Gustav0-Freind/100m · Datasets at Hugging Face

text stringlengths 1 5.12k
"
" This gives us a predicted value for the point.
"
" The result of trilinear interpolation is independent of the order of the interpolation steps along the three axes: any other order, for instance along formula_9, then along formula_10, and finally along formula_11, produces the same value.
"
" The above operations can be visualized as follows: First we find the eight corners of a cube that surround our point of interest. These corners have the values formula_28, formula_41, formula_42, formula_43, formula_44, formula_45, formula_46, formula_47.
"
" Next, we perform linear interpolation between formula_28 and formula_41 to find formula_50, formula_44 and formula_45 to find formula_53, formula_46 and formula_47 to find formula_56, formula_42 and formula_43 to find formula_59.
"
" Now we do interpolation between formula_50 and formula_59 to find formula_62, formula_53 and formula_56 to find formula_65. Finally, we calculate the value formula_66 via linear interpolation of formula_62 and formula_65
"
" In practice, a trilinear interpolation is identical to two bilinear interpolation combined with a linear interpolation:
"
" An alternative way to write the solution to the interpolation problem is
"
" where the coefficients are found by solving the linear system
"
" yielding the result
"
"
"
"= = = New Hanover = = =
"
"
"
" New Hanover may refer to:
"
"
"
"= = = Little League World Series = = =
"
"
"
" The Little League Baseball World Series is an annual baseball tournament in the eastern United States (held in Williamsport, PA) for children (typically boys) aged 10 to 12 years old. Originally called the National Little League Tournament, it was later renamed for the World Series in Major League Baseball. The Series was first held in 1947 and is held every August in South Williamsport, Pennsylvania. (Although the postal address of the organization is in Williamsport, the Series itself is played at Howard J. Lamade Stadium and Volunteer Stadium at the Little League headquarters complex in South Williamsport.)
"
" Initially, only teams from the United States competed in the Series, but it has since become a worldwide tournament. The tournament has gained popular renown, especially in the United States, where games from the Series and even from regional tournaments are broadcast on ESPN. The United States collectively as a country has won a plurality of the series, although from 1969 to 1991 teams from Taiwan dominated the series, winning in 15 out of those 23 years. Taiwan's dominance during those years has been attributed to a national effort to combat its perceived diplomatic isolation around the world. From 2010 through 2018, teams from Tokyo, Japan, have similarly dominated the series, winning five of those matchups.
"
" While the Little League Baseball World Series is frequently referred to as just the Little League World Series, it is actually one of twelve tournaments sponsored by Little League International, in twelve different locations. Each of them brings community teams from different around the world together in baseball (five age divisions), girls' softball (four age divisions), and boys' softball (three divisions). The tournament structure described here is that used for the Little League Baseball World Series. The structure used for the other World Series is similar, but with different regions.
"
" In the summer months leading up to the Little League World Series, held each year in August, Little Leagues around the world select an All-Star team made up of players from its league. It is these All-Star teams that compete in district, sectional and/or divisional, and regional tournaments, hoping to advance to Williamsport for the Little League World Series. How many games a team has to play varies from region to region. In the United States, the tournaments at the lowest (district) level lack nationwide standardization. Some use pool play or double elimination, while others use single elimination.
"
" In the United States, the fate of district winners varies widely from state to state. In some larger states such as Pennsylvania, New York, and California, the district winners advance to one of many sectional tournaments. The winners of each sectional tournament then advance to a state or divisional tournament, the latter only being held in Texas and California and are similar to the state tournaments held in less populous states. Most smaller states lack competition at the sectional level and go straight from district to state tournaments. A handful of states are composed of only one district, and the district champion is the automatic state champion.
"
" With two exceptions, every state as well as the District of Columbia crowns a state champion, and sends that team to represent it to one of eight regional tournaments. The exceptions involve California and Texas. Because of their large geographic and population sizes, California and Texas send two representatives to their regional tournament; Northern California and Southern California in the West region tournament and Texas East and Texas West (whose areas encompass more than the geographical areas of East Texas and West Texas, splitting roughly along the I-35/I-37 corridor) compete in the Southwest region tournament. Up through 2018, the Dakotas had one district spanning the two states, and its winner became the joint champion when advancing to the Midwest region tournament. However, beginning in 2019, North Dakota and South Dakota are represented by individual teams in the regional tournament—creating an odd number of seven teams in the Midwest Regional.
"
" The state champions (as well as the Northern California, Southern California, Texas East, Texas West, and District of Columbia teams) compete in one of eight different regional tournaments. Each regional tournament winner then advances to the Little League World Series. A comprehensive breakdown of current and historical US regional tournament locations, participants and results is available online. Since the geographical boundaries of District of Columbia are exactly the same as the capital city of Washington, this District is usually identified specifically as ""Washington, DC.""
"
" Other countries and regions pick their own way of crowning a champion. Little League Canada holds tournaments at the provincial and divisional level to field six champions (four provincial and two divisional) at the national tournament: Alberta, Ontario, Quebec, British Columbia, the Prairie Provinces (Saskatchewan and Manitoba), and the Atlantic Provinces. The host site of the national tournament varies from year to year, and the host team gets an automatic berth as the seventh team. The tournament is played as a round robin and uses the page playoff format. The winner of the national tournament earns the right to represent Canada at the Little League World Series.
"
" The eight regional tournament winners which compete in the United States Bracket of the Little League World Series, as well as the states those regional champions could possibly hail from are as follows:
"
" Known as Gulf States during the 2001 LLWS
"
" The eight divisions which compete in the International Bracket are as follows:
