Vladimir Bourmeister (22 January 1904 – 5 March 1971) was a Soviet choreographer best known for his choreography of Swan Lake, a ballet dance by Peter Tchaikovsky. Made in 1952, his choreography of the dance, unlike other choreographies at the time, was designed to be closely related to the original dance by Tchaikovsky whilst also being modern. The most recognized change in his choreography to the ballet was adding a prologue that showed Odette being turned into a swan by Rothbart. By the end of Bourmeister's choreography, she gets restored to herself. In the Ballroom scene of the dance, Bourmeister made Odile more like an attractive and respectable girl than a seductive vamp to make Siegreid portraying Odette more realistic. Bourmeister's choreography had been played over by the Stanislavsky orchestra. In 1960 the choreography was adopted by the Paris Opera Ballet. When he was invited to choreograph The Snow Maiden (mus. Tchaikovsky) for London Festival Ballet in 1961, he became the first Soviet choreographer to work with a Western company.

References

1904 births
1971 deaths
Soviet male ballet dancers

Vladimir Bourmeister


Native Americans (also called Aboriginal Americans, American Indians, Amerindians or indigenous peoples of the Americas) are the indigenous peoples and their descendants, who were in the Americas before Europeans arrived.

Sometimes these people are called Indians, but this may be confusing, because it is the same word used for people from India. When Christopher Columbus explored, he did not know about the Americas. He was in the Caribbean but thought he was in the East Indies, so he called the people Indians. Today, some think that calling a Native American an Indian is racist.

There are many different tribes of Native American people, with many different languages. Some tribes were hunter-gatherers who moved from place to place. Others lived in one place and built cities and kingdoms.

Many Native Americans died after the Europeans came to the Americas. There were diseases that came with the Europeans but were new to the Native Americans. There were battles with the Europeans. Many native people were hurt, killed, or forced to leave their homes by settlers who took their lands.

Today, there are more than three million Native Americans in Canada and the U.S. combined. About 51 million more Native Americans live in Latin America. Many Native Americans still speak native languages and have their own cultural practices, while others have adopted some parts of Western culture. Many Native Americans face problems with discrimination and racism.

Origins
The ancestors of Native Americans came to the Americas from Asia. Some of them may have come to America 15,000 years ago when Alaska was connected to Siberia by the Bering land bridge.

The earliest people in the Americas came from Siberia when there was an ice bridge across the Bering Strait. The cold but mainly grassy plain which connected Siberia with Canada is called Beringia.  It is reckoned that a few thousand people arrived in  Beringia from eastern Siberia during the Last Glacial Maximum before moving into the Americas sometime after 16,500 years before the present (BP). This would have occurred as the American glaciers blocking the way southward melted, but before the bridge was covered by the sea about 11,000 years BP.

Before European colonization, Beringia was inhabited by the Yupik peoples on both sides of the straits. This culture remains in the region today, with others. In 2012, the governments of Russia and the United States announced a plan to formally establish "a transboundary area of shared Beringian heritage". Among other things this agreement would establish close ties between the Bering Land Bridge National Preserve and the Cape Krusenstern National Monument in the United States and Beringia National Park in Russia.

Native Americans are divided into many small nations, called First Nations in Canada and tribes elsewhere.

Culture
Each Native American tribe has their own culture. The cultures can be grouped together depending on region. For example, the tribes living in Mesoamerica have similar cultures.

Food
Native Americans ate many different things depending on where they lived.

Native Americans from Mesoamerica introduced vanilla, avocados, and chocolate to the world.

Religion
Before Europeans came, the native peoples of the Americans practiced many different religions. Each tribe had their own different beliefs.

Today, many Native Americans practice Christianity, a religion that was brought to the Americas by Europeans. Meanwhile, others still practice their own religions.

Languages
Native Americans today speak over a thousand different languages. Some of these languages had writing systems before Europeans came.

Many of these languages are endangered because more people are speaking European languages and not teaching Native American languages to their kids.

Music
Native Americans make musical instruments using the things around them.

Art
Native Americans made a lot of different art.

Today

North America

United States
According to the 2010 United States census, 0.9% of Americans say they are Native American, 2.9 million people, and 0.8% of Americans say they are both Native American and something else.  They are not evenly spread out through the United States.  About a third of the people in Alaska are Native Alaskan and about a sixth of the people in Oklahoma are Native American.

In the United States, most Native Americans live in cities.  About 28% of Native Americans live on Indian reservations.  Many Native Americans are poor, and 24% are extremely poor.  The history of violence against Native Americans persists today in higher rates of violence against Native American people than white people.

Mexico
Many Mexicans are of Native American or mestizo ancestry. Mexico has the largest and most diverse Native American population in Latin America.

Canada
In the 2016 census, More than 1.67 million people in Canada identified as Indigenous, making them 4.9 per cent of Canada's population.

Central America

Guatemala
About 40% of the people of Guatemala identify as Native American. Many indigenous groups in the country are descendants of the Maya.

Many Native Americans in Guatemala are poor. Many of them have left the country to find better jobs elsewhere.

South America

Bolivia
The majority of Bolivians belong to indigenous groups. Many are Aymara and Quechua.

Peru
Peru has a large indigenous population, around 80% of Peru's population identify as indigenous or mestizo.

Indigenous activism
In the later half of the 20th century, many Native Americans started to protest the unfair treatment they experienced from the societies they lived in.

Some Native Americans have become famous in politics. For example, an Aymara man named Evo Morales was elected as president of Bolivia in 2005. He was the first indigenous presidential candidate in Bolivia and South America.

Related pages
First Nations
Plains Indians
Native Americans in the United States

References

Native American


Drew Denbaum (born December 12, 1949 in Brooklyn, New York) is an  American writer, actor, director, and educator, with credits in theater, film, and television.

Early life and career
Denbaum graduated cum laude with honors from The Lawrenceville School (1967) and Yale University (1971), where he was awarded the Saybrook Fellows' Prize  and was close friends with the author and critic, William A. Henry III, and the poet and psychologist, Steve Benson.

Theater
Denbaum's playwriting credits include Ways of Loving and Secrets, both based on stories by Brendan Gill and produced in New York City at West Park Theater and Stage 73. Denbaum's play, The Last of Wilhelm Reich was developed at Theatre Artists Workshop  after more than a decade of research on the controversial psychoanalyst, scientist, and social activist, Wilhelm Reich.

Denbaum's directing credits in the theater include Hatful of Rain by Michael V. Gazzo at the Samuel Beckett Theatre, The Poet and the Rent by David Mamet at the Henry Street Settlement Theatre, and Secrets at Stage 73, all in New York City. Notable theater performances by Denbaum include Marat in Marat/Sade by Peter Weiss, directed by Lynne Meadow; Uriah in Mann ist Mann by Bertolt Brecht, directed by Evangeline Morphos; Sir Andrew Aguecheek in Shakespeare's Twelfth Night, directed by Leland Starnes; Wilhelm Reich in The Last of Wilhelm Reich, directed by Denbaum; and August Strindberg in Strindberg's Dollhouse by Vivian Sorvall, directed by Mark Graham.

Film
Denbaum began his film career as a story analyst at Columbia Pictures and joined Cannon Films as assistant to the President in Charge of Production, Christopher C. Dewey. Denbaum was Associate Producer of the feature films, Jump!, directed by Joe Manduke, and Who Killed Mary What'sername?, directed by Ernest Pintoff.  While attending the Institute of Film and Television at New York University, Denbaum won First Prize in the 20th Century Fox Screenwriting Competition in 1975 for his original screenplay, Caught in the Act, about the Bay of Pigs invasion by the Central Intelligence Agency.  Denbaum's next screenplay was the science fiction dark comedy, The Sky is Falling, developed by director John G. Avildsen for Universal Pictures.

In 1983, Denbaum adapted and directed John Gardner's novel Nickel Mountain as a feature film, which was released by Warner Bros./Lorimar. His short films, Lovesick (starring Austin Pendleton) and The Last Straw (based on the play by Charles Dizenzo), were featured in the New York Museum of Modern Art's Cineprobe Series  and won awards in numerous film festivals, including the Silver Plaque at the Chicago Film Festival and the Grand Prize at the Virgin Islands International Film Festival.

Television
Denbaum wrote the scripts for two television movies, I-75 (CBS) and The Westport Women's Bank Heist & Frolic (NBC). As an actor, he appeared in Barnaby Jones as Stan Nesbit in the episode Dangerous Gambit and in Cannon as Bill in the episode The Quasar Kill. Denbaum also appeared on Saturday Night Live as the husband of Gilda Radner in the classic commercial spoof, Royal Deluxe II, which also featured Dan Aykroyd and Garrett Morris, and was written by Al Franken and Tom Davis.

Author
After decades of practicing Jain meditation, Denbaum co-authored the nonfiction book, Chi Fitness, with his wife, the dancer/choreographer, Sue S. Benton. Their book, influenced by the works of Moshé Feldenkrais, Gary Zukav, Carolyn Myss, and studies of the chakra energy system, was published by HarperCollins in 2001.

Educator
In 2007, Denbaum earned a Master of Teaching degree and Connecticut certification (English, Grades 7-12) from Sacred Heart University and began teaching high school students in English, Film Studies, and Dramatic Literature and Performance, heavily influenced by the progressive education theories of Ken Robinson and Native American Circle of Courage principles. In 2010, he began teaching Literature and Composition at Housatonic Community College, where he was elected to the College Senate in 2014. In 2017, Denbaum was named Director of the Stamford YMCA LEAD College and Career Readiness Summer Institute, an enrichment program for teenagers that includes classroom sessions at the Stamford campus of the University of Connecticut and briefings at corporate, cultural, and educational institutions, as well as trips to New York City and Washington, D.C. In keeping with his pedagogical focus on higher-order critical thinking, Denbaum expanded the LEAD After-School Program at Westhill High School by creating the first high school curriculum based on Thinking, Fast and Slow by the noted psychologist Daniel Kahneman, winner of the Nobel Prize in Economics. In 2019, Denbaum received the Stamford Public Education Foundation Spotlight Award for Excellence in Teaching.

References

External links
 Denbaum biography at The Dramatists Guild

 Denbaum biography at Theatre Artists Workshop

1949 births
20th-century American dramatists and playwrights
20th-century American male actors
21st-century American educators
21st-century American non-fiction writers
American male dramatists and playwrights
American male screenwriters
American male stage actors
American male television actors
American television writers
American theatre directors
Film directors from New York City
Living people
Male actors from New York City
People from Brooklyn
Sacred Heart University alumni
Screenwriters from New York (state)
Yale University alumni
20th-century American male writers
20th-century American non-fiction writers
American male non-fiction writers
Educators from New York City
American male television writers
21st-century American male writers

Drew Denbaum


Sir Richard Lloyd (1634–1686) was an English jurist and politician. He was Admiralty Advocate from 1674 to 1686, and appointed Judge of the High Court of Admiralty from 1685 to 1686.

Life

He was the second son of Andrew Lloyd of Aston, Shropshire. A fellow of All Souls' College, Oxford, he proceeded B.C.L. in 1659 and D.C.L. in 1662. He was admitted to Gray's Inn at 1655, and an advocate at Doctors' Commons in 1664.

He was admiralty Advocate in 1674–1685, and chancellor of the dioceses of Llandaff and Durham. He was M.P. for Durham city in 1679–1681, 1681 and 1685, and was knighted on 16 January 1677. He was dean of the arches in 1684–6, and a judge of the high court of admiralty in 1685–6.

He died 28 June 1686, and was buried in the church of St. Bennet, Paul's Wharf. Nathaniel Lloyd was his son by Elizabeth, his wife.

Footnotes

References

1634 births
1686 deaths
English legal professionals
Members of Doctors' Commons
English MPs 1680–1681
English MPs 1681
English MPs 1685–1687
Members of the Parliament of England for the City of Durham

Richard Lloyd (Durham politician)


Benjamin Chew Tilghman (October 26, 1821  July 3, 1901) was an American soldier and inventor. He is best known as the inventor of the process of sandblasting.

Early life
He was born in Philadelphia, Pennsylvania, on October 26, 1821, the third child of Benjamin and Anne Marie (McMurtie). His father was descended from Richard Tilghman, a surgeon in the British Navy; he was related to William Tilghman, Chief Justice of Philadelphia.

Tilghman was educated at Bristol College and later at the University of Pennsylvania, where he was graduated with a degree in law in 1839, though he never practiced this profession. With his brother, Richard, he spent much time before the war journeying through Europe, visiting laboratories, chemical works and mills. He was elected as a member to the American Philosophical Society in 1871.

Civil War career
At the outbreak of the American Civil War, he volunteered as a Captain in the 26th Pennsylvania Infantry Regiment, rising to Colonel and commander of the 29th Pennsylvania Volunteer Infantry. He was severely wounded in the thigh at the Battle of Chancellorsville in 1863 and sent home to recover. Upon his recovery, he accepted the role of Colonel and commander of the 3rd United States Colored Troops. He was brevetted Brigadier General, US Volunteers on April 13, 1865 for "meritorious services".

Invention of the sandblasting process
Legend has it that Tilghman had seen the effect of wind-blown sand on windows in the desert while a general in the army, and that this was the basis of his sandblasting invention.

Around 1870, he invented the Sandblasting process and filed a patent for it in the US (US patent 108,408.), detailing many of the applications for which this technique is uniquely suited, such as sharpening files, engraving bottles, cleaning boilers or bringing out the grain in wood. Later that year a patent was issued in the UK.

In 1871, at the 40th Exhibition of the American Institute of the City of New York, he was awarded the institute's Great Medal of Honor for his invention; shortly after, he was also awarded the Elliott Cresson Medal by the Franklin Institute.

He refined the technique for various purposes, and in 1877 took out a patent (US patent 252,279) for sharpening files, which he marketed as "Liquid Grindstone".

Further patents and developments followed.

Commercial ventures

His first company was formed with his brother in Philadelphia—B. C. & R. A. Tilghman—for the production of chilled iron shot for the stone industry. Around 1879, Benjamin moved to London forming a new company, Tilghman's Patent Sand Blast Co. at Gray's Inn Road. This company used one of his patent methods for sharpening files and rasps. From London he moved to Sheffield, the centre of steel production in England at the time, and later moved to Altrincham in Cheshire, being resident there around 1885, having invested in the machine tool company George Richards Ltd.

In 1879, he opened the gates of his new works in Broadheath, Altrincham, which became the hub of the sand blasting industry in Great Britain. This lastly formed company, later called Wheelabrator Tilghman, and since 2005, Wheelabrator Group, still trades.

Other inventions

While working on the sandblasting process, he was also engaged in the working of stone, which caused him to invent a production method for iron shot - pouring a stream of molten metal onto a revolving surface, from which the globules would be propelled into cold water (US patent 187,239, 1872). This material was in great demand for the cutting of stone.

Around 1880, he invented the sulfite method of fiber reduction for paper production; this was a critical part of the production of paper from wood pulp, competing with the Kraft process.

He also patented a design for a torpedo to be propelled "rocket fashion" by a slow burning powder. It was not successful. He was assisted in this venture by his nephew, Benjamin C. Tilghman II.

He died on July 3, 1901, and is buried in the churchyard of Church of St. James the Less in Philadelphia.

Known Patents
 U.S. Patent No. 108,408 - sandblasting (1870)
U.S. Patent No. 133,501, "Improvement in cutting in stone and other hard substances" (1872) - cutting stone by means of steel shot
U.S. Patent No. 174,167, "Improvement in process of producing designs upon hard surfaces" (1875)
 U.S. Patent No. 187,239 - production of iron shot (1872)
 U.S. Patent no. 252,279 - sharpening of files (1877)
U.S. Patent No. 446,988
U.S. Patent No. RE7,499
 U.S. Patent no. 702,040, "Sand-blast tumbling barrel" (attributed to "Benjamin C. Tilghman Jr.")
 U.S. patent No. 416,873  "Cutting metal by electricity" (1889)
 UK Patent no. 2147 (1870) - sandblasting
 UK Patent no. 2900 (1870) - blast wheel
 UK Patent no. 13,510 (1885) - roughening iron and steel rolls

Footnotes

.

References
 "Studies in the Land: The Northeast Corner" by David C Smith (Routlegde 2002) - quoted from Google Books

External links

 Wheelabrator Group website

1821 births
1901 deaths
Businesspeople from Philadelphia
University of Pennsylvania Law School alumni
Union Army colonels
19th-century American inventors
Engineers from Pennsylvania
Burials at the Church of St. James the Less
People of Pennsylvania in the American Civil War
Military personnel from Philadelphia
19th-century American businesspeople
Tilghman family

Benjamin Chew Tilghman


Walter Giffard, Lord of Longueville in Normandy, 1st Earl of Buckingham (died 1102) was an Anglo-Norman magnate.

He was the son of Walter Giffard, Lord of Longueville (one of the few proven companions of William the Conqueror at the Battle of Hastings in 1066)  and Ermengarde daughter of Gerald Flaitel. His father had been given 107 lordships, 48 of which were in Buckinghamshire which Giffard inherited by 1085. The caput of his feudal honor was at Crendon, Buckinghamshire.

He held an important castle at Longueville overlooking the River Scie as well as vast estates in Buckinghamshire. As he held lands in both England and Normandy he was a vassal to both Robert Curthose and William Rufus. But Rufus purchased his loyalty along with several other key cross-Channel barons and fortified Giffard's and the other castles, garrisoning them with knights in the king's employ who could now ravage northeastern Normandy. Giffard also served Rufus as Justiciar of England, and it was probably Rufus who created him Earl of Buckingham in 1097. Giffard was one of the great magnates who joined Robert Curthose's 1101 invasion of England against Henry I of England. He died 15 July 1102 in England and his body was returned to Normandy, where it was interred at St. Mary's Church at Longueville-sur-Scie, the caput of his Norman honors.

Giffard was married to Agnes de Ribemont, sister of Anselm de Ribemont. His heir was his son,  Walter Giffard, 2nd Earl of Buckingham.

Notes

References

Sources
William M. Aird, Robert Curthose Duke of Normandy (Woodbridge: The Boydell Press, 2008)
George Edward Cokayne, The Complete Peerage of England Scotland Ireland Great Britain and the United Kingdom, Extant Extinct or Dormant, Vol. II, Ed. Vicary Gibbs (London: The St. Catherine Press, Ltd., 1912)

11th-century births
1102 deaths
11th-century English nobility
12th-century English nobility
01
Anglo-Normans
Year of birth unknown

Walter Giffard, 1st Earl of Buckingham


Google Business Photos (now called "Indoor Street View") is a virtual tour service started by Google.  It uses the same photography technique used in Google Street View in order to offer 360˚ interactive panoramas inside businesses. Once the virtual tour is published by Google, the link to the tour is displayed directly on the search results page. The tour is also published on Google+ Local (now just called Google+) pages and Google Maps. A user visiting a business published virtual tour can navigate inside the business in the same way a user of Google Street View can navigate roads, streets and highways.

History
Google Business Photos first established by Google in April 2010, and at first was available in approximately 30 cities across the US, Australia, and Japan.  By January, 2013, 100,000 businesses had arranged for Google Maps users to tour inside their premises. Google re-branded Google Business Photos to Business View in 2014. In 2015, Google announced that they are again re-branding Business View to Street View.

At the Street View Summit in May 2016, Google announced several changes to the program. In order to become Trusted, photographers must publish 50 high-quality maps-approved photo spheres that are 14MP or larger, without any significant stitching errors or artifacts.

Photography
The virtual tours are photographed by Google Trusted Photographers or Google Trusted Agencies. These photographers are independent contractors and are not employed by Google. Google has certified them because they meet Google's standards of quality for taking the feature pictures and panoramic pictures. Businesses pay the photographers to take the interior photos.

References

Google Search
Google services
Computer-related introductions in 2010
Google Street View
Google Maps

Street View Trusted


In the law of the United States, diversity jurisdiction is a form of subject-matter jurisdiction that gives United States federal courts the power to hear lawsuits that do not involve a federal question. For a federal court to have diversity jurisdiction over a lawsuit, two conditions must be met. First, there must be "diversity of citizenship" between the parties, meaning the plaintiffs must be citizens of different U.S. states than the defendants. Second, the lawsuit's "amount in controversy" must be more than $75,000. If a lawsuit does not meet these two conditions, federal courts will normally lack the jurisdiction to hear it unless it involves a federal question, and the lawsuit would need to be heard in state court instead.

