especially associated with the sky. In Egyptian religion, the sky was deified as the goddess Nut and as the god Horus. Dyeus is reconstructed as the god of the sky, or the sky personified, in Proto-Indo-European religion, whence Zeus, the god of the sky and thunder in Greek mythology and the Roman god of sky and thunder Jupiter.


title: Sky

text: In Australian Aboriginal mythology, Altjira (or Arrernte) is the main sky god and also the creator god. In Iroquois mythology, Atahensic was a sky goddess who fell down to the ground during the creation of the Earth. Many cultures have drawn constellations between stars in the sky, using them in association with legends and mythology about their deities.


title: The Hundred (cricket)

text: The Hundred is a professional franchise 100-ball cricket tournament involving eight men's and eight women's teams located in major cities across England and Wales. The tournament is run by the England and Wales Cricket Board (ECB) and took place for the first time in July and August 2021.


title: The Hundred (cricket)

text: The format was invented with the expectation that each match lasts around two-and-a-half hours. The BBC showed free-to-air broadcasts of the competition, while all of the women's matches and some of the men's matches were available to stream for free on Sky Sports' YouTube channel.


title: The Hundred (cricket)

text: Almost all the matches take place as back-to-back double-headers at the same venue on the same day. One ticket gives access to both the men's and women's games. The men's salaries are four times higher than the women's, but the tournament prize money is equal.


title: The Hundred (cricket)

text: A new city-based cricket Twenty20 competition similar to the Indian Premier League was first proposed by the England and Wales Cricket Board (ECB) in September 2016. Following early discussions between the 18 first-class counties, the Professional Cricketers' Association (PCA) and the Marylebone Cricket Club (MCC) they voted 16–3 in favour of developing the competition. On 26 April 2017, members of the ECB voted by 38-3 to push ahead with the new competition.


title: The Hundred (cricket)

text: The idea of switching the competition from the established Twenty20 format to an entirely new type of cricket was first proposed by Sanjay Patel, the ECB's chief commercial officer, in a private October 2017 meeting with senior cricket officials. He argued that the hundred ball format would be simpler to understand for new audiences that the competition wants to attract.


title: The Hundred (cricket)

text: Former England player and Northern Superchargers head coach Dani Hazell stated that the tournament would help with investment into the women’s regional structure and the tournament would be an important learning experience for domestic players.


title: The Hundred (cricket)

text: One-hundred-ball cricket is a form of limited overs cricket, played by two teams each playing a single innings made up of 100 balls. Games last approximately two and a half hours.


title: The Hundred (cricket)

text: Eight city-based teams compete during the school summer holidays. All men's and women's matches are held on the same day at the same grounds. In total there were 32 matches in the league. Each team played four matches at home and four matches away, This will include one match against every other side and then a second bonus match against their nearest regional rivals.


title: The Hundred (cricket)

text: The team that ultimately finishes top of the men's and women's league progresses straight into the final. The teams finishing second and third will compete in the Eliminator (or semi-final), with the winner progressing into the final.


title: The Hundred (cricket)

text: The decision to create an entirely new format of cricket, with teams based in just seven major cities, has split opinion between traditionalists who favour the historic county cricket structure and those who wish to see change.


title: The Hundred (cricket)

text: Some current England players have been positive about the Hundred. England's Test captain at the time, Joe Root, welcomed the ECB's plans, believing it would attract a completely new audience to the game. ODI and T20 captain Eoin Morgan expressed a similar opinion. Former T20 captain Stuart Broad said he was hugely optimistic about the new format. Michael Vaughan echoed Broad's comments, believing that it would be an appealing concept to broadcasters, and Michael Atherton stated while a T20 match was rarely completed in a three-hour window, this can be achieved with the Hundred.


title: The Hundred (cricket)

text: However, former MCC chief Keith Bradshaw said he hoped the 100-ball tournament would not be "innovation for innovation's sake", and voiced his concern that the new format would mean that the ECB could not exploit the T20 boom. The England and Wales Professional Cricketers' Association announced that, overall, players were "open-minded" about the tournament. India captain Virat Kohli cited concerns about the commercialisation of cricket and was not entirely in favour of the new version of the game.


title: The Hundred (cricket)

text: After the teams and branding was announced, anti-obesity groups criticised the sponsorship from snack food company KP Snacks.


title: The Hundred (cricket)

text: Social media reaction has also been split. During the player draft on the 20 October 2019, the Twitter hashtag "#OpposeThe100" began trending, with a vocal section of cricket fans dismayed at the format of the competition, particularly fans of counties whose home grounds are not among the eight used by city franchises. Wisden noted that the response on Twitter and Facebook "has usually been cutting" but there has been less negativity on Instagram which is "mainly used by a younger age group".


title: The Hundred (cricket)

text: Women cricketers have been particularly enthusiastic about the new format and the decision to run both competitions in parallel, with the same prize money, allowing many to turn professional for the first time.


