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G. H. Hardy

Godfrey Harold Hardy was an English mathematician, known for his achievements in number theory and mathematical analysis. In biology, he is known for the Hardy -- a basic principle of population genetics. G. H. Hardy is known by those outside the field of mathematics for his 1940 essay A Mathematician's Apology considered one of the best insights into the mind of a working mathematician written for the layperson. Starting in 1914, Hardy was the mentor of the Indian mathematician Srinivasa Ramanujan, a relationship that has become celebrated. Hardy immediately recognised Ramanujan's extraordinary albeit untutored brilliance, Hardy and Ramanujan became close collaborators. In an interview by Paul Erdős, when Hardy was asked what his greatest contribution to mathematics was, Hardy unhesitatingly replied that it was the discovery of Ramanujan. In a lecture on Ramanujan, Hardy said that "my association with him is the one romantic incident in my life". G. H. Hardy was born on 7 February 1877, in Cranleigh, England, into a teaching family.

His father was Art Master at Cranleigh School. Both of his parents were mathematically inclined. Hardy's own natural affinity for mathematics was perceptible at an early age; when just two years old, he wrote numbers up to millions, when taken to church he amused himself by factorising the numbers of the hymns. After schooling at Cranleigh, Hardy was awarded a scholarship to Winchester College for his mathematical work. In 1896 he entered Cambridge. After only two years of preparation under his coach, Robert Alfred Herman, Hardy was fourth in the Mathematics Tripos examination. Years he sought to abolish the Tripos system, as he felt that it was becoming more an end in itself than a means to an end. While at university, Hardy joined an elite, intellectual secret society. Hardy cited as his most important influence his independent study of Cours d'analyse de l'École Polytechnique by the French mathematician Camille Jordan, through which he became acquainted with the more precise mathematics tradition in continental Europe.

In 1900 he passed part II of the Tripos, in the same year he was elected to a Prize Fellowship at Trinity College. In 1903 he earned his M. A., the highest academic degree at English universities at that time. When his Prize Fellowship expired in 1906 he was appointed to the Trinity staff as a lecturer in mathematics, where teaching six hours per week left him time for research. In 1919 he left Cambridge to take the Savilian Chair of Geometry at Oxford in the aftermath of the Bertrand Russell affair during World War I. Hardy spent the academic year 1928–1929 at Princeton in an academic exchange with Oswald Veblen, who spent the year at Oxford. Hardy gave the Josiah Willards Gibbs lecture for 1928. Hardy left Oxford and returned to Cambridge in 1931, becoming again a fellow of Trinity College and holding the Sadleirian Professorship until 1942, he was on the governing body of Abingdon School from 1922-1935. Hardy is credited with reforming British mathematics by bringing rigour into it, a characteristic of French and German mathematics.

British mathematicians had remained in the tradition of applied mathematics, in thrall to the reputation of Isaac Newton. Hardy was more in tune with the cours d'analyse methods dominant in France, aggressively promoted his conception of pure mathematics, in particular against the hydrodynamics, an important part of Cambridge mathematics. From 1911 he collaborated with John Edensor Littlewood, in extensive work in mathematical analysis and analytic number theory; this led to quantitative progress on Waring's problem, as part of the Hardy–Littlewood circle method, as it became known. In prime number theory, they proved some notable conditional results; this was a major factor in the development of number theory as a system of conjectures. Hardy's collaboration with Littlewood is among the most successful and famous collaborations in mathematical history. In a 1947 lecture, the Danish mathematician Harald Bohr reported a colleague as saying, "Nowadays, there are only three great English mathematicians: Hardy and Hardy–Littlewood."Hardy is known for formulating the Hardy–Weinberg principle, a basic principle of population genetics, independently from Wilhelm Weinberg in 1908.

