ejaasaari/simplewiki-2025-04-01 huggingface dataset:
The kernel of a group homomorphism from "G" to "H" is the subset of the elements from "G" that arrive to the Identity element of "H".  Mathematically: formula_1. Since a group homomorphism preserves identity elements, the identity element of "G" must belong to the kernel subset. Property. The homomorphism is injective if and only if its kernel is only the identity elements of "G". Proof: If "f" were not injective, then the non-injective elements can form a distinct element of its kernel: there would exist formula_2 such that formula_3 and formula_4. Thus formula_5. "f" is a group homomorphism, so inverses and group operations are preserved, giving formula_6; in other words, formula_7, and ker "f" would not be the singleton. Conversely, distinct elements of the kernel violate injectivity directly: if there would exist an element formula_8, then formula_9, thus "f" would not be injective.
Judah is a person from the Book of Genesis. He was the ancestor of the tribe that became the Kingdom of Judah. Birth. It is written in the Torah, in the Book of Genesis that Jacob married both Leah and her sister Rachel. He loved Rachel but not Leah. So Leah prayed to the Lord for a son so that she wouldn’t be hated. Then Leah became pregnant and gave birth to a son and she said “now my husband shall love me” and named him Reuben. Then Leah gave birth to a second son and said that the Lord had heard her voice so she named him Simeon. Then Leah gave birth to a third son and said “I have poured my heart unto the Lord” and named him Levi. Then Leah gave birth to a fourth son. She said “this time I will thank the Lord” and she named him Judah. Family History. After Judah was born, Rachel came to Jacob and said “give me children otherwise I am dead”. Jacob told her that he couldn’t give her a miracle like that since he was only human. So Rachel told Jacob to marry her servant Bilhah. Bilhah gave birth to two sons named Dan and Naphtali. Leah then told Jacob to marry her servant Zilpah. Zilpah gave birth to two sons named Gad and Asher. Then Leah gave birth to Zebulun and Issachar. Then Leah gave birth to a daughter Dinah and Rachel gave birth to a son Joseph. Later, Rachel died in childbirth and her son was named Benjamin.  Sale of Joseph. Jacob loved Joseph more than all of his other children. Joseph was born when he was an old man. It took many years for Rachel to be able to give birth. So Jacob gave Joseph a coat with many colours. And Joseph had dreams about his brothers all bowing to him so they became jealous and they took Joseph and threw him in a big hole in the ground and left him to die. But then Judah felt guilty about that. He told his brothers that instead of letting Joseph die, they should take him and sell him as a slave to the Ishmaelites and they did. And when
"Death or Freedom" () was the anthem of the Chechen Republic of Ichkeria, a former partially-recognised country in the Caucasus within Russia. Lyrics. The lyrics are highly Islamic, reflecting the fact that most Chechens are Muslims.
Civitella del Tronto is a "comune" in the Province of Teramo in the Abruzzo region in central Italy. Twin towns. Civitella del Tronto is twinned with:
Spacecraft propulsion is the method that a spacecraft uses to control its movement through outer space. A spacecraft with no means of propelling itself is typically considered derelict.  The problem of propelling a spacecraft has, predictably, existed since spacecraft themselves. Most spacecraft are propelled by rocket engines, which combust an explosive liquid fuel with liquid oxidizer (oxygen in a liquid state) to generate hot gas which expands and propels the spacecraft forward. Methods. Many methods of spacecraft propulsion have been developed and practiced. Most work by accelerating a propellant to a very high speed and ejecting it from the spacecraft through a nozzle. Chemical rocket. A chemical rocket works by mixing an explosive propellant with liquid oxygen and burning it under pressure. This releases a great amount of heat. It results in a rapidly expanding gas. This gas is then funneled out of the rocket's nozzle (usually a bell shape) and off into space. Ion thruster. An ion thruster works by using static electricity or magnetism to accelerate ions (atoms with an electric charge) to very high speeds, and out of the thruster's nozzle. Ion thrusters make very little thrust but are very efficient. Nuclear thermal rocket. A nuclear thermal rocket heats a propellant with heat from a nuclear reactor before expelling it through a nozzle. Nuclear thermal rockets are currently experimental, but will have decent thrust and high efficiency once put into practice.
