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Kerala School of Astronomy and Mathematics

The Kerala School of Astronomy and Mathematics was a school of mathematics and astronomy founded by Madhava of Sangamagrama in Kerala, which included among its members: Parameshvara, Neelakanta Somayaji, Achyuta Pisharati, Melpathur Narayana Bhattathiri and Achyuta Panikkar. The school flourished between the 14th and 16th centuries and the original discoveries of the school seems to have ended with Narayana Bhattathiri. In attempting to solve astronomical problems, the Kerala school independently discovered a number of important mathematical concepts, their most important results—series expansion for trigonometric functions—were described in Sanskrit verse in a book by Neelakanta called Tantrasangraha, again in a commentary on this work, called Tantrasangraha-vakhya, of unknown authorship. The theorems were stated without proof, but proofs for the series for sine and inverse tangent were provided a century in the work Yuktibhasa, written in Malayalam, by Jyesthadeva, in a commentary on Tantrasangraha.

Their work, completed two centuries before the invention of calculus in Europe, provided what is now considered the first example of a power series. However, they did not formulate a systematic theory of differentiation and integration, nor is there any direct evidence of their results being transmitted outside Kerala; the Kerala school has made a number of contributions to the fields of infinite series and calculus. These include the following geometric series: The Kerala school made intuitive use of mathematical induction, though the inductive hypothesis was not yet formulated or employed in proofs, they used this to discover a semi-rigorous proof of the result: for large n. They applied ideas from differential and integral calculus to obtain infinite series for sin ⁡ x, cos ⁡ x, arctan ⁡ x; the Tantrasangraha-vakhya gives the series in verse, which when translated to mathematical notation, can be written as: where, for r = 1, the series reduce to the standard power series for these trigonometric functions, for example: The Kerala school made use of the rectification of the arc of a circle to give a proof of these results.

They made use of the series expansion of arctan ⁡ x to obtain an infinite series expression for π: Their rational approximation of the error for the finite sum of their series are of particular interest. For example, the error, f i, for the series: They manipulated the terms, using the partial fraction expansion of: 1 n 3 − n to obtain a more converging series for π: They used the improved series to derive a rational expression, 104348 / 33215 for π correct up to nine decimal places, i.e. 3.141592653. They made use of an intuitive notion of a limit to compute these results; the Kerala school mathematicians gave a semi-rigorous method of differentiation of some trigonometric functions, though the notion of a function, or of exponential or logarithmic functions, was not yet formulated. In 1825 John Warren published a memoir on the division of time in southern India, called the Kala Sankalita, which mentions the discovery of infinite series by Kerala astronomers; the works of the Kerala school were first written up for the Western world by Englishman C. M. Whish in 1835.

According to Whish, the Kerala mathematicians had "laid the foundation for a complete system of fluxions" and these works abounded "with fluxional forms and series to be found in no work of foreign countries". However, Whish's results were completely neglected, until over a century when the discoveries of the Kerala school were investigated again by C. T. Rajagopal and his associates, their work includes commentaries on the proofs of the arctan series in Yuktibhasa given in two papers, a commentary on the Yuktibhasa's proof of the sine and cosine series and two papers that provide the Sanskrit verses of the Tantrasangrahavakhya for the series for arctan and cosine. In 1952 Otto Neugebauer wrote on Tamil astronomy. In 1972 K. V. Sarma published his A History of the Kerala School of Hindu Astronomy which described features of the School such as the continuity of knowledge transmission from the 13th to the 17th century: Govinda Bhattathiri to Parameshvara to Damodara to Nilakantha Somayaji to Jyesthadeva to Acyuta Pisarati.

Transmission from teacher to pupil conserved knowledge in "a practical, demonstrative discipline like astronomy at a time when there was not a proliferation of printed books and public schools." In 1994 it was argued that the heliocentric model had been adopted about 1500 A. D. in Kerala. A. K. Bag suggested in 1979 that knowledge of these results might have been transmitted to Europe through the trade route from Kerala by traders and Jesuit missionarie

Attleborough Academy

Attleborough Academy Norfolk is a coeducational secondary school and sixth form with academy status, located in Attleborough in the English county of Norfolk. A community school administered by Norfolk County Council, Attleborough High School became a specialist Mathematics and Computing College in 2008; as part of this, the school became a Microsoft®Academy in 2010. In May 2013 the school launched a consultation on the possibility of converting to academy status. Attleborough High School formally became an academy on 1 January 2014, was renamed Attleborough Academy Norfolk; the school is now sponsored by the TEN Group. Attleborough Academy offers GCSEs, NVQs and BTEC First Certificates as programmes of study for pupils; the sixth form centre offers A Levels and advanced BTECs, some of which are offered in partnership with Wymondham College. For the school's 2016 GCSE results, the Progress 8 score of 0.04, in line with the average Progress 8 for schools in England, 65% of students achieved grades A*-C in GCSE English and Maths.

A-Level results were below the national average, with a progress score of -0.27 and an average grade of D. In March 2009, a 16-year-old student posted a threat on the website Newgrounds stating that he would go to the school with a gas canister, set fire to the building and commit other acts of violence. A Newgrounds user from Montreal, Canada notified English authorities via Skype after seeing the threat; the student was found carrying a knife, matches and a plastic gas canister containing flammable liquid, was arrested for threats to commit criminal damage and possession of an offensive weapon, to which he admitted. He was held under the Mental Health Act. Attleborough Academy official website

Von Dutch

Von Dutch is an American multinational apparel brand named after Kenny Howard, a.k.a. "Von Dutch", an American artist and pinstriper of the Kustom Kulture movement. After Howard's death in 1992, his daughters sold the Von Dutch name to Michael Cassel and Robert Vaughn; the clothing brand gained popularity in the US and attracted the attention of celebrities such as Paris Hilton, Whitney Houston, Britney Spears, Justin Timberlake, Jay-Z, Lance Pedersen and Ashton Kutcher and Eric Church. The French stylist Christian Audigier helped popularize the brand, left it in 2004; the company was purchased in 2009 by Groupe Royer S. A. through its Luxembourg subsidiary Royer Brands International S.a.r.l. Groupe Royer is the largest shoe distributor in Europe, distributing brands including Converse, New Balance, Charles Jourdan; the Von Dutch Brand has licensees in the U. S. Europe, Malaysia, China, the Philippines and Brazil; the brand is headquartered in Los Angeles for marketing, social media and collections approval activities.

The C. E. O. is Olivier Mercier. Tonny Sorensen Official website

Type 89 grenade discharger

The Type 89 Grenade Discharger and colloquially known as a knee mortar by Allied forces, is a Japanese grenade launcher or light mortar, used in the Pacific Ocean theatre of World War II. The Japanese Army, noting that grenades were short-ranged weapons, began efforts to optimize these weapons for close-in infantry fighting. After studying employment of grenades and mortars on the battlefield, the Japanese Army developed hand grenades, rifle grenades, grenade/mortar shell dischargers suited to warfare in typical short-range combat environments such as urban and jungle warfare; as part of this effort, the Japanese Army had adopted by 1932 a set of fragmentation grenades with universal adaptability. The Type 91 fragmentation grenade could be thrown by hand, fired from a spigot-type launcher, or used in a mortar-like grenade discharger, the Type 89; the Type 89 Heavy Grenade Discharger was adopted in 1929 but production did not begin until 1932. It differs from the earlier Type 10 grenade discharger.

The Type 89 could fire two types of grenades or shells: the Type 91 Grenade, a normal infantry fragmentation grenade adapted to the Type 89 discharger, the Type 89 50 mm shell, an impact-detonated shell with more explosive power. When fired from the Type 89 discharger, the Type 91 fragmentation grenade was fitted with a propellant base and time fuse, it was designed to ignite its fuse while in flight. A weak creep spring inside the grenade firing mechanism allowed the firing pin to be thrown back upon launching, igniting a time fuse with a 7-8 second delay. Using this system, the Type 91 grenades could be launched through jungle cover or through small openings without the danger of premature detonation in the event the grenade struck an object on its way to the target. Although the Type 89 could be fired by a single person, it was operated with a crew of 3, enabling it to reach a rate of fire of about 25 rounds per minute; the Type 89 discharger could be used with a more powerful impact-detonated shell approaching the power of a light mortar.