He played cricket with the geneticist Reginald Punnett, who introduced the problem to him in purely mathematical terms. Hardy, who had no interest in genetics and described the mathematical argument as "very simple", may never have realized how important the result became. Hardy's collected. Hardy preferred his work to be considered pure mathematics because of his detestation of war and the military uses to which mathematics had been applied, he made several statements similar to that in his Apology: I have never done anything "useful". No discovery of mine has made, or is to make, directly or indirectly, for good or ill, the least difference to the amenity of the world. However, aside from formulating the Hardy–Weinberg principle in population genetics, his famous work on integer partitions with his collaborator Ramanujan, known as the Hardy–Ramanujan asymptotic formula, has been applied in physics to find quantum partition functions of atomic nuclei and to derive thermodynamic functions of non-inte

Land reform in the Philippines

Land reform in the Philippines has long been a contentious issue rooted in the Philippines's Spanish Colonial Period. Some efforts began during the American Colonial Period with renewed efforts during the Commonwealth, following independence, during Martial Law and following the People Power Revolution in 1986; the current law, the Comprehensive Agrarian Reform Program, was passed following the revolution and extended until 2014 Much like Mexico and other Spanish colonies in the Americas, the Spanish settlement in the Philippines revolved around the encomienda system of plantations, known as haciendas. As the 19th Century progressed, industrialization and liberalization of trade allowed these encomiendas to expand their cash crops, establishing a strong sugar industry in the Philippines in the Visayan island of Negros; the United States of America took possession of the Philippines following the Spanish–American War in 1898 and after putting down the subsequent rebellion in the Philippine–American War.

The Second Philippine Commission, the Taft Commission, viewed economic development as one of its top three goals. In 1901 93% of the islands' land area was held by the government and William Howard Taft, Governor-General of the Philippines, argued for a liberal policy so that a good portion could be sold off to American investors. Instead, the United States Congress, influenced by agricultural interests that did not want competition from the Philippines, in the 1902 Land Act, set a limit of 16 hectares of land to be sold or leased to American individuals and 1,024 hectares to American corporations; this and a downturn in the investment environment discouraged the foreign-owned plantations common in British Malaya, the Dutch East Indies, French Indochina. Further the U. S. Federal Government faced the problem of much of the private land being owned by the Roman Catholic Church and controlled by Spanish clerics; the American government—officially secular, hostile to continued Spanish control of much of the land of the now-American colony, long hostile to Catholics—negotiated a settlement with the Church handing over its land.

The 1902 Philippine Organic Act was a constitution for the Insular Government, as the U. S. civil administration was known. This act, among other actions, disestablished the Catholic Church as the state religion; the United States government, in an effort to resolve the status of the friars, negotiated with the Vatican. The church agreed to sell the friars' estates and promised gradual substitution of Filipino and other non-Spanish priests for the friars, it refused, however, to withdraw the religious orders from the islands partly to avoid offending Spain. In 1904 the administration bought for $7.2 million the major part of the friars' holdings, amounting to some 166,000 hectares, of which one-half was in the vicinity of Manila. The land was resold to Filipinos, some of them tenants but the majority of them estate owners. During the American Colonial Period, tenant farmers complained about the sharecropping system, as well as by the dramatic increase in population which added economic pressure to the tenant farmers' families.

As a result, an agrarian reform program was initiated by the Commonwealth. However, success of the program was hampered by ongoing clashes between landowners. An example of these clashes includes one initiated by Benigno Ramos through his Sakdalista movement, which advocated tax reductions, land reforms, the breakup of the large estates or haciendas, the severing of American ties; the uprising, which occurred in Central Luzon in May 1935, claimed about a hundred lives When the Philippine Commonwealth was established, President Manuel L. Quezon implemented the Rice Share Tenancy Act of 1933; the purpose of this act was to regulate the share-tenancy contracts by establishing minimum standards. The Act provided for better tenant-landlord relationship, a 50–50 sharing of the crop, regulation of interest to 10% per agricultural year, a safeguard against arbitrary dismissal by the landlord; the major flaw of this law was that it could be used only when the majority of municipal councils in a province petitioned for it.