Simeon is a person in the Torah and Old Testament. Simeon was the second son of Jacob and Leah and the ancestor of one of the Twelve Tribes of the Israelites. Birth. After Leah gave birth to her second son she said that the Lord had heard her voice so she named her son Simeon. She then gave birth to another son and said “I have poured out my heart to the Lord” and named him Levi. The story of Dinah. When a prince named Shechem raped Dinah after having kidnapped her, he and his father Hamor wanted Shechem to marry her. So Jacob’s sons told him to tell Hamor to tell the men of Shechem to circumcise themselves. And then they did, so Shechem could marry Dinah. Then Simeon and his brother Levi killed every adult male in Shechem and rescued Dinah. But Jacob was angry with Simeon and Levi since he thought that the Canaanites would kill them all for it. So they asked him “should our sister be treated as a whore”.  Story of Joseph. Simeon was the one of Joseph’s brothers that he jailed to get the others to bring Benjamin to Egypt.  Land Distribution. When Jacob died, he told Simeon and Levi that because of the massacre of Shechem they wouldn’t have land of their own as part of their inheritance but would instead be contained by the lands of the other tribes. So the tribe of Simeon had its lands surrounded on all sides by land belonging to the tribe of Judah.
The Nigerian Civil War was a civil war fought between the government of Nigeria and the Republic of Biafra. "Food was cut off from the 13 million inhabitants of Biafra"; Furthermore, "At the height of the war, an estimated 10,000 people (including 6,000 children) died from starvation every day".
Levi was a person in the Book of Genesis who was a son of Jacob and Leah. Along with his brother Simeon he killed the men of Shechem for the rape of Dinah. Because of that, his father Jacob told him that his tribe would not have his land as part of their inheritance but would live on the land of other tribes. Children. Levi had three sons and they were named Gershon, Kehath and Merari. Moses and Aaron. Kehath had a son named Amaram. Amaram married a woman named Yocheved and became the father of Miriam, Aaron and Moses. Moses became the prophet to the Israelites and Aaron became the High Priest.  Levites. While the sons of Aaron and their male descendants became the priests, the rest of Levi’s descendant known as the Levites helped the priests in the sanctuary. Their tribe didn’t get any land of their own because they instead had to be the religious ministers to everyone in the other tribes who had to let the Levites live on their land.
Lusigliè is a "comune" in the Metropolitan City of Turin in the Piedmont region in Italy.
Benjamin was the youngest son of Jacob and the second son of Rachel. When Rachel gave birth to Joseph she prayed that the Lord would one day give her another child. And when Jacob and his family left Aramea, Rachel stole the idols of her father Laban without telling Jacob so when Laban came to Jacob and asked him “why did you steal my gods” Jacob said that he didn’t do it and curses the person who did it to die. Later, Rachel became pregnant and gave birth to a son and since she was dying in childbirth she named him Ben-Oni, son of my suffering, and after Rachel died, Jacob named the boy Benjamin, the son of the right. Story of Joseph. After the sale of Joseph, Jacob thought Joseph was dead so he decided always to keep Benjamin by his side to protect him so that nothing could happen to him. But Judah (Biblical personage) still convinced him to let him bring Benjamin to Egypt with a promise to keep him safe. Then Benjamin was framed for stealing a cup from Joseph and Joseph said that he would enslave Benjamin as punishment but Judah and his brothers asked Joseph to have mercy on Benjamin and take them instead. Then Joseph told them he was their long lost brother and forgave them. Tribe of Benjamin. Benjamin became the ancestor of an Israelite tribe called the Benjaminites. The Midrash. According to a Midrash in the Talmud, Benjamin was one of only four people who never sinned in their entire life.
The National Anthem of Mongolia was created in 1950. This was known before 1991 as the State Anthem of the Mongolian People's Republic. The words of the song were written by a Mongolian author named Tsendiin Damdinsüren, and the melody to his words were made by two composers by the names of Bilegiin Damdinsüren and Luvsanjambyn Mördorj. Lyrics. The lyrics (words) of this song has been changed three times. First the lyrics were changed in 1961 to remove mentions of specific leaders; then in 1991, when communism came to an end, the lyrics no longer mentioned communism nor the Soviet Union; and finally in 2006, the lyrics were changed slightly, and this is the current version used till this day.
"Dirty Laundry" is a 1982 song by Don Henley. It was taken from his debut studio album "I Can't Stand Still". It went to number 1 in Canada, number 2 in South Africa, number 3 in the United States, number 7 in New Zealand and number 8 in Austria.