title: The Hundred (cricket)

text: At the conclusion of the inaugural season, it was revealed that 55% of tickets were bought by people who had never bought one before, and that several records were set with regards to television viewing and match attendance figures, particularly for the women's matches. Former England women's captain Charlotte Edwards said that the tournament had "single-handedly changed women’s cricket in this country".


title: The Hundred (cricket)

text: Before the eight teams were confirmed, it was reported that they would carry a different identity from the long-established county teams and would not be named after cities, counties or venues. However, in May 2019, the team names were revealed to be:


title: The Hundred (cricket)

text: Each male and female team is made up of 15 players, of whom a maximum of four can be overseas players. Players are signed using a draft system common in other franchise leagues. At least one England cricket team player is signed to each of the teams competing in The Hundred. The salary cap per team for the 2022 season is £1,000,000.


title: The Hundred (cricket)

text: All games are televised by Sky Sports, with the BBC also showing 10 men's and 8 women's games free-to-air.


title: The Hundred (cricket)

text: In Germany, Sky Sport streamed the initial tournament on their website. They used the signal from Sky Sports UK.


title: Western Christianity

text: Western Christianity is one of two sub-divisions of Christianity (Eastern Christianity being the other). Western Christianity is composed of the Latin Church and Western Protestantism, together with their offshoots such as the Old Catholic Church, Independent Catholicism and Restorationism.


title: Western Christianity

text: The large majority of the world's 2.3 billion Christians are Western Christians (about 2 billion – 1.2 billion Latin Catholic and 800 million Protestant). The original and still major component, the Latin Church, developed under the bishop of Rome. Out of the Latin Church emerged a wide variety of independent Protestant denominations, including Lutheranism and Anglicanism, starting from the Protestant Reformation in the 16th century, as did Independent Catholicism in the 19th century. Thus, the term "Western Christianity" does not describe a single communion or religious denomination, but is applied to distinguish all these denominations collectively from Eastern Christianity.


title: Western Christianity

text: The establishment of the distinct Latin Church, a particular church "sui iuris" of the Catholic Church, coincided with the consolidation of the Holy See in Rome, which claimed primacy since Antiquity. The Latin Church is distinct from the Eastern Catholic Churches, also in full communion with the Pope in Rome, and from the Eastern Orthodox Church and Oriental Orthodox Churches, which are not in communion with Rome. These other churches are part of Eastern Christianity. The terms "Western" and "Eastern" in this regard originated with geographical divisions mirroring the cultural divide between the Hellenistic east and Latin West, and the political divide between the Western and Eastern Roman empires. During the Middle Ages adherents of the Latin Church, irrespective of ethnicity, commonly referred to themselves as "Latins" to distinguish themselves from Eastern Christians.


title: Western Christianity

text: Western Christianity has played a prominent role in the shaping of Western civilization. With the expansion of European colonialism from the Early Modern era, the Latin Church, in time along with its Protestant secessions, spread throughout the Americas, much of the Philippines, Southern Africa, pockets of West Africa, and throughout Australia, and New Zealand. Thus, when used for historical periods after the 16th century, the term "Western Christianity" does not refer to a particular geographical area, but is rather used as a collective term for all these.


title: Western Christianity

text: Today, the geographical distinction between Western and Eastern Christianity is not nearly as absolute as in Antiquity or the Middle Ages, due to the spread of Christian missionaries, migrations, and globalisation. As such, the adjectives "Western Christianity" and "Eastern Christianity" are typically used to refer to historical origins and differences in theology and liturgy, rather than present geographical locations.


title: Western Christianity

text: While the Latin Church maintains the use of the Latin liturgical rites, Protestant denominations and Independent Catholicism use a wide variety of liturgical practices.


title: Western Christianity

text: For most of its history the church in Europe has been culturally divided between the Latin-speaking west, whose centre was Rome, and the Greek-speaking east, whose centre was Constantinople. Cultural differences and political rivalry created tensions between the two churches, leading to disagreement over doctrine and ecclesiology and ultimately to schism.


title: Western Christianity

text: Like Eastern Christianity, Western Christianity traces its roots directly to the apostles and other early preachers of the religion. In Western Christianity's original area Latin was the principal language. Christian writers in Latin had more influence there than those who wrote in Greek, Syriac, or other Eastern languages. Though the first Christians in the West used Greek (such as Clement of Rome), by the fourth century Latin had superseded it even in the cosmopolitan city of Rome, while there is evidence of a Latin translation of the Bible in the 2nd century (see also Vetus Latina) in southern Gaul and the Roman province of Africa.


