the-french-artist/wikipedia_20220301.simple_sentence_split huggingface dataset:
Possible date - John the Baptist was beheaded by King Herod Antipas.
Livia, wife of Caesar Augustus
31 is a year in the 1st century.
At the time, it was known as the Year of the Consulship of Augustus and Seianus.
Aelius Sejanus named co-Consul to the Emperor Tiberius.
Tiberius has Sejanus arrested for treachery and executed.
April 6 - possible crucifixion of Jesus
Naevius Sutorius Macro becomes the leader of the Praetorian Guard
Tiberius returns to Rome from Capri
Musonius Rufus, Roman philosopher
October 18 - Aelius Sejanus, Roman politician
Marcus Velleius Paterculus, Roman historian
Livilla, niece and daughter-in-law of the emperor Tiberius
32 is a year in the 1st century.
It was a leap year starting on Tuesday of the Julian calendar.
At the time, it was known as the Year of the Consulship of Ahenobarbus and Camillus.
Saint Peter traditionally becomes first pope
Symbolic interpretation of the Old Testament by Philo
Ban Chao, Chinese general and cavalry commander (d. 102)
Otho, Roman emperor (d. 69)
Lucius Calpurnius Piso, consul under Caesar Augustus
33 is a year in the 1st century.
At the time, it was known in the Roman world as the Year of the Consulship of Ocella and Sulla.
Tiberius founds a credit bank in Rome
A financial crisis hits Rome.
Many aristocratic families are ruined.
Traditional date for Crucifixion,  Resurrection and Ascension of Jesus.
30 and 28 are also suggested as a date for these events.
Traditionally, Christianity was founded
Saint Peter became Pope - possible date
Gaius Rubellius Plautus, son of Gaius Rubellius Blandus and Julia.
Gaius Asinius Gallus, widower of Vipsania Agrippina and potential lover of Agrippina the elder
Agrippina the Elder, wife of Germanicus
Nero Caesar, son of Germanicus and Agrippina the Elder
Drusus Caesar, son of Germanicus and Agrippina the Elder
Marcus Aemilius Lepidus, senator
34 is a year in the 1st century.
At the time, it was known as the Year of the Consulship of Persicus and Vitellius.
Roman start to build a three tier aqueduct.
It began in Nîmes and ran for 269 miles.
Naevius Sutorius Macro gained prestige by prostituting his wife Eunius to Tiberius
Romans invaded Armenia
The people of Dacia revolt against the Sarmatian tribe of Iazyges who had enslaved them.
Aulus Persius Flaccus, Roman poet
Stephen, the first martyr of Christianity
36 is a year in the 1st century.
It was a leap year starting on Sunday of the Julian calendar.
At the time, it was known as the Year of the Consulship of Allenius and Plautius.
Pontius Pilate is called back to Rome.
He had stopped a Samaritan uprising.
L. Vitellius defeated Artabanus of Parthia in support of another clamaint to the throne, Tiridates III.
Herod Antipas is remarried.
Marcellus becomes governor of Judaea and Samaria.
In MesoAmerica, last calendar monument created for about a century and a half.
Thrasyllus of Mendes
Jesus (according to some theories)
38 is a year in the 1st century.
At the time, it was known as the Year of the Consulship of Iulianus and Asprenas.
Probable year of the marriage of Claudius and Messalina
Apion represents a group to complain to Caligula about the Jews in Alexandria
Anti-Jewish riot starts in Alexandria during a visit by Agrippa I. The mob wants to place statues of Caligula in every synagogue.
Phaedrus writes his popular collection of fables
Stachys the Apostle becomes the second patriarch of Constantinople
Marcus Valerius Martialis, Latin epigrammatist
June 10 - Drusilla, sister of Caligula
Saint Andrew, apostle
Naevius Sutorius Macro, commander of the Roman Praetorian Guard
Law was elected to Parliament in 1900 as a member of the Conservative Party.
He became leader of the Party in 1911.
He was Lloyd George's Chancellor of the Exchequer and Leader of the House of Commons while Lloyd George served as Prime Minister during World War I.
Law became Prime Minister in October 1922.
He found out he had throat cancer and resigned in May 1923.
He died in October 1923.
British chess players
Canadian Christians
39 is a year in the 1st century.
At the time, it was known as the Year of the Consulship of Augustus and Corbulo.
Tigellinus, minister and favorite of the later Roman emperor Nero, is banished for adultery with Caligula's sisters.
Domitius Afer becomes a consul.
Caligula is also a consul.
Agrippa I, king of Iudaea, is called back to Rome.
Legio XV Primigenia and XXII Primigenia are levied by Caligula for the German frontier.
Caligula's campaign into Germany was stopped by a conspiracy led by Cassius Chaerea.
Caligula orders that a statue of himself be placed in the temple in Jerusalem.
Jews protest.
They are able to stop construction of the statue until the death of Caligula (January 24, 41).
Philo leads a Jewish delegation to Rome to protest the anti-Jewish conditions in Alexandria.
The Trung Sisters resist Chinese influence in Vietnam.
November 3 – Lucan, Roman poet
December 30 – Titus Flavius, Roman emperor (79–81)
Julia Drusilla, daughter of current Roman Emperor Caligula
Britannicus, son of later Roman emperor Claudius and his third wife Messalina
Seneca the Elder, Roman rhetorician
The pulmonary artery is a blood vessel that connects the heart to the lungs.
The pulmonary artery carries blood that does not have much oxygen.
The blood from throughout the body is taken into the heart by the right atrium into the right ventricle.
The blood is pumped into the pulmonary artery and into the lung capillaries.