Since landowners controlled such councils, no province asked that the law be applied. Therefore, Quezón ordered. However, contracts were good only for one year. By refusing the renew their contract, landlords were able to eject tenants; as a result, peasant organizations agitated in vain for a law that would make the contract automatically renewable for as long as the tenants fulfilled their obligations. In 1936, this Act was amended to get rid of its loophole, but the landlords made its application relative and not absolute, it was never carried out in spite of its good intentions. In fact, by 1939, thousands of peasants in Central Luzon were being threatened with wholesale eviction. By the early 1940s, thousands of tenants in Central Luzon were ejected from their farmlands and the rural conflict was more acute than ever. Therefore, during the Commonwealth period, agrarian problems persisted; this motivated the government to incorporate a cardinal principle on social justice. Dictated by the social justice program of the government, expropriation of landed estates and other landholdings commenced.

The National Land Settlement Administration began an orderly settlement of public agricultural lands. At the outbreak of the Second World War, major settlement areas containing more than 65,000 hectares were established; when the Philippines gained its independence in 1946, much of the land was held by a small group of wealthy landowners. There was much pressure on the democratically elected government to redistribute the

Nemanja Mitrović (basketball)

Nemanja Mitrovic is a Canadian-Bosnian professional basketball player who last played for Araberri of the Spanish LEB Oro. He has been a member of the Bosnia and Herzegovina national basketball team, he played college basketball for four years at the University of Portland. Mitrovic played for Northern Secondary School in Canada, his senior season he averaged 21 points, 7 rebounds and 4 assists per game, while leading his team to a 20–11 record, was named to the All-District All-Star Team. In 2007, he participated in the All-Canada All-Star game. Mitrovic went on to play at the University of Portland, which plays in the West Coast Conference, between 2008 and 2012, he appeared in 101 career games for the Pilots and is 4th all-time in school history in 3-point field goals made, as well as 6th all-time in 3-point percentage. During his freshman season, Mitrovic did not receive much playing time, appearing in only 16 games for the Pilots for a total of 43 minutes played; the Pilots finished the season 19–13.

His best game came on December 22 against Howard, where he came off the bench to score 5 points and grab 2 rebounds in 9 minutes. During his second season as a Pilot, Mitrovic became a bigger part of the rotation, appearing in 25 games while averaging 12.5 minutes per game. The Pilots finished the season 21–11 and were ranked in the Top 25 for the first time in school history after finishing 2nd at the 76 Classic in Anaheim. Mitrovic averaged 4.2 points and 1.5 rebounds per game while shooting 35.2% from 3. In conference play, that season, Mitrovic's averages jumped to 7.0 points and 2.4 rebounds in 17.2 minutes per game, while shooting 40.6% from 3. His best game came against San Francisco on February 25, where he came off the bench to score 20 points and grab 6 rebounds in 25 minutes. Mitrovic's breakout season came in his junior year, he started 31 out of 32 games while averaging 30.5 minutes per game helping the Pilots to a 20–12 record. After a slow start in the first 4 games, Mitrovic began to put up good performances for the Pilots, including being named the WCC's Player Of The Month during the month of December after which the Pilots were 12–2 going into conference play.

During the month, he averaged 17.4 points while shooting 62.5% from 3. He finished the season averaging 13.5 points, 3.3 rebounds and 1.6 assists while shooting 46.3% from 3 and was named to the WCC All-Conference 1st Team along with teammate Luke Sikma. His best game of the season came against San Francisco on February 17 where he scored 26 points and grabbed 6 rebounds, he finished the season ranked 6th in the nation in 3-point percentage. Before his senior season, Mitrovic was named to the WCC preseason All-Conference 1st team, he went on to start 25 out of 31 games that season while averaging 22 minutes per game, as the Pilots finished with a 7–24 record. Mitrovic averaged 7.9 points and 3.1 rebounds while shooting 31.5% from 3 and was named to the All-Star team at the World Vision Basketball Classic in November 2011. His best game came against Anthony Davis and the Kentucky Wildcats on November 26, where he scored 20 points and grabbed 6 rebounds in 28 minutes, he graduated in 2012 with a degree in finance.