title: Western Christianity

text: With the decline of the Roman Empire, distinctions appeared also in organization, since the bishops in the West were not dependent on the Emperor in Constantinople and did not come under the influence of the Caesaropapism in the Eastern Church. While the see of Constantinople became dominant throughout the Emperor's lands, the West looked exclusively to the see of Rome, which in the East was seen as that of one of the five patriarchs of the Pentarchy, "the proposed government of universal Christendom by five patriarchal sees under the auspices of a single universal empire. Formulated in the legislation of the emperor Justinian I (527–565), especially in his Novella 131, the theory received formal ecclesiastical sanction at the Council in Trullo (692), which ranked the five sees as Rome, Constantinople, Alexandria, Antioch, and Jerusalem."


title: Western Christianity

text: Over the centuries, disagreements separated Western Christianity from the various forms of Eastern Christianity: first from East Syriac Christianity after the Council of Ephesus (431), then from that of Oriental Orthodoxy after the Council of Chalcedon (451), and then from Eastern Orthodoxy with the East-West Schism of 1054. With the last-named form of Eastern Christianity, reunion agreements were signed at the Second Council of Lyon (1274) and the Council of Florence (1439), but these proved ineffective.


title: Western Christianity

text: Historian Paul Legutko of Stanford University said the Catholic Church is "at the center of the development of the values, ideas, science, laws, and institutions which constitute what we call Western civilization". The rise of Protestantism led to major divisions within Western Christianity, which still persist, and wars—for example, the Anglo-Spanish War of 1585–1604 had religious as well as economic causes.


title: Western Christianity

text: In and after the Age of Discovery, Europeans spread Western Christianity to the New World and elsewhere. Roman Catholicism came to the Americas (especially South America), Africa, Asia, Australia and the Pacific. Protestantism, including Anglicanism, came to North America, Australia-Pacific and some African locales.


title: Western Christianity

text: Today, the geographical distinction between Western and Eastern Christianity is now much less absolute, due to the great migrations of Europeans across the globe, as well as the work of missionaries worldwide over the past five centuries.


title: Western Christianity

text: Original sin, also called ancestral sin, is a Christian belief in a state of sin in which humanity has existed since the fall of man, stemming from Adam and Eve's rebellion in the Garden of Eden, namely the sin of disobedience in consuming the forbidden fruit from the tree of the knowledge of good and evil. Theologians have characterized this condition in many ways, seeing it as ranging from something as insignificant as a slight deficiency, or a tendency toward sin yet without collective guilt, referred to as a "sin nature", to something as drastic as total depravity or automatic guilt of all humans through collective guilt.


title: Western Christianity

text: Most Western Christians use a version of the Nicene Creed that states that the Holy Spirit "proceeds from the Father and the Son", where the original text as adopted by the First Council of Constantinople had "proceeds from the Father" without the addition of either "and the Son" or "alone". This Western version also has the additional phrase "God from God" (in Latin "Deum de Deo"), which was in the Creed as adopted by the First Council of Nicaea, but which was dropped by the First Council of Constantinople.


title: Western Christianity

text: The date of Easter usually differs between Eastern and Western Christianity, because the calculations are based on the Julian calendar and Gregorian calendar respectively. However, before the Council of Nicea, various dates including Jewish Passover were observed. Nicea "Romanized" the date for Easter and anathematized a "Judaized" (i.e. Passover date for) Easter. The date of observance of Easter has only differed in modern times since the promulgation of the Gregorian calendar in 1582; and further, the Western Church did not universally adopt the Gregorian calendar at once, so that for some time the dates of Easter differed between the Eastern Church and the Roman Catholic Church, but not necessarily as between the Eastern Church and the Western Protestant churches. For example, the Church of England continued to observe Easter on the same date as the Eastern Church until 1753.


title: Western Christianity

text: Today, Western Christianity makes up close to 90% of Christians worldwide with the Catholic Church accounting for over half and various Protestant denominations making up another 40%.


title: Western Christianity

text: Hussite movements of 15th century Bohemia preceded the main Protestant uprising by 100 years and evolved into several small Protestant churches, such as the Moravian Church. Waldensians survived also, but blended into the Reformed tradition.


title: Disulfiram

text: Disulfiram is a medication used to support the treatment of chronic alcoholism by producing an acute sensitivity to ethanol (drinking alcohol). Disulfiram works by inhibiting the enzyme acetaldehyde dehydrogenase, causing many of the effects of a hangover to be felt immediately following alcohol consumption. Disulfiram plus alcohol, even small amounts, produces flushing, throbbing in the head and neck, a throbbing headache, respiratory difficulty, nausea, copious vomiting, sweating, thirst, chest pain, palpitation, dyspnea, hyperventilation, fast heart rate, low blood pressure, fainting, marked uneasiness, weakness, vertigo, blurred vision, and confusion. In severe reactions there may be respiratory depression, cardiovascular collapse, abnormal heart rhythms, heart attack, acute congestive heart failure, unconsciousness, convulsions, and death.


title: Disulfiram

text: In the body, alcohol is converted to acetaldehyde, which is then broken down by acetaldehyde dehydrogenase. When the dehydrogenase enzyme is inhibited, acetaldehyde builds up, causing unpleasant side effects. Disulfiram should be used in conjunction with counseling and support.


title: Disulfiram

text: Disulfiram is used as a second-line treatment, behind acamprosate and naltrexone, for alcohol dependence.


title: Disulfiram

text: Under normal metabolism, alcohol is broken down in the liver by the enzyme alcohol dehydrogenase to acetaldehyde, which is then converted by the enzyme acetaldehyde dehydrogenase to a harmless acetic acid derivative (acetyl coenzyme A). Disulfiram blocks this reaction at the intermediate stage by blocking acetaldehyde dehydrogenase. After alcohol intake under the influence of disulfiram, the concentration of acetaldehyde in the blood may be five to 10 times higher than that found during metabolism of the same amount of alcohol alone. As acetaldehyde is one of the major causes of the symptoms of a "hangover", this produces immediate and severe negative reaction to alcohol intake. About 5 to 10 minutes after alcohol intake, the patient may experience the effects of a severe hangover for a period of 30 minutes up to several hours. Symptoms include flushing of the skin, accelerated heart rate, shortness of breath, nausea, vomiting, throbbing headache, visual disturbance, mental confusion, postural syncope, and circulatory collapse.


title: Disulfiram

text: Disulfiram should not be taken if alcohol has been consumed in the last 12 hours. There is no tolerance to disulfiram: the longer it is taken, the stronger its effects. As disulfiram is absorbed slowly through the digestive tract and eliminated slowly by the body, the effects may last for up to two weeks after the initial intake; consequently, medical ethics dictate that patients must be fully informed about the disulfiram-alcohol reaction.


title: Disulfiram

text: Disulfiram does not reduce alcohol cravings, so a major problem associated with this drug is extremely poor compliance. Methods to improve compliance include subdermal implants, which release the drug continuously over a period of up to 12 weeks, and supervised administration practices, for example, having the drug regularly administered by one's spouse.


title: Disulfiram

text: Although disulfiram remained the most common pharmaceutical treatment of alcohol abuse until the end of the 20th century, today it is often replaced or accompanied with newer drugs, primarily the combination of naltrexone and acamprosate, which directly attempt to address physiological processes in the brain associated with alcohol abuse.


title: Disulfiram

text: The most common side effects in the absence of alcohol are headache, and a metallic or garlic taste in the mouth, though more severe side effects may occur. Tryptophol, a chemical compound that induces sleep in humans, is formed in the liver after disulfiram treatment. Less common side effects include decrease in libido, liver problems, skin rash, and nerve inflammation. Liver toxicity is an uncommon but potentially serious side effect, and risk groups e.g. those with already impaired liver function should be monitored closely. That said, the rate of disulfiram-induced hepatitis are estimated to be in between 1 per 25,000 to 1 in 30,000, and rarely the primary cause for treatment cessation.


title: Disulfiram

text: Cases of disulfiram neurotoxicity have also occurred, causing extrapyramidal and other symptoms. Disulfiram can produce neuropathy in daily doses of less than the usually recommended 500 mg. Nerve biopsies showed axonal degeneration and the neuropathy is difficult to distinguish from that associated with ethanol abuse. Disulfiram neuropathy occurs after a variable latent period (mean 5 to 6 months) and progresses steadily. Slow improvement may occur when the drug's use is stopped; often there is complete recovery eventually.


title: Disulfiram

text: Disulfiram disrupts metabolism of several other compounds, including paracetamol (acetaminophen), theophylline and caffeine. However, in most cases, this disruption is mild and presents itself as a 20–40% increase in the half-life of the compound at typical dosages of disulfiram.


title: Disulfiram

text: In medicine, the term "disulfiram effect" refers to an adverse effect of a particular medication in causing an unpleasant hypersensitivity to alcohol, similar to the effect caused by disulfiram administration.


title: Disulfiram

text: The synthesis of disulfiram, originally known as tetraethylthiuram disulfide, was first reported in 1881. By around 1900, it was introduced to the industrial process of sulfur vulcanization of rubber and became widely used. In 1937 a rubber factory doctor in the US published a paper noting that workers exposed to disulfiram had negative reactions to alcohol and could be used as a drug for alcoholism; the effects were also noticed in workers at a Swedish rubber boot factory.


title: Disulfiram

text: In the early 1940s it had been tested as a treatment for scabies, a parasitic skin infection, as well as intestinal worms.


title: Disulfiram

text: Around that time, during the German occupation of Denmark, Erik Jacobsen and Jens Hald at the Danish drug company Medicinalco picked up on that research and began exploring the use of disulfiram to treat intestinal parasites. The company had a group of enthusiastic self-experimenters that called itself the "Death Battalion", and in the course of testing the drug on themselves, accidentally discovered that drinking alcohol while the drug was still in their bodies made them mildly sick.