"
" The eight divisions which compete in the United States bracket represent 96% of the players in Little League with over 2.2 million players while the eight divisions in the International bracket represent 4% of the Little League or less than 130 thousand players.
"
" Prior to 2008, instead of two separate geographic regions, Europe, the Middle East, and Africa held two coterminous regions:
"
" The Transatlantic and EMEA regions were geographically identical. Leagues from the Transatlantic region generally consisted of children and other dependents of American expatriates, typically Armed Forces personnel, international organization members, and oil company workers (such as the team representing the Saudi Aramco Residential Camp in Dhahran, which advanced to the World Series 19 times through 2007, including all the tournaments from 2001 through 2007). The leagues within the ""EMEA"" region consisted of players native to the league's own country. Representative teams for the Trans-Atlantic region had to have at least 51% nationals of Canada, the U.S. or Japan, while teams for the EMEA region could have no more than three players from those three countries.
"
" Teams in the reorganized Europe and MEA regions did not have nationality restrictions, as evidenced by the 2009 series. In that year, both regions were won by teams made up primarily of children of American expatriates. Europe was represented by a team from Ramstein Air Base, a United States Air Force base in Germany, while MEA was represented for the second time in its two-year existence by the team from the Saudi Aramco camp.
"
" On August 29, 2012, Little League announced a significant realignment of the international regions, which took effect in 2013:
"
" As part of a scheduled expansion to 20 teams in 2021, Cuba, Panama, and Puerto Rico are planned to get alternating automatic bids to the LLWS on a rotating basis, with two teams getting a bid while the other plays through the region it is currently in (Cuba or Puerto Rico through the Caribbean or Panama through Latin America). The U.S. is planned to add two more regions:
"
" Along with the new regions, the expansion will move Wisconsin from the Great Lakes region to the Midwest region.
"
" The Little League World Series currently consists of 16 teams; eight from the United States, and eight from other countries. From the inaugural 1947 tournament through 1956, there were predominantly U.S.-based teams, usually eight, competing in a single-elimination format. One Canadian team played in 1952, and one in 1953. Regions were introduced in 1957, and that tournament included the first non-U.S. champion, Monterrey, Mexico, although they represented the U.S. South region. International regions were added in 1958. From 1962 through 2000, the eight teams in the tournament came from four U.S and four international regions:
"
" Through 1975, all teams competed in one bracket. That year, the tournament was held with only the teams from the U.S. regions. The international teams returned in 1976, when two brackets were established, one with U.S. teams, and the other with international teams. The U.S. bracket winner and the international bracket winner would then meet in the championship game, an arrangement that has continued to the present, independent of subsequent changes made to early rounds of the tournament.
"
" In 2001, the number of regions was doubled to 16. The tournament started with eight U.S. teams, randomly assigned into two four-team pools; and eight international teams, also randomly assigned into two four-team pools. Teams competed round-robin within their own pool, with the top two teams of each pool advancing to single-elimination play for a spot in the U.S. final or international final, followed by the U.S champion and international champion meeting in the World Championship game.
"
" In 2010, round-robin play was replaced by a double-elimination bracket in each four-team pool. The winners of each pool advanced to a single-elimination U.S. championship or international championship game, with those winners advancing to the World Championship game. Additionally, each team in the tournament played a minimum of three games, as any team that lost its first two games would play in a consolation U.S. vs. international game.
"
" In 2011, pools were eliminated, with the eight U.S. teams continuing to compete in one bracket and the eight international teams in another bracket. The tournament is double-elimination until the U.S. championship and international championship games, which remain single-elimination, with those winners advancing to the World Championship game. Each team in the tournament still plays a minimum of three games, via consolation games as noted above.
"
" In August 2019, organizers announced that the tournament would expand to 20 teams in 2021, by adding two U.S. participants and two international participants.
"
" Two venues host World Series games: Howard J. Lamade Stadium and Little League Volunteer Stadium. Lamade Stadium has hosted games since 1959 and added lights in 1992. Volunteer Stadium opened in 2001 when the field expanded to 16 teams. Prior to 1959, the Little League World Series was held at Original Little League on West Fourth Street in Williamsport.
"
" Both fields have symmetrical fences, with a distance of 68.6 m (225 feet) from home plate to each of the outfield positions. That distance had been 62.5 m (205 feet) before 2006.
"
" Admission to all LLWS games is free for all spectators. However, stadium seats for the championship game are distributed in a random drawing of all interested parties due to high demand. Some early round games, mostly games with Pennsylvania teams, will use first-come, first-served admission if a big crowd is to be expected. Lamade Stadium has a berm beyond the fences that has allowed the facility to hold up to 45,000 spectators.
"
" From 1947 to 2005, the age limit for players was set at children who turned 13 on August 1 of that year or later. In 2006, the age limit was loosened to include players who turn 13 after April 30. As the Series takes place in August, this led to many of the players having already turned 13 before the Series started. In 2014 Little League voted to change the age cutoff from April 30 to December 31. However, this caused outrage by parents because the players born between May 1 and August 31, 2005 would have lost their 12-year-old season because they would be considered to be 13 years old even though they have not reached their 13th birthday. Effective November 2015, a new implementation plan was established, which ""grandfathered"" players born between May 1 and August 31, 2005 as 12-year-olds for the 2018 season, using April 30 age determination date for the 2018 season. Beginning in 2019, a new determination date of August 31 will be used, which will effectively ban 13-year-old players from participating in the Series.
"
" A total of 19 girls have participated in the Little League Baseball World Series:<br>
"
" 1984 – Victoria Roche (Brussels, Belgium)<br>
"
" 1989 – Victoria Brucker (San Pedro, CA, US)<br>
"
" 1990 – Kelly Craig (Trail, BC, Canada)<br>
"
" 1991 – Giselle Hardy (Dharan, Saudi Arabia)<br>
"
" 1994 – Krissy Wendell (Brooklyn Center, MN, US)<br>