When the blood passes through the capillaries slowly to absorb the oxygen from the lungs.
The oxygenated blood is taken through the pulmonary vein back into the heart through the left atrium and the left ventricle.
It is then pumped throughout the body.
The pulmonary artery is an extension of the pulmonary trunk (lat.
truncus pulmonaris), extending from the right ventricle; it is located in front and to the left of all the vessels that flow in and out of the heart, and brings venous blood to the lungs (the only one of the human arteries, except for the umbilical arteries of the fetus).
The initial lobe of the pulmonary artery goes up and back and somewhat covers the beginning of the aorta.
Next, lying to the left of the ascending aorta and in front of the left atrium, the pulmonary artery lies at the level of the IV thoracic vertebra under the concavity of the aortic arch.
Here the pulmonary trunk is divided into:
right branch, right pulmonary artery (lat.
arteria pulmonaris dextra);
left branch, left pulmonary artery (lat.
arteria pulmonaris sinistra).
This is the remnant of the Botal duct (Latin ductus arteriosus (Botalli)), through which the fetus and blood entering the right ventricle are redirected from the pulmonary artery to the aorta: a small circle in the fetal stage of development does not function.
In the future, the duct is obliterated (parallel overgrowth of the oval hole in the atrial septum).
An artery is a blood vessel that carries blood away from the heart to other parts of the body.
Almost all arteries carry blood with a lot of oxygen in it.
The only arteries that do not carry oxygen-rich blood are the pulmonary artery, and (in a fetus) the umbilical artery.
Every artery has three layers.
The outer layer is a thick covering made of stretchy tissue.
The middle layer is made of muscle, so the artery can get wider or get smaller when the body needs it to.
The inner lining is made of the same cells that line the heart.
Arteries are deep under the skin.
They do not have valves to prevent blood from flowing backwards.
Instead, every time the heart beats, the arteries stretch out so the blood has room to go through.
Once the walls have completely stretched out, the muscles in the arteries make them shrink back to their normal size.
This pushes the blood through.
Arteries split down into small vessels called arterioles.
Important arteries
The aorta
The aorta is the main artery in the human body.
It starts in the left ventricle of the heart, which is full of blood that just picked up oxygen in the lungs.
(This is called oxygenated blood - meaning it has a lot of oxygen in it.)
The left ventricle pumps this oxygen-rich blood out through the aorta.
The aorta brings this blood to every organ in the body.
The aorta runs all the way from the heart to the bottom of the abdomen.
Along the way, smaller arteries split off the aorta, like branches on a tree, to bring blood to different parts of the body.
The aorta finally ends by splitting off into the two arteries that bring blood to the legs.
Except for the pulmonary artery, every artery in the body is connected to the aorta.
Some other important arteries include:
The carotid arteries, which bring blood to the brain, head, and face
The femoral arteries, which bring blood to the legs
The coronary arteries, which bring blood to the heart
The pulmonary artery
Does not connect to the aorta; and
Carries blood that does not have much oxygen in it.
(This is called deoxygenated blood.)
The body uses the oxygen carried in the other arteries to make energy.
The blood in these arteries becomes deoxygenated - it does not have much oxygen left in it.
This blood then travels through capillaries to get from the arteries to the veins.
The veins' job is to carry the deoxygenated blood back to the right side of the heart.
The pulmonary artery carries this blood from the heart's right ventricle to the lungs.
In the lungs, the blood can pick up more oxygen.
After picking up more oxygen, the blood travels back to the left side of the heart and is pumped out to the body by the aorta.
This cycle continues, over and over again.
Problems with arteries
Arterial bleeding
Because the heart pumps blood right into the arteries, the arteries are under a lot of pressure.
Unlike the veins, the arteries are always stretching and then squeezing to push blood through them to the body.
Because of this, an arterial bleed - bleeding from an artery - can be a medical emergency, especially if the artery is big.
Arterial bleeding can happen very quickly.
For example, if a person's femoral artery is cut, they can bleed to death.
Arteriosclerosis and atherosclerosis
When a person has arteriosclerosis, the walls of their arteries get harder, stiffer, and less stretchy.
This makes it more difficult for blood and oxygen to get through the arteries to the body's important organs.
One type of arteriosclerosis is atherosclerosis.
Atherosclerosis is a disease where the arteries get narrower because they are clogged up with things like cholesterol and fat.
Like a clog in sink pipes makes it harder for water to get through the pipes, clogs in arteries make it more difficult for blood to get through.
This makes the heart have to work harder to push blood through the arteries.
Atherosclerosis is a big risk factor for high blood pressure and heart disease.
When atherosclerosis happens in the coronary arteries, it can cause coronary heart disease.
If these arteries get too clogged, the heart will not get the blood and oxygen it needs to survive.
This can cause angina, a heart attack, heart failure, or even sudden death.
Aneurysms
An aneurysm is a bulge in the wall of an artery.
It is like a little balloon, filled with blood, coming off the artery.
As the aneurysm gets bigger, it is more likely to break.
If the aneurysm breaks ("ruptures"), the artery will start bleeding.
If the artery is big, a person could bleed to death.
Also, if an artery is bleeding, blood cannot get through it.
The part of the body that the artery is supposed to feed will not get the blood and oxygen it needs.
A ruptured aneurysm is a medical emergency.
Jönköping is a city in Sweden.
About 90,000 people live there.
It is in southern Sweden near the lake Vättern.
Jönköping was actually 3 towns that grew into one large town.
The 3 towns were, Jönköping (55.000), Huskvarna (22.000) and Norrahammar (9.000).
HV71, ishockey club
Jönköping Bandy IF, bandy club
Jönköpings IK, floor ball club
Jönköpings Södra IF, soccer club
Warwickshire (pronounced //, //, or //) is a county in central England.
The county town is Warwick.
The shape of the administrative area Warwickshire differs considerably from that of the historic county.
Commonly used abbreviations for the county are Warks or Warwicks.
Warwickshire is perhaps best known for being the birthplace of William Shakespeare from Stratford-upon-Avon.
The county has also produced other literary figures such as George Eliot (from near Nuneaton), Rupert Brooke (from Rugby), and Michael Drayton from Hartshill.
The market towns of northern and eastern Warwickshire were industrialised in the 19th century, and include Atherstone, Bedworth, Nuneaton, and Rugby.
Major industries included coal mining, textiles, engineering, and cement production, but heavy industry is in decline.
Of the northern and eastern towns, only Nuneaton and Rugby (as the birthplace of Rugby football) are well-known outside of Warwickshire.
The rich towns of central and western Warwickshire include Leamington Spa, Stratford-upon-Avon, Kenilworth, Alcester, and Warwick.
They have light to medium industries, services, and tourism as major employers.
The south of the county is largely rural and has little population, and includes a small area of the Cotswolds.
The only town in the south of Warwickshire is Shipston-on-Stour.
The highest point in the county, at 261 m (856 ft), is Ebrington Hill on the border with Gloucestershire, GR SP187426 at its southwest extremity.
There are no cities in Warwickshire since both Coventry and Birmingham were incorporated into the West Midlands county in 1974.
The largest towns in Warwickshire as of 2004 are: Nuneaton (pop.
77,500), Rugby (62,700), Leamington Spa (45,300), and Bedworth (32,500).
Stratford, Warwick, and Kenilworth all house populations with more than 20,000 inhabitants, the smaller towns of Atherstone, Alcester, Coleshill, Southam, Bulkington, Polesworth, Kingsbury, Henley-in-Arden, Studley, Shipston and Whitnash have populations between 5,000 and 12,000.
Historically much of western Warwickshire, was covered by the ancient Forest of Arden (although most of this was cut down to provide fuel for industrialisation in the 17th to 19th centuries).
For this reason, the names of a number of places in the northwestern part of Warwickshire end with the phrase "-in-Arden".
Historic boundaries
Areas historically part of Warwickshire include Coventry, Solihull, and most of Birmingham.
These became part of the West Midlands metropolitan county following local government re-organisation in 1974.
Coventry is effectively in the centre of the Warwickshire area, and still has strong ties with the county.
Coventry and Warwickshire are sometimes treated as a single area and share a single NHS trust and ambulance service as well as other institutions.
Main settlements
This is a list of the main settlements in Warwickshire, including towns, or villages with a population of over 5,000.
For a complete list see List of places in Warwickshire.
Alcester, Atherstone
Bedworth, Bulkington
Coleshill
Henley-in-Arden
Kenilworth, Kingsbury
Leamington Spa
Polesworth
Shipston-on-Stour, Southam, Stratford-upon-Avon, Studley
Warwick, Wellesbourne, Whitnash
Warwick Chamber of Trade - An invaluable reference to the unspoilt town of Warwick
Warwickshire County Council
The Doppler effect is a change in frequency and wavelength of a wave.
It is caused by the change in distance between the thing creating the wave (causer) and whatever is measuring seeing or hearing the wave (watcher or observer).
Another word for "causer" is "sender" or "source".
Another word for "change in distance" is "speed" or "relative velocity".
A common example is sitting in a car while another car goes by the watcher.
The watcher will hear a change in pitch, while the sender will not.
For waves read all the waves that can send out or reflected by an object.
And for reflection read change of direction of a wave.
Effects of changes in distance
For light, this causes a shift in colour towards the blue end of the spectrum called a blue shift.
The faster something is moving toward us, the greater the blue shift.
For sound, this causes the sound to become higher in pitch
For light, this causes a shift towards the red end of the spectrum called a red shift, the faster something is moving away, the greater the red shift.
For sound, this causes the sound to become lower in pitch.
blue shift
Rubén León  (1988–1992)
Rumualdo Romero (1993–1995)
Jesús Salgado (1995–1996)
Rafael Castellín Osuna  (1997)
Claudio González  (2000–2001)
Roicis Pérez  (2001–2003)
Antonio del Moral
Antonio Núñez
Manuel Villalba
Ramón Caballero (–2006)
Nelson Núñez  (2006–)
Joaquín (Fariñas) Da Silva
Víctor Pignanelli
Antonio Mejías
Radamel García
Manolo Contreras
Eduardo Borrero
Daniel Lanata
Alí Cañas
Franco Fasciana
Del Valle Rojas
Bernardo Redín
José (Cuervito) Rivas
Rafael Castellín
José Fasciana
José (el Papi) Rivas
Carlos (Pomada) Bravo
Current roster 2007
José Bottini
Andrés Rivas
Juan Carlos Guazá
Lenín Díaz
Pedro Agustín Duval
Frank José Presilla
Luis Salazar
Benzon Rovira
Robert Alexander Varrone
Ever Avendaño
Edward Leonett
Williams Lacle
John Mancilla
Jarvy Mejía
Timshel Tábarez
Néstor Sánchez
Laynecker Zafra
Ricardo Wisniewski
Alexis Acuña
Luis Alberto Moreno
Hermes Orejuela
Jamerson Rentería
Venezuelan football clubs
Vättern is the second biggest lake in Sweden.
The lake's total surface area is about  .
The deepest known point is .
The average depth of the lake is .
Vättern is famous for the quality of its transparent water.
Many of the people living in the area get their drinking water directly from Vättern.
The lake water does not need to have many things done to it before it is used in nearby cities and towns.
The water can be safely drunk from almost any point in the lake.
It has been said that Vättern is the largest body of potable water in the world.
Vättern is also noted for its fishing.
Tourist sport fishermen and people on vacation are allowed to fish in the lake as long as they do not use nets.
Lakes of Sweden
Uppsala is a city in Sweden.
It is the 4th biggest city in Sweden, and the center of the Church of Sweden.
The city is home to the well-known student residential area of Flogsta.
It is the largest student residence in the city.
It is also known for the 'Flogsta scream'.
At 10 pm every evening, students scream their frustrations from windows and balconies.
The Summer of Love is the name for the summer of 1967 in the United States, especially in the Haight-Ashbury district of San Francisco, California.
Thousands of young people from all over the world went to San Francisco to help create a hippie counterculture.
The Summer of Love made the rest of America much more aware of the hippie movement.
The Human Be-In is often called the start of the Summer of Love, although it happened in January of that year.
During the Summer of Love, as many as 100,000 young people from around the world travelled to San Francisco's Haight-Ashbury district, Berkeley, California, and other cities in the San Francisco area.
Once there, they joined in a popular version of the hippie experience.
The people who were a part of the Summer of Love are sometimes called "Flower Children".
When these new Flower Children returned home at the end of summer, they brought their new clothing, ideas and behaviors to most major cities in the U.S., Canada, Britain, Western Europe, Australia and New Zealand.
Appenzell Innerrhoden is one of the twenty-six cantons of Switzerland.
It is the smallest canton by population and the second smallest by area.
Appenzell, population 5587 (2002)
Gonten, population 1398 (2002)
Oberegg, population 1831 (2002)
Rüte, population 3036 (2002)
Schlatt-Haslen, population 1160 (2002)
Schwende, population 2094 (2002)
Official Statistics
Säntis (German)
A cataphile, also known as an urban explorer or "kata", is a person who illegally explores the catacombs underneath Paris, France.
The catacombs go on for approximately 186 miles.
The cataphiles carry maps, usually made by hand.
Staffordshire (abbreviated Staffs) is a county in the West Midlands region of England.
The county town is Stafford.
Part of the National Forest is there.
It is next to the counties of Cheshire, Derbyshire, Leicestershire, Warwickshire, West Midlands, Worcestershire and Shropshire.
Staffordshire County Council
Staffordshire Past Track - Historical archive about the county
The story of a Staffordshire Home Guard Battalion, 1940-1944
Staffordshire Photographs
Staffordshire Tourism website
The Upper Cretaceous is the last geological epoch in the Cretaceous.
It began 100.5 million years ago, and ended 66 million years ago.
The Cretaceous is traditionally divided into Lower Cretaceous (early), and Upper Cretaceous (late), because of the different rocks.
The rocks reflect the conditions in which they were formed.
From lowest to highest, it is subdivided into the Cenomanian, Turonian, Coniacian, Santonian, Campanian, and Maastrichtian ages.
The Upper Cretaceous is the time of chalk.
Chalk is composed of countless millions of calcareous (CaCO3) plates called coccoliths.
They are so small they can only just be seen with a light microscope; details require an electron microscope.
The plates are formed by single-celled planktonic algae called coccolithophores, and were laid down in the off-shore seas.
The only other rock found in chalk is the flint, which is siliceous (silica, SiO2).
This derives from those algae and animals which have skeletons of silica.
Undoubtedly, this marks periods when the climate was somewhat different.
The Cretaceous was the last period when dinosaurs were the dominant land animals.
Triceratops, Tyrannosaurus and Velociraptor lived at this time.
The huge Mosasaurus was the dominant marine predator.
In the Cretaceous period, birds became more diverse.
Flowering plants developed more, and became the dominant plants on land.
The Upper Cretaceous ended with the K/T extinction event.
The end of the Cretaceous period is marked by the huge extinction event which marked the end of the dinosaurs.
However, many groups had already disappeared long before then.
There was an earlier extinction event in the Upper Cretaceous at the CenomanianTuronian boundary, about 95 to 90 million years ago.
All we know about it is that there was huge volcanic activity which led to changes in sea life.
The event brought about the extinction of the pliosaurs, and most ichthyosaurs, and most lines of pterosaurs.
Although the cause is uncertain, the result starved the Earth's oceans of oxygen for nearly half a million years.
This caused the extinction of about 27 percent of marine invertebrates, including certain planktonic and benthic foraminifera, mollusks, bivalves, dinoflagellates and calcareous nannofossils.
This global environmental disturbance increased atmospheric and oceanic temperatures.
Boundary sediments show an enrichment of trace elements, and elevated δ13C values.
Higher carbon-13 shows a time of lesser biological productivity.
This means the seas were no longer so favourable for life at that time, and many species went extinct.
Late Cretaceous
Ocean-wide
Mosasaurus
Dracorex
Hesperonychus
Alexornis
Alphadon
The Thai language is the national and official language of Thailand.
It is the first language of the Thai people, Thailand's main ethnic group.
Thai is closely related to the Lao language.
In fact, some dialects of Thai and Lao are mutually intelligible, meaning that speakers of one language can talk with and understand speakers of the other language without knowing the other's language.
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thai-language.com English speakers' online resource for the Thai language
Thai Online Web Application with 105 Interactive Lessons of which the first 10 are free to access.
Thai Flashcards, online flashcards with sound.
The New England Patriots is an American football team in the National Football League or the NFL.
They are in the American Football Conference or the AFC.
Their starting quarterback is Mac Jones.
Cody Kessler plays the second string quarterback.
The Patriots play in Gillette Stadium on Foxborough, midway between Boston, Massachusetts and Providence, Rhode Island.
In the 2007 season, the Patriots have won all 16 games and became the first team with 16 wins and no losses.
They would win 2 more playoff games and enter the Super Bowl at 18-0.
However, they did not complete a historic 19-0 season, because they lost to the Giants.
The Giants scored 17 points when David Tyree made a helmet catch and the Patriots scored 14 points.
The New England Patriots won the Super Bowl in 2001, 2003, 2004, 2014, 2016, and 2018.
They play in Foxboro, Massachusetts.
They lost to the New York Giants in Super Bowl XLVI on February 5, 2012 in a rematch of Super Bowl XLII which their perfect season got spoiled.
This time, the Giants scored 21 points and the Patriots scored 17 points.
The Patriots also won Super Bowl XLIX against the Seattle Seahawks when Russell Wilson threw an interception on the final play.
The Patriots scored 28 points and the Seahawks scored 24 points.
The Patriots were originally called the "Boston Patriots", and played in Fenway Park.
Their name comes from the city of Boston's importance in the American Revolution.
Digenea are a type of flatworms.
They are parasites.
They have two suckers, usually.
One of them is ventral (on the belly), and the other is oral (where the mouth is).
The Aspidogastrea (gr.
aspid - shield, gaster - stomach/pouch) is a small group of flukes.
There are about 80 species.
The group is a subclass of the Trematoda, and sister group to the Digenea.
Species are between approximately one mm to several cm long.
They are parasites of freshwater and marine molluscs and vertebrates (cartilaginous and bony fishes and turtles).
Aspidogastrea from Tree of Life
Checklist of European aspidogastreans
Fishdisease.net
Today, they are represented by 10,000 living species of birds, which evolved in the Upper Jurassic from small feathered coelurosaurian theropods.
Early theropods
Theropods first appear in the earliest part of the Upper Triassic about 230 million years ago.
They were the sole large terrestrial carnivores from the Lower Jurassic until the close of the Cretaceous, about 66 million years ago.
Some of the earliest and most primitive of the theropod dinosaurs were:
coelophysids, a family including Coelophysis
In number theory, Iwasawa theory is a Galois module theory of ideal class groups, started by Kenkichi Iwasawa, in the 1950s, as part of the theory of cyclotomic fields.
In the early 1970s, Barry Mazur thought about generalizations of Iwasawa theory to Abelian Varieties.
Later, in the early 90s, Ralph Greenberg has suggested an Iwasawa theory for motives.
The first thing Iwasawa noticed was that there are towers of fields in algebraic number theory, having Galois group isomorphic with the additive group of p-adic integers.
That group, usually written Γ in the theory and with multiplicative notation, can be found as a subgroup of Galois groups of infinite field extensions (which are by their nature pro-finite groups).
The group  is the inverse limit of the additive groups , where p is the fixed prime number and .
We can express this by Pontryagin duality in another way: Γ is dual to the discrete group of all -power roots of unity in the complex numbers.
Let  be a primitive -th root of unity and look at the following tower of number fields:
where  is the field generated by a primitive -th root of unity.
This tower of fields has a union .
Then the Galois group of  over  is isomorphic with ; because the Galois group of  over  is .
In order to get an interesting Galois module here, Iwasawa took the ideal class group of , and let  be its -torsion part.
There are norm mappings  when , and so an inverse system.
Letting  be the inverse limit, we can say that  acts on , and it is good to have a description of this action.
The motivation here was undoubtedly that the -torsion in the ideal class group of   had already been identified by Kummer as the main obstacle to the direct proof of Fermat's last theorem.
What Iwasawa did that was new, was to go 'off to infinity' in a new direction.
In fact,   is a module over the group ring .
This is a well-behaved ring (regular and two-dimensional), meaning that it is quite possible to classify modules over it, in a way that is not too coarse.
From this beginning, in the 1950s, a good-sized theory has been built up.
A basic connection was noticed between the module theory, and the p-adic L-functions that were defined in the 1960s by Kubota and Leopoldt.
The latter begin from the Bernoulli numbers, and use interpolation to define p-adic analogues of the Dirichlet L-functions.
It became clear that the theory might be able to move ahead finally from Kummer's century-old results on regular primes.
The main conjecture of Iwasawa theory was formulated as an assertion that two ways of defining p-adic L-functions (by module theory, by interpolation) should coincide, as far as that was well-defined.
This was eventually proved by Barry Mazur and Andrew Wiles for Q, and for all totally real number fields by Andrew Wiles.
These proofs were modeled upon Ken Ribet's proof of the converse to Herbrand's theorem (so-called Herbrand-Ribet theorem).
More recently, also modeled upon Ribet's method, Chris Skinner and Eric Urban have announced a proof of a main conjecture for GL(2).
An easier proof of the Mazur-Wiles theorem can be found by using Euler systems as developed by Kolyvagin (see Washington's book).
Other generalizations of the main conjecture proved using the Euler system method have been found by Karl Rubin, amongst others.
Greenberg, Ralph, Iwasawa Theory - Past & Present, Advanced Studies in Pure Math.
30 (2001), 335-385.
Available at .
Coates, J. and Sujatha, R., Cyclotomic Fields and Zeta Values, Springer-Verlag, 2006
Lang, S., Cyclotomic Fields, Springer-Verlag, 1978
Washington, L., Introduction to Cyclotomic Fields, 2nd edition, Springer-Verlag, 1997
In mathematics, a ring is an algebraic structure consisting of a set together with two operations: addition (+) and multiplication (•).
These two operations must follow special rules to work together in a ring.
Mathematicians use the word "ring" this way because a mathematician named David Hilbert used the German word Zahlring to describe something he was writing about.
The integers, the rational numbers, the real numbers and the complex numbers are all famous examples of rings.
There are other, more unusual examples of rings, however they all obey the special rules below.
The operations are used to combine two elements to form a third element.
There are a few rules the set and the operations must obey to qualify as a ring.
These are called ring axioms:
Closure: It is required to check if the suggested operations are actually operations on the set.
If an operation is used on any elements in the ring, the element that is formed will also be part of the ring.
For all a, b in R, the result of the operation a + b is also in R.
For all a, b in R, the result of the operation a • b is also in R.
Additive Identity element: One element of the ring is special.
It is called the additive identity element.
If addition is used with the identity element and another element, the other element will not change.
There exists an element 0 in R, such that for all elements a in R, the equation 0 + a = a + 0 = a holds.
Associativity of Addition: When addition is done many times, it does not matter how it is grouped, the result will be the same.
For all a, b and c in R, the equation (a + b) + c = a + (b + c) holds.
Commutativity of Addition: When addition is done, it does not matter which element is on the right and left, the result will be the same.
For all a and b in R, the equation a + b = b + a holds.
Additive Inverse element: Every element in the ring has another element in the group when addition is performed between them, the result is the additive identity element.
This is known as its additive inverse.
For each a in R, there exists an element -a in R such that a + (-a) = 0, where 0 is the additive identity element.
Associativity of multiplication: When multiplication is done many times, it does not matter how it is grouped, the result will be the same.
For all a, b and c in R, the equation (a • b) • c = a • (b • c) holds.
Distribution: When multiplication and addition are both done, certain rules apply.
For all a, b and c in R, the equation (a + b) • c = (a • c) + (b • c) holds.
For all a, b and c in R, the equation a • (b + c) = (a • b) + (a • c) holds.
Special Kinds of Rings
Commutative Ring: If x • y = y • x holds for every x and y in the ring, then the ring is called a commutative ring.
Ring with Unity: If there is a multiplicative identity element, that is an element e such that for all elements a in R, the equation e • a = a • e = a holds, then the ring is called a ring with unity.
This element is usually written as 1.
Division Ring: If every element of the ring has a multiplicative inverse, that is for each a in R, there exists an element a-1 in R such that a • a-1 = 1, where 1 is the multiplicative identity element, then the ring is called a division ring.
Integral Domain: In a ring, it may be possible to multiply two things which are not zero and get zero as a result.
If this is impossible in a certain ring, then the ring is called an integral domain.
July 5 – Pope Celestine V succeeds Nicholas IV as the 192nd pope.
December 24 – Pope Boniface VIII succeeds Pope Celestine V as the 193rd pope after Celestine V abdicates the papacy on December 13, only five months after reluctantly accepting his surprise election on July 5, wishing to return to his life as an ascetic hermit.
John Balliol, King of Scotland, decides to refuse King Edward I of England's demands for support in a planned invasion of France, and instead informs the French of Edward's plans and negotiates the Auld Alliance with France and Norway.
These actions play a part in precipitating the Scottish Wars of Independence, to begin in 1296.
The Strata Florida Abbey is rebuilt; it had been destroyed some years earlier in King Edward I of England's conquest of Wales.
Architect Arnolfo di Cambio designs the Florentine cathedral Santa Maria del Fiore, better known smply as Il Duomo.
He also begins work on the Basilica di Santa Croce di Firenze, also in Florence.
England and Portugal enter into the first iteration of the Anglo-Portuguese Alliance, the oldest alliance in the world still in force.
The death of Kublai Khan allows the four khanates of the Mongol Empire (the Chagatai Khanate, the Golden Horde, the Ilkhanate, and the Yuan Dynasty of China) to formally become independent; they each had already been moving toward independence during Kublai's reign.
Charles IV of France (died 1328)
Kusunoki Masashige, Japanese samurai (died 1336)
February 18 – Kublai Khan of the Mongol Empire (born 1215)
May 3 – John I, Duke of Brabant
December 25 – Mściwój II of Pomerania
Roger Bacon, English philosopher and scientist
Emperor Yagbe'u Seyon of Ethiopia
Brunetto Latini, Florentine philosopher (born c. 1220)
Dmitri of Pereslavl, Grand Duke of Vladimir-Suzdal
September – Halley's Comet is at perihelion
Sankore University founded in Timbuktu
Adémar de Chabannes (died 1034), monk and historian
Gisela of Swabia (died 1043), Holy Roman Empress
6 September – Sharaf al-Daula, emir of Kerman and Fars
Al-Azhar University is founded in Cairo, Egypt.
It is the 2nd oldest university in the world.
Vladimir I, Prince of Kiev marries Anna, sister of Byzantine emperor Basil II and converts to Christianity.
Baptism of Kievan Rus'.
Abbo becomes abbot at Fleury
Baile Átha Cliath (Dublin, Ireland) was founded.
Liao Dynasty adopts civil service examinations in the Southern Chancellery based on Tang Dynasty models.
King Edmund II of England, English royal (died 1016)
Tilopa, Indian tantric practitioner and mahasiddha
May 19 – Saint Dunstan, Archbishop of Canterbury (b. 909)
Hugh Capet, Count of Paris, crowned King of France
Kukulcan conquers Chichen Itza
Earl Godwin of Wessex, Anglo Saxon nobleman (died 1053)
Liu Yong, Chinese poet of the Song Dynasty
May 21 King Louis V of France
March 2 – Louis V becomes King of the Franks
End of the reign of Emperor Kazan, emperor of Japan
Emperor Ichijō ascends to the throne of Japan
Explorer Bjarni Herjólfsson becomes the first inhabitant of the Old World to sight North America
Sweyn Forkbeard becomes King of Denmark
Song Dynasty sends armies on three fronts against the Liao Dynasty in the Sixteen Prefectures but are defeated on all fronts.
Pablo Neruda (July 12, 1904 – September 23, 1973) was a Chilean poet.
He won the Nobel Prize for literature in 1971.
He wrote in Spanish.
Most of his works have been translated into many other languages.
Neruda was born in the City of Parral in Chile on July 12, 1904 born under the name Ricardo Neftali Reyes.
Neruda’s mother died shortly after he was born, but the child, Neruda came to love his stepmother (Dona Trinidad Candia Malverde) as if she had been his real mother.
Neruda started to write poetry as a young boy against the wishes of his father who wanted him to focus on mathematics - so he could become a teacher.
In his youth he became a great admirer of the poetry of Jan Neruda and Paul Verlaine and chose the pen name of Pablo Neruda after Paul Verlaine (Pablo is the Spanish version of Paul) and Jan Neruda.
Neruda was mainly interested in literature and writing poems, which he would mail out to magazines; to prevent his parents from discovering that he was doing this he changed his name to Pablo Neruda.
In 1920 Neruda moved to Santiago to study French at the University of Chile, which he did to please his parents who wanted him to become a teacher.
Soon Neruda became deeply involved in his poetry and in 1923 he published his first book: Crepusculario(Twilight Book).
Neruda was suffering from cancer when he died of heart failure in hospital at the age of 69 on September 23, 1973 about a fortnight after the overthrow of Salvador Allende by military forces led by Pinochet.
Many people today believe Neruda may have been poisoned by Pinochet's secret police, DINA, who feared Neruda's prominence and influence in creating an opposition to the military dictatorship.
Neruda had a number of siblings, he had a sister that was stillborn when he was 3 or 4 years old and from his father's second marriage, a stepbrother, Ricardo Reyes Candia, and a stepsister, Laura Reyes Candia, - both children from his "mother" Trinidad Candia and his father DonReyes.
Some of Neruda’s dog and also Tierney poetry is very difficult to understand because they are about events of World history such as the colonization of America, the Spanish Civil War, Nazi Germany and other conflicts.
Neruda also references (mentions) important figures of World history.
In some of his poetry Neruda tends to link historical events from different eras (periods of history) and different parts of the world into one major conflict as in his Canto General (1950).
Neruda was very concerned in how his poetry sounded, he liked rhythm and many claim he had a “musical intelligence” i.e. he wrote with music in his mind.
He would record many of his poems on a tape recorder and many of his recordings were sold like records in the Spanish speaking world.
Many academics and scholars consider Neruda to be one of the most important and widely read poets of the 1900s.
Many go as far as to place him alongside Shakespeare and Dante.
This is probably because Neruda wrote poems on all sorts of topics, appealing to people of all ages and interests: poems about love, on historical events (like wars), he wrote about native people, about nature and about simple things.
Neruda was also an avid collector of all sorts of things.
He had one of the largest collections of seashells in the world and collected bottles, model ships, water taps - among other odd objects.
Many of Neruda’s poems have been used in movies and in music, such as in the classical music of the Greek composer Mikis Theodorakis, and in the movies, such as "Il Postino" or "Patch Adams".
Many famous people have also recorded narrations (spoken word) of his poems, such as Julia Roberts, Madonna, Andy Garcia, and Glen Close.
Also, he fought his whole life for the freedom of others.
Pablo Neruda Study Guide - Sources and References
Ode To My Socks hear the poem (English)
Chilean poets
People from Parral
The Truth about Nanjing is a Japanese movie from 2007.
It is thought to be made by fundamental Japanese nationalists.
In this movie they want to deny the fact of the Nanjing Massacre.
'Nanking No Shinjitsu' official website (Japanese language only)
'Nanking No Shinjitsu' Supporting Website ( Automatic translation )
The Nanjing Massacre was a massacre (an unjust killing of many people) that happened in Nanjing, China, in December of 1937 and January of 1938.
It was part of the Second Sino-Japanese War, which was the part of World War II between China and Japan.
At the time, Japan was trying to take over China and Nanjing was the Chinese capital.
The Japanese Army reached Nanjing on 13 December 1937 and began killing thousands upon thousands of men and boys and raping thousands upon thousands of women and girls.
Some Japanese claim the fighting in Nanjing was the same or not much worse than fighting in other places and in other wars.
There is a lot of evidence from the Chinese, from outsiders who were there, from outsiders who have studied it, and from the Japanese themselves that things were much worse.
There were many, many war crimes: soldiers without weapons were killed; people who were not soldiers were killed; many were tortured (hurt very badly), mutilated (hurt ways that can never be fixed), or killed in very cruel ways; many were raped (forced to have sex) or forced to work and treated like things.
We have the orders from the soldier's leaders telling them to do these kinds of things and not to follow rules against them.
The Nanjing Massacre was so bad that some even think of it as a kind of genocide (trying to wipe out an entire group of people).
The Nanjing Massacre is also known as the .
It was known at the time as the  or the .
The name of Nanjing has not changed: it was  then and now, but people have changed the way they spell the sounds of Chinese names using the Latin alphabet. "
Nanking" was the Postal Map spelling, which usually tried to spell words the way local people said them around the year 1900. "
Nanjing" is the pinyin spelling, which spells words the way they should sound in Mandarin Chinese.
The Mandarin Chinese name for the Nanjing Massacre is the Nánjīng Dàtúshā, which means the same thing. (
Part-by-part, dàtúshā could mean "a big butchering and killing" but, taken all together, it is just the Chinese word for "massacre".)
It is written  in traditional Chinese writing and  in the easier Chinese writing now used by mainland China and Singapore.
The Japanese can use similar names but often prefer to call it the Nankin Jiken, which just means "The Thing that Happened in Nanjing".
It is written  in Japanese writing.
The massacre
The Nanjing Massacre lasted over six weeks.
During this time, soldiers of the Imperial Japanese Army:
Murdered Chinese civilians
Murdered Chinese soldiers who had given up their weapons
Stole and looted whatever they wanted
Set buildings on fire to destroy them
Raped and tortured children and adults
Mass murder of civilians
During the six weeks of the Nanjing massacre, the Imperial Japanese Army (IJA) massacred between 40,000 and 300,000 people.
It is difficult to know exactly how many people were killed in this mass murder, because the IJA burnt many bodies, buried others in mass graves, and dumped others in the Yangtze River.
Because of this, scholars and historians do not agree on exactly how many civilians were killed.p.
However, historians agree that the Imperial Japanese Army began massacring Chinese civilians the day they entered Nanjing.
On that day, John Rabe, a German businessman, wrote in his diary: "We come across corpses every 100 to 200 yards.
These people had ... been [running away] and were shot from behind.
In another massacre, Japanese soldiers shot thousands of Chinese people with machine guns.
They left their bodies in a trench they named the "Ten-Thousand-Corpse Ditch."
Most historians think that more than 12,000 people were killed in this massacre.
The IJA also massacred about 100 Hui people (a minority group in China who are mostly Muslim).
Torture of civilians
For the entire six weeks of the Massacre, the Imperial Japanese Army kept killing Chinese civilians.
They killed in cruel, brutal ways and often tortured their victims before killing them.
Throwing them into pots of boiling water
Burying them while they were still alive so they would suffocate
Burying them with only their heads above ground so they would starve
Throwing infants into the air and catching them on bayonets
In 2010, a Japanese woman named Tamaki Matsuoka made a documentary film about the Nanjing Massacre.
In the film, former IJA soldiers admit that they often raped Chinese women and massacred Chinese civilians.
However, out of the 250 former soldiers that Matsuoka interviewed, only three felt bad about what they had done.
One former solder, Sho Mitani, said:
During the Massacre, the Japanese soldiers raped about 20,000 women  including children and the elderly.p.
1012  Soldiers would go from door to door, searching for girls.
When they found one, they would take her and rape her as a group.
If anyone tried to stop the soldiers, the soldiers would shoot them.p.
One survivor of the massacre said that sons were forced to rape their mothers, and fathers were forced to rape their daughters.
One group of soldiers gang-raped a pregnant woman, who gave birth only a few hours later (the baby did not seem to be hurt).
Japanese soldiers also raped Buddhist nuns and forced monks to rape women.
Witnesses' stories
Another witness to the rapes in Nanjing was Robert O. Wilson.
He was a surgeon at an American hospital in Nanjing.
On December 15 and 18, 1937, he wrote to his family:
Killing of prisoners of war
Starting in 1931, an international law called the Third Geneva Convention said it was illegal to treat prisoners of war in certain ways.
It said these prisoners had rights  for example, the right to have a trial before being executed.
However, in August 1937, Hirohito, the Emperor of Japan, had decided that neither he nor the army would not follow any international laws about how Chinese prisoners of war had to be treated.
Right after the IJA took over Nanjing, they started searching for ex-Chinese soldiers.
They took thousands of young men as prisoners.
Some of these men were never soldiers; the IJA just assumed they were.
Without any trials, the IJA took many of these young men to the Yangtze River and killed them with machine guns.
According to confessions made by former IJA soldiers, on December 13 and 14, 1937, a unit of IJA soldiers had taken 14,777 Chinese prisoners of war.
In the next few days, they took another 2,0003,000 prisoners.
In two days, the IJA massacred every one of these prisoners of warover 15,000 people.
In their confessions, the former IJA soldiers said their military leaders had ordered them to do this.
Over the six weeks of the massacre, the IJA killed a total of about 30,000 Chinese prisoners of war.p.
Theft and arson
The Japanese Army left most of the buildings in Nanjing destroyed by looting and arson.
They destroyed newly built government buildings as well as many civilians'  homes.
Soldiers also stole whatever they wanted.
Because the Imperial Japanese Army was so much stronger than the Chinese soldiers and civilians in Nanjing, the Chinese could not fight back.
This meant the Japanese could take all of the city's valuable things for themselves.
End of the massacre
In January 1938, the Imperial Japanese Army announced that Nanjing was in "order" again.
In the first week of February, it created a government that would obey all of Japan's needs.
After that, the IJA left.
The massacre was over.
Trial and punishment
On September 2, 1945, Japan surrendered to the Allied Powers.
This ended World War II.
Soon after this, the Allied Powers began creating international military courts.
To try Japan's leaders for war crimes and crimes against humanity, they created the International Military Tribunal for the Far East (IMTFE).
General Matsui Iwane, who was in charge of all of the Japanese soldiers at Nanjing
General Akira Muto, who led soldiers during the worst part of the massacre
Kōki Hirota, who was the Foreign Minister during the massacre.
He was accused of helping plan the massacre, and not doing anything to stop it
All three of these men were found guilty of "Class A" war crimes.
This meant they had been found guilty of planning and being in charge of the war.