A nuclear thermal rocket (abbreviated to NTR) is a type of rocket engine which heats a propellant (usually liquid hydrogen) using a nuclear reactor. This is different from chemical rockets, which burn their propellant to heat it. NTRs have higher exhaust velocities than chemical rockets, high enough to triple a spacecraft's payload capacity (the amount of cargo or astronauts they can carry to their destination). NTRs have the potential to be very fuel efficient while still providing good thrust, but their thrust-to-weight ratio is very small. A rocket's thrust-to-weight ratio (TWR) is the proportion between the amount of thrust the spacecraft can make and how much the spacecraft weighs. For example, a spacecraft that weighs 100 pounds and can produce 10 pounds of thrust would have a TWR of 1:10. An average chemical rocket has a TWR of about 70:1, but an average NTR has a TWR of 7:1. This means that NTRs have to burn for a long time to get the same acceleration as a chemical rocket. This is balanced by their high fuel efficiency. NTRs have not been tested in space yet, but a special program named DRACO is going to attempt to do so.
The Costa Rica brook frog or red-eyed stream frog ("Duellmanohyla uranochroa") is a frog. It lives in Costa Rica and Panama. Scientists have seen it between 70 and 1740 meters above sea level. The skin of the frog's back is green in color. The belly and neck are bright yellow. The parts of the legs that face the ground are yellow but less bright. There is a yellow-white stripe from the mouth to the place where the legs meet the body, one on each side. The iris of the eye is bright red. The female frog is bigger than the male frog, and she has bigger eardrums. This frog moves at night. They go to mountain streams to look for food. During the day, they sit in bromeliad plants. The frogs lay eggs in May and June. The frog's voice sounds like "boop boop boop boop," but different frogs and frogs in different places can sound different. The female frog lays eggs in pools of water with silt on the bottom instead of sand or mud. Threats. This frog is in danger of dying out. This is because human beings change the places where it lives. Sometimes even small changes can hurt this frog. Climate change and ultraviolet light can also kill this frog.
Caleb son of Jephunneh was a person from the Book of Numbers who was one of the twelve spies that Moses sent to Canaan and aside from Joshua was the only one of them who still thought that the Lord could give the Israelites a victory against Canaan. Because of this Caleb and Joshua were the only adult males of that generation allowed to live long enough to come into the Promised Land.  Book of Joshua. At the end of the Book of Joshua, just before Joshua dies, Caleb asks Joshua for permission to conquer Hebron and Joshua gives it to him.  Judges. In the Book of Judges, Caleb’s daughter marries Othniel, the first judge.  The Midrash. According to a Midrash in the Talmud, Caleb was one of the two spies that Joshua sent to Rahab.
The Sword was an American heavy metal band from Austin, Texas. It was made in 2003 by singer and guitarist John Cronise, guitarist Kyle Shutt, and drummer Trivett Wingo. The band released their first album, "Age of Winters", in 2006. Cronise had written most of the album's music before making the band. Two years later, the band made "Gods of the Earth", which reached number 102 on the "Billboard" 200 music chart. In 2010, the band released "Warp Riders". This was a concept album based on a science fiction story that Cronise made. Drummer Trivett Wingo left the band, and was replaced by Santiago Vega. After signing with a new record label, Razor &amp; Tie, the band made three more albums: "Apocryphon" in 2012, "High Country" in 2015, and "Used Future" in 2018. The band ended in October 2022. When they were first making music, people called The Sword a doom metal band. Members of the band said they were inspired by other bands, such as Sleep and Black Sabbath. Later, people said the band's music sounded more like hard rock and stoner rock. The Sword has toured with many other metal bands, such as Lamb of God, Metallica, and Clutch.
In the Books of Kings, after King Solomon died, his kingdom known as Israel split into two kingdoms one in the North and one in the South. The one in the South was called Judah and the one in the North was called the Kingdom of Israel. It was later conquered and destroyed by the Assyrian emperor Shalmaneser who exiled its people who were known ever since then as the Lost Tribes of Israel. Israel's capital was Samaria. It was richer than Judah but it fell earlier than it. The story of the Northern Kingdom comes from Jeroboam's Revolt. Jeroboam led the 10 tribes to revolt against Rehoboam in a civil war.
The Exploration of the Moon started when the Space Race/Space Age (1957 - 1969/1976) heated up and the Soviet Union and the United States both raced to the moon and later other planets. With the Space Race the world and technology changed, especially the interest of the moon. The Soviet Union was the first country to land on the moon ( Without any Humans ) and the United States was behind in the space race but the United States was the first one to land with a human on the moon which started the exploration. More Satellites and Probes during and after the space race/space age were sent to explore the rocky surface and during the robots and human missions that successfully landed on the moon they found that the moon had craters and had a hard surface. But they also found dead volcanoes, and lava flowing through areas on the moon.