"

" This gives us a predicted value for the point.

"

" The result of trilinear interpolation is independent of the order of the interpolation steps along the three axes: any other order, for instance along formula_9, then along formula_10, and finally along formula_11, produces the same value.

"

" The above operations can be visualized as follows: First we find the eight corners of a cube that surround our point of interest. These corners have the values formula_28, formula_41, formula_42, formula_43, formula_44, formula_45, formula_46, formula_47.

"

" Next, we perform linear interpolation between formula_28 and formula_41 to find formula_50, formula_44 and formula_45 to find formula_53, formula_46 and formula_47 to find formula_56, formula_42 and formula_43 to find formula_59.

"

" Now we do interpolation between formula_50 and formula_59 to find formula_62, formula_53 and formula_56 to find formula_65. Finally, we calculate the value formula_66 via linear interpolation of formula_62 and formula_65

"

" In practice, a trilinear interpolation is identical to two bilinear interpolation combined with a linear interpolation:

"

" An alternative way to write the solution to the interpolation problem is

"

" where the coefficients are found by solving the linear system

"

" yielding the result

"

"= = = New Hanover = = =

"

" New Hanover may refer to:

"

"= = = Little League World Series = = =

"

" The Little League Baseball World Series is an annual baseball tournament in the eastern United States (held in Williamsport, PA) for children (typically boys) aged 10 to 12 years old. Originally called the National Little League Tournament, it was later renamed for the World Series in Major League Baseball. The Series was first held in 1947 and is held every August in South Williamsport, Pennsylvania. (Although the postal address of the organization is in Williamsport, the Series itself is played at Howard J. Lamade Stadium and Volunteer Stadium at the Little League headquarters complex in South Williamsport.)

"

" Initially, only teams from the United States competed in the Series, but it has since become a worldwide tournament. The tournament has gained popular renown, especially in the United States, where games from the Series and even from regional tournaments are broadcast on ESPN. The United States collectively as a country has won a plurality of the series, although from 1969 to 1991 teams from Taiwan dominated the series, winning in 15 out of those 23 years. Taiwan's dominance during those years has been attributed to a national effort to combat its perceived diplomatic isolation around the world. From 2010 through 2018, teams from Tokyo, Japan, have similarly dominated the series, winning five of those matchups.

"

" While the Little League Baseball World Series is frequently referred to as just the Little League World Series, it is actually one of twelve tournaments sponsored by Little League International, in twelve different locations. Each of them brings community teams from different around the world together in baseball (five age divisions), girls' softball (four age divisions), and boys' softball (three divisions). The tournament structure described here is that used for the Little League Baseball World Series. The structure used for the other World Series is similar, but with different regions.

"

" In the summer months leading up to the Little League World Series, held each year in August, Little Leagues around the world select an All-Star team made up of players from its league. It is these All-Star teams that compete in district, sectional and/or divisional, and regional tournaments, hoping to advance to Williamsport for the Little League World Series. How many games a team has to play varies from region to region. In the United States, the tournaments at the lowest (district) level lack nationwide standardization. Some use pool play or double elimination, while others use single elimination.

"

" In the United States, the fate of district winners varies widely from state to state. In some larger states such as Pennsylvania, New York, and California, the district winners advance to one of many sectional tournaments. The winners of each sectional tournament then advance to a state or divisional tournament, the latter only being held in Texas and California and are similar to the state tournaments held in less populous states. Most smaller states lack competition at the sectional level and go straight from district to state tournaments. A handful of states are composed of only one district, and the district champion is the automatic state champion.

"

" With two exceptions, every state as well as the District of Columbia crowns a state champion, and sends that team to represent it to one of eight regional tournaments. The exceptions involve California and Texas. Because of their large geographic and population sizes, California and Texas send two representatives to their regional tournament; Northern California and Southern California in the West region tournament and Texas East and Texas West (whose areas encompass more than the geographical areas of East Texas and West Texas, splitting roughly along the I-35/I-37 corridor) compete in the Southwest region tournament. Up through 2018, the Dakotas had one district spanning the two states, and its winner became the joint champion when advancing to the Midwest region tournament. However, beginning in 2019, North Dakota and South Dakota are represented by individual teams in the regional tournament—creating an odd number of seven teams in the Midwest Regional.

"

" The state champions (as well as the Northern California, Southern California, Texas East, Texas West, and District of Columbia teams) compete in one of eight different regional tournaments. Each regional tournament winner then advances to the Little League World Series. A comprehensive breakdown of current and historical US regional tournament locations, participants and results is available online. Since the geographical boundaries of District of Columbia are exactly the same as the capital city of Washington, this District is usually identified specifically as ""Washington, DC.""

"

" Other countries and regions pick their own way of crowning a champion. Little League Canada holds tournaments at the provincial and divisional level to field six champions (four provincial and two divisional) at the national tournament: Alberta, Ontario, Quebec, British Columbia, the Prairie Provinces (Saskatchewan and Manitoba), and the Atlantic Provinces. The host site of the national tournament varies from year to year, and the host team gets an automatic berth as the seventh team. The tournament is played as a round robin and uses the page playoff format. The winner of the national tournament earns the right to represent Canada at the Little League World Series.

"

" The eight regional tournament winners which compete in the United States Bracket of the Little League World Series, as well as the states those regional champions could possibly hail from are as follows:

"

" Known as Gulf States during the 2001 LLWS

"

" The eight divisions which compete in the International Bracket are as follows:

"

" The eight divisions which compete in the United States bracket represent 96% of the players in Little League with over 2.2 million players while the eight divisions in the International bracket represent 4% of the Little League or less than 130 thousand players.

"

" Prior to 2008, instead of two separate geographic regions, Europe, the Middle East, and Africa held two coterminous regions:

"

" The Transatlantic and EMEA regions were geographically identical. Leagues from the Transatlantic region generally consisted of children and other dependents of American expatriates, typically Armed Forces personnel, international organization members, and oil company workers (such as the team representing the Saudi Aramco Residential Camp in Dhahran, which advanced to the World Series 19 times through 2007, including all the tournaments from 2001 through 2007). The leagues within the ""EMEA"" region consisted of players native to the league's own country. Representative teams for the Trans-Atlantic region had to have at least 51% nationals of Canada, the U.S. or Japan, while teams for the EMEA region could have no more than three players from those three countries.

"

" Teams in the reorganized Europe and MEA regions did not have nationality restrictions, as evidenced by the 2009 series. In that year, both regions were won by teams made up primarily of children of American expatriates. Europe was represented by a team from Ramstein Air Base, a United States Air Force base in Germany, while MEA was represented for the second time in its two-year existence by the team from the Saudi Aramco camp.

