cahya/wikipedia-simple-en huggingface dataset:
Dave Fortman

Dave Fortman (born July 11, 1967) is an American music producer. He used to play rhythm guitar in California-based hard rock band, Ugly Kid Joe, through the 1990s. Fortman also co-owns a recording studio called Balance Productions which is in Louisiana. He recently worked with Slipknot on their new fourth studio album called All Hope Is Gone.

Other websites
 Official Ugly Kid Joe MySpace page
 Balance Productions 
 Ugly Kid Joe Fan Site 

American rock guitarists
Living people
1967 births
Sampler (musical instrument)

A sampler is an electronic musical instrument that is similar to the synthesizer. What a sample does is that instead of creating sounds from scratch however, a sampler starts with more than one recording (or "samples") of different sounds added by the user, and then plays each back based on how the instrument is configured.  Because these samples are usually stored in RAM, the information can be quickly accessed.

Electronic musical instruments
Headbangers Ball

Headbangers Ball is a television program about heavy metal and hardcore punk music airing on MTV2, and other channels.

Other websites
 Official show sites
 United States  – Official blog
 UK 
 Denmark
 Finland 
 Sweden 
 Australia 
 Myspace site
 Official site for albums spawned from Headbangers Ball 
 
 
 Jump The Shark – Headbangers Ball
 Headbangers Ball Tribute Site 

Music television series
English-language television programs
Solar cooker

A solar cooker is a device that uses energy from sunlight. They use no fuel and cost nothing to run. They also help slow deforestation and desertification. Another benefit of solar cooking is that unlike cooking with fire, Solar cookers don't pollute the air. Solar cookers are also sometimes used for cooking outside, especially when using fire is risky or there is no fuel. The solar cooker is very useful. It is a renewable source of energy

Solar box cookers can be made of materials or be manufactured in a factory for sale. There are many kinds of solar box cookers, from small cardboard boxes, that can be used to cook a single meal, to wood and glass boxes built into the sunny side of a house. Although the solar cooker was invented by Horace de Saussure, a Swiss naturalist, as early as 1767, solar box cookers have only become popular since the 1970s. They are found in almost every country of the world.

References

Solar energy
House of mirrors

A house of mirrors or hall of mirrors is a traditional attraction at carnivals and amusement parks.

Entertainment
Phonograph

The phonograph is a device for the mechanical recording and reproduction of sound.  It was the most common device for playing recorded music from the 1870s through the 1980s. It was invented by Thomas Edison, after other inventors had studied the idea.  Early phonographs recorded sound on cylinders, in addition to playing sound.  In its later forms, it is also called a gramophone (as a trademark since 1887, as a generic name in the UK since 1910) or, since the 1940s, a record player.

Creation
Thomas Edison made his first phonograph with the mouth piece of the early telephone and some tinfoil. He thought he could talk into the mouth piece to make a disk vibrate, as the disk vibrated a needle would put grooves in the tinfoil. When Edison adjusted the machine to play and cranked the lever, he was surprised to hear his voice play back to him. He said his ideas rarely worked the first time. These cylinders could record sound, but due to their cylindrical shape, they could not be copied cheaply with a mold.

The phonograph was soon replaced by the graphophone by Alexander Graham Bell in his Volta Laboratory.  Later it was replaced with the disc phonograph, cassette tapes, compact discs, audio files and other devices.  These later inventions made stereo sound.

Gramophone
The gramophone, invented by Emile Berliner, plays sounds from a flat disk record. The record is placed onto the turntable. The turntable spins the record while a lever with a small needle on the bottom lies between the little grooves in the disk. When the grooves make the needle vibrate, music is played. These machines do not record, but the disks could be copied quickly onto vinyl disks in a factory with a mold, called a master.
Social Democratic Party (Romania)

The Social Democratic Party is a big political party in Romania.  It started in January of 2001.It has been in a political association called "Uniunea Socială Liberală" along with the National Liberal Party that in 2014 has ended. Now it is in association with PC and UNPR (commonly known as USD).

Other websites 
 Official website

Socialist International
Social democratic parties in Europe
Political parties in Romania
2001 establishments in Europe
2000s establishments in Romania
James Dewees

James Dewees (born March 13, 1976) is an American musician who has been involved in many musical projects including The Get Up Kids, Reggie and the Full Effect, Coalesce, New Found Glory, and My Chemical Romance.

Discography

Reggie and the Full Effect
Studio albums
 Greatest Hits 1984-1987 (April 20, 1999)
 Promotional Copy (April 25, 2000)
 Under the Tray (February 18, 2003)
 Songs Not to Get Married To (March 29, 2005)
 Last Stop: Crappy Town (June 17, 2008)
 No Country for No Musicians (November 19, 2013)
 41 (February 23, 2018)

American drummers
American keyboard players
American rock musicians
Punk musicians
Musicians from Missouri
1976 births
Living people
Resaca Confederate Cemetery

Resaca Confederate Cemetery in Resaca, Georgia is home to over 400 confederate soldiers who died during the American Civil War, also known as the War Between the States. This particular cemetery is designated for the soldiers that fought in the Battle of Resaca which took place May 14 and 15, 1864. Although the battle lasted two days, there are only three graves where the death date is listed as May 15, 1864. The remaining graves are listed as May 14, 1864. There are 424 graves marked 'unknown'.

History 

After the battle, a family known as the Green family returned to their plantation and the sight that met them there was almost more than they could bear. The bodies of confederate soldiers were buried in crude makeshift graves all across the yard. Compelled by a since of respect to those who had fallen in action, Mary J. Green and her sister began collecting the bodies to bury properly. Though poverty was rampant the Green daughters wrote friends asking for any amount money they could give. Col. John Green gave his daughters 2.5 acres of land for use as a cemetery for these soldiers. With the money collected and the land provided, the Green daughters and their mother began work on what we now call the Resaca Confederate Cemetery.

The Resaca Confederate Cemetery was founded on October 25, 1866. This cemetery and one in Winchester, Virginia were both dedicated on the same day. Each group thought they were the first confederate cemetery.

References 

Cemeteries in the United States
Buildings and structures in Georgia (U.S. state)
1866 establishments in the United States
19th-century establishments in Georgia (U.S. state)
Palm Sunday

Palm Sunday is a Christian festival. It is always happens on a Sunday but the date each year changes. It is a day to celebrate the day that Jesus entered the city of Jerusalem in Israel as was written about in the Bible in Mark 11:1-11, Matthew 21:1-11, Luke 19:28-44, and in John 12:12-19. During Palm Sunday many Christians celebrate with Crosses made out of Palm leaves and by going to church.

Many Christian churches mark Palm Sunday as the beginning of Holy Week which ends on Easter Sunday. It is an event celebrated by some churches by cutting branches of palm trees and attending mass. Palm Sunday is celebrated by most Christian churches all over the world including Roman Catholics and Protestants. However, Orthodox churches observe Palm Sunday at a later date following the Julian calendar. In some countries, palm leaves that were blessed during mass are displayed on the door of their houses believing that it will also bring blessings to their household. Some churches traditionally gather the palm leaves to be burned and used during the Ash Wednesday services.

References

Related pages
 Roman Catholicism
 Eastern Orthodox

Other websites 
 BBC - Palm Sunday
 Christian calendar for 2009 

Christian holidays
Passive solar building design

In passive solar building design, windows, walls, and floors are made to collect, store, and distribute solar energy in the form of heat in the winter and reject solar heat in the summer. This is called passive solar design or climatic design because, unlike active solar heating systems, it doesn't involve
the use of mechanical and electrical devices.

The key to designing a passive solar home is to best take advantage of the local climate. Elements to be considered include window placement and glazing type, thermal insulation, thermal mass, and shading.  Passive solar design techniques can be applied most easily to new buildings, but existing buildings can be adapted or "retrofitted".

References

Energy
Vickie Guerrero

Vickie Lynn Guerrero (maiden name Lara)(born March 16, 1968) is an American professional wrestling authority figure. She is best known for her time with the WWE. She is the widow of professional wrestler and WWE Hall of Famer Eddie Guerrero. During her time in the WWE, she was known for yelling the catchphrase "Excuse Me!" which received negative reactions from the fans. She was also an occasional wrestler. she was also a manger for laycool 

On June 23, 2014 episode of Raw, Guerrero was fired after she lost a pudding match against Stephanie McMahon with her job on the line. McMahon won with help from Alicia Fox, Layla, and Rosa Mendes. Guerrero would get revenge on McMahon by throwing her into mud pool. She then pointed to the sky, said "this was for you"; as a tribute to her late husband, Eddie, and did Eddie's taunt before leaving.

References

Other websites
Official website 
WWE profile

1968 births
Female professional wrestlers
Former WWE wrestlers
Living people
Sportspeople from El Paso, Texas
All Elite Wrestling
Renewable energy in developing countries

Most developing countries have good renewable energy resources, including solar energy, wind power, geothermal energy, and biomass. These can help developing countries reduce their dependence on oil and natural gas. Investments in renewables can be less expensive than fossil fuel energy systems.

Importance of renewables
Renewable energy can be particularly suitable for developing countries. In rural and remote areas, transmission and distribution of energy generated from fossil fuels can be difficult and expensive. Producing renewable energy locally can offer a viable alternative.

Interest in renewable energies has increased in recent years due to environmental concerns about global warming and air pollution, reduced costs of renewable energy technologies, and improved efficiency and reliability.

Poverty reduction
Renewable energy projects in many developing countries contribute to poverty alleviation by providing the energy needed for creating businesses and employment. Renewable energy technologies can also make indirect contributions to alleviating poverty by providing energy for cooking, space heating, and lighting.

Education
Renewable energy can also contribute to education, by providing electricity to schools. Renewable energy for cooking and heating can reduce the time that children, spend out of school collecting fuel. In addition, the displacement of traditional fuels reduces the health problems from indoor air pollution produced by burning those fuels.

Health
Renewable energy can also contribute to better health by providing energy to refrigerate medicine and sterilize medical equipment. It can also provide power for supplying the fresh water and sewerage services needed to reduce infectious disease.

Kenya
Kenya is the world leader in the number of solar power systems installed per capita. More than 30,000 small solar panels, each producing 12 to 30 watts, are sold in Kenya
annually. For an investment of as little as $100 for the panel and wiring, the PV system can be used to charge a car battery, which can then provide power to run a fluorescent lamp or a small television for a few hours a day. More Kenyans adopt solar power every year than make connections to the country’s electric grid.

Related pages
Indian Solar Loan Programme
Ashden Awards for Sustainable Energy
Solar powered refrigerator

References

Other websites
Solar Offers A Future for Kenya’s Youth 
Clean Energy Investment 
The Renewable Energy & Energy Efficiency Partnership (REEEP) Tackles Energy Poverty 
Milk Cooler Powered by Renewable Energy Could Help Ugandan Dairy Farmers

Renewable energy
Sustainable development
Papaveraceae

Papaveraceae is a family of flowering plants. The family has been universally recognized by taxonomists, and is also known as the "poppy family". Most are herbaceous plants, but a few are shrubs and small trees.

Ranunculales
Myristicaceae

Myristicaceae is the botanical name for a family of flowering plants, mostly from Africa, Asia, Pacific islands, and the Americas. The family has been recognised by most taxonomists, and it is sometimes called the "nutmeg family", after its most famous member, the nutmeg (Myristica fragrans). It has about 21 genera and 520 species. They are mostly trees and shrubs.

References 

Magnoliales
Dirac delta function

The Dirac delta function, often written as , is a made-up concept by mathematician Paul Dirac. It is a really pointy and skinny function that pokes out a point along a wave. Loosely speaking, it has the value of zero everywhere except at , in such a way that the area between the function and the x-axis adds up to 1. The delta function is often used in sampling theory, where its pointiness is useful for getting clean samples.

The integral of the Dirac delta function is the Heaviside function. Thus Dirac delta function can be view as the derivative of Heaviside function.

Related pages 

 Special functions

References 

Digital signal processing
Newton's method

Newton's method provides a way for finding the real zeros of a function. This algorithm is sometimes called the Newton–Raphson method, named after Sir Isaac Newton and Joseph Raphson.

The method uses the derivative of the function in order to find its roots. An initial "guess value" for the location of the zero must be made. From this value, a new guess is calculated by this formula:

Here xn is the initial guess and xn+1 is the next guess. The function f (whose zero is being solved for) has the derivative f'.

By repeatedly applying this formula to the generated guesses (that is by setting the value of xn to the formula's output and recomputing), the value of the guesses will approach a zero of the function.

Newton's method can be explained graphically by looking at intersections of tangent lines with the x-axis. First, a line tangent to the f at xn is calculated. Next, the intersection between this tangent line and the x-axis is found. Finally, the x-position of this intersection is recorded as the next guess, xn+1.

Problems with Newton's Method 
Newton's method can find a solution quickly if the guess value begins sufficiently near the desired root. However, when the initial guess value is not close, and depending on the function, Newton's method may find the answer slowly or not at all.

Further reading
 Fernández, J. A. E., & Verón, M. Á. H. (2017). Newton’s method: An updated approach of Kantorovich’s theory. Birkhäuser.
 Peter Deuflhard, Newton Methods for Nonlinear Problems. Affine Invariance and Adaptive Algorithms, Second printed edition. Series Computational Mathematics 35, Springer (2006)
 Yamamoto, T. (2001). "Historical Developments in Convergence Analysis for Newton's and Newton-like Methods". In Brezinski, C.; Wuytack, L. (eds.). Numerical Analysis : Historical Developments in the 20th Century. North-Holland. pp. 241–263.

Related pages
 Kantorovich theorem (Statement about the convergence of Newton's method, found by Leonid Kantorovich)

Functions and mappings
Asimo

Asimo was a robot that was built by Honda. The current models could walk, run, and go up and down stairs. Engineers planned to add laser capabilities. Its height was 130 centimeters (4 feet 3 inches) and weight 54 kilograms (119 pounds). Asimo was just like an astronaut wearing a backpack and could walk or run on two feet.

Development 
ASIMO was created at Honda's Research & Development Wako Fundamental Technical Research Center in Japan. Honda will not confirm how much it costs.

Name 
ASIMO is an acronym.  ASIMO stands for "Advanced Step in Innovative MObility". It should be pronounced “ah she moh” to match the original Japanese pronunciation.

As of February 2009, there are over 100 ASIMO units in existence.

Public appearances

ASIMO has made lots of public appearances.

Robots
Fahrenheit 451

Fahrenheit 451 is an American dystopian fiction novel. It was written by Ray Bradbury and first published in 1953.

The novel is about a future American society in which people are hedonistic (meaning they live only for pleasure), and reading is against the law because it makes them think. The main character, Guy Montag, has a job as a "fireman" (which, in this future, means "book burner"). The number "451" refers to the temperature (in Fahrenheit) at which the books burn when the "firemen" burn them "for the good of humanity". Written in the early years of the Cold War, the novel is a critique of what Bradbury saw as an increasingly dysfunctional American society.

The idea began with Bradbury's short story "Bright Phoenix," written in 1947 but first published in the Magazine of Fantasy and Science Fiction in 1963. The original short story was reworked into the novella, The Fireman, and published in the February 1951 issue of Galaxy Science Fiction. The novel was also serialized in the March, April, and May 1954 issues of Playboy magazine. Bradbury wrote the entire novel on a pay typewriter in the basement of UCLA's Powell library. His original idea in writing Fahrenheit 451 was to show his great love for books and libraries. He has often referred to Montag as an allusion to himself.

Over the years, the novel has been subject to various interpretations, primarily focusing on the historical role of book burning in suppressing dissenting ideas. Bradbury has said that the novel is not about censorship; he says that Fahrenheit 451 is a story about how television destroys interest in reading literature, which leads to people thinking that knowledge is made up of "factoids", partial information without context, such as Napoleon's birth date alone, without an indication of who he was.

A movie version of the novel was released in 1966, and at least two BBC Radio 4 dramatizations have also been aired, both of which follow the book very closely.

References 

1953 books
20th-century American novels
English-language novels
Fantasy books
Fiction set in the future
Hugo_Award_winners
Science fiction books
Collingwood School

Collingwood School is a private school in West Vancouver, British Columbia, Canada. It teaches from Junior Kindergarten to Grade 12.

History

Collingwood School was opened in 1984 by West Vancouver and North Vancouver parents who wanted a private school nearby. The school was named after a ship called the HMCS Collingwood. The school used the buildings from the old Glenmore Elementary School. Now the school has buildings in two different parts of West Vancouver.

Facilities 

The "Morven" campus is the oldest part of the school. This is where they teach the older children, from Grade 6 to Grade 12. It is in a part of West Vancouver called the British Properties. The address is 70 Morven Drive, West Vancouver. The "Wentworth" campus was built later. This is where they teach the younger children, from Junior Kindergarten to Grade 5. It is right below Cypress Provincial Park in West Vancouver.

References

Other websites
Collingwood School Official Site
Round Square Official Site

Schools in Canada
1984 establishments in Canada
Stack (data structure)

The stack is one of the most important data structures in computer science. To understand how a stack works, think of a deck of playing cards that is face down. We can only easily access the card that is on top. When we want to look at the top card, there are two things we can do: we can peek at it, but leave it on the stack, or we can pop it off. When we pop off the top object, we are taking it off the stack. If we want to add another card to the top of the stack, we push. 

A stack is called a last-in-first-out (LIFO) collection. This means that the last thing we added (pushed) is the first thing that gets pulled (popped) off. If the last card we put on our stack of cards was an ace, then the first card we pulled from the top is that same ace.

History 
The stack was first proposed in 1955, and then patented in 1957, by the German Friedrich L. Bauer. The same concept was developed independently, at around the same time, by the Australian Charles Leonard Hamblin.

Other operations 
In modern computer languages, the stack is usually implemented with more operations than just "push" and "pop". Some implementations have a function which returns the current length of the stack. Another typical helper operation is "top" (also known as "peek"), which can return the current top element of the stack without removing it. Another common operation is "dup," which makes a copy of the element at the top of the stack.

Related pages
 Stack machine

Computer science
Data structures
Nocturnal emission

A nocturnal emission or wet dream is the condition in which a person has an orgasm while sleeping. It often leads to ejaculation. Wet dreams can begin after a person goes through puberty. Many young people have their first orgasm this way. They might not understand what has happened to them, if they have not been taught anything about sex.

Nocturnal emissions are called wet dreams in males because of the dampness caused by ejaculation and because the orgasm and ejaculation often happen during a sexually exciting dream. Scientists are not sure what causes them. Most sexual dreams do not cause orgasms.

It is harder for women to tell, because vaginal lubrication is not always associated with orgasm.

Wet dreams are natural and harmless. They do not mean that anything is wrong with you. Many people stop having wet dreams if they masturbate often, or once they begin having sexual intercourse on a regular basis.

If you urinate while asleep, this is called wetting the bed, not a wet dream.

Sleep
Tevatron

The Tevatron was a giant Particle accelerator in Illinois that was used by scientists to make protons go very fast, almost the speed of light in some cases. Scientists looked at what happens when the protons hit antiprotons to see if they are right about their ideas as to what protons are made of.

The Tevatron was a circular particle accelerator at the Fermi National Accelerator Laboratory (also known as Fermilab), just east of Batavia, Illinois. It was the second highest energy particle collider in the world after the Large Hadron Collider (LHC). The Tevatron is a synchrotron that accelerates protons and antiprotons in a 6.28 km (3.90 miles) ring to energies of up to 1 TeV, hence its name. The Tevatron was completed in 1983 at a cost of $120 million ($ today) and has been regularly upgraded since then. (The 'Energy Doubler', as it was known then, produced its first accelerated beam — 512 GeV —  on July 3, 1983.)  The Main Injector was the most substantial addition, built over five years from 1994 at a cost of $290 million.  The Tevatron was shut down on September 30, 2011.

The Large Hadron Collider was later built in Switzerland to look for one of those pieces, called the Higgs Boson. The LHC broke and is now being fixed. The Tevatron scientists also tried to find the Higgs Boson. They need to do this before the LHC is fixed, because the LHC is much better at finding things.

The scientists at the Tevatron had a year's headstart on the scientists at the LHC. Whoever finds the Higgs will be honored by other scientists. That is why the scientists at the Tevatron wanted to find it before the scientists at the LHC.

The Tevatron discovered three of the 17 fundamental particles including the top quark.  The main ring of the Tevatron will probably be reused in future experiments, and its components may be transferred to other particle accelerators.

References

Nuclear physics
Fermilab
First Punic War

The First Punic War started in 264 BC. It lasted for 23 years, ending in 241 BC. It was the first of three wars fought between ancient Carthage and the Roman Republic. They were rivals for trade and influence in the Mediterranean. For more than 20 years the two powers struggled for supremacy. Key areas were the island of Sicily and its surrounding waters, and also North Africa. Rome eventually won control of Sicily.

With the help of her own allies and rebels among the indigenous African allies of Carthage, Rome won the First Punic War after 23 years. In the end it became the dominant naval power of the Mediterranean. To get terms for peace, the Carthaginians had to pay a large amount of money (in silver), and give up a number of islands in the Mediterranean. They kept Sardinia and Corsica.

References 

264 BC
Punic Wars
Wars and battles of Ancient Rome
Scott Westerfeld

Scott Westerfeld (born May 5, 1963) is an American author of science fiction and young adult literature. One of his most famous book series was Uglies.

Books

Adults
Polymorph (1997)
Fine Prey (1998)
Evolution's Darling (2000)

Succession series 
 The Risen Empire (2003)
The Killing of Worlds (2003)
The two books were re-published in 2005 in one volume, also titled The Risen Empire.

Young adults 
So Yesterday (2004)
Afterworlds (2014)
Horizon (2017)

Midnighters trilogy
The Secret Hour (2004)
Touching Darkness (2005)
Blue Noon (2006)

Peeps series 
Peeps (2005) (also known as Parasite Positive in Britain and V-Virus or Peeps in Canada)
The Last Days (2006)

Uglies series
Uglies (2005)
Pretties (2005)
Specials (2006)
Extras (2007)
Impostors (2018)
Shatter City (2019)
Mirror's Edge (2021)
Youngbloods (2022)

Related works 
Bogus to Bubbly: An Insider's Guide to the World of Uglies (2008)
Graphic novel retellings from Shay's point of view:
Uglies: Shay's Story (with Devin Grayson and Steven Cummings) (2012)
Uglies: Cutters (with Devin Grayson and Steven Cummings) (2012)

Leviathan series (illustrated by Keith Thompson) 
Leviathan (October, 2009)
Behemoth (October, 2010)
Goliath (September, 2011)

Related works 
The Manual of Aeronautics (illustrated guide) (August, 2012)

Spill Zone graphic novel series (illustrated by Alex Puvilland) 
 Spill Zone (May, 2016)
 Spill Zone: The Broken Vow (July, 2019)

Related works 
 Spill Night (short story for Free Comic Book Day) (March 2017)

Zeroes trilogy (with Margo Lanagan and Deborah Biancotti)  
 Zeroes (2015)
 Swarm (2016)
 Nexus (2018)

References

Other websites

1963 births
Living people
Writers from Dallas, Texas
Partial differential equation

Partial Differential equations (abbreviated as PDEs) are a kind of mathematical equation. They are related to partial derivatives, in that obtaining an antiderivative of a partial derivative involves integration of partial differential equations.

Numerical methods

Since PDEs have appeared in mathematics and physics, many scientists have studied methods to solve them. But unfortunately, no one could establish methods to solve any kind of PDE. Therefore, numerical methods for PDEs (such as the finite element method) are widely studied since the appearance of computers.

Related pages
Differential equation
Functional analysis
Ordinary differential equation
Navier–Stokes equations

People who studied about partial differential equations

 Kyuya Masuda
 Peter Lax
 Ryogo Hirota
 Shinichi Oishi
 Sofya Kovalevskaya
 Terence Tao

Literature
 Partial Differential Equations (Graduate Studies in Mathematics) Lawrence C. Evans, American Mathematical Society, 2010/04/.
 Egorov, Y. V., & Shubin, M. A. (2013). Foundations of the classical theory of partial differential equations. Springer Science & Business Media.
 Olver, P. J., Introduction to partial differential equations. Berlin: Springer.
 Partial Differential Equations I-III (Applied Mathematical Sciences) Michael Taylor, Springer.

References

Mathematical analysis
Trade paperback (comics)

Trade paperbacks, or "trades" as they are commonly called, are collections of comic books that are usually bound in a better format than the comic magazines, using the same materials and methods as printed books. They are generally sold in bookstores and specialty comic book shops rather than at newsstands. 

Unlike graphic novels, the material in a trade paperback is reprinted from comic magazines that were released in the standard 32-page format. Unlike comic books, which only tell one small part of a story, trade paperbacks usually collect a complete story, story arc, or a large part of a story. They usually reprint the material from 4 to 12 comic books, depending on the size of the trade and the story being collected.

Some famous examples of trade paperbacks:
 Watchmen
 V for Vendetta
 Batman: Year One

Comics
Mathematical induction

Mathematical induction is a special way of proving a mathematical truth. It can be used to prove that something is true for all the natural numbers (or all positive numbers from a point onwards). The idea is that if:

 Something is true for the first case (base case); 
 Whenever that same thing is true for a case, it will be true for the next case (inductive case),

then
 That same thing is true for every case by induction.

In the careful language of mathematics, a proof by induction often proceeds as follows:
 State that the proof will be by induction over . ( is the induction variable.)
 Show that the statement is true when  is 1.
 Assume that the statement is true for any natural number . (This is called the induction step.)
 Show then that the statement is true for the next number, .

Because it is true for 1, then it is true for 1+1 (=2, by the induction step), then it is true for 2+1 (=3), then it is true for 3+1 (=4), and so on.

Examples of proof by induction

Sum of the first n natural numbers

Prove that for all natural numbers n:

Proof:

First, the statement can be written as:

    (for all natural numbers n)

By induction on n,

First, for n=1:
,

so this is true.

Next, assume that for some n=n0 the statement is true. That is,:

Then for n=n0+1:

can be rewritten as

Since 

Hence the proof is complete by induction.

The sum of the interior angles of a polygon
Mathematical induction is often stated with the starting value 0 (rather than 1). In fact, it will work just as well with a variety of starting values. Here is an example when the starting value is 3: "The sum of the interior angles of a -sided polygon is  degrees."

The initial starting value is 3, and the interior angles of a triangle is  degrees. 
Assume that the interior angles of a -sided polygon is  degrees. Add on a triangle which makes the figure a -sided polygon, and that increases the count of the angles by 180 degrees  degrees. Since both the base case and the inductive case are handled, the proof is now complete.

There are a great many mathematical objects for which proofs by mathematical induction works. The technical term is a well-ordered set.

Inductive definition

The same idea can work to define a set of objects, as well as to prove statements about that set of objects.

For example, we can define th degree cousin as follows:
A st degree cousin is the child of a parent's sibling.
A st degree cousin is the child of a parent's th degree cousin.

There is a set of axioms for the arithmetic of the natural numbers which is based on mathematical induction. This is called "Peano's Axioms". The undefined symbols are | and =.
The axioms are
| is a natural number.
 If  is a natural number, then  is a natural number.
If  then .

One can then define the operations of addition and multiplication and so on by mathematical induction. For example:

Related pages 
 Mathematical proof
 Proof by contradiction

References 

Mathematics
Kader Abdolah

Hossein Sadjadi Ghaemmaghami Farahani (, better known by his pen name Kader Abdolah () (Arak, 12 November 1954), is a Dutch author who was born in Iran.

Kader Abdolah was born Hossein Sadjadi Ghaemmaghami Farahani () in Arak, Iran. Since 1988 he has been living in the Netherlands.

His books are often written in Dutch.  He adds ideas from Persian literature.  He wrote "De reis van de lege flessen", "The journey of the empty bottles".  The book is about an Iranian who goes to live in the Netherlands.  "The House of the Mosque" was voted second best Dutch novel ever in Holland. "My Father's Notebook: A Novel of Iran" and "The House of the Mosque" are available in English.

Honours and awards
 Knight in the Order of the Netherlands Lion
 Knight in the French Order of Arts and Literature

References

Other websites

1954 births
Living people
Iranian writers
Naturalised citizens of the Netherlands
Dutch columnists
Dutch novelists
Persian people
Pseudonyms
Wigan

Wigan is a town located within the Metropolitan Borough of Wigan in Greater Manchester, North West England. It is home to Wigan Athletic football club and Wigan Warriors rugby league team. It is about twenty miles from Liverpool, Manchester and Preston.

Wigan
Towns in Greater Manchester
Polymerization

Polymerization or polymerisation is the process in which small molecules, called monomers, join chemically to produce a very large chain-like or network molecules, called a polymer. The monomer molecules may all be alike, or they may represent two, three, or more different compounds. Usually at least 100 monomer molecules must be combined to make a product that has certain unique physical properties—such as elasticity, high tensile strength, or the ability to form fibres—that differentiate polymers from substances composed of smaller and simpler molecules. Often, many thousands of monomer units are incorporated in a single molecule of a polymer. The formation of stable covalent chemical bonds between the monomers sets polymerization apart from other processes, such as crystallization, in which large numbers of molecules aggregate under the influence of weak intermolecular forces.
Alkene molecules can react with themselves, by adding polymerization to form 'plastic' or polymeric materials. When a catalyst (a substance that speeds up chemical processes) is added to the reaction, or it is heated under pressure, unsaturated alkenes link together, when the double bond partially breaks.

Uses of polymers: Polyethene- it is a cheap and useful plastic used for plastic bags and bottles, it is also very flexible and quite strong.

Polymer chemistry
Final Crisis

Final Crisis is was a seven issue miniseries published by DC Comics from May 2008 to January 2009 written by Grant Morrison and drawn by JG Jones, Carlos Pacheco and Doug Mahnke.

In Final Crisis, the bad guys win. But after some fighting, Superman deep freezes the Earth's population. After he defeats a vampire god called the Dark Monitor, he brings the world back with his imagination.

DC Comics
Portishead

This article is about the town. For the band with the same name, see Portishead (band).

Portishead is a town near the sea in North Somerset, England, where about 21000 people live (Local council update July 24, 2007).

Portishead has had a history since Roman times. Its name comes from the words ‘port at the head of the river’.  The town was built on the mouth of a small river; the main road in the town once met the water at the top of the river.

Lots of buildings in the town are of a Victorian style.

Portishead's dock and railway lines

Portishead dock

In the 1860s, in the middle of the iron and steel era, a pier and a dock were built for the big boats that could not easily get to Bristol Harbour. The ships brought in expensive items from around the world and took items made in the town to other countries. Many ships carried coal.

In the 1880s Portishead Dock was bought by Bristol Corporation, and was managed as part of the Port of Bristol until it closed.

Portishead power stations
The Portishead power stations were coal power stations built near the dock. The first power station was built in 1926. It began making electricity in 1929 for the Bristol Corporation. The power station was made bigger in 1948.

A 2nd power station was started in 1949 and began making electricity in 1955.

After 1949, the power stations became part of the country's electricity industry. They used some local coal produced in the Somerset coalfield which was moved by train along the Portishead Railway. The line had opened on 12 April 1867 as the Bristol and Portishead Pier and Railway Company; it opened to the dock on 5 July 1879.

The 1st power station closed in 1976, and the 2nd closed in 1982. The dock was closed in 1992.

Railway stations
Portishead had two train stations for people who lived in the town. The main station was near the centre of Portishead, and the other was at the Pier. The construction of the 2nd power station caused the 1st train station to be removed and another station was opened in the main street of the town on 2 January 1954. The new station closed on 7 September 1964. People who live in Portishead now want the train station to be opened again.

References

Further reading
 Awdry, Christopher, (1990). Encyclopaedia of British Railway Companies. London: Guild Publishing.
 Crowhurst, Ken, (2001). Images of England: Portishead, Stroud: Tempus Publishing. .
 Smith, Martin, (1992).  The Railways of Bristol & Somerset, Sherton: Ian Allan Ltd. .
 Winter, Michael T., (2005). The Portishead Coal Boats: A History of Osborn & Wallis Ltd, Bristol. Lydney: Black Dwarf Publications. .

Other websites

 
 Weston, Clevedon & Portishead Railway
 Portishead and Bristol Lifeboat
 Photos of Portishead in 3d (Anaglyphs) 

Towns in Somerset
Adverse possession

Adverse possession is a rule in property law. This rule says that if property is not being used by its owner while another person is using the property, this other person (called an "adverse possessor") becomes the new owner of the property. To get these rights, the adverse possessor usually must use the property in the way a normal owner would do for a period of time, typically 20 years. In some jurisdictions, a form of adverse possession exists in which the adverse possessor ends up with sharing some rights to property with the owner, such as a right-of-way, instead of getting all the rights.

Legal terms
Property
Rule against perpetuities

The Rule against Perpetuities is one of the most complicated rules in property law and wills and trusts.  In general, the rule states that a gift of a will (or a trust) will not be enforced if the subject of the gift is to be given to a person who can not be known now, and will not be able to be known, by the end of 21 years after the death of everyone who was alive (including children in their mother's uterus but not yet born) at the time the gift was created.  

For example, if a woman says in her will that her house is to be given "to the children of her children when they graduate from college" this would not be enforced by a court. It would not be enforced because one (or more) of her children's children might not graduate from college until 21 years after everyone who was alive at the time of the woman's death has died.  

The purpose of the rule is to prevent property from being tied up for "perpetuity" (a very long time).  The courts (and many people in society) do not want to hold property to see who will receive it after a complicated set of rules from the gift-giver. First, this would result in a waste of the courts' time and resources. Second, it would be a waste of the property that is being given through the gift.  If a gift in a will violates the Rule against Perpetuities, the court will simply strike that gift and transfer the subject of the gift as if the will had not mentioned it.

However, many countries and states have changed this rule, and it does not apply at all, or in a changed way, in those countries and states.

Property
Polypeptide

A polypeptide is a string or linear chain of amino acids linked together. Amino acids are the basic building blocks of proteins.  A single polypeptide chain might make up the entire primary structure of a simple protein; more complex proteins are formed when two or more polypeptides link together. Each protein is a polymer of amino acids.

Polypeptides are made when mRNA is translated, a process involving ribosomes, tRNA and amino acids.

References

Biochemistry
Solipsism

Solipsism ( ) is the view that a person has no reason to believe anything exists except their own mind. It is a philosophical position that first appeared in ancient philosophy. It mainly means to reject or doubt that other people exist. "" and "" are the Latin words for "alone" and "self", which is where the word "solipsism" comes from. Some kinds of solipsism say that everything outside a person's own mind (including other people) is only imaginary. Other kinds of solipsism instead say that nothing outside a person's own mind is certain.

To only reject that the physical world exists is not solipsism. Solipsism also rejects or doubts that other people exist. As an epistemological position, it is the concept that nothing but one's own mind can be certain to exist. The existence of other minds, in this position, is considered a possibility, but not a certainty. Including time, which does not stop just because there would be nobody being to experience it (which is probably going to happen in the end of the universe when there would be simply nothing)

Related pages 
 Egoism
 Idealism
 Nihilism

References 

Epistemology
Philosophical movements and positions
Dipstick

A dipstick is a tool which can be dipped into liquid to measure how much of it there is, or to test it for things.

Testing dipstick 
A testing dipstick is usually made of paper or cardboard. It contains substances which change colour when something is found in a liquid.

Measuring dipstick 

 
Measuring dipsticks show the amount of liquid in a container. These containers are usually hard to access. Measuring dipsticks are used by inserting and removing the stick and then checking how much of the stick is covered by the liquid. The oil level dipstick is an example of a measuring dipstick found on most internal combustion engines.

Science
Engineering
Tools
Elliptic curve

An elliptic curve is a plane curve of degree 3 that can be described using the following formula:

,

where  and  are integers.

Geometry
Northrop Grumman B-2 Spirit

The Northrop Grumman B-2 Spirit, also called the Stealth Bomber, is an American strategic bomber. It has a lot of stealth technology, and it is designed to get through many anti-aircraft defenses. It can drop both conventional and nuclear weapons. Two people fly the bomber, and it can drop up to 80 -class JDAM GPS-guided bombs, or sixteen  B83 nuclear bombs. 

The bomber began being designed as the "Advanced Technology Bomber" (ATB) during the Carter administration. The designing of the ATB continued during the Reagan administration. The bomber was designed and is made by Northrop Grumman, with help from Boeing. Each aircraft cost US$737 million (in 1997 dollars). 

Because the bomber is very expensive, the project was controversial in the U.S. Congress. The end of the Cold War meant that the bomber was not really needed anymore. Congress wanted to buy 132 bombers, but during the late 1980s and 1990s, Congress reduced this to 21. In 2008, a B-2 was destroyed in a crash shortly after takeoff. The crew got out safely. 20 B-2s are being used by the United States Air Force. 

Although the B-2 was supposed to be a mainly nuclear bomber, it was first used in combat to drop normal bombs on Serbia during the Kosovo War in 1999. It was used during the Iraq War and it is being used in the war in Afghanistan.

References

Other websites 

 B-2 Spirit fact sheet and gallery on U.S. Air Force site 
 B-2 Spirit page on Northrop Grumman site 
 B-2 Spirit Stealth bomber on airforce-technology.com
 B-2 Stealth Bomber article on How It Works Daily
 B-2 Spirit page at GlobalSecurity.org

United States Air Force aircraft
Diapause

Diapause is a delay in development which has evolved in response to regular periods of adverse environmental conditions.

It is a physiological state with very specific conditions. Diapause is a mechanism used as a means to survive predictable, unfavourable environmental conditions, such as temperature extremes, drought or reduced food availability. It is most often observed in arthropods, especially insects, and in the embryos of many of the oviparous species of fish in the order Cyprinodontiformes.

Not only is diapause started by specific stimuli or conditions, but once it is started, only certain other stimuli are capable of bringing the organism out of diapause. This distinguishes diapause from other forms of dormancy such as hibernation.

Activity levels of diapausing stages can vary considerably among species. Diapause may occur in a completely immobile stage, such as the pupae and eggs, or it may occur in very active stages that undergo extensive migrations, such as the adult Monarch butterfly, Danaus plexippus. In cases where the insect remains active, feeding is reduced and reproductive development is slowed or halted.

References 

Physiology
Electric field

An electric field is a vector field that shows the direction that a positively charged particle will move when placed in the field. More precisely, if a particle has an electric charge  and is in an electric field , the electric force the charge will feel is  .Electric fields are produced around objects that have electrical charge, or by a magnetic field that changes with time. Electric field lines are used to represent the influence of electric field.  The idea of an electric field was first made by Michael Faraday.

Electric fields are caused by electric charges, described by Gauss's law, or varying magnetic fields, described by Faraday's law of induction.  The equations of both fields are coupled and together form Maxwell's equations that describe both fields as a function of charges and currents.

References 

Electromagnetism
Audiobook

Audiobooks or "talking books" are books that have been read aloud by someone and recorded. Nowadays, they are usually recorded onto compact discs (CDs), although some older editions remain on cassette tapes. (This is why many texts in this format were first called books-on-tape.) More recently, audiobooks have been available to download from the internet (free or paid-for) and pre-recorded on special MP3 players.

While audiobooks can be used by anyone, they serve as a main resource for people who are blind or cannot see well.

Many popular books are often chosen to be turned into audiobooks. The original author may or may not be involved in choosing the narrator for the reading. Some authors often use the same reader for many books, so that their audiobooks have a similar sound or style.

References

Disability
Books
Power spectrum

The power spectrum of a signal is the power or more simply the energy of the signal at each frequency that it contains. It can also be considered as the range or spectra of energy or power of the given signal derived from the signals' range of frequencies. For example, white noise, which contains all frequencies at the same power, has a flat power spectrum. The power spectrum of the sound of the bottom key on a piano would have a high value at the frequency corresponding to its note, and low values elsewhere.

Electronics
Slovak Wikipedia

The Slovak Wikipedia (In Slovak: Slovenská Wikipédia) is the Slovak-language edition of Wikipedia. This edition began in October 2003.

As of October 2015, it is the 37th largest edition of Wikipedia by number of articles.

It has over 120,000 articles.

References

Other websites 

 Slovak Wikipedia main page

Wikipedias