The Ozone Disco fire occurred at 11:35 pm on March 18, 1996 in South Avenue, Quezon City, Philippines. It killed 162 people and injured 95 others. It is considered the worst fire in Philippine 20th century history. It is also one of the worst nightclub fires in the world. History. The Ozone Disco was a famous club located at Tomas Morato in Quezon City. It was established in the year 1991. It was developed and operated by Westwood Entertainment Company, Inc. Incident. The fire broke out at 11:35 pm on March 18, 1996. There were more than 350 people in the building when the incident occurred. Most of them were young male high school graduates.
Charlie DePew, (born on May 22, 1996 in Pasadena, California) is an American actor. Career. In 2012, DePew first role was "The Amazing Spider-Man" (2012) at The Amazing Spider-Man 2 (2014), alongside with Emma Stone, He was then in "Awkward" (2014), "The Goldbergs" (2015) and "Mad Men's Midseason 7" - finale (2014).
Djent is a type of progressive metal. It is known for its difficult rhythm patterns, and is inspired by free jazz music. The electric guitar is one of the main instruments in djent. In djent, the guitar is played with high gain (power) and distortion. Djent guitarists also do things such as down-tune their guitar strings and palm mute. The word "djent" comes from how the music sounds. It is similar to math rock. Fredrik Thordendal, the guitarist for Meshuggah, is known for being the first person to play djent music. Other bands that play djent music are Animals as Leaders, Periphery, and Tesseract.
Mappano is a "comune" in the Metropolitan City of Turin in the Piedmont region in Italy. Geography. Mappano is in the northwestern area of the metropolitan area of Turin, about km in south of Turin-Caselle Airport. It is next to these municipalities: Borgaro Torinese, Caselle Torinese, Leinì, Settimo Torinese and Turin. History. It was created on 30 January 2013, from territories which previously had been "frazioni" of the "comuni" of Borgaro Torinese, Caselle Torinese, Leinì and Settimo Torinese.
Roure is a "comune" in the Metropolitan City of Turin in the Piedmont region in Italy. It is about west of Turin. Roure is next to these municipalities: Bussoleno, Coazze, Fenestrelle, Massello, Mattie, Perosa Argentina, Perrero, and San Giorio di Susa.
Perosa Argentina is a "comune" in the Metropolitan City of Turin in the Piedmont region in Italy. It is about northwest of Turin. Perosa Argentina is next to these municipalities: Coazze, Giaveno, Roure, Pinasca, Perrero, Pomaretto, and Inverso Pinasca.
Ennetières-en-Weppes is a commune in the Nord department in northern France.
Escaudœuvres is a commune in Nord in north France. In 2019, 3,218 people lived there.
Godspeed You! Black Emperor (sometimes called GY!BE or Godspeed) is a Canadian post-rock band. They formed in Montreal, Canada in 1994. After making their first album in 1997, the group played at concerts from 1998 to 2003. In 2000, they released "Lift Your Skinny Fists Like Antennas to Heaven". It was called one of the best albums of the 2000s. In 2003, the band took a break so that the members could play other kinds of music. They came back together in 2010, and released five more albums. Their newest album is "No Title as of 13 February 2024 28,340 Dead" . It was released in 2024. The band is known for being very important in post-rock music. Their music is usually instrumental, and is about ideas such as war and anarchism. The band often puts monologues into their songs. In 2013, the album "'Allelujah! Don't Bend! Ascend!" won the Polaris Music Prize.
Mazzè is a "comune" in the Metropolitan City of Turin in the Piedmont region in Italy.
Sauze d'Oulx is a "comune" in the Metropolitan City of Turin in the Piedmont region in northern Italy. It was the site of the freestyle skiing events of the 2006 Olympic Winter Games. Together with the villages of Pragelato, Sestriere, Claviere, Cesana Torinese, San Sicario and Montgenèvre, in France which makes up the Via Lattea (Milky Way) skiing area.
Montanaro is a "comune" in the Metropolitan City of Turin in the Piedmont region in Italy. Twin towns. Montanaro is twinned with:
Nichelino is an Italian city in Piedmont. About 47,700 people live there. Twin towns. Nichelino is twinned with:
Caluire-et-Cuire is a commune. It is in Auvergne-Rhône-Alpes in the Metropolis of Lyon in east France. It is the fifth-largest suburb of the city of Lyon.