The United States Constitution, in Article III, Section 2, grants Congress the power to permit federal courts to hear diversity cases through legislation authorizing such jurisdiction. The provision was included because the Framers of the Constitution were concerned that when a case is filed in one state, and it involves parties from that state and another state, the state court might be biased toward the party from that state. Congress first exercised that power and granted federal trial circuit courts diversity jurisdiction in the Judiciary Act of 1789. Diversity jurisdiction is currently codified at .

In 1969, the American Law Institute explained in a 587-page analysis of the subject that diversity is the "most controversial" type of federal jurisdiction, because it "lays bare fundamental issues regarding the nature and operation of our federal union."

Statute

Diversity of parties
Mostly, in order for diversity jurisdiction to apply, complete diversity is required, where none of the plaintiffs can be from the same state as any of the defendants. A corporation is treated as a citizen of the state in which it is incorporated and the state in which its principal place of business is located. A partnership or limited liability company is considered to have the citizenship of all of its constituent partners/members. Thus, an LLC or partnership with one member or partner sharing citizenship with an opposing party will destroy diversity of jurisdiction. Cities and towns (incorporated municipalities) are also treated as citizens of the states in which they are located, but states themselves are not considered citizens for the purpose of diversity. U.S. citizens are citizens of the state in which they are domiciled, which is the last state in which they resided and had an intent to remain.

A national bank chartered under the National Bank Act is treated as a citizen of the state in which it is "located". In 2006, the Supreme Court rejected an approach that would have interpreted the term "located" to mean that a national bank is a citizen of every state in which it maintains a branch. The Supreme Court concluded that "a national bank ... is a citizen of the State in which its main office, as set forth in its articles of association, is located". The Supreme Court, however, left open the possibility that a national bank may also be a citizen of the state in which it has its principal place of business, thus putting it on an equal footing with a state-formed corporation. This remains an open question, with some lower courts holding that a national bank is a citizen of only the state in which its main office is located, and others holding that a national bank is also a citizen of the state in which it has its principal place of business.

The diversity jurisdiction statute also allows federal courts to hear cases in which:
Citizens of a U.S. state are parties on one side of the case, with nonresident alien(s) as adverse parties;
Complete diversity exists as to the U.S. parties, and nonresident aliens are additional parties;
A foreign state (i.e., country) is the plaintiff, and the defendants are citizens of one or more U.S. states; or
Under the Class Action Fairness Act of 2005, a class action can usually be brought in a federal court when there is just minimal diversity, such that any plaintiff is a citizen of a different state from any defendant. Class actions that do not meet the requirement of the Class Action Fairness Act must have complete diversity between class representatives (those named in the lawsuit) and the defendants.

A U.S. citizen who is domiciled outside the U.S. is not considered to be a citizen of any U.S. state, and cannot be considered an alien. The presence of such a person as a party completely destroys diversity jurisdiction, except for a class action or mass action in which minimal diversity exists with respect to other parties in the case.

If the case requires the presence of a party who is from the same state as an opposing party, or a party who is a U.S. citizen domiciled outside the country, the case must be dismissed, the absent party being deemed "indispensable". The determination of whether a party is indispensable is made by the court following the guidelines set forth in Rule 19 of the Federal Rules of Civil Procedure.

Diversity is determined at the time that the action is filed
Diversity is determined at the time that federal court jurisdiction is invoked (at time of filing, if directly filed in U.S. district court, or at time of removal, if removed from state court), and on the basis of the state citizenships of the parties at that time. A change in domicile by a natural person before or after that date is irrelevant. However, in Caterpillar, Inc. v. Lewis (1996), the Supreme Court also held that federal jurisdiction predicated on diversity of citizenship can be sustained even if there did not exist complete diversity at the time of removal to federal court, so long as complete diversity exists at the time the district court enters judgment. The court in Caterpillar sustained diversity as an issue of "fairness" and economy, given a lower court's original mistake that allowed removal.

Corporate citizenship based on principal place of business

Before 1958, a corporation for the purpose of diversity jurisdiction was deemed to be a citizen only of the state in which it had been formally incorporated.  This was originally not a problem when a corporation could be chartered only by the enacting of a private bill by the state legislature (either with the consent of the governor or over his veto).  It became a problem when general incorporation laws were invented around 1896, state legislatures began a race to the bottom to attract out-of-state corporations, and corporations began to incorporate in one state (usually Delaware) but set up their headquarters in another state.  During the 20th century, the traditional rule came to be seen as extremely unfair in that corporate defendants actually headquartered in a state but incorporated elsewhere could remove diversity cases against them from state courts to federal courts, while individual and unincorporated defendants physically based in that same state (e.g., partnerships) could not.  Therefore, during the 1950s, various proposals were introduced to broaden the citizenship of corporations in order to reduce their access to federal courts.

In 1957, conservative Southern Democrats, as part of their larger agenda to protect racial segregation and states' rights by greatly reducing the power of the federal judiciary, introduced a bill to limit diversity jurisdiction to natural citizens.  Liberals in Congress recognized this was actually a form of retaliation by conservative Southerners against the Warren Court, and prevailed in 1958 with the passage of a relatively narrow bill which deemed corporations to be citizens of both their states of incorporation and principal place of business.  The two proposals, respectively, promised to reduce the federal civil caseload by 25% versus 2%.

However, Congress never defined what exactly is a "principal place of business". The question of what that phrase meant became hotly disputed during the late 20th century as many areas of the American economy came under the control of large national corporations. Although these corporations usually had a headquarters in one state, the majority of their employees, assets, and revenue were often physically located at retail sites in the states with the largest populations, and hence a circuit split developed in which some judges held that the latter states could also be treated as the corporation's principal place of business. The rationale was that those states were where the business was actually occurring or being transacted.  This issue was finally resolved by a unanimous Supreme Court in Hertz Corp. v. Friend (2010), which held that a corporation's principal place of business is presumed to be the place of the corporation's "nerve center" from where its officers conduct the corporation's important business.

Amount in controversy
The United States Congress has placed an additional barrier to diversity jurisdiction: the amount in controversy requirement. This is a minimum amount of money which the parties must be contesting is owed to them. Since the enactment of the Federal Courts Improvement Act of 1996, 28 U.S.C. §1332(a) has provided that a claim for relief must exceed the sum or value of $75,000, exclusive of interest and costs and without considering counterclaims. In other words, the amount in controversy must be equal to or more than $75,000.01, and (in a case which has been removed from a state court to the federal court) a federal court must remand a case back to state court if the amount in controversy is exactly $75,000.00.

A single plaintiff may add different claims against the same defendant to meet the amount. Two plaintiffs, however, may not join their claims together to meet the amount, but if one plaintiff meets the amount standing alone, the second plaintiff can piggyback as long as the second plaintiff's claim arises out of the same facts as the main claim.  More detailed information may be obtained from the article on federal supplemental jurisdiction.

The amount specified has been regularly increased over the past two centuries. Courts will use the legal certainty test to decide whether the dispute is over $75,000. Under this test, the court will accept the pled amount unless it is legally certain that the pleading party cannot recover more than $75,000. For example, if the dispute is solely over the breach of a contract by which the defendant had agreed to pay the plaintiff $10,000, a federal court will dismiss the case for lack of subject matter jurisdiction, or remand the case to state court if it arrived via removal.

In personal injury cases, plaintiffs will sometimes claim amounts "not to exceed $75,000" in their complaint to avoid removal of the case to federal court.  If the amount is left unspecified in the ad damnum, as is required by the pleading rules of many states, the defendant may sometimes be able to remove the case to federal court unless the plaintiff's lawyer files a document expressly disclaiming damages in excess of the jurisdictional requirement. Because juries decide what personal injuries are worth, compensation for injuries may exceed $75,000 such that the "legal certainty" test will not bar federal court jurisdiction. Many plaintiffs' lawyers seek to avoid federal courts because of the perception that they are more hostile to plaintiffs than most state courts.

Domestic relations and probate exceptions
A longstanding judge-made rule holds that federal courts have no jurisdiction over divorce or other domestic relations cases, even if there is diversity of citizenship between the parties and the amount of money in controversy meets the jurisdictional limit. As the Supreme Court has stated, "[t]he whole subject of the domestic relations of husband and wife, parent and child, belongs to the laws of the states, and not to the laws of the United States." The court concluded "that the domestic relations exception ... divests the federal courts of power to issue divorce, alimony, and child custody decrees."  In explaining this exception, the high court noted that domestic cases frequently required the issuing court to retain jurisdiction over recurring disputes in interpreting and enforcing those decrees. State courts have developed expertise in dealing with these matters, and the interest of judicial economy required keeping that litigation in the courts most experienced to handle it. However, federal courts are not limited in their ability to hear tort cases arising out of domestic situations by the doctrine.

A similar exception has been recognized for probate and decedent's estate litigation, which continues to hold for the primary cases; diversity jurisdiction does not exist to probate wills or administer decedent's estates directly. Diversity jurisdiction is allowed for some litigation that arises under trusts and other estate planning documents, however.

Removal and remand

If a case is originally filed in a state court, and the requirements for federal jurisdiction are met (diversity and amount in controversy, the case involves a federal question, or a supplemental jurisdiction exists), the defendant (and only the defendant) may remove the case to a federal court.

A case cannot be removed to a state court. To remove to a federal court, the defendant must file a notice of removal with both the state court where the case was filed and the federal court to which it will be transferred. The notice of removal must be filed within 30 days of the first removable document. For example, if there is no diversity of citizenship initially, but the non-diverse defendant is subsequently dismissed, the remaining diverse defendant(s) may remove to a federal court. However, no removal is available after one year of the filing of the complaint.

A party's citizenship at the time of the filing of the action is considered the citizenship of the party. If a defendant later moves to the same state as the plaintiff while the action is pending, the federal court will still have jurisdiction. However, if any defendant is a citizen of the state where the action is first filed, diversity does not exist. 28 U.S.C. §1441(b).

If a plaintiff or a co-defendant opposes removal, he may request a remand, asking the federal court to send the case back to the state court. A remand is rarely granted if the diversity and amount in controversy requirements are met. A remand may be granted, however, if a non-diverse party joins the action, or if the parties settle some claims among them, leaving the amount in controversy below the requisite amount.

Law applied

The United States Supreme Court determined in Erie Railroad Co. v. Tompkins (1938) that the law to be applied in a diversity case would be the law of whatever state in which the action was filed. This decision overturned precedents that had held that federal courts could create a general federal common law, instead of applying the law of the forum state. This decision was an interpretation of the word "laws" in 28 U.S.C. 1652, known as the Rules of Decision Act, to mean not just statutes enacted by the legislature but also the common law created by state courts.

Under the Rules of Decision Act, the laws of the several states, except where the constitution or treaties of the United States or Acts of Congress otherwise require or provide, shall be regarded as rules of decision in civil actions in the courts of the United States, in cases where they apply.

The Court interpreted "laws" to include the states' judicial decisions, or "common law". Thus, it is an overstatement to state that Erie represents the notion that there is no federal common law. Federal courts do adjudicate "common law" of federal statutes and regulations.

Because the RDA provides for exceptions and modifications by Congress, it is important to note the effect of the Rules Enabling Act (REA), 28 U.S.C. 2072. The REA delegates the legislative authority to the Supreme Court to ratify rules of practice and procedure and rules of evidence for federal courts. Thus, it is not Erie but the REA which created the distinction between substantive and procedural law.

Thus, while state substantive law is applied, the Federal Rules of Civil Procedure and the Federal Rules of Evidence still govern the "procedural" matters in a diversity action, as clarified in Gasperini v. Center for Humanities (1996). The REA, 28 U.S.C. 2072(b), provides that the Rules will not affect the substantive rights of the parties. Therefore, a federal court may still apply the "procedural" rules of the state of the initial filing, if the federal law would "abridge, enlarge, or modify" a substantive right provided for under the law of the state.

See also

Class Action Fairness Act of 2005
Federal question jurisdiction
Federalist No. 80
Saadeh v. Farouki (1997)
Strawbridge v. Curtiss (1806)
Supplemental jurisdiction

References

External links
28 U.S.C § 1332. Diversity of Citizenship

United States civil procedure
Jurisdiction

Article Three of the United States Constitution
American legal terminology

Diversity jurisdiction


Joseph Aloysius Corbett (December 4, 1875 – May 2, 1945) was a Major League Baseball starting pitcher who played in the National League. He was born in San Francisco, California.

Corbett, the younger brother of World Heavyweight Boxing Champion James J. Corbett, played baseball at Saint Mary's College of California from 1890 to 1893 before breaking into the major leagues in 1895. He went 3–0 with a 2.20 earned run average for the Baltimore Orioles in 1896 and then won two games in the Temple Cup series. He had his best season in 1897 when he posted career-highs in wins (24), strikeouts (149), ERA (3.11), starts (37), complete games (34) and innings pitched (313.0). However, Corbett had gotten angry over a dispute with manager Ned Hanlon, and he refused to report to the team the following season. Hanlon welched on a bet and refused to buy Corbett a new suit for winning 20 games.

For the next five years, Corbett was a sportswriter for the San Francisco Call and pitched semi-professional ball. He signed with the Pacific Coast League's Los Angeles Angels in 1903. It was the league's inaugural season, and the Angels won the pennant by 27.5 games. Corbett went 23–16, 2.36, led the PCL in strikeouts (196), and tied for the lead in shutouts (8). He also hit .336 in 262 at-bats. Corbett went back to the majors in 1904 with the St. Louis Cardinals, where went 5–8, 4.39. Arm trouble developed because of rheumatism and he was released in August. He then joined the PCL's San Francisco Seals and went 14–10 with a 1.86 ERA during the rest of the season. He also pitched for the Seals in 1905 and then retired except for a brief comeback attempt in 1909.

He later coached baseball at Santa Clara University.

Corbett died in San Francisco aged 69.  He was interred in the Holy Cross Cemetery in Colma, California.

References

External links

1875 births
1945 deaths
19th-century baseball players
Baltimore Orioles (NL) players
Baseball players from San Francisco
Burials at Holy Cross Cemetery (Colma, California)
Los Angeles Angels (minor league) players
Major League Baseball pitchers
Saint Mary's Gaels baseball players
St. Louis Cardinals players
San Francisco Seals (baseball) players
Washington Senators (1891–1899) players
Piedmont (minor league baseball) players
Petaluma Poison Oaks players
Toronto Canucks players
Scranton Coal Heavers players
Imperials of San Francisco players
Norfolk Braves players
Scranton Miners players
Minneapolis Millers (baseball) players
Stockton Millers players
San Jose Prune Pickers players

Joe Corbett


The County Palatine of Veldenz was a principality in the contemporary Land Rhineland-Palatinate with full voting rights to the Reichstag. The county was located partially between Kaiserslautern, Sponheim and Zweibrücken, partially on the Mosel in the Archbishopric of Trier. A municipality of the same name, Veldenz, and a castle, Schloss Veldenz, are located in the district of Bernkastel-Wittlich.

History
The Counts of Veldenz separated from the Wildgraves of Kyrburg and Schmidburg family in 1112. The direct male line of the first comital house ceased in 1260 with the death of Gerlach V of Veldenz and his daughter Agnes of Veldenz inherited the county in 1260. Her husband Heinrich of Geroldseck became the founder of the second line of Counts of Veldenz or the House of Veldenz-Geroldseck (Hohengeroldseck).

In 1444 the county came under the rule of Stephen, Count Palatine of Simmern-Zweibrücken by his marriage to Anna of Veldenz, the only heiress of Count Frederick III of Veldenz. As of 1532, the entire County Palantine of Zweibrücken passed to the child Wolfgang. In 1543, when Wolfgang reached majority and took on the responsibilities of office, he enacted the Marburg Contract, giving his uncle Rupert, who had served as his regent and guardian for 11 years, the County of Veldenz.

When Rupert died in 1544, son George John succeeded him as Count Palatine of Veldenz. George married Anna Maria of Sweden, a daughter of Gustav I of Sweden, in 1563. This was the joining of the House of Wittelsbach with the Swedish Vasa royal family which was strengthened by a further marriage when Johann Casimir of Pfalz-Zweibrücken married Catharina of Sweden, a sister of Gustavus Adolphus in the 17th century. Wolfgang had in 1553 with the Heidelberg Succession agreement regulated the mutual inheritance of all Wittelsbach lines reaching from Veldenz-Palatinate to the county Lützelstein in Alsace.  The grandson of Georg Hans, Leopold Ludwig von Lützelstein, died in 1694 as a poor man without legitimate offspring and the county-Palatinate of Veldenz, which was in ruins after many French attacks, reverted to the Zweibrücken line, specifically King of Sweden Charles XI, who ruled in personal union with the duchy of Palatine Zweibrücken. However, even bordering Electoral Palatinate wanted the ruins, and it obtained the goal.

In 1801 it was incorporated into the Saardepartement of the First French Empire. The Congress of Vienna, 1815, gave the smaller part of the county lying on the Mosel to Prussia and the remainder to Bavaria.

Counts of Veldenz

First Veldenz Line
 Emicho, Count of Kyrburg and Schmidburg (1086–1113)
 Gerlach I, Count of Veldenz (1113–1146)
 Gerlach II, Count of Veldenz (1146–1186)
 Gerlach III, Count of Veldenz (1186–1214)
 Gerlach IV, Count of Veldenz (1214–1254)
 Gerlach V, Count of Veldenz (1254–1260)
 Agnes, Countess of Veldenz (1260–1277)

Veldenz-Geroldseck Line
 Henry, Count of Geroldseck (1277–1298) ∞ Agnes of Veldenz (1258–?)
 Walter, Count of Veldenz (1298–1327)
 George I, Count of Veldenz (1327–1347)
 Henry II, Count of Veldenz (1347–1378)
 Frederick II, Count of Veldenz (1378–1396)
 Henry III, Count of Veldenz (1378–1389)
 Henry IV, Count of Veldenz (1389–1393)
 Frederick III, Count of Veldenz (1393–1444)

Palatine Zweibrücken Line
Stephen (briefly in 1444), widower of Anna of Veldenz (died 1439, daughter of Frederick III), separated Veldenz from his other holdings and gave it to his younger son
Louis (1444–1489)
Alexander (1489–1514)
Louis II (1514–1532)
Wolfgang (1532–1543). Wolfgang rewarded his uncle and regent, Rupert, with Veldenz. Wolfgang's other counties and duchies were split amongst his own sons upon his death in 1569.

Palatine Veldenz Line
 Rupert, Count Palatine of Veldenz (1543–1544)
 George John I, Count Palatine of Veldenz (1544–1592)
 George Gustavus, Count Palatine of Veldenz (1592–1634)
 Leopold Louis, Count Palatine of Veldenz (1634–1694), died without heir, Veldenz reabsorbed by the Palatine Zweibrücken line (King of Sweden Charles XI)

Veldenz ruins
Sweden and Palatinate disputed the Veldenz ruins for years. When the personal Union of Sweden and Zweibrücken ended, following agreements between the Wittelsbach family, Veldenz went to bordering Palatinate.

Literature
  Crollius, Georg Christian: Vorlesung: Von dem ersten geschlecht der alten graven von Veldenz und dessen gemeinschaftlichen abstammung mit den ältern Wildgraven von den graven im Nohgau. Historia et Commentationes. Academiae Electoralis Scientiarvm et Elegantiorvm Litterarvm Theodoro-Palatinae. Mannhemii Typis Academicis 1770 (complete at Google Books)
  Crollius, Georg Christian: Vorlesung: von dem zweiten geschlechte der grafen von Veldenz, aus dem hause der herren von Geroldseck in der Ortenau. Historia et Commentationes. Academiae Electoralis Scientiarvm et Elegantiorvm Litterarvm Theodoro-Palatinae. Mannhemii Typis Academicis 1778 (complete at Google Books)
  Gerbert, Martin: Pragmatische Geschichte des Hauses Geroldsek, wie auch derer Reichsherrschaften Hohengeroldsek, Lahr und Mahlberg in Schwaben. Frankfurt und Leipzig 1766 (complete at Google Books)

External links

 www.schlossveldenz.com
 List of the county's belonging locations ca. 1350
 Historical map (Veldenzer Aufgebot 1462)

1801 disestablishments
States and territories established in 1112
Counts of Veldenz
Subdivisions of the Holy Roman Empire

County Palatine of Veldenz


A softail (shortened form of soft tail) motorcycle intentionally looks like vintage motorcycles with a rigid hard-tail frame that has a triangle of steel tubes at the rear axle, as on a bicycle frame, but on a Softail these tubes are actually a triangular swingarm, with the shock absorber(s) hidden, as opposed to clearly visible regular twin shocks on both sides of the rear wheel on standard bikes. Since the introduction of the Harley-Davidson FXST Softail in 1983 as a registered trademark of the Motor Company, softail has become a genericized trademark for other models of cruiser motorcycles with rear suspensions hidden for retro style reasons. This was done even though the rear wheel was often hidden behind bags or exhaust pipes.

The hard tail becomes obsolete

The first rear suspensions on motorcycles were introduced before World War I, and many companies offered fully suspended motorbikes before World War II, but most designs were either expensive, prone to wear and tear, or added more instability than comfort or better roadholding, especially when damping was insufficient. The models that remained hard tails offered suspended bicycle-like seats for a minimum of rider comfort. After World War II, imported British bikes with rear suspension and good handling became popular. Harley-Davidson replaced the Springer leading link fork in 1949 with a telescopic hydraulically dampened Hydra Glide front fork that offered more travel, a design that is still state-of-the-art today. After the all-new entry-level 1952 Harley-Davidson Model K adopted the by now standard rear swingarm with twin shock absorbers, the Big Twin FL continued to rely on the big suspended seat until the 1958 Duo Glide got twin shocks, too.

The hard tail becomes cult

In the 1950s and 1960s, customized motorcycles appeared, many of them based on old Harleys, like surplus US Army Harley-Davidson WLA, or other brands, and often with hard tail frames rather than suspended ones. While the earlier bobbers still used the suspended single seat, the 1960s choppers had a small seat cushion directly on the hard tail frame, giving the rider a position much lower and rearward than on stock Harleys, which at the time were mainly ridden by Police officers. This position was without doubt uncomfortable, but it looked cool and gave the rider a tough guy, outlaw image. Some other obsolete and risky features were still used for coolness, like the so-called suicide clutch that was operated by left foot, with the left hand working a jockey shift, or the kick starter, even after electric starters were available. Even the front brake was removed for a good clean look, like on the more famous of the Easy Rider Harleys, the "Captain America". As seen in the movie, these hard tails were not easy to ride on bad roads and could be painful if sat on over bumps such as railway crossings. Even after suspension was available for over 20 years, in the 1970s many riders preferred these old style tough guy frames, and even new hard tail frames were made by aftermarket companies.

In 1970, Harley only had the big twin full-dresser touring bike, the FLH Electra Glide, and the small XL Sportster. With the FX Super Glide, the Big Twin Harley-Davidson Shovelhead engine was offered without the extras of the E-Glide, and with the narrow front end of the Sportster, later offered as the FXRS Low Rider. By the end of the decade, the FXWG Wide Glide was kind of a factory chopper, with a wide telescopic fork like on the FLH, narrow 21 inch wheel, buckhorn handle bar, bobbed fender, a small sissy bar, and even flames  paint job. It still had twin shocks, though, and many bikers wanted the clean look of the hard tail frame, with the frame forming a straight line from the steering head to the rear axle.

The hard tail becomes resurrected as FXST Softail

Bill Davis, an avid Harley rider and engineer from St. Louis, Missouri, designed his softail in the mid-1970s. His first design, which he worked on in 1974 and 1975, had a cantilever swingarm like on vintage Vincent Motorcycles that pivoted at the bottom and sprung at the top with the springs and shock absorber hidden under the seat. Davis then built a prototype based on his 1972 Super Glide. He patented the design and arranged to meet Willie G. Davidson August 1976. Davidson was impressed, but made no commitments, and six months later, said Harley-Davidson was interested but would not use the design at that time.

In April 1980, Harley-Davidson started work on its own rear suspension design that would have the look of a hard-tail motorcycle. The job was given a low priority until later in the year it was transferred to Jim Haubert Engineering, a firm that Harley-Davidson contracted yearly to custom build motorcycles and prototypes. Haubert built a prototype using his own rear suspension design that closely followed the look of the earlier Harley rigid frames. This version was completed enough for review by Harley-Davidson in January 1981.

Davis continued to develop the design, switching the pivot and the springing points around so that the springs and shock absorber were under the frame and the pivot point was at the top of the triangular swingarm. This allowed the traditional horse shoe shaped Harley-Davidson oil tank to be placed under the seat. Davis attempted to produce the new design independently as the Road Worx Sub-Shock, but the partnership he had put together for this purpose collapsed. Harley-Davidson executive Jeffrey Bleustein contacted Davis shortly afterward and began negotiations to buy Davis's design. Davis sold his patents, prototype, and tooling to Harley-Davidson in January 1982.

After further testing and development, Davis's design was introduced in June 1983 as the 1984 Harley-Davidson FXST Softail. This basically was an FXWG Wide Glide, but instead of the visible twin shocks, the softail swingarm was used, with the shocks hidden under the gearbox, which at the time was still 4-speed with kickstarter and chain. Other companies had introduced rear suspension designs with invisible shocks, but for performance reasons. The Harley Softail was the first modern motorcycle intentionally designed to look as if it was decades older. Between gearbox and seat, the rather dull asymmetric battery box (right side) and black oil tank (left side) was replaced by the symmetric horse-shoe shaped chrome oil tank around the battery in the middle, another feature of the old hard tail era.

In addition, Harley had just completed the "buy back" from AMF, and had developed the all-aluminium Harley-Davidson Evolution engine that was more reliable that the Shovelhead, and had heads that looked like square versions of the round Panheads. It was first offered in the Softail, and helped making it a success.

Other Harley-Davidson Softails

From 1986 onwards, Harley offered the Heritage Softail that copies the look of the 1950s Hydra Glide full dresser, with big front wheel, big head lights plus additional lights, big fenders, floor boards, saddle bags, windshield. By 1988, even the Springer front fork that was discontinued in 1948 was offered again, as a modern design with better bushings and a central damper. Even Heritage Springers were offered, that looked like the 1936 to 1948 Knuckleheads.

There have been many Harley-Davidson models with the Softail frame, including the Softail Standard, Custom, Springer Softail, Heritage Softail, Heritage Springer, Night Train, Deluxe, Deuce, Fat Boy, Softail Slim, the Dark Custom Cross Bones, the Dark Custom Blackline and Breakout. With the exception of the Deuce, which has a  longer tank, these motorcycles have the same engines, transmissions, and frames, differing mainly in the fork, wheels, and accessories.

Front forks
The Softail model line has multiple front fork configurations. Historically, they have had Springer leading link forks, reminiscent of the sprung front-ends that were used before the Hydra-Glide in 1949. The FXST designation is used for 21" front wheel bikes or when the Springer fork is used with a 21" wheel, while the FLST designation is used for 16" front wheel bikes or when the Springer fork is used with a 16" wheel.

Engines
Because Softail models do not have rubber-mounted engines, they transmit more of the engine's vibration to the rider than the Touring or Dyna models (which have rubber engine mounts). To compensate, later Softail models used a counterbalanced version of the Twin Cam engine, the 88B, instead of the regular Twin Cam engine used in the Touring and Dyna models. This counterbalanced engine was enlarged to 96B and 103B before it was replaced by a variant of the Harley-Davidson Milwaukee-Eight engine for the 2018 model year.

New Softail from 2018 onwards

In 2017, Harley unveiled a completely redesigned Softail frame for the 2018 model year, the first major change since the introduction of the Twin Cam engine in 2000. The 2018 Softail frame uses a differently shaped swingarm suspended by a single rear shock absorber, mounted underneath the seat in a similar fashion to the original Haubert and Davis designs. Harley claims that the new chassis is significantly stiffer and lighter than the previous-generation Softail and Dyna platforms, the latter being discontinued with some of its models being carried over to the new Softail chassis. The 2017 Street Bob 103 ci was dyno tested and made  and  at the rear wheel. The new 2018  Street Bob 107 ci makes  and  at the rear wheel. The 114 ci motor such as in the 2018 Heritage Classic produces  and  at the rear wheel.

Customizing
The Softail is the most popular Harley-Davidson model family for heavy customizing and is often used for show bikes. Many aftermarket manufacturers around the globe have specialized in Softail parts & accessories like wheels, fenders or tanks to change the look of the custom motorcycle. Harley-Davidson also started an Inspiration Gallery to show their latest factory custom parts on all new models  - many have their origin in CVO Softails, which are handmade Limited-Editions of the regular models.

Softails by other brands
Other softail-style motorcycles:
Honda VT600C (Shadow VLX)
Kawasaki Vulcan 800, 900
Suzuki VL 1500 Intruder LC / Boulevard C90
Victory Vegas
Yamaha Royal Star, Royal Star Venture
Yamaha XV1600A (Road Star, XV1700)
Yamaha DragStar 650, 950, 1100
Zero Engineering Type 9
Daelim VL Daystar

See also
 Bicycle suspension
 List of Harley-Davidson motorcycles

References

External links
Cruelworld Softail at Von Dutch Kustom Cycles.

Motorcycle suspension technology
Bicycle parts
Harley-Davidson motorcycles

Softail


The Battle of Kabul was a series of intermittent battles and sieges over the city of Kabul during the period of 1992–1996.

Throughout the Soviet–Afghan War from 1979 to 1989, and subsequent civil war (1989–1992) the city of Kabul saw little fighting. The collapse of Mohammad Najibullah's regime in April 1992 led to a peace treaty between the Afghan political parties and the establishment of the Islamic State of Afghanistan. But soon after, the undisciplined commanders from both former mujahideen and Communist ranks started to vie for power, abetted by foreign powers, namely Pakistan, Saudi Arabia, Iran and Uzbekistan, who began arming their Afghan proxies to fight for control and influence.

Political background

With the breakup of the Soviet Union in 1991, the Soviet-supported government of Najibullah lost credibility. In 1992, Russia agreed to end fuel shipments to the Democratic Republic of Afghanistan, which triggered the collapse of Najibullah's regime. In April 1992, General Abdul Rashid Dostum defected to the forces of Ahmed Shah Massoud, and began to take control of Kabul. By April 14, 1992, Massoud and his forces took control of Charikar and Jabalussaraj in Parwan Province without significant fighting. At this point, it was reported that Massoud had approximately 20,000 troops stationed around Kabul. It was also reported that the government's Second Division had joined Massoud. General Mohammad Nabil Azimi then proceeded to reinforce Bagram Air Base, and sent further reinforcements to the outer perimeter of Kabul. By mid-April, the air force command at Bagram capitulated to Massoud. With no army to defend it, Kabul had become completely helpless.

As soon as he announced his willingness, on March 18, to resign in order to make way for a neutral interim government, Najibullah immediately lost control. As the government broke into several factions, the issue was how to carry out a transfer of power to a new government. Najibullah resigned on April 14 and attempted to flee from Kabul on April 17, but was stopped by Dostum's troops, who controlled Kabul International Airport. Najibullah then took refuge at the United Nations mission where he remained until 1995. A group of Parchami generals and officials, led by acting President Abdul Rahim Hatif, declared themselves an interim government for the purpose of handing over power to the dominant and most popular military force: Massoud.

Massoud hesitated to enter Kabul, waiting for the political parties to reach a peace and power-sharing agreement first. In April 1992, the Peshawar Accord was signed. It established the Islamic State of Afghanistan and stipulated that an interim government would be formed with a supreme leadership council. A transitory presidency was given to Sibghatullah Mojaddedi for two months, after which Burhanuddin Rabbani was to succeed him. Gulbuddin Hekmatyar was given the post of prime minister, but he did not accept this position as he did not want to share power and Pakistan was urging him to take power for himself. Massoud, in a recorded conversation, tried to convince Hekmatyar to join the peace agreement and not to enter Kabul. But Hekmatyar replied he would enter the capital with "our naked sword. No-one can stop us". Hekmatyar's Hezb-i Islami forces began to infiltrate Kabul. This forced Massoud to advance on the capital in order to preserve the Peshawar Accord and prevent the establishment of a Hekmatyar dictatorship.

Eleven armed groups in total entered Kabul and its vicinities, which included the seven Sunni Afghan mujahideen; the Shi'ite Islamic Movement of Asif Mohseni and Hezbe Wahdat of Abdul Ali Mazari; and the Junbish-i Milli of ex-communist Abdul Rashid Dostum. The different groups entered the city in different directions. Hezb-i Islami made the first move and entered the city from the south. With soldiers armed and financed by Pakistan, Hekmatyar had asked other groups such as Harakat-Inqilab-i-Islami and the Khalis faction to join him while entering Kabul, but they declined his offer and instead backed the Peshawar Accord. Jamiat-i Islami had seized massive amount of weapons while overrunning the Communist garrisons in Bagram, Charikar, Takhar, Kunduz, Fayzabad and other northern cities. Adding to that, all the forces of Junbish-i Milli had aligned themselves to the Jamiat, and the former Communist government of Afghanistan had decided to surrender all its weapons to Jamiat, instead of Hezb. All the Parchamis had fled abroad through the Jamiat-controlled areas. Jamiat had seized massive stockpiles of heavy weapons such as T-62 and T-55 tanks, Scud missiles and MiG-21s.

Hekmatyar's Hezb forces were very far from key points of the city such as the presidential palace, the prime minister's office, Kabul International Airport, the ministry of defense and many other important government offices. Much of the city lies on the North Bank of the Kabul River. Burhanuddin Rabbani's Jamiat forces quickly took control of these strategically important offices. Although Hezb forces got to the gates of the ministry of justice and took control of the ministry of the interior, they were quickly repulsed after bombing from the Afghan Air Force, which was supported by artillery shells fired from a TV tower onto Jade Maiwand. Hundreds of Hezb fighters were killed or taken prisoners, including some foreign fighters.

In the western sector of the city, the Hezb forces crossed the Kabul River and arrived at the northern bank after taking control of the Karte Seh area. While charging towards the Kote Sangi and Kabul University, Sayyaf's forces attacked Hezb forces from the Ghazi School area in a surprise move, and the Hezb forces were separated into two groups after being cut off by Jamiat troops. Throughout the night, the exhausted and demoralized forces of Hezbi Islami fought. After suffering heavy casualties, Hezb forces on the southern bank deserted their positions, fleeing out of Kabul towards Logar.

Kabul came completely under Islamic State control on April 30, 1992, but the situation was far from stabilised. The Hezb-i Islami had been driven out, but they were still within artillery range, and soon started firing tens of thousands of Pakistan-supplied rockets into the city.

When Hekmatyar's forces had overrun Pul-e-Charkhi prison, while still in the centre of Kabul, they had set free all the inmates, including many criminals who were able to take arms and commit gruesome actions against the population. With the government institutions either collapsing or participating in the factional fighting, maintaining order in Kabul became almost impossible. The scene was set for the next phase of the war.

Timeline

1992
April–May

The immediate objective of the interim government was to defeat the forces acting against the peace agreement (the Peshawar Accord), particularly Hekmatyar's Hezb-i Islami (backed by Pakistan) but later to include Mazari's Wahdat (backed by Iran) and Dostum's Junbish (backed by Uzbekistan).

The forces of Jamiat and Shura-e Nazar entered the city, with agreement from Nabi Azimi and the commander of the Kabul garrison, General Abdul Wahid Baba Jan, that they would enter the city through Bagram, Panjshir, Salang and Kabul Airport. Many government forces, including generals, joined Jamiat, including the troops of General Baba Jan, who was at the time in charge of the garrison of Kabul. On April 27, all major parties had entered the city.

Meanwhile, in Western Kabul, an area that would later see some of the fiercest fighting and greatest massacres of the war, Sayyaf's mostly Pashtun forces began to enter the city from Paghman and Maidan Shar.

As mentioned above, Kabul came completely under the control of the interim government on April 30, 1992, and hopes were rising for a new era. But the situation was far from stabilized. The Hezb-i Islami had been driven out, but they were still within artillery range, and soon started firing tens of thousands of rockets into the city. Fighting between Hezb-i Islami and Junbish occurred in the Shashdarak area of Kabul. On May 5–6, 1992, Hizb-i Islami subjected Kabul to a heavy artillery bombardment, killing and injuring an unknown number of civilians. On May 23, 1992, despite a cease-fire, the forces of Junbish-i Milli bombarded Hizb-i Islami positions in Bini Hissar, Kalacha and Kart-iNau.

Peace talks on May 25, 1992, originally agreed to give Hekmatyar the position of prime minister. However, this lasted less than a week after Hekmatyar had attempted to shoot down the plane of President Sibghatullah Mojaddedi. Furthermore, as part of the peace talks, Hekmatyar was demanding the departure of Dostum's forces, which would have tilted the scales.

On May 30, 1992, during fighting between the forces of Junbish-i Milli and Hizb-i Islami in the southeast of Kabul, both sides used artillery and rockets killing and injuring an unknown number of civilians. Shura-e Nazar forces were said to have been around the customs post on Jalalabad Road under the command of Gul Haidar and Baba Jalandar, who also were active in the areas such as the military university.

June–July

In June 1992, as scheduled, Burhanuddin Rabbani became President of Afghanistan.

From the onset of the battle, Jamiat and Shura-e Nazar controlled the strategic high areas, and were thus able to develop a vantage point within the city from which opposition forces could be targeted. Hekmatyar continued to bombard Kabul with rockets. Although Hekmatyar insisted that only Islamic Jihad Council areas were targeted, the rockets mostly fell over the houses of innocent civilians of Kabul, a fact which has been well-documented. Artillery exchanges quickly broke out, escalating in late May-early June. Shura-i Nazar was able to immediately benefit from heavy weapons left by fleeing or defecting government forces and launched rockets on Hekmatyar's positions near the Jalalabad Customs Post, and in the districts around Hood Khil, Qala-e Zaman Khan and near Pul-i Charkhi prison. On June 10, it was reported that Dostum's forces had also begun nightly bombardments of Hezb-i Islami positions.

Particularly noticeable in this period was the escalation of the fight in West Kabul between the Shi'a Wahdat forces supported by Iran and those of the Wahhabist Ittihad militia supported by Saudi Arabia. Wahdat was somewhat nervous about the presence of Ittihad posts which were deployed in Hazara areas such as Rahman Baba High school. According to reports by Nabi Azimi, who at the time was a high ranking governor, the fighting began on May 31, 1992, when four members of Hezb-e Wahdat's leadership were assassinated near the Kabul Silo. Those killed were Karimi, Sayyid Isma'il Hosseini, Chaman Ali Abuzar and Vaseegh, the first three being members of the party's central committee. Following this, the car of Haji Shir Alam, a top Ittihad commander, was stopped near Pol-e Sorkh, and although Alem escaped, one of the passengers was killed. On June 3, 1992, heavy fighting between forces of Ittihad-i Islami and Hizb-I Wahdat in West Kabul broke out. Both sides used rockets, killing and injuring civilians. On June 4, interviews with Hazara households stated that Ittihad forces looted their houses in Kohte-e Sangi, killing six civilians. The gun battles at this time had a death toll of over 100 according to some sources. On June 5, 1992, further conflicts between forces of Ittihad and Hizb-i Wahdat in West Kabul were reported. Here, both sides used heavy artillery, destroying houses and other civilian structures. Three schools were reportedly destroyed by bombardment, and an unknown number of civilians were injured or killed. Gunmen were reported killing people in shops near the Kabul Zoo. On June 24, 1992, the Jamhuriat hospital located near the interior ministry was bombed and closed. Jamiat and Shura-e Nazar forces sometimes joined the conflict when their positions came under attack by Wahdat forces and in June and July bombarded Hizb-i Wahdat positions in return. Harakat forces also sometimes joined the fight.

August–December

In the month of August, a bombardment of artillery shells, rockets and fragmentation bombs killed over 2,000 people in Kabul, most of them civilians. On August 1 the airport was attacked by rockets. One hundred and fifty rockets were launched the following day, and according to one author, these missile attacks killed as many as 50 people and injured 150. In the early morning on August 10 Hezb-e Islami forces attacked from three directions—Chelastoon, Darulaman and Maranjan mountain. A shell also struck a Red Cross hospital. On April 10–11 nearly a thousand rockets hit parts of Kabul including about 250 hits on the airport. Some estimate that as many as 1,000 were killed, with the attacks attributed to Hekmatyar's forces. By August 20 it was reported that 500,000 people had fled Kabul. On August 13, 1992, a rocket attack was launched on Deh Afghanan in which cluster bombs were used. Eighty were killed and more than 150 injured, according to press reports. In response to this, Shura-e Nazar forces hit Kart-I Naw, Shah Shaheed and Chiilsatoon with aerial and ground bombardment. In this counterattack, more than 100 were killed and 120 wounded.

Hezb-i Islami was not, however, the only perpetrator of indiscriminate shelling of civilians. Particularly in West Kabul, Wahdat, Ittihad and Jamiat all have been accused of deliberately targeting civilian areas. All sides used non-precision rockets such as Sakre rockets and the UB-16 and UB-32 S-5 airborne rocket launchers.

In November, in a very effective move, Hekmatyar's forces, together with guerrillas from some of the Arab groups, barricaded a power station in Sarobi, 30 miles east of Kabul, cutting electricity to the capital and shutting down the water supply, which is dependent on power. His forces and other Mujahideen were also reported to have prevented food convoys from reaching the city.

On November 23, Minister of Food Sulaiman Yaarin reported that the city's food and fuel depots were empty. The government was now under heavy pressure. At the end of 1992 Hizb-i Wahdat officially withdrew from the government and opened secret negotiations with Hizb-I Islami. In December 1992, Rabbani postponed convening a shura to elect the next president. On December 29, 1992, Rabbani was elected as president and he agreed to establish a parliament with representatives from all of Afghanistan. Also notable during this month was the solidification of an alliance between Hezb-i Wahdat and Hezb-i Islami against the Islamic State of Afghanistan. While Hizb-i Islami joined in bombardments to support Wahdat, Wahdat conducted joint offensives, such as the one to secure Darulaman. On December 30, 1992, at least one child was apparently killed in Pul-i Artan by a BM21 rocket launched from Hezb-i Islami forces at Rishkor.

About the bombardments

Throughout the war, the most devastating aspect of it remained the indiscriminate shelling of the city by Gulbuddin Hekmatyar and later Rashid Dostum. Although most sides engaged in bombardments, some were more indiscriminate in their targeting.

As Jamiat-i controlled the strategic high areas, they were better able to target specific military objectives rather than resorting to indiscriminate shelling as other factions such as Hezb-i Islami had done. According to the officer, the 3rd Regiment deployed in the Darulaman area, where Wahdat Corps had based their artillery commander, as well as the area near the Russian Embassy where Wahdat's Division 096, were particularly targeted by the long ranged rockets. Charasyab, which housed Hizb-i Islami's artillery, Shiwaki, where the intelligence department was deployed and the Rishkor Division were also targeted, in addition to the Dasht-I Saqawa airport in Logar Province.

By far the worst perpetrator of attacks against non-military targets were the forces of Hizb-i Islami. These included attacks against hospitals and a bombing attack on the headquarters of the International Red Cross. There was general indiscriminate bombing starting in August.

In 1994 the forces of Rashid Dostum were involved in indiscriminate shelling.

Kandahar at the same time

Kandahar was filled with three different local Pashtun commanders Amir Lalai, Gul Agha Sherzai and Mullah Naqib Ullah who engaged in an extremely violent struggle for power and who were not affiliated with the interim government in Kabul. The bullet-riddled city came to be a center of lawlessness, crime and atrocities fuelled by complex Pashtun tribal rivalries.

1993
January–February
On January 3, 1993, Burhanuddin Rabbani, the leader of the Jamiat-i Islami Party, was sworn in as president. However, Rabbani's authority remained limited to only part of Kabul; the rest of the city remained divided among rival militia factions. On January 19, a short-lived cease-fire broke down when Hezb-i Islami forces renewed rocket attacks on Kabul from their base in the south of the city supervised by Commander Toran Kahlil. Hundreds were killed and wounded while many houses were destroyed in this clash between Hizb-i Islami and Jamiat-i Islami.

Heavy fighting was reported around a Wahdat post held by Commander Sayid Ali Jan near Rabia Balkhi girls' school. Most notable during this period was the rocket bombardments which would start against the residential area of Afshar. Some of these areas, such as Wahdat's headquarters at the Social Science Institute, were considered military targets, a disproportionate number of the rockets, tank shells and mortars fell in civilian areas. Numerous rockets were reportedly launched from Haider-controlled frontlines of Tap-I Salaam towards the men of Division 095 under Ali Akbar Qasemi. One attack during this time from Wahdat killed at least nine civilians. Further rockets bombardments took place on February 26, 1993, as Shura-e Nazar and Hezb-i Islami bombarded each other's positions. Civilians were the main victims in the fighting which killed some 1,000 before yet another peace accord was signed on March 8. However, the following day rocketing by Hekmatyar's Hezb-i Islami and Hezb-i Wahdat in Kabul left another 10 dead.

Afshar

The Afshar Operation was a military operation by Burhanuddin Rabbani's Islamic State of Afghanistan government forces against Gulbuddin Hekmatyar's Hezb-i Islami and Hezb-i Wahdat forces that took place in February 1993. The Iran-controlled Hezb-i Wahdat, together with the Pakistani-backed Hezb-i Islami of Hekmatyar, were shelling densely populated areas in Kabul from their positions in Afshar. To counter these attacks, Islamic State forces attacked Afshar in order to capture the positions of Wahdat, capture Wahdat's leader Abdul Ali Mazari and to consolidate parts of the city controlled by the government. The operation took place in a densely populated district of Kabul, the Afshar District. The Afshar District is situated on the slopes of Mount Afshar in West Kabul. The district is predominantly home to the Hazara ethnic group. The Ittihad troops of Abdul Rasul Sayyaf escalated the operation into a rampage against civilians. Both Ittihad and Wahdat forces severely targeted civilians in the war. The Wahhabist Ittihad supported by Saudi Arabia was targeting Shias, while the Iran-controlled Wahdat was targeting Sunni Muslims as well as their own people.

March–December

Under the March accord, brokered by Pakistan and Saudi Arabia, Rabbani and Hekmatyar agreed to share power until elections could be held in late 1994. Hekmatyar's condition had been the resignation of Massoud as minister of defense. The parties agreed to a new peace accord in Jalalabad on May 20 under which Massoud agreed to relinquish the post of defense minister. Massoud had resigned in order to gain peace. Hekmatyar at first accepted the post of prime minister but after attending only one cabinet meeting he left Kabul again starting to bomb Kabul leaving more than 700 dead in bombing raids, street battles and rocket attacks in and around Kabul. Massoud returned to the position of minister of defense to defend the city against the rocket attacks.

1994
January–June
The war changed dramatically in January 1994. Dostum, for different reasons, joined with the forces of Gulbuddin Hekmatyar.
Hezb-i Islami, along with their new allies of Wahdat and Junbish-i Milli, launched the Shura Hamaghangi campaign against the forces of Massoud and the interim government. During this, Hezb-i Islami was able make use of Junbish's air force in both bombing the positions of Jamiat and in resupplying their men. This led to greater artillery bombardment on behalf of Hezb-i Islami. Hezb-i Islami and Junbish were able to hold parts of central Kabul during this time. Junbish forces were particularly singled out for committing looting, rape and murder. Some commanders such as Shir Arab, commander of the 51st Regiment, Kasim Jangal Bagh, Ismail Diwaneh ["Ismail the Mad"], and Abdul Cherikwere particularly singled out. According to the Afghanistan Justice Project, during this period until June 1994, 25,000 people were killed. Areas around Microraion were particularly bloody. By now the population of Kabul had dropped from 2 million during Soviet times to 500,000 due to a large exodus from Kabul.

However, by the end of 1994 Junbish and Dostum were on the defensive, and Massoud's forces had ousted them from most of their strongholds. Massoud more and more gained control of Kabul. At the same time, Junbish was able to push Jamiat out of Mazar-e Sharif.

July–December
Significant changes occurred in 1994 in how the war was conducted and who fought which side. The Taliban movement first emerged on the military scene in August 1994, with the stated goal of liberating Afghanistan from its present corrupt leadership of warlords and establishing a pure Islamic society. By October 1994, the Taliban movement had attracted the support of Pakistan, which was unhappy with the unsuccessful Hekmatyar, which saw in the Taliban a way to secure trade routes to Central Asia and establish a government in Kabul friendly to its interests. Pakistani traders who had long sought a secure route to send their goods to Central Asia quickly became some of the Taliban's strongest financial backers. The Pakistanis also wished for a stable government to take hold in Afghanistan, regardless of ideology, in hopes that the 3 million Afghans who for 15 years had taken refuge in Pakistan would return to their homeland since the refugee population became increasingly viewed as a burden.

In October 1994, a bomb struck a wedding ceremony in Qala Fathullah in Kabul, killing 70 civilians. No fighting had been witnessed in the area in several days according to reports.

Also in October 1994, the Taliban revolted in Kandahar, capturing the city on November 5, 1995, and soon going on to capture most of the south.

1995
The Taliban soon began to approach Kabul, capturing Wardak in early February and Maidshahr, the provincial capital on February 10, 1995. On February 14, 1995, Hekmatyar was forced to abandon his artillery positions at Charasiab due to the advance of the Taliban. The Taliban were therefore able to take control of this weaponry. In March, Massoud launched an offensive against Hezb-e Wahdat. Mazari allied himself with the Taliban, allowing them to enter Kabul, although many of Wahdat's forces joined Massoud instead. Massoud's forces heavily bombarded Western Kabul driving Wahdat out. According to other reports the forces of Jamiat-e Islami also committed mass rape and executions on civilians in this period. The Taliban retreated under this, taking Mazari with them and throwing him from a helicopter en route to Kandahar. The Taliban then continued to launch offensives against Kabul, using the equipment of Hezbe Islami. While the Taliban retreated, large amounts of looting and pillaging was said to have taken place in southwestern Kabul by the forces under Rabbani and Massoud.

In March 1995, Massoud's forces were able to drive out the Taliban from the area around Kabul, and retake Charasiab, leading to a relative period of calm for a few months. The battle left hundreds of Taliban dead and the force suffered its first defeat.

In October, the Taliban retook Charasiab. Between November 11–13, 1995, at least 57 unarmed civilians were killed and over 150 injured when rockets and artillery barrages fired from Taleban positions south of Kabul pounded the civilian areas of the city. On November 11, 36 civilians were killed when over 170 rockets as well as shells hit civilians areas. A salvo crashed into Foruzga Market. Rockets struck the Taimani District where many people from other parts of Kabul had settled. Other residential areas hit by artillery and rocket attacks were the Bagh Bala District in the northwest of Kabul and Wazir Akbar Khan where much of the city's small foreign community live.

On November 20, 1995, the forces of the Taliban gave the government a five-day ultimatum after which they would resume bombardment if Rabbani and his forces did not leave the city. This ultimatum was eventually withdrawn.

By the end of November and December, more than 150 people had died in Kabul due to the repeated rocketing, shelling and high-altitude bombing of the city, reportedly by Taliban forces.

1996

In September 1996 the Taliban seized Kabul. In its first action, the Islamic militant group publicly hanged former president, Najibullah, and his brother, perceiving them to be puppets loyal to nations other than Afghanistan. All key government installations appeared to be in the Taliban's hands within hours, including the presidential palace and the ministries of defense, security and foreign affairs. The Islamic Emirate of Afghanistan was proclaimed, securing recognition from Saudi Arabia, Pakistan, the United Arab Emirates and the partially recognized Chechen Republic of Ikheria. A rigidly strict version of Sharia was imposed upon the population.

Massoud's militia and other groups decided to retreat to the north to reduce civilian casualties. The United Islamic Front for the Salvation of Afghanistan, a coalition of various armed factions known in the Pakistani and Western media as the "Northern Alliance", was constituted in opposition to the Taliban under the leadership of Massoud.

References

Bibliography

External links
Afghanistan – the Squandered Victory (documentary film) by the BBC
(documentary film directly from the year 1989 explaining the beginning of the turmoil to follow)

Massoud's Conversation with Hekmatyar (original document from 1992)

Commander Massoud's Struggle (documentary film) by Nagakura Hiromi
(from 1992, one month after the collapse of the communist regime, after Hekmatyar was repelled to the southern outskirts of Kabul, before he started the heavy bombardment of Kabul with the support of Pakistan)

Starving to Death Afghanistan (documentary report) by Journeyman Pictures/ABC Australia
(from March 1996)

20th century in Kabul
1990s conflicts
1990s in Afghanistan
Afghan Civil War (1992–1996)
Afghanistan conflict (1978–present)
First Siege of Kabul (1992–1995)
History of Afghanistan (1992–present)
Military history of Afghanistan
Modern history of Afghanistan
Taliban
Warlordism

Battle of Kabul (1992–1996)


In computer science, amortized analysis is a method for analyzing a given algorithm's complexity, or how much of a resource, especially time or memory, it takes to execute.  The motivation for amortized analysis is that looking at the worst-case run time can be too pessimistic.  Instead, amortized analysis averages the running times of operations in a sequence over that sequence.
As a conclusion: "Amortized analysis is a useful tool that complements other techniques such as worst-case and average-case analysis."

For a given operation of an algorithm, certain situations (e.g., input parametrizations or data structure contents) may imply a significant cost in resources, whereas other situations may not be as costly.  The amortized analysis considers both the costly and less costly operations together over the whole sequence of operations.  This may include accounting for different types of input, length of the input, and other factors that affect its performance.

History
Amortized analysis initially emerged from a method called aggregate analysis, which is now subsumed by amortized analysis. The technique was first formally introduced by Robert Tarjan in his 1985 paper Amortized Computational Complexity, which addressed the need for a more useful form of analysis than the common probabilistic methods used. Amortization was initially used for very specific types of algorithms, particularly those involving binary trees and union operations. However, it is now ubiquitous and comes into play when analyzing many other algorithms as well.

Method

Amortized analysis requires knowledge of which series of operations are possible. This is most commonly the case with data structures, which have state that persists between operations. The basic idea is that a worst-case operation can alter the state in such a way that the worst case cannot occur again for a long time, thus "amortizing" its cost.

There are generally three methods for performing amortized analysis: the aggregate method, the accounting method, and the potential method. All of these give correct answers; the choice of which to use depends on which is most convenient for a particular situation.

Aggregate analysis determines the upper bound T(n) on the total cost of a sequence of n operations, then calculates the amortized cost to be T(n) / n.
The accounting method is a form of aggregate analysis which assigns to each operation an amortized cost which may differ from its actual cost.  Early operations have an amortized cost higher than their actual cost, which accumulates a saved "credit" that pays for later operations having an amortized cost lower than their actual cost.  Because the credit begins at zero, the actual cost of a sequence of operations equals the amortized cost minus the accumulated credit.  Because the credit is required to be non-negative, the amortized cost is an upper bound on the actual cost.  Usually, many short-running operations accumulate such credit in small increments, while rare long-running operations decrease it drastically.
The potential method is a form of the accounting method where the saved credit is computed as a function (the "potential") of the state of the data structure.  The amortized cost is the immediate cost plus the change in potential.

Examples

Dynamic array

Consider a dynamic array that grows in size as more elements are added to it, such as  in Java or  in C++.  If we started out with a dynamic array of size 4, we could push 4 elements onto it, and each operation would take constant time.  Yet pushing a fifth element onto that array would take longer as the array would have to create a new array of double the current size (8), copy the old elements onto the new array, and then add the new element.  The next three push operations would similarly take constant time, and then the subsequent addition would require another slow doubling of the array size.

In general if we consider an arbitrary number of pushes n + 1 to an array of size n, we notice that push operations take constant time except for the last one which takes  time to perform the size doubling operation.  Since there were n + 1 operations total we can take the average of this and find that pushing elements onto the dynamic array takes: , constant time.

Queue
Shown is a Python3 implementation of a Queue, a FIFO data structure:
# Define a class named Queue
class Queue:
  # Define the constructor method that initializes two empty lists
  def __init__(self):
    self.input = [] # This list will store the elements that are enqueued
    self.output = [] # This list will store the elements that are dequeued

  # Define a method named enqueue that takes an element as a parameter
  def enqueue(self, element):
    self.input.append(element) # Append the element to the input list

  # Define a method named dequeue that returns the first element that was enqueued
  def dequeue(self):
    if not self.output: # If the output list is empty
      while self.input: # While the input list is not empty
        self.output.append(self.input.pop()) # Pop the last element from the input list and append it to the output list

    return self.output.pop() # Pop and return the last element from the output list

The enqueue operation just pushes an element onto the input array; this operation does not depend on the lengths of either input or output and therefore runs in constant time.

However the dequeue operation is more complicated.  If the output array already has some elements in it, then dequeue runs in constant time; otherwise, dequeue takes  time to add all the elements onto the output array from the input array, where n is the current length of the input array.  After copying n elements from input, we can perform n dequeue operations, each taking constant time, before the output array is empty again. Thus, we can perform a sequence of n dequeue operations in only  time, which implies that the amortized time of each dequeue operation is .

Alternatively, we can charge the cost of copying any item from the input array to the output array to the earlier enqueue operation for that item.  This charging scheme doubles the amortized time for enqueue but reduces the amortized time for dequeue to .

Common use
 In common usage, an "amortized algorithm" is one that an amortized analysis has shown to perform well.
 Online algorithms commonly use amortized analysis.

References

Literature

Analysis of algorithms
Articles with example Ruby code

Amortized analysis


Thin Ice is a 1937 American romantic comedy movie directed by Sidney Lanfield and starring Sonja Henie, Tyrone Power, Arthur Treacher, Raymond Walburn, Joan Davis. It was distributed by 20th Century Fox and was nominated for an Academy Award in 1938.

Plot
The film's plot revolves around Lili Heiser, a skate instructor working at a luxurious hotel in the Swiss Alps. Lili falls in love with a man who regularly goes skiing in the mornings, believing him to be an ordinary tourist. However, she is unaware that he is actually a prince trying to escape the pressures of his royal life.

The movie prominently showcases the skating talents of Sonja Henie, who had previously won gold in the Winter Olympics. Henie transitioned to a successful career as a professional film actress in 1936. The film also features Tyrone Power, who was in the early stages of his acting career at the time.

Other websites

1937 comedy movies
American romantic comedy movies
20th Century Fox movies
Movies directed by Sidney Lanfield

Thin Ice (1937 movie)


Guerrant House is a historic home located near Arvonia, Buckingham County, Virginia. It was built about 1835, and consists of a -story, two room frame house with a separate kitchen set perpendicular to the rear of the main block.  It features typical Federal period decorative and construction details.  They include beaded weatherboards, a boxed cornice with dentils, and shouldered chimneys.

It was listed on the National Register of Historic Places in 2000.

References

Federal architecture in Virginia
Houses completed in 1835
Houses on the National Register of Historic Places in Virginia
Houses in Buckingham County, Virginia
National Register of Historic Places in Buckingham County, Virginia

Guerrant House (Arvonia, Virginia)


Edward Holmes (1797 – 28 August 1859) was an English musicologist, music critic, pianist, and music educator. Born just outside London, he was a pupil of Vincent Novello. He spent his early career earning a living as a piano teacher. In 1827 he visited Germany, and upon returning to England published his first book, A Ramble among the Musicians of Germany (1828; 3d ed., 1838). Impressed with his skills as a writer on music, the owner of The Atlas hired him as a music critic where he remained for many years. In 1849 he immigrated to the United States where he spent the last ten years of his life working as an editor and music critic. He also contributed articles to several music journals during his career, including The Musical Times. His other works include The Life of Mozart (1845), Life of Purcell, for Novello's Sacred Music, and Analytical and Thematic Index of Mozart's Piano-works.

References

Notes

1797 births
1859 deaths
English music critics
English musicologists
19th-century musicologists

Edward Holmes (musicologist)