title: Disulfiram

text: They made that discovery in 1945, and did nothing with it until two years later, when Jacobsen gave an impromptu talk and mentioned that work, which was discussed afterwards in newspapers at the time, leading them to further explore the use of the drug for that purpose. That work included small clinical trials with Oluf Martensen-Larsen, a doctor who worked with alcoholics. They published their work starting in 1948.


title: Disulfiram

text: The chemists at Medicinalco discovered a new form of disulfiram while trying to purify a batch that had been contaminated with copper. This form turned out to have better pharmacological properties, and the company patented it and used that form for the product that was introduced as Antabus (later anglicized to Antabuse).


title: Disulfiram

text: This work led to renewed study of the human metabolism of ethanol. It was already known that ethanol was mostly metabolized in the liver, with it being converted first to acetaldehyde and then acetaldehyde to acetic acid and carbon dioxide, but the enzymes involved were not known. By 1950 the work led to the knowledge that ethanol is oxidized to acetaldehyde by alcohol dehydrogenase and acetaldehyde is oxidized to acetic acid by aldehyde dehydrogenase (ALDH), and that disulfiram works by inhibiting ALDH, leading to a buildup of acetaldehyde, which is what causes the negative effects in the body.


title: Disulfiram

text: The drug was first marketed in Denmark and as of 2008, Denmark is the country where it is most widely prescribed. It was approved by the FDA in 1951. The FDA later approved other drugs for treatment of alcoholism, namely naltrexone in 1994 and acamprosate in 2004.


title: Disulfiram

text: Though the Occupational Safety and Health Administration (OSHA) in the US has not set a permissible exposure limit (PEL) for disulfiram in the workplace, the National Institute for Occupational Safety and Health has set a recommended exposure limit (REL) of 2 mg/m and recommended that workers avoid concurrent exposure to ethylene dibromide.


title: Disulfiram

text: Disulfiram has been studied as a possible treatment for cancer, parasitic infections, anxiety disorder, and latent HIV infection.


title: Disulfiram

text: When disulfiram creates complexes with metals (dithiocarbamate complexes), it is a proteasome inhibitor and as of 2016 it had been studied in "in vitro" experiments, model animals, and small clinical trials as a possible treatment for liver metastasis, metastatic melanoma, glioblastoma, non-small cell lung cancer, and prostate cancer. Various clinical trials of copper depletion agents have been carried out.


title: Disulfiram

text: In the body, disulfiram is rapidly metabolized to diethyldithiocarbamate (ditiocarb), which binds to metal ions such as zinc or copper to form zinc or copper diethyldithiocarbamate (zinc or copper ditiocarb). The zinc diethyldithiocarbamate (zinc-ditiocarb) metabolite of disulfiram is extremely potent against the diarrhea and liver abscess-causing parasite "Entamoeba histolytica" and might be active against other deadly parasites.


title: Disulfiram

text: Disulfiram has also been identified by systematic high-throughput screening as a potential HIV latency reversing agent (LRA). Reactivation of latent HIV infection in patients is part of an investigational strategy known as "shock and kill" which may be able to reduce or eliminate the HIV reservoir. Recent phase II dose-escalation studies in patients with HIV who are controlled on antiretroviral therapy have observed an increase in cell-associated unspliced HIV RNA with increasing exposure to disulfiram and its metabolites. Disulfiram is also being investigated in combination with vorinostat, another investigational latency reversing agent, to treat HIV.


title: Disulfiram

text: Disulfiram has been shown to inhibit the papain-like proteases of MERS-CoV and SARS-CoV. It has been examined in a small inconclusive retrospective observational study for its effects on COVID-19 symptoms and is currently in Phase 2 clinical trials.


title: George Herbert, 8th Earl of Carnarvon

text: George Reginald Oliver Molyneux Herbert, 8th Earl of Carnarvon (born 10 November 1956), styled Lord Porchester from 1987 to 2001, is a British peer and arable farmer.


title: George Herbert, 8th Earl of Carnarvon

text: His family seat, Highclere Castle, has achieved notability as the primary filming location for the television series "Downton Abbey". Carnarvon and his family live in part of the house, while the rest is used as a venue for hire and is also open to the public much of the summer and on some dates during other months.


title: George Herbert, 8th Earl of Carnarvon

text: Herbert was born in Lambeth, London, the son of Henry Herbert, 7th Earl of Carnarvon and an American mother, Jean Margaret Wallop (1935–2019). His mother was born in Big Horn, Wyoming, the granddaughter to Oliver Wallop, 8th Earl of Portsmouth, who had not expected to inherit the title and moved to the American west to become a rancher. His maternal uncle Malcolm Wallop, a rancher in Wyoming, served three terms in the United States Senate. His parents were close friends with Queen Elizabeth II, his godmother. Herbert was a Page of Honour to the Queen. He was educated at Eton and St John's College, Oxford.


title: George Herbert, 8th Earl of Carnarvon

text: He succeeded to the title of Earl of Carnarvon when his father died on 11 September 2001 in Winchester, Hampshire.


title: George Herbert, 8th Earl of Carnarvon

text: On 16 December 1989, he married Jayne M. Wilby, daughter of racehorse owner Kenneth A. Wilby and Princess Prospero Colonna di Stigliano ("née" Frances Loftus). They had two children before divorcing in 1998:


title: George Herbert, 8th Earl of Carnarvon

text: Then, on 18 February 1999, he married fashion designer Fiona Jane Mary Aitken, daughter of Ronnie Aitken and Frances Farmer; they have one son:


title: George Herbert, 8th Earl of Carnarvon

text: The current Countess of Carnarvon is also a historian who has written two biographies about her predecessors – the first about her husband's great-grandmother, Almina, Countess of Carnarvon, and the second about his grandparents. She is the 'godmother' for the cruise ship "Viking Mars".


title: Ethernet over twisted pair

text: Ethernet over twisted-pair technologies use twisted-pair cables for the physical layer of an Ethernet computer network. They are a subset of all Ethernet physical layers.


title: Ethernet over twisted pair

text: Early Ethernet used various grades of coaxial cable, but in 1984, StarLAN showed the potential of simple unshielded twisted pair. This led to the development of 10BASE-T and its successors 100BASE-TX, 1000BASE-T and 10GBASE-T, supporting speeds of 10 and 100 megabit per second, then 1 and 10 gigabit per second respectively.


title: Ethernet over twisted pair

text: Two new variants of 10 megabit per second Ethernet over a "single" twisted pair, known as 10BASE-T1S and 10BASE-T1L, were standardized in IEEE Std 802.3cg-2019. 10BASE-T1S has its origins in the automotive industry and may be useful in other short-distance applications where substantial electrical noise is present. 10BASE-T1L is a long-distance Ethernet, supporting connections up to 1 km in length. Both of these standards are finding applications implementing the Internet of things.


title: Ethernet over twisted pair

text: The earlier standards use 8P8C modular connectors, and supported cable standards range from Category 3 to Category 8. These cables typically have four pairs of wires for each connection, although early Ethernet used only two of the pairs. Unlike the earlier -T standards, the -T1 interfaces were designed to operate over a single pair of conductors and introduce the use of two new connectors referred to as IEC 63171-1 and IEC 63171-6.


title: Ethernet over twisted pair

text: The first two early designs of twisted-pair networking were StarLAN, standardized by the IEEE Standards Association as IEEE 802.3e in 1986, at one megabit per second, and LattisNet, developed in January 1987, at 10 megabit per second. Both were developed before the 10BASE-T standard (published in 1990 as IEEE 802.3i) and used different signalling, so they were not directly compatible with it.


title: Ethernet over twisted pair

text: In 1988, AT&T released StarLAN 10, named for working at 10 Mbit/s. The StarLAN 10 signalling was used as the basis of 10BASE-T, with the addition of "link beat" to quickly indicate connection status.


title: Ethernet over twisted pair

text: Using twisted-pair cabling in a star topology addressed several weaknesses of the previous Ethernet standards:


title: Ethernet over twisted pair

text: Although 10BASE-T is rarely used as a normal-operation signaling rate today, it is still in wide use with network interface controllers in Wake-on-LAN power-down mode and for special, low-power, low-bandwidth applications. 10BASE-T is still supported on most twisted-pair Ethernet ports with up to Gigabit Ethernet speed.


title: Ethernet over twisted pair

text: The common names for the standards derive from aspects of the physical media. The leading number ("10" in 10BASE-T) refers to the transmission speed in Mbit/s. "BASE" denotes that baseband transmission is used. The "T" designates twisted-pair cable. Where there are several standards for the same transmission speed, they are distinguished by a letter or digit following the T, such as "TX" or "T4", referring to the encoding method and number of lanes.


title: Ethernet over twisted pair

text: Most Ethernet cables are wired "straight-through" (pin 1 to pin 1, pin 2 to pin 2, and so on). In some instances the "crossover" form (receive to transmit and transmit to receive) may still be required.


title: Ethernet over twisted pair

text: Cables for Ethernet may be wired to either the T568A or T568B termination standards at both ends of the cable. Since these standards differ only in that they swap the positions of the two pairs used for transmitting and receiving, a cable with T568A wiring at one end and T568B wiring at the other results in a crossover cable.


title: Ethernet over twisted pair

text: A 10BASE-T or 100BASE-TX host uses a connector wiring called medium dependent interfaces (MDI), transmitting on pins 1 and 2 and receiving on pins 3 and 6 to a network device. An infrastructure node (a hub or a switch) accordingly uses a connector wiring called MDI-X, transmitting on pins 3 and 6 and receiving on pins 1 and 2. These ports are connected using a straight-through cable so each transmitter talks to the receiver on the other end of the cable.