Böllen is a municipality in Lörrach in Baden-Württemberg, Germany.
Fröhnd is a municipality in Lörrach in Baden-Württemberg in Germany.
Häg-Ehrsberg is a municipality in Lörrach in Baden-Württemberg, Germany.
Schliengen is a municipality in Lörrach in Baden-Württemberg, Germany.
Charvieu-Chavagneux is a commune in the Isère department in southeastern France.
Isny im Allgäu is a town in Ravensburg in Baden-Württemberg, Germany. It is in the Allgäu region. Isny was a Free Imperial City ("Freie Reichsstadt") until the mediatisation of 1803.
J. Cole (born Jermaine Lamarr Cole; January 28, 1985) is an American rapper and record producer. Early life. Cole was born at a United States Army base in Frankfurt, West Germany. His father is an African American who served in the United States Army. Cole's mother is white. Eight months later, Cole moved to Fayetteville, North Carolina, where he was raised by his mother, aunt and cousin. His father left the family when Cole was still young. Discography. Cole began gaining popularity after his first mixtape, "The Come Up", was released in 2007. In 2009, he was signed to Jay-Z's record label Roc Nation. Cole released two additional mixtapes, "The Warm Up" in 2009 and "Friday Night Lights" in 2010. Albums. Cole released his first studio album, "", in 2011. It peaked at number one on the US "Billboard" 200. His next two albums, "Born Sinner" (2013) and "2014 Forest Hills Drive" (2014), also topped the "Billboard" 200. "2014 Forest Hills Drive" earned Cole a Best Rap Album nomination at the 2015 Grammy Awards.  His fourth album, "4 Your Eyez Only" (2016), peaked at number one on the "Billboard" 200. Cole's other albums, "KOD" (2018) and "The Off-Season" (2021), also topped the "Billboard" 200. Altogether, Cole has earned six number-one album on the "Billboard" 200. As producer. As a producer, he has worked with famous musicians such as Kendrick Lamar and Janet Jackson. Dreamville Records. He founded his own record label Dreamville Records. The label's compilation album "Revenge of the Dreamers III" (2019) charted at number one on the "Billboard" 200. It was nominated for Best Rap Album at the 2020 Grammy Awards. Awards and nominations. Cole has won a Grammy Award for Best Rap Song, a "Billboard" Music Award for Top Rap Album, three Soul Train Music Awards, and eight BET Hip Hop Awards.
Al Pitrelli is an American guitarist. He is known for playing music with Megadeth, Alice Cooper, Savatage, and the Trans-Siberian Orchestra. Pitrelli joined Savatage in 1995. He played guitar on three of the band's albums. Paul O'Neill asked him to join another rock band named "Trans-Siberian Orchestra", He has played on every album with the band. He joined Megadeth in 2000, but left in 2002.
Megadeth is an American thrash metal band. It was made by Dave Mustaine and David Ellefson in 1983. Albums. In 1985, Megadeth made its first album, named "Killing is My Business... and Business is Good!." The Combat Records record label released the album. After the album came out, larger record labels noticed Megadeth, and the band joined Capitol Records. Their first album with Capitol Records, "Peace Sells... but Who's Buying?", was released in 1986. Some Megadeth band members were addicted to drugs, so they got a lot of bad publicity during the 1980s. Still, the band released many popular albums, such as "So Far, So Good... So What!" in 1988, "Rust in Peace" in 1990, and "Countdown to Extinction" in 1992. The band took a break in 2002, but came back together later. They have released six albums since then. Members. Megadeth has had many different guitarists, drummers, and bassists. Mustaine is the last member of the original group who is still in the band. Megadeth's current members are guitarist and singer Dave Mustaine, guitarist Kiko Loureiro, drummer Dirk Verbeuren and bassist James LoMenzo. Session. A session musician is someone hired by a band to help make music.
"Love Spreads" is a 1994 song by British indie rock band The Stone Roses. It was taken from their second studio album "Second Coming". It went to number 2 in the United Kingdom, number 8 in Ireland, number 13 in Sweden, number 23 in New Zealand and number 36 in Australia. Track listing. 7-inch vinyl (Geffen GFS 84)&lt;br&gt; Cassette (Geffen GFSC 84) 12-inch vinyl (Geffen GFST 84) CD (Geffen GFSTD 84)
Bob Brown (born 1944) is the former Australian Greens parliamentary leader. Bob Brown may also refer to:
Bobby Brown (born 1969) is an American R&amp;B singer. Bobby, Bobbie or Bobbi Brown may also refer to: