cahya/simple-wikipedia huggingface dataset:
Lilac is a light violet colour. It is named after the colour of the lilac flower.  The actual colour of the flowers of the plant may range from the colour of the lilac flowers shown at left to a richer or deeper colour.  These colours, such as rich lilac and deep lilac, are shown in the colour chart below.

The first written use of lilac as a colour name in English was in 1775.

Meaning of lilac
 Lilac is a soft dainty colour that is often associated with grandparents or grandchildren and used on greeting cards addressed to grandparents or grandchildren.

Tones of lilac and Persian lilac colour comparison charts
Some lilac flowers are coloured tones of lilac and other lilac flowers are coloured tones of red-violet.  Those lilac flowers that are coloured red-violet are said to be coloured Persian lilac.  Therefore, two different colour comparison charts are provided.

Tones of lilac colour comparison chart

Tones of Persian lilac colour comparison chart
See also red-violet

Related pages
 List of colors

References
A freedom fighter is a person who thinks their native ethnic group is not free, and is working to have freedom for their group. Most often this means that a freedom fighter wants their people to have own nation and independence and/or get rid of oppressors. People who think like this are said to think in a nationalist way

Freedom fighter is a relativistic term - this means a person decides by his or her point of view if he call some persons or groups freedom fighters or not. Freedom fighter is a positive term - this means that he or she calls a person "freedom fighter" only if he or she supports the goals of the freedom fighter. If people do not support his goals, they probably use more negative terms like insurgent, terrorist, rebel or criminal.

Freedom fighters are often called terrorists by their opponents if they hurt civilians. However, not all freedom fighters hurt civilians. Some freedom fighters damage the opposing military. Some freedom fighters damage property - this is called sabotage. There are also freedom fighters who do not use violence at all. For example, the Mahatma Gandhi and the Dalai Lama.

Groups 
These are examples of groups who call themselves freedom fighters.
 The African National Congress, c.f. Alfred Nzo's Address to the British Trades Union Congress at its Presentation of a Gold Medal to Nelson Mandela , 1988.
 Al-Qaeda
 Aryan Nations
 Babbar Khalsa (Sikh separatists)
 CNRT Conselho Nacional de Resistência Timorense
 The Continuity Irish Republican Army
 Earth Liberation Front
 ETA Euskadi Ta Askatasuna - Basque nationalist organization
 GAM Gerakan Aceh Merdeka
 Hamas
 Hezbolla
 Hizbul Mujahideen - Kashmiri separatists
 The Irish National Liberation Army
 The Irish People's Liberation Organisation
 The Irish Republican Army
 Liberation Tigers of Tamil Eelam (Tamil Separatists)
 Mahdi Army a milita force created by and loyal to the Iraqi Shiite cleric Muqtada al-Sadr
 The New Peoples' Army
 The Real Irish Republican Army
 The Scottish National Liberation Army
 The Ulster Defence Regiment
 The Ulster Freedom Fighters
 The Ulster Volunteer Force

Other examples 
 The Dalai Lama: "We are freedom fighters unique in our peaceful approach to liberation."
 Sitting Bull
 Nelson Mandela
 Mahatma Gandhi
 Michael Collins (Irish leader)
 Red Cloud
 William the Silent
 George Washington
 Bangabandhu Sheikh Mujibur Rahman

Human rights
Freedom
Wood grain describes the ,  and appearance of the wood . This is often important in its effect on woodworking techniques (e.g. against the grain).

In describing the alignment of the wood in the tree a distinction may be made. Basic grain descriptions and types include:
 straight - grain which runs in a single direction along the cut wood, a product of a straight growing tree
 cross - grain in which some cells grow out from the major growth axis of the tree
 spiral - grain which develops as the trunk of the tree twists in development
 interlocked (roey grain) A step beyond spiral grain occurring when growth rings in a twisting trunk develop misaligned grain

In addition, there are a few special grain alignments. Their rarity often promotes the value of both the raw material, and the finished work it becomes a part of. These include:

 bird's eye
 quilted
 fiddleback
 curly
 tiger

In describing the application of a woodworking technique to a given piece of wood, the direction of the technique might be:
 with the grain
 against the grain
 across the grain

In a wider sense, the term grain may also be applied to the orientation of the cut, the way a given piece of wood has been sawn: 
 flat-grain: flat-sawn or plain sawn,
 edge grain: quarter-sawn or rift-sawn or straight-grained, and
 end grain.

Wood
In joinery, a groove is a slot or trench cut into a member which runs parallel to the grain. A groove is something else than  a dado, which runs across the grain. 

Grooves are used for several purposes in cabinet making and other woodworking fields. Typically, a groove is used to house the panels in frame and panel construction and the bottoms drawers.

A groove may be through, meaning that it passes all the way through the surface and its ends are open, or stopped, meaning that one or both of the ends finish before the groove meets edge of the surface.

Methods
A groove can be cut by the following methods:
electric router using a straight or rebate bit
circular saw with multiple passes (depending on width and depth)
dado set in a single pass
spindle moulder (wood shaper)
hand saw and chisel
router plane

Manufacturing

da:Not (træ)
Sepultura is a thrash metal/death metal/groove metal band from Brazil that has sold over 15 million albums worldwide. The brothers Max and Igor Cavalera started it in Belo Horizonte in 1984. The two brothers have left the band since, Max in 1996, and Igor in 2006, with American singer Derrick Green and drummer Jean Dolabella replacing them after their exits, although Dolabella left in 2011 to be replaced with Eloy Casagrande.

History
The band's name is Portuguese for the word "grave". The Cavalera brothers chose this name after translating English band Motorhead's song called "Dancing On Your Grave".

Singer Wagner Lamounier and bass player Paulo Jr. were the first stable members to join the band along the Cavaleras. Lamounier left after a year and Max decided to sing as well as play guitar. The band added a second guitar player named Jairo Guedez. These members recorded their first album "Morbid Visions" in 1986. The song "Troops of Doom" from this album gave the band a small amount of popularity.

Guedez left after the album was released, being replaced by Andreas Kisser. This line-up lasted until 1996 and accomplished several things. They recorded five more albums, where they began to play a more thrash metal sound than death/black metal in the first three albums, Schizophrenia (1987), Beneath The Remains (1989) and Arise (1991), and then moved on to groove metal with the last two of these five albums, Chaos A.D. (1993) and Roots (1996). Popular songs from the Chaos A.D. include Refuse/Resist and Roots Bloody Roots. On Roots, they also included a song they recorded with the Brazilian Xavantes tribe called Itsari, who also toured with them.

Conflicts between Max and the other members led to Max leaving the band. He was replaced with American singer Derrick Green. Although the band's album sales have lowered with each album released with Green, he remains in the group today, having recorded the albums Against (1998), Nation (2001), Roorback (2003), Dante XXI (2006), A-Lex (2009) and Kairos (2011) with the band.

Igor Cavalera left the band in 2006 after Dante XXI. A year later, he made up with his brother Max, and the two formed The Cavalera Conspiracy. Igor's first replacement in Sepultura was Jean Dolabella, who recored A-Lex and Kairos with the band before quitting. The band's drummer today is Eloy Casagrande.

Members 
 Paulo Jr. - bass guitar (1984-)
 Andreas Kisser - guitar (1987-)
 Derrick Green - vocals, guitar (1997-)
 Eloy Casagrande - drums (2011-)
 Max Cavalera - vocals, guitar (1984-1996)
 Igor Cavalera - drums (1984-2006)
 Jairo Guedez - guitar (1984-1986)
 Jean Dolabella - drums (2006-2011)

Albums 
 Morbid Visions (1986)
 Schizophrenia (1987)
 Beneath the Remains (1989)
 Arise (1991)
 Chaos A.D. (1993)
 Roots (1996)
 Against (1998)
 Nation (2001)
 Roorback (2003)
 Dante XXI (2006)
 A-Lex (2009)
 Kairos (2011)
 The Mediator Between Head and Hands Must Be the Heart (2013)
 Machine Messiah (2017)
Quadra (2020)

Other websites 
 http://www.sepultura.com.br/

Thrash metal bands
Heavy metal bands
Death metal bands
Groove metal bands
Belo Horizonte
1984 establishments
1980s establishments in Brazil
The Dalai Lama  is a religious figure in Tibetan Buddhism. He is its highest spiritual teacher of the Gelugpa school. A new Dalai Lama is said to be the reborn old Dalai Lama. This line goes back to 1391. The 14th and current Dalai Lama is Tenzin Gyatso.

Between the 17th century and 1959, the Dalai Lama was the head of the Tibetan government. During winter, the Dalai Lamas stayed in the Potala palace. In summer they were in the Norbulingka palace. These two palaces are both in Lhasa, Tibet. In 1959, the Dalai Lama had to flee from Tibet to Dharamsala, India. This is still his base today.

The current Dalai Lama is His Holiness Tenzin Gyatso.

Dalai Lama is the title of Tibetan Buddhism leader. "Dalai" is original from Mongolian which means "ocean" and "Lama" is original from Tibetan which means "the highest principle". In 1653, during the Qing Dynasty, this title was authorized to Dalai Lama V by the Chinese Emperor for the first time.

Modern history 
The 13th Dalai Lama, Thubten Gyatso, expelled all Chinese civilians from the country, and instituted many measures to modernise Tibet. These included provisions to curb excessive demands on peasants and tax evasion by the nobles, setting up an independent police force, the abolishment of the death penalty, extension of secular education, and the provision of electricity throughout the city of Lhasa in the 1920s. Thubten Gyatso died in 1933.

The 14th Dalai Lama was not formally enthroned until 17 November 1950, during the People's Republic of China invasion of Tibet (1950–1951). Fearing for his life, the 14th Dalai Lama fled to India where he has led a government-in-exile since. With the aim of launching guerrilla operations against the Chinese, the Central Intelligence Agency funded the Dalai Lama $1.7 million a year in the 1960s. In 2001, he gave up his absolute power over the government to an elected parliament of selected Tibetan exiles. His original goal was full independence for Tibet, but by the late 1980s, he was seeking high-level autonomy instead. He is still seeking greater autonomy from China, although Dolma Gyari, deputy speaker of the parliament-in-exile has stated "If the middle path fails in the short term, we will be forced to opt for complete independence or selfdetermination as per the UN charter".

References 

Asian people
Joinery often refers to the part of woodworking that involves the joining together of parts of wood.

Traditional wood joinery techniques use
the distinctive material properties of wood, often without mechanical fasteners. There are different types of joinery for different structures, for example the joinery used
to build a house is different from that used to make puzzle toys,
although elements overlap.

Wood is strong when stressed along the grain (longitudinally), but weak across it (radially and tangentially). It expands and contracts in response to humidity.
This change is very small longitudinally.  It is considerable, but unequal,
in the radial and tangential directions.

Images of different types of joints

Styles of joinery
Two of the most common traditions of joinery are Japanese and European. The Japanese in particular developed hundreds of types of joints and their furniture was often held together without glue or nails.

Related pages
Woodworking

References
 Bernard Jones (Ed.) (1980). The Complete Woodworker.   
 Peter Korn (1993). Working with Wood.   
 Sam Allen (1990). Wood Joiner's Handbook. Sterling Publishing. 
 Wolfram Graubner (1992). Encyclopedia of Wood Joints. Taunton Press. 

Woodworking
George Grenville (14 October 1712–13 November 1770) was Prime Minister of Great Britain. He was a member of the Whig Party. He was one of the few prime ministers who never was given a title of nobility.

Grenville was the second son of Richard Grenville and Hester Temple. His older brother was Richard Grenville-Temple.  Grenville went to school at Eton College and at Christ Church College, Oxford.  He entered Parliament in 1741 as member for Buckingham, and represented Buckingham until his death.

As Treasurer of the Navy in 1758 he introduced and carried a bill which established a fairer system of paying the wages of sailors. He stayed in office in 1761, when Pitt resigned, and in the administration of Lord Bute acted as Leader of the House of Commons. In May 1762 he became Secretary of State for the Northern Department, and in October First Lord of the Admiralty; and in April 1763 he became First Lord of the Treasury and Chancellor of the Exchequer. 

While Prime Minister, his government oversaw the prosecution of John Wilkes and the passing of the American Stamp Act 1765, which led to the first disagreements between American colonies and Great Britain that led to the American Revolutionary War.  

After many years of being Prime Minister, he began to have disagreements with young king George III.  The king started to think that the Prime Minister was using him as a puppet.  The king convinced Rockingham to become the new Prime Minister and Grenville never held an office again.

Grenville was called the "gentile shepherd" because he bored the House by asking over and over again, during the debate on the Cider Bill of 1763, that somebody should tell him "where" to lay the new tax if it was not to be put on cider. Pitt whistled the air of the popular tune Gentle Shepherd, tell me where, and the House laughed. Though few excelled him in a knowledge of the forms of the House or in mastery of administrative details, he lacked tact in dealing with people and with affairs.

In 1749 Grenville married Elizabeth Wyndham (before 1731-5 December 1769), daughter of Sir William Wyndham. They had seven children.

1712 births
1770 deaths
Politicians from London
Whig party (UK) politicians
Prime Ministers of Great Britain
Harald Sigurdsson was also known as Harald of Norway (;  – 25 September 1066). He was also called Hardrada (, modern Norwegian:  ("stern counsel" or "hard ruler") in the sagas). 

Harald was King of Norway (as Harald III) from 1046 to 1066. Also, he unsuccessfully claimed the Danish throne until 1064 and the English throne in 1066. Before becoming king, Harald had spent about fifteen years in exile as a mercenary and military commander in Kievan Rus' and of the Varangian Guard in the Byzantine Empire.

When he was fifteen years old, in 1030, Harald fought with his half-brother Olaf against Cnut (Canute). Olaf sought to reclaim the Norwegian throne, which he had lost to the Danish king Cnut the Great two years before. In the battle, Olaf and Harald were defeated by forces loyal to Cnut.  Harald was forced into exile to Kievan Rus' (early form of Russia). After some time in the army of Grand Prince Yaroslav the Wise, he moved on to Constantinople with his companions around 1034. In Constantinople, he commanded the Byzantine Varangian Guard. 

Harald got wealthy during his time in the Byzantine Empire. He shipped the money to Yaroslav in Kievan Rus' for safekeeping. He finally left the Byzantines in 1042. He arrived back in Kievan Rus' to prepare his campaign of reclaiming the Norwegian throne. In his absence Olaf's illegitimate son Magnus the Good had got the throne. Magnus had also become king of Denmark.

In 1046, Harald joined forces with Magnus's rival in Denmark the pretender Sweyn II of Denmark, and started raiding the Danish coast. Magnus, unwilling to fight his uncle, agreed to share the kingship with Harald, since Harald in turn would share his wealth with him. The co-rule ended abruptly the next year as Magnus died, so Harald became the sole ruler of Norway. 

Domestically, Harald crushed all opposition, and outlined the union of Norway under a national rule. Harald's reign was probably one of relative peace and stability, and he set up a viable coin economy and foreign trade. Probably seeking to restore Cnut's "North Sea Empire", Harald also claimed the Danish throne, and spent nearly every year until 1064 raiding the Danish coast and fighting his former ally, Sweyn. Although the campaigns were successful, he was never able to conquer Denmark.

Not long after Harald had renounced his claim to Denmark, the former Earl of Northumbria, Tostig Godwinson, brother of the English king Harold Godwinson, pledged his allegiance to Harald and invited him to claim the English throne. Harald invaded Northern England with 10,000 troops and 300 longships in September 1066, raided the coast and defeated English regional forces of Northumbria and Mercia in the Battle of Fulford near York. Although initially successful, Harald was defeated and killed in an attack by Harold Godwinson's forces in the Battle of Stamford Bridge, which wiped out almost his entire army. Modern historians have often considered Harald's death, which brought an end to his invasion, as the end of the Viking Age.  The famous Anglo-Saxon Chronicle records these events.

References

1015 births
1066 deaths
Kings and Queens of Norway
The Normans were Vikings who settled in northern France. There they made a kingdom called Normandy.

In 1066 the Normans attacked England and took over. The battle was called The Battle Of Hastings. They ruled England for about 300 years. There they built the Tower of London, Windsor Castle and many other stone castles.

Norman life

Clothes 
The Normans wore woollen tunics and sometimes they wore a waistband to keep the tunic in place. The men also wore long cloaks.

Food 
Normans ate dairy, oatmeal porridge, green vegetables and sometimes meat. They often used honey as a sweetener and for mead (an alcoholic drink).

Castles 
Norman built many stone castles that often had moats around them to protect them from intruders.

Houses 
Norman houses had a wooden frame with sticks and twigs woven in between, which is called wattle, and then it was all covered in a layer of daub which was made from mud, wet clay, dung and straw. The roofs were usually thatched.

Normans in Ireland 
Diarmuid MacMurrough, King of Leinster kidnapped the King of Breifne’s wife. Then Rory O’Connor, the High King of Ireland fired him from being the King of Leinster. Diarmuid still wanted to be king so he hired some Normans, lead by Strongbow to help him get the throne back. Diarmuid had to pay Strongbow so he said that he could marry his daughter and become king when Diarmuid died. Strongbow agreed to this. They first came to Ireland at Bannow Bay, Wexford in 1169 and soon they got the throne back for Diarmuid. King Henry II, King of England and part of France, thought that Strongbow was getting too powerful since Strongbow wasn’t actually the king, so Henry decided to take over the whole of Ireland. He sent over some other Normans who arrived at Ireland in Baginbun, Wexford in 1170. Then King Henry II became King of Ireland as well.

While the Normans were in Ireland they built the original Dublin castle and many other stone castles.

Normans probably introduced rabbits and fallow deer to Ireland for meat and skins.

References 

Ethnic groups in Europe
Germanic tribes
Middle Ages
Normans
Captain is a military rank.  

Captains are officers in an army.  In a navy, captains command an entire ship. A Navy Captain is equal to the army rank of colonel. Another type of captain is a commander of a ship who is not in the military. 

There are also captains in other uniformed organisations, including the police. A leader of a sports team is also called a captain, as well as the pilot of an airliner.

Military ranks
Law enforcement occupations
Ships
Wire rope consists of several strands laid (or 'twisted') together like a helix. Each strand is likewise made of metal wires laid together like a helix. Initially wrought iron wires were used, but today steel is the main material used for wire ropes.

History & materials
Modern wire rope was invented by the German mining engineer Wilhelm Albert in the years between 1831 and 1834 for use in mining in the Harz Mountains in Clausthal, Lower Saxony, Germany. It was quickly accepted because it was better than ropes made of hemp or to metal chains, such as had been used before.

Wilhelm Albert's first ropes consisted of wires twisted about a hemp rope core, six such strands then being twisted around another hemp rope core in alternating directions for extra stability. Earlier forms of wire rope had been made by covering a bundle of wires with hemp.

In America wire rope was later manufactured by John A. Roebling, forming the basis for his success in suspension bridge building. Roebling introduced a number of innovations in the design, materials and manufacture of wire rope.

Manufacturing a wire rope is similar to making one from natural fibres. The individual wires are first twisted into a strand, then six or so such strands again twisted around a core. This core may consist of steel, but also of natural fibres such as sisal, manila, henequen, jute, or hemp. This is used to cushion off stress forces when bending the rope.

Construction & specification
The specification of a wire rope type, including the number of wires per strand, the number of strands, and the lay of the rope, are is documented using a commonly accepted coding system, with abbreviations. For example, the rope shown in the figure "Wire rope construction" is designated:

6x19 FC RH OL FSWR

Each of the sections of the wire rope designation described above is variable. There are therefore a large number of combinations of wire rope that can be specified in this manner. The following abbreviations are commonly used to specify a wire rope.

Other websites 
 Modern history of wire rope

Hardware (mechanical)
Ropework
Liekkiö ("flamey") or Ihtiriekko is a ghost of a bastard child in Finnish mythology.

Stories tells that a woman had sex with someone else than her husband. Maybe she did not even have a husband. She then get pregnant and gave birth to a baby. This way to make a baby was not accepted by church and society - that kind of baby is called bastard. Mother had to kill her bastard child to avoid being blamed by priests or other people. Mother then buried child outside graveyard and without priests blessing the body. Soul of baby could not go to heaven because his/her body was not at graveyard and was not blessed by a priest. This is why she became a ghost.

This ghost could make terrible noise until somebody dugs up his/her body and buries it in graveyard. Such ghost people call Ihtiriekko. Ghosts could also be quiet, but she/he might be seen as a flame in forest, like will o' the wisp. Such ghost people call Liekkiö.

Finnish mythology

es:Ihtiriekko
A bastard is a person who was born of parents who are not married to one another. It is considered by some cultures and individuals as a nasty or insulting word today, or sometimes even profanity, with the term illegitimate being a little more polite. Some cultures see illegitimate children as dirty or bad, and only accept sexual relations between married couples.

Related pages
 Illegitimacy

Pejoratives
English profanity
In formal number theory a Gödel numbering is a function which assigns to each symbol and formula of some formal language a unique natural number called a Gödel number (GN). The concept was first used by Kurt Gödel for the proof of his incompleteness theorem. 

A Gödel numbering can be interpreted as an encoding where a number is assigned to each symbol of a mathematical notation, and a stream of natural numbers can then represent some form or function. A numbering of the set of computable functions can then be represented by a stream of Gödel numbers (also called effective numbers). Rogers' equivalence theorem states   criteria for which those numberings of the set of computable functions  are Gödel numberings.

Definition

Given a countable set S, a Gödel numbering is an injective function

with both f and  (the inverse of f) being computable functions.

Examples

Base notation and strings
One of the simplest Gödel numbering schemes is used every day: The correspondence between integers and their representations as strings of symbols. For example, the sequence 2 3 is understood, by a particular set of rules, to correspond to the number twenty-three. Similarly, strings of symbols from some alphabet of N symbols can be encoded by identifying each symbol with a number from 0 to N and reading the string as the base N+1 representation of an integer.

References 

 Gödel, Kurt, "Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I", Monatsheft für Math. und Physik 38, 1931, pages 173–198.

Further reading
 Gödel, Escher, Bach: an Eternal Golden Braid, by Douglas Hofstadter.  This book defines and uses an alternative Gödel numbering.
Gödel's Proof by Ernest Nagel and James R. Newman.  This book provides a good introduction and summary of the proof, with a large section dedicated to Gödel's numbering.

Mathematics
Numbers
In mathematics, computer science and linguistics, a formal language is one that has a particular set of symbols, and whose expressions are made according to a particular set of rules. The symbol  is often used as a variable for formal languages in logic.

Unlike natural languages, the symbols and formulas in formal languages are syntactically and semantically related to one another in a precise way. As a result, formal languages are completely (or almost completely) void of ambiguity.

Examples 
Some examples of formal languages include:

 The set of all words over 
 The set , where  is a natural number and  means  repeated  times
 Finite languages, such as 
 The set of syntactically correct programs in a given programming language
 The set of inputs upon which a certain Turing machine halts

Specification 
A formal language can be specified in a great variety of ways, such as:

 Strings produced by some formal grammar (see Chomsky hierarchy)
 Strings described or matched by a regular expression
 Strings accepted by some automaton, such as a Turing machine or finite state automaton
 Strings indicated by a decision procedure (a set of related yes/no questions) where the answer is 'yes'

Related pages
 Language for languages in general
 Syntax for the form of a language in general
 Semantics for the meanings in a language
 Natural language for languages that are not formal
 Computer language for application of formal languages in computing
 Programming language for the application of formal languages to program computers

References

Further reading

Other websites 
 http://icalp06.dsi.unive.it/  ICALP 2006 33rd International Colloquium on Automata, Languages and Programming.
 http://www.cs.auckland.ac.nz/CDMTCS/conferences/dlt/DLTConfSeries.html International Conferences on Developments in Language Theory

Mathematics
Programming languages
In computer science, an alphabet is a finite non-empty set. The elements of an alphabet are called the letters or symbols of the alphabet.

An example of an alphabet is  which may be used for Morse code or {begin, if, else, for, while} which may be the keywords of a Programming language.

The set of natural numbers is not an alphabet because as it is not finite.

The alphabet which is used the most in computer science is {0,1}. It is called the binary alphabet because it contains two symbols. An alphabet can be used to make a string (or word). This is a finite Sequence of letters from the alphabet. For example, a string of length 5 over {0,1} is 01101.

The empty string is the string containing no letters (it is often written as ). The empty string is a string over any alphabet.

If we have an alphabet called , then we write the set of all strings that can be made from  as . This is called the Kleene star (or Kleene closure) of . It is named after the mathematician Stephen Cole Kleene.

The Kleene star of the binary alphabet is . The three dots after 001, show that we cannot write the Kleene star of an alphabet in full because it is an infinite set.

Alphabets are important because they are used in studying formal languages, finite automata and very difficult questions in computer science about what can be computed and what can not.

Related pages
Formal language
Syntax
Semantics

References 

 Arto Salomaa, Formal Languages, (1973): Chapter 1
 Michael A. Harrison, Introduction to Formal Language Theory, (1978): Chapter 1.2
 John E. Hopcroft and Jeffrey D. Ullman, Introduction to Automata Theory, Languages, and Computation, Addison-Wesley Publishing, Reading Massachusetts, (1979). .
 György E. Révész, Introduction to Formal Languages, (1991): Chapter 1.1
 Grzegorz Rozenberg and Arto Salomaa, Handbook of Formal Languages: Volume 1. Word, Language, Grammar, (1997): Chapter 2.1
 Dan A. Simovici and Richard L. Tenney, Theory of Formal Languages with Applications, (1999): Chapter 2.1
 Keijo Ruohonen, Formal Languages, (2009): Chapter 1.1
 John Martin: Introduction to Languages and the Theory of Computation (2010): Chapter 1.5

Computer science
Mathematics
Concatenation is a simple concept from computer science. It is a way of making a new word (or String), by putting together two other Strings. Given the words foo and bar, the two new words foobar and barfoo can be made that way. 

Computer science
In mathematics, the identity element (or neutral element) of a set is a special element of that set. It is special because if it is combined with another element of that set, it does not change the other element.

With addition, the identity element is 0, because adding 0 to some number does not change the number. With multiplication, it is 1. In a group (an algebraic structure in mathematics), the identity element is sometimes denoted by the symbol .

Further Examples

Related pages 

 Identity (mathematics)
 Null vector
 One
 Zero

References 

Mathematics

fa:عمل دوتایی#عضو خنثی
An inverse function is a concept of mathematics. A function will calculate some output , given some input . This is usually written . The inverse function does the reverse. Let's say  is the inverse function of , then . Or otherwise put, . An inverse function to  is usually called . It is not to be confused with , which is a reciprocal function.

Examples
If  over real , then 

To find the inverse function, swap the roles of  and  and solve for . For example,  would turn to , and then . This shows that the inverse function of  is .

Not all functions have inverse functions: for example, function  has none (because , and  cannot be both 1 and -1), but every binary relation has its own inverse relation.

In some cases, finding the inverse of a function can be very difficult to do.

Related pages
 Inverse element
 Inverse triangle function
 Inverse hyperbolic function
 Invertible matrix
 Reciprocal

References 

Mathematics
In mathematics (particularly set theory), a countable set is a set whose elements can be counted. A set with one thing in it is countable, and so is a set with one hundred things in it. A set with all the natural numbers (counting numbers) in it is countable too. This is because even if it is infinite, someone who counts forever would not miss any of the numbers. The sets which has the same size as the natural numbers are therefore called countably infinite. The size of these sets are then written as (aleph-null)—the first of the aleph numbers. Sometimes when people say 'countable set' they mean countable and infinite. Georg Cantor coined the term.

Examples of countable sets 

Countable sets include all sets with a finite number of members, no matter how many.

Countable sets also include some infinite sets, such as the natural numbers. Since it is impossible to actually count infinite sets, we consider them countable if we can find a way to list them all without missing any. The natural numbers have been nicknamed "the counting numbers", since they are what we usually use to count things with.

You can count the natural numbers with 

You can count the whole numbers with 

You can count the integers with 

You can count the square integer numbers with

A more-complex example

The rational numbers are also countable, but its counting becomes tricky. We can't just list the fractions as (0/1, 1/1, -1/1, 2/1, -2/1...) since we will never get to 1/2 this way. However, we can list all of the rational numbers in the form of a table. The horizontal rows are the numerators, while the vertical columns are the denominators. We can then zigzag through the list, starting at 1/1, then 2/1, then 1/2, then 1/3, then 2/2, then 3/1, then 4/1, then 3/2, then 2/3, etc.  If we keep this up, we will get to all of the numbers on the table in due time. Each time we hit a new rational number that is new, we add it to the list of counted numbers. We don't want to count numbers twice, so when we hit 3/6, for example, we can skip it, because we already counted the rational number 1/2. In this way, we produce an infinite list with all the rational numbers. Therefore, the rational numbers are countable.

Not all counting schemes will yield a countable list
Suppose the integers are counted differently, as

This does not prove that the integers are uncountable, but it does illustrate what one might call a "failed" effort to count a set, because it is never possible to reach .  Not all sets are countable. For example, the interval  and the set of real numbers can be proven to be uncountable.

Related pages 

 Cantor's diagonal argument
 Cardinality
 Uncountable set

References

Set theory
A pharmacist is a person who works in a pharmacy. Pharmacists have to be trained to work there, and have knowledge about the drugs package. Pharmacists interact with customers, give the prescribed medication and telling them about the drugs.

Related pages
 Pharmaconomist
 Pharmacy
 Pharmacologist

Pharmacology
Drugs
Healthcare occupations
Perch is a type of fish.  Perch are the fish in the genus Perca.

Perch have "rough" scales. When looking through a microscope, the scales look like a plate with growth rings and spikes on the top edges. On the top side of the fish, there is a mouth, a pair of nostrils, and two lidless eyes. On the bottom sides are the operculum, which are used to protect the gills. Also perch have a lateral line system, which a set of sense organs that are sensitive to vibrations in the water. They have a pair of pectoral and pelvic fins. On the front end of the fish, there are two dorsal fins. The first one is spiny and the second is soft. There is also an anal fin, which is also considered spiny, and a caudal fin.

Perciformes
Edible fish
Scarlet is a slight brilliant red colour.  It is a colour of the rainbow.  It is redder than vermilion.  The colour's name comes from the Persian saqirlat. 

An early recorded use of scarlet as a color name in the English language dates to 1250.

Meaning of Scarlet
  
 Traditionally, scarlet is the colour of flame.  People also call the colour of the blood of a living person scarlet, even though the actual color of blood is crimson.  

 Scarlet may represent sin.

 Scarlet represents sensual pleasure and fun.  Scarlet represents partying.

Tones of scarlet color comparison chart

Related pages
List of colors

References
Nero (Nerō Claudius Caesar Augustus Germanicus; 15 December 37 AD – 9 June 68 AD) was the fifth and last Roman Emperor of the Julio-Claudian dynasty. He was born Lucius Domitius Ahenobarbus. 

Nero was the adopted son of his grand-uncle Claudius. He became emperor on 13 October 54, after Claudius died. Claudius was probably assassinated by Nero's mother Agrippina the Younger. Agrippina had motive in ensuring the succession of Nero before Britannicus (Claudius' natural son) could gain power.

Nero as Emperor 

During his reign, Nero focused much of his attention on diplomacy, trade, and improving the cultural capital of the empire. He ordered the building of theatres and promoted athletic games.

His reign included a successful war and negotiated peace with the Parthian Empire; the suppression of a revolt in Britain; and the beginning of the First Roman–Jewish War.

In 64, most of Rome was destroyed in the Great Fire of Rome. In 68, the rebellion of Vindex in Gaul and later the acclamation of Galba in Hispania (Spain) drove Nero from the throne. Facing assassination, he died by suicide on 9 June 68.

Nero's rule is often associated with tyranny and extravagance. He is known for a number of executions, including those of his mother and stepbrother.

Nero is known as the emperor who played a fiddle while Rome burned. In reality, the violin had not yet been invented, Nero wasn't in Rome at the time, and when he heard of the fire he returned to direct relief efforts. 

He also persecuted Christians. However, some ancient sources show that Nero was popular with the common people during and after his reign.

Sources
Tacitus, Histories, I-IV (c. 105)
Tacitus, Annals, XIII–XVI (c. 117)
Josephus, War of the Jews, Books II-VI (c. 94)
Josephus, Antiquities of the Jews, Book XX (c. 94)
Cassius Dio, Roman History, Books 61–63 (c. 229)
Plutarch, The Parallel Lives, The Life of Galba (c. 110)
Philostratus II, Life of Apollonius Tyana, Books 4–5, (c. 220)
Suetonius, The Lives of Twelve Caesars, the Life of Nero (c. 121)

Other sources
 Nero Nero:The Actor-Emperor
 Nero entry in historical sourcebook by Mahlon H. Smith
 Nero basic data & select quotes posted by Romans On Line
 Nero Caesar biographical sketch archived in Bible History Online
 Nero biography by Herbert W. Benario in De Imperatoribus Romanis
 Grant, Michael. Nero. New York: Dorset Press, 1989 ().
 Nero Claudius Drusus Germanicus entry in the Illustrated History of the Roman Empire
 Griffin, Miriam T. Nero: The End of a Dynasty. New Heaven, CT; London: Yale University Press, 1985 (hardcover, ); London; New York: Routledge, 1987 (paperback, ).
 Warmington, Brian Herbert. Nero: Reality and Legend (Ancient Culture and Society). London, Chatto & Windus, 1969 (hardcover, ); New York: W.W Norton & Company, 1970 (paperback, ); New York: Vintage, 1981 (paperback, ).

References

37 births
68 deaths
Roman Emperors
Gallery Dutta Geneve
The tachi is a Japanese sword, which has a strongly curved blade and is longer than a katana. It was used on the battlefield before katana was, so it is considered to be older. The word Tachi translates as "the soul of bushi" (soul of samurai). 

When the katana began to be widely used the tachi sword became a court sword for ceremonies. It looks very richly decorated with traditional cord wrappings and a specially designed handle. The length of a tachi blade was around 30.70 inches (about 75cm) Because of its length the tachi was a cavalry sword and was mainly worn by horsemen. The strongly curved blade also made it easy to make slicing blows. Even if the tachi is a very long sword it is light enough to be handled with one hand. The tachi had a long enough hilt to hold it with two hands. It was especially useful for warriors who were not riding.

The tachi was worn hung to the belt with the cutting-edge down, unlike the katana which was worn with the cutting-edge pointing upwards. Not all tachi were the standard size. Small ones were called ko-dachi. If the sword was longer than the standard one it was called o-dachi.
 
The tachi that can be seen in museums have one or more chips along the back of the sword, while the cutting edge looks almost untouched and mirror polished. The experts explain that Samurai made the smallest possible moves with their tachi to kill the enemy. Thus when both swords were about to collide, the samurai both turned their swords and let only the blunt back (mune) of the blades hit one another. The cutting edge was used for finish touches, namely for cutting the human body.

Related pages
Katana
Samurai
Japanese sword schools

Japanese swords
Machaira was a rare mythic sword used in the Basileus cult.  Basileus cult is the cult of the king, because in ancient Rome the word basileus was translated as "king". To get a Basileus title a person should  kill a lion with a special  weapon. So this weapon was called - Machaira.

Machaira had a very curved blade, which reminded a sickle. The  shape of a machaira is often compared to a lion claw. The cutting edge was on the inside part of the blade. The legends say that it has a length from about . The blade was secured in a wooden cage (sheath).  This sword was kept by ancient priests called sacerdotes. They used to decorate the sheath with golden ornaments. The sword was kept in special places and used in important rituals. 

The meaning of machaira sword was ideological. A king who was at the same time a sacerdotus and owned a machaira, made rituals before the battle. Its power showed to the army the right path and saved from enemies' traps. It was supposed that the sword kept the troubles away. It was very important that the machaira  to be used only by a  sacerdotus, otherwise it was only a beautiful but powerless weapon.  

The well known king Macedonian Alexander Hephaistion was a sacerdotus. He belonged to the lion cult and used machaira for rituals. Later in 324 B.C. happened the official burial of the machaira sword and Alexander the Great left his sacerdotal powers. The cult of  machaira sword and the cult of Basileus were restarted in 301 B.C.

Other websites 
More on the mythical machaira 

Swords
Field can mean:
an area of land in a farm, which may be used for crops or animals; also a meadow or area that is empty of trees, and has mostly grass.
in computing, a field is an item/category of data, e.g. first name; a field contains data about one aspect of the table, e.g. a field can contain all of the first names of a table. An individual entry in a field, e.g. Anna for the first name field, is called a field value. A record contains all of the field values about a particular subject, such as an employee.
field of vision, the area in sight of a person.
in mathematics, a certain kind of algebraic structure: field (mathematics)
in physics, a field is seen as extending throughout a large region of space so that it influences everything: field (physics).
magnetic field,  the area around a magnet in which there is magnetic force

See also: force field

Basic English 850 words
Lucerne (, Swiss German: Lozärn, French: Lucerne, Italian: Lucerna, Romansh: Lucerna) is a city in Switzerland. It is the capital of the Canton of Lucerne and seat of the district with the same name. The city has a population of about 60,000. Lucerne is the biggest and most important city in Central Switzerland. The city's metropolitan area consists of 17 municipalities in three cantons. It has an overall population of nearly 200,000 people.

Since 2010, Littau part of the city.

Geography 
Lucerne is located in central Switzerland on the northern end of Lake Lucerne. The river Reuss flows from the lake through the city. The city is surrounded by hills and mountains, for example the mountains Pilatus and Rigi.

History 
Lucerne joined Switzerland in 1332.

Sights and attractions 
Due to its location on the shore of Lake Lucerne () within sight of the mountains Pilatus and Rigi, Lucerne is mainly a tourist destination. One of the city's famous landmarks is Chapel Bridge (Kapellbrücke), a wooden bridge from the 14th century. Many tourists choose Lucerne as their place to stay because the city is close to the alps in in the center of the country.

Lucerne is also famous for it's traditional Fasnacht (carneval) celebration which takes place every spring.

Gallery

References

Other websites 

 City of Lucerne official website
 Luzern Tourismus AG - tourist office 

 
Imperial free cities
The Eastern hemisphere is a geographical term for the half of the Earth that is east of the Prime Meridian and west of the 180th Meridian.  It is the opposite of the Western hemisphere. It can be also used to describe Europe, Asia, Australia, Africa and Oceania.

Hemispheres

he:המיספירה#חצי הכדור המזרחי
Hertfordshire is a county in England. It is one of the so-called Home Counties, those counties that border or surround Greater London. The county is also surrounded by Essex, Cambridgeshire, Buckinghamshire and Bedfordshire. The county town is Hertford; the oldest city is St Albans.

Leading towns (2001 census)

Education
Hertfordshire has 26 independent schools and 73 state secondary schools.
The state secondary schools are entirely comprehensive, although seven schools in the south and southwest of the county are partially selective.

The University of Hertfordshire, formerly the Hatfield Polytechnic, is a modern university. It is mostly in Hatfield, and has more than 23,000 students.

Independent schools 
Some of the most notable secondary schools are:
 Abbot's Hill School (secondary, Hemel Hempstead)
 Aldenham School (secondary boarding school, Elstree)
 Berkhamsted School (primary and secondary, Berkhamsted)
 Bishop's Stortford College (secondary, Bishop's Stortford)
 Haberdashers' Aske's School for Girls (secondary, Elstree)
 Haberdashers' Aske's School (secondary, Elstree)
 Merchant Taylors' School (secondary, Northwood)
 Queenswood School (secondary, Hatfield)
 St Albans High School for Girls (secondary, St Albans)
 St Albans School (secondary, St Albans)

Fame & fortune 
Hertfordshire has been home to many famous people, including George Michael and Geri Halliwell. Victoria Beckham, born in Essex, was raised near Broxbourne in Hertfordshire. The Beckhams bought a £2.5 million house in Sawbridgeworth when they married in 1999. They sold it last year to insurance entrepreneur Neil Uttley for £11.4 million.

The richest person in Hertfordshire is Mike Ashley, a retailing tycoon. His fortune is estimated as £3,650 million. He owns Newcastle United F.C. and has an 8.9% share in owning Glasgow Rangers F.C.

References 

 
Ceremonial counties of England
The Lower Jurassic is the first geological epoch in the Jurassic that began 201.3 million years ago, and ended at 174.1 million years ago. 

The Jurassic period is divided into Lower, Middle and Upper. The Lower Jurassic started after the end-Triassic extinction event at 201.3 million years ago (mya). Its rocks form in Europe the Lias group of marine strata consisting mostly of limestone, with some clays and siltstone. It was in this formation on the Dorset Jurassic Coast that Mary Anning did much of her work. The mudstones of the earliest Jurassic (Blue Lias)  give way to carbonate rocks as the water deepens in the Middle Jurassic.

The Jurassic period was one of the time periods when dinosaurs were on the Earth. By this time, many groups of the Triassic period had become extinct.

Britain 
At the start of the Jurassic, Britain was warm temperate to subtropical, between 30° and 40° north of the equator. Temperature would have been in the range of 12–29°C. 

Shallow seas were over southern England; higher ground like the Mendip Hills were a string of islands stretching westwards South Wales.

North America 

The Lower Jurassic in western North America is quite different. It is continental in origin, sandstones laid down in shifting streams and rivers. These sandstones were laid down over a long period from the later Permian to the Lower Jurassic.

Related pages 
Blue Lias
Jurassic
Middle Jurassic
Upper Jurassic

References
 

Jurassic