In August 2012, Mitrovic signed with Kavala B. C. of the A1 league in Greece. In 25 games in the A1 Greek league, Mitrovic posted averages of 9.2 points per game to go along with 2.5 rebounds per game in 25.4 minutes per game. He shot 39% from 3. In 11 games in the Balkan league, he averaged 10.6 points per game to go along with 2.8 rebounds while shooting 47% from 3. In September 2013, Mitrovic signed a one-year contract with Sutor Montegranaro in Italy, to play for legendary Italian coach Carlo Recalcati. In 29 games in Serie A, Mitrovic posted averages of 6.8 points per game to go along with 2.4 rebounds per game in 19.9 minutes per game while shooting 39.4% from 3. In January 2015, he signed with Panelefsiniakos of the Greek Basket League. In 13 games in the A1 Greek League, he averaged 8.5 points and 2 rebounds per game in 16.5 minutes per game, while shooting 53% from 2 and 39.6% from 3. In January 2016, Mitrovic signed with Berck Basket in France. In 15 games with the club, he averaged 11.3 points, 2.5 rebounds and 2.1 assists in 22.7 minutes per game, while shooting 36% from 3.

In August 2016, Mitrovic signed with Ourense Provincia Termal of the Liga Española de Baloncesto. In 37 games in the Spanish Leb Oro League, he averaged 11.8 points, 3 rebounds and 1 assist in 28.5 minutes per game while shooting 53% from 2, 40% from 3 and 84% from the free throw line. On October 18, 2016, in a game against GBC, Mitrovic tied a league record by making 9 three-pointers in one game. He finished the game with 8 rebounds while shooting 9/12 from three-point range. Ourense Provincia Termal lost to Union Financeria Baloncesto Oviedo in the first round of the playoffs. In October 2017, Mitrović signed with Araberri of the Spanish LEB Oro. Mitrovic attended training camps with Senior National Teams of Canada. In 2011, he travelled with the Senior team on an international tour to Europe to play games against France and Czech Republic. Mitrovic is a member of the Bosnia & Herzegovina National Team. In 2012, he was on the 12 man roster which qualified for Eurobasket 2013, finishing first in their group.

In 5 games, he averaged 2.8 points per game in 8 minutes per game. In 2014, he was on the 12 man roster led by coach Duško Ivanović, which finished first in their group and qualified for EuroBasket 2015. In 4 games, he averaged 3.3 rebounds in 19.3 minutes per game. Mitrović resides in Canada, his father, Miroljub "Miki", played professionally

2007 Mil Milhas Brasil

The 2007 Mil Milhas Brasil was the 35th running of the Mil Milhas Brasil and was the sixth and final round of the 2007 Le Mans Series season. It took place at the Autódromo José Carlos Pace, Brazil, on 10 November 2007, it is the first round of the Le Mans Series held outside of Europe, as well as the first event longer than 1000 kilometers. The race lasted 8 hours 58 minutes. Class winners in bold. Cars failing to complete 70% of winner's distance marked as Not Classified. Pole position - #7 Team Peugeot Total - 1:41.867 Fastest lap - #8 Team Peugeot Total - 1:18.787 Average speed - 179.607 km/h Le Mans Series - Mil Milhas Brasil Mil Milhas Brasil - Official website

Suppressor mutation

A suppressor mutation is a second mutation that alleviates or reverts the phenotypic effects of an existing mutation in a process defined synthetic rescue. Genetic suppression therefore restores the phenotype seen prior to the original background mutation. Suppressor mutations are useful for identifying new genetic sites which affect a biological process of interest, they provide evidence between functionally interacting molecules and intersecting biological pathways. Intragenic suppression results from suppressor mutations that occur in the same gene as the original mutation. In a classic study, Francis Crick used intragenic suppression to study the fundamental nature of the genetic code. From this study it was shown. Researchers showed that mutations caused by either a single base insertion or a single base deletion could be "suppressed" or restored by a second mutation of the opposite sign, as long as the two mutations occurred in the same vicinity of the gene; this led to the conclusion that genes needed to be read in a specific "reading frame" and a single base insertion or deletion would shift the reading frame in such a way that the remaining DNA would code for a different polypeptide than the one intended.

Therefore, researchers concluded that the second mutation of opposite sign suppresses the original mutation by restoring the reading frame, as long as the portion between the two mutations is not critical for protein function. In addition to the reading frame, Crick used suppressor mutations to determine codon size, it was found that while one and two base insertions/deletions of the same sign resulted in a mutant phenotype, deleting or inserting three bases could give a wild type phenotype. From these results it was concluded that an inserted or deleted triplet does not disturb the reading frame and the genetic code is in fact a triplet. Intergenic suppression relieves the effects of a mutation in one gene by a mutation somewhere else within the genome; the second mutation is not on the same gene as the original mutation. Intergenic suppression is useful for identifying and studying interactions between molecules, such as proteins. For example, a mutation which disrupts the complementary interaction between protein molecules may be compensated for by a second mutation elsewhere in the genome that restores or provides a suitable alternative interaction between those molecules.

Several proteins of biochemical, signal transduction, gene expression pathways have been identified using this approach. Examples of such pathways include receptor-ligand interactions as well as the interaction of components involved in DNA replication and translation. Suppressor mutations occur in genes that code for virus structural proteins. To create a viable phage T4 virus, a balance of structural components is required. An amber mutant of phage T4 contains a mutation that changes a codon for an amino acid in a protein to the nonsense stop codon TAG. If, upon infection, an amber mutant defective in a gene encoding a needed structural component of phage T4 is weakly suppressed, it will produce a reduced number of the needed structural component; as a consequence few if any viable phage are formed. However, it was found that viable phage could sometimes be produced in the host with the weak nonsense suppressor if a second amber mutation in a gene that encodes another structural protein is present in the phage genome.

It was found that the reason the second amber mutation could suppress the first one is that the two numerically reduced structural proteins would now be in balance. For instance, if the first amber mutation caused a reduction of tail fibers to one tenth the normal level, most phage particles produced would have insufficient tail fibers to be infective. However, if a second amber mutation is defective in a base plate component and causes one tenth the number of base plates to be made, this may restore the balance of tail fibers and base plates, thus allow infective phage to be produced. In microbial genetics, a revertant is a mutant that has reverted to its former genotype or to the original phenotype by means of a suppressor mutation, or else by compensatory mutation somewhere in the gene. Synthetic viability The mutations chapter of the WikiBooks General Biology textbook Examples of Beneficial Mutations


Meiderich is a quarter of the city of Duisburg. It is divided into Mittel - and Obermeiderich. Meiderich belongs to the city district Meiderich/Beeck, which started in 1975, during the course of municipal reorganization. On 31 December 2004, 75,000 people lived in the district. Meiderich/Beeck has seven quarters: Beeck, Bruckhausen, Mittel-, Ober- and Untermeiderich. Meiderich was first mentioned in the beginning of the 10th century as "Medriki", that means "moist area", in a document of the Werden Abbey; the first church was built in the 13th century. In the Middle Ages there was the village Meiderich surrounded by seven areas of accumulated farms: Berchum, Borkhofen, Dümpten, Lakum, Lösort and Vohwinkel; the association-football club MSV Duisburg taking part in the second division in Germany is based in Meiderich. Meiderich Bf. is a terminus station of Verkehrsverbund Rhein-Ruhr line U79, connecting Meiderich with Duisburg Hbf and Düsseldorf-Stadtmitte. Heinrich Averdunk / Walter Ring: Geschichte der Stadt Duisburg.

Essen: Baedeker Verlag, 1927, S. 304 - 330 Peter Cinka: Berühmte Meidericher Persönlichkeiten aus den letzten beiden Jahrhunderten. Duisburg: Borath Verlag, 1997 Günter von Roden: Geschichte der Stadt Duisburg. Bd. II: Die Ortsteile von den Anfängen. Die Gesamtstadt seit 1905. Duisburg: Walter Braun Verlag, 1974, p. 124 - 184 Website of the quarter