Weighing two pounds, it was known as the Type 89 50mm shell, was made in high explosive and smoke variants. To fire the shell, it was dropped base-down inside the tube of the discharger. By setting the Type 89 discharger at a fixed angle of 45 degrees, varying distance to target by adjusting the size of a variable chamber space inside the discharger mechanism, soldiers could adjust fire onto multiple targets at varying ranges while firing the contact-detonated 50 mm shell through a single small clearing in the jungle canopy; the method worked well when firing from deep trenches or pits, or between various building obstructions when fighting inside a built-up town or city. With its curved support plate, the Type 89 was designed to be placed on the ground or against a log or trunk at a fixed firing angle of 45 degrees. However, since it used a spring-loaded, lanyard-operated firing pin mechanism, in an emergency it could fire grenades or shells at point targets while braced horizontally against a tree or building.

The Type 89 discharger first saw service in Manchuria. During World War II, the weapon was used in Burma and the Pacific islands; the Japanese Navy paratroopers carried special containers for the Type 89 clipped to their harnesses to provide fire support right on the landing zone. Allied troops soon learned to hit the ground when they heard the telltale "pop" of the weapon launching its grenades or shells, in some cases from more than 200 yards away; some Allied infantrymen mistakenly assumed that the launcher's curve plate was propped on the leg to fire and thereafter referred to it as a "knee mortar." However, any soldier or marine who tried to fire a captured Type 89 in this fashion received a severe bruise from the hefty recoil. After World War II the Type 89 was used by Indonesian National Army and militias against Dutch forces in the Indonesian National Revolution, with copies of the weapon manufactured in Demakijo, Yogyakarta. Others were used by Communist forces during Chinese Civil Korean War.

Some were used by the Việt Minh during First Indochina War and by the Viet Cong during the Vietnam War. Type 89 50mm HE mortar shell. Type 91 Fragmentation Grenade. Type 94 50mm practice shell Smoke shell weight: 0.9 kg containing 0.11 kg of HC type smoke mixture. Incendiary shell weight: 0.57 kg containing 0.32 kg of incendiary material. China Japan: Imperial Japanese Army Indonesia: Indonesian National Army North Korea Vietnam Leo J. Daugherty III, Fighting Techniques of a Japanese Infantryman 1941–1945, ISBN 1-86227-162-3 Gordon L Rottman, Japanese Infantryman 1937-45 Sword of the empire, ISBN 1-84176-818-9 US Army field manual TM-E 30-480 at hyperwar Taki U. S. World War II Intel Report on Japanese Smoke Grenades Lance-grenade individuel Mle F1, a French close-support weapon infantry weapon designed to be used by one man. Commando mortar, a class of infantry light mortars designed for maximum portability and rapid deployment, at the expense of accuracy and repeatability. Nambu World: Type 89 “Knee Mortar” Type 91 grenade at Type 89 grenade at Colour pictures of the Type 89 and Type 10 at

Tom Cullerton

Tom Cullerton is a member of the Illinois Senate representing the 23rd district since 2013. The 23rd district spans northern DuPage County and includes all or parts of Addison, Bartlett, Carol Stream, Glendale Heights, Hanover Park, Roselle, Villa Park, West Chicago and Wood Dale. Prior to his service in the Illinois Senate he was the Village President of Villa Park from 2009 to 2013 and served one term as a village trustee from 2005 to 2009. After graduating high school from Loyola Academy Cullerton went to Kansas University. In 1990 Cullerton enlisted in the US Army and served as an 11H TOW Gunner until being honorably discharged in 1993. After moving to DuPage County, Cullerton decided to become active in the community, he served as a captain a local neighborhood watch. He became a member of the Knights of Columbus, the American Legion, coaches little league with his team winning the 2011 Farm League World Series, he is married to his wife and they have three sons. A distant cousin, John Cullerton, served as President of the Senate.

In 2005 Tom Cullerton was elected a trustee for Villa Park. He served one term before defeating incumbent Joyce Stupegia in a three-way race to become Village President in 2009. While in office he was an active member of the DuPage Mayors & Managers Conference and the Metropolitan Mayors. While Village President, the other mayors from municipalities in DuPage County Board District 2 elected him to serve as their representative on the DuPage Water Commission; that year, Cullerton was recognized by the Sierra Club for reducing the village's carbon footprint via Cool Cities. In the 2013 municipal elections, Cullerton was succeeded as Village President by Deb Bullwinkle. In November 2011 Tom Cullerton announced his candidacy for state senate in the newly redrawn 23rd district. In the March 2012 primary he won the Democratic nomination defeating two perennial candidates. In the general election he faced incumbent State Senator Carole Pankau, the winner of the Republican nomination against State Representative Randy Ramey.

Cullerton was endorsed by the Illinois AFL-CIO, Personal PAC, Planned Parenthood, Equality Illinois and the Illinois Sierra Club. Tom Cullerton won the general election defeating 20 year Springfield incumbent Senator Pankau by a margin of a little over 2,000 votes to become the first Democratic member of the Illinois Senate from DuPage County. Senator Cullerton was first sworn in to represent the 23rd district on January 9, 2013. At the beginning of the General Assembly, Senator Cullerton joined a bipartisan group of lawmakers who turned down a pension as part of the effort to fix the state's pension system. In January 2013, Senator Cullerton proposed his first bill which would allow county boards to more reduce crime in residential areas by adopting crime free rental housing ordinances. In 2012, DuPage County performed a review that found a variety of small units of government that provide mosquito abatement and street lighting services cost taxpayers $300 million annually; these districts included small entities such as the one square mile Century Hill Street Lighting District whose board members had wanted to dissolve the district, but were unable to.

In response, Cullerton introduced SB 494 as a pilot program to allow for consolidation of these types of government bodies. The bill would allow the DuPage County Board to pass ordinances to dissolve thirteen small units of government after an audit issued by the County Board Chair was completed; the dissolution of a district could to be overturned via referendum by voters in that district. The bill’s cosponsors included suburban legislators and it was supported by Republican County Board Chair Dan Cronin. On April 25, the bill was passed unanimously in the Illinois Senate and on May 6, its house counterpart sponsored by Deb Conroy passed the Illinois House of Representatives with 108 yes votes; the bill was signed into law by Pat Quinn in August. Since DuPage County has been able to pass an ordinance to dissolve the Fairview Fire Protection District. In 2015, Representative Jack Franks a co-sponsor of SB 494 proposed legislation to give McHenry and Lake counties the same ability to consolidate small, special purpose districts.

Concerned that Illinois had some of the weakest civic education programs in the country and State Representative Deb Conroy proposed the creation of the Task Force on Civic Education. The commission recommended Illinois establish a requirement for a civics course as a part of a broader revision of the state’s social studies standards, that the state establish a project-based and/or service learning requirement, student involvement in elections and professional development for teachers who teach civics. After the task force released its findings, Cullerton introduced a bill which would put the task force’s recommendations into place; the bill passed the House with 81 votes. The McCormick Foundation and other non-profit organizations pledged $3 million to cover the costs of civics education training for teachers in poorer school districts; the bill was signed into law by Bruce Rauner on August 21, 2015 to take effect during the 2016-2017 school year. Citing the rising costs associated with a college education, Cullerton served as the co-sponsor of a bill that would allow students who achieve at least a 3 on an AP test to receive post-secondary level course credit at public colleges and universities.

This would make Illinois competitive with neighboring states. The colleges themselves would be allowed to decide the number of credits granted for a particular score. DuPage County, the bulk of Cullerton’s district, has seen an increase in heroin use in the county; this was accompanied by an epidemic of overdoses and at one poi

Processor sharing

Processor sharing or egalitarian processor sharing is a service policy where the customers, clients or jobs are all served each receiving an equal fraction of the service capacity available. In such a system all jobs start service immediately; the processor sharing algorithm "emerged as an idealisation of round-robin scheduling algorithms in time-shared computer systems". A single server queue operating subject to Poisson arrivals with a processor sharing discipline has a geometric stationary distribution; the sojourn time jobs experience has no closed form solution in an M/M/1 queue. Generalized processor sharing is a multi-class adaptation of the policy which shares service capacity according to positive weight factors to all non-empty job classes at the node, irrespective of the number of jobs of each class present, it is assumed that the jobs within a class form a queue and that queue is served on a first-come, first-served basis, but this assumption is not necessary for many GPS applications.

In processor scheduling, generalized processor sharing is "an idealized scheduling algorithm that achieves perfect fairness. All practical schedulers approximate GPS and use it as a reference to measure fairness." In multilevel processor sharing a finite set of thresholds are defined and jobs partitioned according to how much service they have received. The lowest level has higher levels monotonically decreasing priorities. Within each level an internal discipline is used