title: Ethernet over twisted pair

text: Nodes can have two types of ports: MDI (uplink port) or MDI-X (regular port, 'X' for internal crossover). Hubs and switches have regular ports. Routers, servers and end hosts (e.g. personal computers) have uplink ports. When two nodes having the same type of ports need to be connected, a crossover cable may be required, especially for older equipment. Connecting nodes having different types of ports (i.e., MDI to MDI-X and vice versa) requires a straight-through cable. Thus connecting an end host to a hub or switch requires a straight-through cable. Some older switches and hubs provided a button to allow a port to act as either a normal (regular) or an uplink port, i.e. using MDI-X or MDI pinout, respectively.


title: Ethernet over twisted pair

text: Many modern Ethernet host adapters can automatically detect another computer connected with a straight-through cable and then automatically introduce the required crossover if needed; if neither of the adapters has this capability, then a crossover cable is required. Most newer switches have auto MDI-X on all ports allowing all connections to be made with straight-through cables. If both devices being connected support 1000BASE-T according to the standards, they will connect regardless of whether a straight-through or crossover cable is used.


title: Ethernet over twisted pair

text: A 10BASE-T transmitter sends two differential voltages, +2.5 V or −2.5 V. A 100BASE-TX transmitter sends three differential voltages, +1 V, 0 V, or −1 V. Unlike earlier Ethernet standards using broadband and coaxial cable, such as 10BASE5 (thicknet) and 10BASE2 (thinnet), 10BASE-T does not specify the exact type of wiring to be used but instead specifies certain characteristics that a cable must meet. This was done in anticipation of using 10BASE-T in existing twisted-pair wiring systems that did not conform to any specified wiring standard. Some of the specified characteristics are attenuation, characteristic impedance, propagation delay, and several types of crosstalk. Cable testers are widely available to check these parameters to determine if a cable can be used with 10BASE-T. These characteristics are expected to be met by 100 meters of 24-gauge unshielded twisted-pair cable. However, with high-quality cabling, reliable cable runs of 150 meters or longer are often achievable and are considered viable by technicians familiar with the 10BASE-T specification.


title: Ethernet over twisted pair

text: 100BASE-TX follows the same wiring patterns as 10BASE-T, but is more sensitive to wire quality and length, due to the higher bit rates.


title: Ethernet over twisted pair

text: 1000BASE-T uses all four pairs bi-directionally using hybrid circuits and cancellers. Data is encoded using 4D-PAM5; four dimensions using pulse-amplitude modulation (PAM) with five voltages, −2 V, −1 V, 0 V, +1 V, and +2 V. While +2 V to −2 V may appear at the pins of the line driver, the voltage on the cable is nominally +1 V, +0.5 V, 0 V, −0.5 V and −1 V.


title: Ethernet over twisted pair

text: 100BASE-TX and 1000BASE-T were both designed to require a minimum of category 5 cable and also specify a maximum cable length of . Category 5 cable has since been deprecated and new installations use Category 5e.


title: Ethernet over twisted pair

text: 10BASE-T and 100BASE-TX require only two pairs (pins 1–2, 3–6) to operate. Since common Category 5 cable has four pairs, it is possible to use the spare pairs (pins 4–5, 7–8) in 10- and 100-Mbit/s configurations for other purposes. The spare pairs may be used for power over Ethernet (PoE), for two plain old telephone service (POTS) lines, or for a second 10BASE-T or 100BASE-TX connection. In practice, great care must be taken to separate these pairs as 10/100-Mbit/s Ethernet equipment electrically terminates the unused pins ("Bob Smith Termination"). Shared cable is not an option for Gigabit Ethernet as 1000BASE-T requires all four pairs to operate.


title: Ethernet over twisted pair

text: In addition to the more computer-oriented two and four-pair variants, the 10BASE-T1, 100BASE-T1 and 1000BASE-T1 single-pair Ethernet physical layers are intended for industrial and automotive applications or as optional data channels in other interconnect applications. The single pair operates at full duplex and has a maximum reach of (100BASE-T1, 1000BASE-T1 link segment type A) or up to (1000BASE-T1 link segment type B) with up to four in-line connectors. Both physical layers require a balanced twisted pair with an impedance of 100 Ω. The cable must be capable of transmitting 600 MHz for 1000BASE-T1 and 66 MHz for 100BASE-T1. 2.5 Gb/s, 5 Gb/s, and 10 Gb/s over a 15 m single pair is standardized in 802.3ch-2020. As of 2021, the P802.3cy Task Force is examining having 25, 50, 100 Gb/s speeds at lengths up to 11 m.


title: Ethernet over twisted pair

text: Ethernet over twisted-pair standards up through Gigabit Ethernet define both full-duplex and half-duplex communication. However, half-duplex operation for gigabit speed is not supported by any existing hardware. Higher speed standards, 2.5GBASE-T up to 40GBASE-T running at 2.5 to 40 Gbit/s, consequently define only full-duplex point-to-point links which are generally connected by network switches, and do not support the traditional shared-medium CSMA/CD operation.


title: Ethernet over twisted pair

text: Many different modes of operations (10BASE-T half-duplex, 10BASE-T full-duplex, 100BASE-TX half-duplex, etc.) exist for Ethernet over twisted pair, and most network adapters are capable of different modes of operation. Autonegotiation is required in order to make a working 1000BASE-T connection.


title: Ethernet over twisted pair

text: When two linked interfaces are set to different duplex modes, the effect of this duplex mismatch is a network that functions much more slowly than its nominal speed. Duplex mismatch may be inadvertently caused when an administrator configures an interface to a fixed mode (e.g. 100 Mbit/s full-duplex) and fails to configure the remote interface, leaving it set to autonegotiate. Then, when the auto-negotiation process fails, half-duplex is assumed by the autonegotiating side of the link.


title: Singer Corporation

text: Singer Corporation is an American manufacturer of consumer sewing machines, first established as I. M. Singer & Co. in 1851 by Isaac M. Singer with New York lawyer Edward C. Clark. Best known for its sewing machines, it was renamed Singer Manufacturing Company in 1865, then the Singer Company in 1963. It is based in La Vergne, Tennessee, near Nashville. Its first large factory for mass production was built in 1863 in Elizabeth, New Jersey.


title: Singer Corporation

text: Singer's original design was the first practical sewing machine for general domestic use. It incorporated the basic eye-pointed needle and lock stitch, developed by Elias Howe, who won a patent-infringement suit against Singer in 1854.


title: Singer Corporation

text: Singer obtained in August 1851 for an improved sewing machine that included a circular feed wheel, thread controller, and power transmitted by gear wheels and shafting.


title: Singer Corporation

text: Singer consolidated enough patents in the field to enable him to engage in mass production, and by 1860 his company was the largest manufacturer of sewing machines in the world. In 1885 Singer produced its first "vibrating shuttle" sewing machine, an improvement over contemporary transverse shuttle designs (see bobbin drivers). The Singer company began to market its machines internationally in 1855 and won first prize at the Paris world's fair that year. The company demonstrated the first workable electric sewing machine at the Philadelphia electric exhibition in 1889 and began mass-producing domestic electric machines in 1910. Singer was also a marketing innovator and a pioneer in promoting the use of installment payment plans.


title: Singer Corporation

text: By 1876, Singer was claiming cumulative sales of two million sewing machines and had put the two millionth machine on display in Philadelphia.


title: Singer Corporation

text: In 1867, the Singer Company decided that the demand for their sewing machines in the United Kingdom was sufficiently high to open a local factory in Glasgow on John Street. The Vice President of Singer, George Ross McKenzie selected Glasgow because of its iron making industries, cheap labour, and shipping capabilities. Demand for sewing machines outstripped production at the new plant and by 1873, a new larger factory was completed on James Street, Bridgeton. By that point, Singer employed over 2,000 people in Scotland, but they still could not produce enough machines.


title: Singer Corporation

text: In 1882, McKenzie, by then President-elect of the Singer Manufacturing Company, undertook the ground breaking ceremony on of farmland at Kilbowie, Clydebank. Originally, two main buildings were constructed, each long, wide and three storeys high. These were connected by three wings. Built above the middle wing was a tall clock tower with the "Singer" name clearly displayed for all to see for miles around. A total of of railway lines were laid throughout the factory to connect the different departments such as the boiler room, foundry, shipping and the lines to main railway stations. Sir Robert McAlpine was the building contractor and the factory was designed to be fire proof with water sprinklers, making it the most modern factory in Europe at that time.


title: Singer Corporation

text: With nearly a million square feet of space and almost 7,000 employees, it was possible to produce on average 13,000 machines a week, making it the largest sewing machine factory in the world. The Clydebank factory was so productive that in 1905, the U.S. Singer Company set up and registered the Singer Manufacturing Company Ltd. in the United Kingdom. Demand continued to exceed production, so each building was extended upwards to 6 storeys high. A railway station with the company name was established in 1907 with connections to adjoining towns and central Glasgow to assist in transporting the workforce to the facility. Increased productivity came from 'scientific management' techniques which increased workloads whilst keeping salary overheads low, and in 1911, a mass walk out of 10,000 workers, the 'Singer Strike', took place in support of twelve women polishers, who had seen three staff dismissed, but the workload remained the same with no extra pay. It was significant in its recognition of the rights of women workers and 'collective bargaining' and predated the labour movement known as 'Red Clydeside'. A centenary film was made by the BBC about the female workers who stood up to the American management.


title: Singer Corporation

text: In the First World War, sewing machine production gave way to munitions. The Singer Clydebank factory received over 5000 government contracts, and made 303 million artillery shells, shell components, fuses, and aeroplane parts, as well as grenades, rifle parts, and 361,000 horseshoes. Its labour force of 14,000 was about 70% female at war's end.