"

" On August 29, 2012, Little League announced a significant realignment of the international regions, which took effect in 2013:

"

" As part of a scheduled expansion to 20 teams in 2021, Cuba, Panama, and Puerto Rico are planned to get alternating automatic bids to the LLWS on a rotating basis, with two teams getting a bid while the other plays through the region it is currently in (Cuba or Puerto Rico through the Caribbean or Panama through Latin America). The U.S. is planned to add two more regions:

"

" Along with the new regions, the expansion will move Wisconsin from the Great Lakes region to the Midwest region.

"

" The Little League World Series currently consists of 16 teams; eight from the United States, and eight from other countries. From the inaugural 1947 tournament through 1956, there were predominantly U.S.-based teams, usually eight, competing in a single-elimination format. One Canadian team played in 1952, and one in 1953. Regions were introduced in 1957, and that tournament included the first non-U.S. champion, Monterrey, Mexico, although they represented the U.S. South region. International regions were added in 1958. From 1962 through 2000, the eight teams in the tournament came from four U.S and four international regions:

"

" Through 1975, all teams competed in one bracket. That year, the tournament was held with only the teams from the U.S. regions. The international teams returned in 1976, when two brackets were established, one with U.S. teams, and the other with international teams. The U.S. bracket winner and the international bracket winner would then meet in the championship game, an arrangement that has continued to the present, independent of subsequent changes made to early rounds of the tournament.

"

" In 2001, the number of regions was doubled to 16. The tournament started with eight U.S. teams, randomly assigned into two four-team pools; and eight international teams, also randomly assigned into two four-team pools. Teams competed round-robin within their own pool, with the top two teams of each pool advancing to single-elimination play for a spot in the U.S. final or international final, followed by the U.S champion and international champion meeting in the World Championship game.

"

" In 2010, round-robin play was replaced by a double-elimination bracket in each four-team pool. The winners of each pool advanced to a single-elimination U.S. championship or international championship game, with those winners advancing to the World Championship game. Additionally, each team in the tournament played a minimum of three games, as any team that lost its first two games would play in a consolation U.S. vs. international game.

"

" In 2011, pools were eliminated, with the eight U.S. teams continuing to compete in one bracket and the eight international teams in another bracket. The tournament is double-elimination until the U.S. championship and international championship games, which remain single-elimination, with those winners advancing to the World Championship game. Each team in the tournament still plays a minimum of three games, via consolation games as noted above.

"

" In August 2019, organizers announced that the tournament would expand to 20 teams in 2021, by adding two U.S. participants and two international participants.

"

" Two venues host World Series games: Howard J. Lamade Stadium and Little League Volunteer Stadium. Lamade Stadium has hosted games since 1959 and added lights in 1992. Volunteer Stadium opened in 2001 when the field expanded to 16 teams. Prior to 1959, the Little League World Series was held at Original Little League on West Fourth Street in Williamsport.

"

" Both fields have symmetrical fences, with a distance of 68.6 m (225 feet) from home plate to each of the outfield positions. That distance had been 62.5 m (205 feet) before 2006.

"

" Admission to all LLWS games is free for all spectators. However, stadium seats for the championship game are distributed in a random drawing of all interested parties due to high demand. Some early round games, mostly games with Pennsylvania teams, will use first-come, first-served admission if a big crowd is to be expected. Lamade Stadium has a berm beyond the fences that has allowed the facility to hold up to 45,000 spectators.

"

" From 1947 to 2005, the age limit for players was set at children who turned 13 on August 1 of that year or later. In 2006, the age limit was loosened to include players who turn 13 after April 30. As the Series takes place in August, this led to many of the players having already turned 13 before the Series started. In 2014 Little League voted to change the age cutoff from April 30 to December 31. However, this caused outrage by parents because the players born between May 1 and August 31, 2005 would have lost their 12-year-old season because they would be considered to be 13 years old even though they have not reached their 13th birthday. Effective November 2015, a new implementation plan was established, which ""grandfathered"" players born between May 1 and August 31, 2005 as 12-year-olds for the 2018 season, using April 30 age determination date for the 2018 season. Beginning in 2019, a new determination date of August 31 will be used, which will effectively ban 13-year-old players from participating in the Series.

"

" A total of 19 girls have participated in the Little League Baseball World Series:

"

" 1984 – Victoria Roche (Brussels, Belgium)

"

" 1989 – Victoria Brucker (San Pedro, CA, US)

"

" 1990 – Kelly Craig (Trail, BC, Canada)

"

" 1991 – Giselle Hardy (Dharan, Saudi Arabia)

"

" 1994 – Krissy Wendell (Brooklyn Center, MN, US)