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In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order does matter. Like a set, it contains members; the number of elements is called the length of the sequence. Unlike a set, the same elements can appear multiple times at different positions in a sequence, order does matter. Formally, a sequence can be defined as a function whose domain is either the set of the natural numbers or the set of the first n natural numbers; the position of an element in a sequence is its index. The first element has 1, depending on the context or a specific convention; when a symbol is used to denote a sequence, the nth element of the sequence is denoted by this symbol with n as subscript. For example, is a sequence of letters with the letter'M' first and'Y' last; this sequence differs from. The sequence, which contains the number 1 at two different positions, is a valid sequence. Sequences can be finite, as in these examples, or infinite, such as the sequence of all positive integers.

In computing and computer science, finite sequences are sometimes called strings, words or lists, the different names corresponding to different ways to represent them in computer memory. The empty sequence is included in most notions of sequence, but may be excluded depending on the context. A sequence can be thought of as a list of elements with a particular order. Sequences are useful in a number of mathematical disciplines for studying functions and other mathematical structures using the convergence properties of sequences. In particular, sequences are the basis for series, which are important in differential equations and analysis. Sequences are of interest in their own right and can be studied as patterns or puzzles, such as in the study of prime numbers. There are a number of ways to denote a sequence, some of which are more useful for specific types of sequences. One way to specify a sequence is to list the elements. For example, the first four odd numbers form the sequence; this notation can be used for infinite sequences as well.

For instance, the infinite sequence of positive odd integers can be written. Listing is most useful for infinite sequences with a pattern that can be discerned from the first few elements. Other ways to denote a sequence are discussed after the examples; the prime numbers are the natural numbers bigger than 1 and themselves. Taking these in their natural order gives the sequence; the prime numbers are used in mathematics and in number theory. The Fibonacci numbers comprise the integer sequence whose elements are the sum of the previous two elements; the first two elements are 1 and 1 so that the sequence is. For a large list of examples of integer sequences, see On-Line Encyclopedia of Integer Sequences. Other examples of sequences include ones made up of rational numbers, real numbers, complex numbers; the sequence approaches the number 1. In fact, every real number can be written as the limit of a sequence of rational numbers, e.g. via its decimal expansion. For instance, π is the limit of the sequence.

A related sequence is the sequence of decimal digits of π, i.e.. This sequence does not have any pattern, discernible by eye, unlike the preceding sequence, increasing. Other notations can be useful for sequences whose pattern cannot be guessed, or for sequences that do not have a pattern such as the digits of π. One such notation is to write down a general formula for computing the nth term as a function of n, enclose it in parentheses, include a subscript indicating the set of values that n can take. For example, in this notation the sequence of numbers could be written as n ∈ N; the sequence of squares could be written as n ∈ N. The variable n is called an index, the set of values that it can take is called the index set, it is useful to combine this notation with the technique of treating the elements of a sequence as individual variables. This yields expressions like n ∈ N, which denotes a sequence whose nth element is given by the variable a n. For example: a 1 = 1 st element of n ∈ N a 2 = 2 nd element a 3 = 3 rd element ⋮ a n − 1 =

Johann Caspar Bosshardt

Johann Caspar Bosshardt, or Kaspar Boßhardt was a Swiss history painter who spent most of his life in Germany. His father was a cooper. Despite objections from his parents, he was allowed, at the age of fifteen, to go to Zürich, where he was apprenticed to the engraver, Georg Christoph Friedrich Oberkogler, he studied portrait painting with Johann Rudolf Obrist. He obtained the sponsorship of Ludwig Vogel who, in 1841, recommended him to Theodor Hildebrandt for his classes at the Kunstakademie Düsseldorf. There, he came under the influence of Hildebrandt, Friedrich Wilhelm Schadow and Carl Friedrich Lessing. Due to an unspecified nervous disorder, he had to quit the Akademie in 1844 and return home to recover.. When he had improved, the government of Zürich granted him a scholarship to study history painting in Munich, he moved there in 1845 and, due to the disturbances surrounding the Sonderbund War and its aftermath, he decided to stay. He would remain for the rest of his life, although he travelled extensively and visited Switzerland on business.

In 1847, he completed his first historical scene, depicting Hans Waldmann saying goodbye to his fellow prisoners. The painting was purchased by the Cantonal government of Zürich and was displayed at a major exhibition of the Schweizerischer Kunstverein, he continued to create large historical scenes from the 16th century, but most of his income was derived from portraits. He had hoped to receive a major commission for decorations in the new Federal Palace of Switzerland but, in 1865, his proposals were rejected; as a result, in the early 1870s, he turned to genre painting and travelled throughout Tyrolia doing study sketches. In his final years, he became reclusive. After his death, his work was considered old-fashioned and was forgotten until a major retrospective was held for his centennial in 1987. Hyacinth Holland, "Boßhardt, Kaspar", Allgemeine Deutsche Biographie, 47, Leipzig: Duncker & Humblot, pp. 138–139 Bosshardt, Johann Caspar in German and Italian in the online Historical Dictionary of Switzerland.

"Bosshardt, Johann Caspar". SIKART dictionary and database

Australia at the 2014 Summer Youth Olympics

Australia competed at the 2014 Summer Youth Olympics, in Nanjing, China from 16 August to 28 August 2014. Medals awarded to participants of mixed-NOC teams are represented in italics; these medals are not counted towards the individual NOC medal tally. Australia qualified two archers from its performance at the Oceania Continental Qualification Tournament. IndividualTeam Australia qualified 20 athletes. Qualification Legend: Q=Final A. SinglesDoubles Australia qualified a girls' team by their performance at the AVC Qualification Tournament. Australia qualified two boxers based on its performance at the 2014 AIBA Youth World Championships BoysGirls Australia qualified one boat based on its performance at the 2013 World Junior Canoe Sprint and Slalom Championships. Boys Australia qualified a rider. Australia qualified one athlete based on its performance at the 2014 Cadet World Championships. BoysMixed Team Australia qualified a boys' team based on its performance at the Oceania Qualification Tournament.

Roster Group Stage QuarterfinalSemifinalGold medal match Australia qualified one team of two athletes based on the 8 June 2014 IGF Combined World Amateur Golf Rankings. IndividualTeam Australia qualified one athlete based on its performance at the 2014 Oceania Artistic Gymnastics Championships. Boys Australia qualified one athlete based on its performance at the Oceania Qualifying Event. Individual Australia qualified one athlete based on its performance at the 2014 Oceania Trampoline Championships. Australia qualified two athletes based on its performance at the 2013 Cadet World Judo Championships. IndividualTeam Australia qualified two athletes based on its performance at the Asian and Oceania YOG Qualifiers. Australia qualified two boats based on its performance at the 2013 World Rowing Junior Championships. Qualification Legend: FA=Final A. Roster Group Stage Semifinal Gold Medal Match Australia qualified two boats based on its performance at the Byte CII Oceania Continental Qualifiers. Australia qualified four shooters based on its performance at the 2013 Oceania Shooting Championships.

IndividualTeam Australia qualified eight swimmers. BoysGirlsMixed Australia qualified two athletes based on its performance at the Oceania Qualification Event. SinglesTeamQualification Legend: Q=Main Bracket. SinglesDoubles Australia qualified two athletes based on its performance at the 2014 Oceania Youth Olympic Games Qualifier. IndividualRelay Australia qualified 1 quota in the boys' and girls' events based on the team ranking after the 2014 Weightlifting Oceania Championships. BoysGirls Australia qualified one athlete based on its performance at the 2014 Oceania Cadet Championships. Key: VT - Victory by Fall. PP - Decision by Points - the loser with technical points. PO - Decision by Points - the loser without technical points. Boys

History of Fenn College

The history of Fenn College tells the story of Fenn College from its founding until the present. 1870: Cleveland YMCA offered free classes. 1881: YMCA program formalized. 1906: Reorganized as the Association Institute. 1921: Renamed Cleveland YMCA School of Technology, or Y-Tech for short. 1923: Y-Tech first offers courses toward a bachelor's degree. This is now the claimed founding date of Fenn College. 1929: Renamed Fenn College after Sereno Peck Fenn. Fenn College took over several buildings in the area including Fenn Tower, Stilwell Hall, Foster Hall. In 1930 Nash Junior College was created. In 1932 Nash became Fenn's school of arts & sciences, joining the original engineering and business schools; the origins of Fenn College date from 1870 when Cleveland YMCA created an Educational Committee to provide free evening classes in French and German for the benefit of young men coming to YMCA. After offering other courses sporadically throughout the 1870s, YMCA moved to establish a formal evening educational in the 1880s.

In 1906 YMCA combined its evening school with a newly created day school under the name of the Association Institute. By 1909 YMCA was operating four different day schools: The School of Commerce and Finance, The Technical School, The Preparatory School, the Special School; the schools admitted their first female students in 1918. In 1921 YMCA's educational branch was designated Cleveland YMCA School of Technology. Finding a demand following the First World War YMCA first began offering college credit courses in engineering and business in 1923; these early classes were conducted at Central YMCA building on Prospect Avenue andEast 22nd Street and in three converted residences on Prospect east of the Central YMCA: the Johnson Building. Two significant events marked 1927. Y-Tech's first college class graduated, planning began for a junior college program that would become Nash Junior College in 1931. In 1928 the first building built for the college, the laboratory and classroom Fenn Building, was constructed adjacent to Central YMCA, behind the Johnson Building.

The need to achieve accreditation for its academic programs prompted the YMCA in 1929 to re-organize again its education program. On January 1, 1930 Y-Tech took the name Fenn College in honor of Sereno Peck Fenn, who had served on the YMCA board of directors and as YMCA’s president for 25 years. College lore holds that among the reasons for the name change was that the school’s graduates felt the name, YMCA, put them at a disadvantage in competing against graduates from other colleges in the job market. In 1935 YMCA Preparatory School and the Nash Junior College ceased operations and a School of Arts and Science was added to the Engineering and Business Administration schools. Dr. Cecil Vincent Thomas, who served as YMCA's Executive Director and as Fenn's first President, 1923-1947, guided Fenn's early development. With several notable private colleges established in the Cleveland area, including Case Institute of Technology and Western Reserve University, Fenn College sought to attract those students for whom college otherwise would have been financially unattainable by offering a low-cost quality education.

In line with this Fenn in 1923 became the fourth college in Ohio to adopt the cooperative education program. This program of alternating periods of classroom work with on-the-job work experience was required for all day students and was optional for evening division students. In need of additional classroom and laboratory space Fenn College purchased the National Town and Country Club building at East 24th Street and Euclid Avenue Street in 1937, becoming only the third college in America to have a skyscraper on campus. Dedicated as Fenn Tower in 1938, the new building provided much needed office space. Additionally it gave Fenn amore prestigious "Euclid Avenue" address. Fenn's reputation was further enhanced when it received accreditation from the North Central Association in 1940. During the administration of Dr. Edward Hodnett, 1948-1951, Fenn constructedFoster Hall, an engineering classroom and laboratory building funded by a donation from Cleveland entrepreneur Claude Foster in 1949, at the recommendation of the North Central Association, separated its operations from those of YMCA in 1950.

Dr. G. Brooks Earnest served as Fenn’s President from 1951 until the State of Ohio's takeover of the College in 1965. Under Dr. Earnest Fenn expanded again purchasing the three story Ohio Motors building on East 24th Street in 1953. Renovated for classroom and laboratory work the building opened in 1958 and was dedicated in January 1959 as Stilwell Hall in honor of Board of Trustees Chairman Charles Stilwell. Throughout its history Fenn College had always managed to operate without incurring a budget deficit. However, by 1963 the College administration was confronted with mounting financial difficulties due to rising operating costs, direct competition from a new community college, persistent rumors of a possible state takeover; that year the College issued The Fenn Plan for Unified Higher Education in Cleveland-Northeastern Ohio calling upon the State of Ohio to develop a state university in Cleveland using Fenn College as its nucleus. During the 1962 Ohio gubernatorial campaign candidate James Rhodes had proposed that there should be a state university within a 30-mile radius of every citizen.

At that time the nearest state university to Cleveland was Kent State University in Ohio. On 18 December 1964, Governor Rhodes signed Ohio General Assembly Amended House Bill No. 2 creating Ohio's seventh state university, Cleveland State University and announced the appointment of a board of trustees. On March 10, 1965 the Fenn College and CS

Noel Clough

Noel Stanley Clough is an Australian former track and field athlete who competed in the 400 metres, 800 metres, 400 metres hurdles. Hailing from Victoria, Australia, he enjoyed success at national level in the mid-1960s, taking runner-up spots three times in the 800 m at the Australian Athletics Championships, he had top three finishes in the 400 m and the 400 m hurdles. Clough competed at one major international competition in his career, running in the 880-yard run, individual and relay 440-yard events, he was a finalist in the 440 yd, taking eighth place, helped the Australian 4 × 440 yard relay team to fifth. His career peak came in the 880 yd final, in which he broke the games record to take the gold medal in a time of 1:46.9 minutes, beating Kenya's Wilson Kiprugut and the home favourite George Kerr, a former Commonwealth champion. The time was a full second faster than Clough had managed before; this was the last time that the event was staged, thus Clough's winning time remains the games record for the now-defunct distance.

His run ranked him joint fifth on the global rankings that year, alongside compatriot Ralph Doubell. He continued to compete in his years as a masters athlete, he won a 400 m/400 m hurdles double in the men's over-40 category at the 1977 World Masters Athletics Championships. His winning times of 49.5 seconds and 54.3 seconds were world records for the over-40s 400 m and 400 m hurdles respectively. List of middle-distance runners

Gymnastics at the 2000 Summer Olympics – Women's artistic qualification

These are the results of the women's qualification round, the preliminary round which decided the finalists for all six events for women in artistic gymnastics at the 2000 Summer Olympics in Sydney. The qualification round took place on September 17 at the Sydney SuperDome; the top twelve teams from the 1999 World Artistic Gymnastics Championships completed for places in the team final. Each team was allowed to bring up to six gymnasts. During qualification, each team could have up to five gymnasts compete on each apparatus, could count the four highest scores for the team total; the six teams with the highest scores in the qualification round advanced to the team final. Individual gymnasts, including those who were not part of a team, competed for places in the all-around and apparatus finals; the twenty-four gymnasts with the highest scores in the all-around advanced to that final, except that each country could only send three gymnasts to the all-around final. The eight gymnasts with the highest scores on each apparatus advanced to those finals, except that each country could only send two gymnasts to each apparatus final.

In total, 97 gymnasts from 32 countries competed in the qualification round. Note: In April 2010, the IOC and FIG disqualified the Chinese team from the all-around team event after discovering member Dong Fangxiao was only 14 years old at the time of the Olympics. Dong's results from the 1999 World Championships and 2000 Olympic Games were struck from the records. Note: In April 2010, the IOC and FIG disqualified the Chinese team after discovering team member Dong Fangxiao was only 14 at the time of the Olympics. Note: In April 2010, the results of Dong Fangxiao from this event were struck from the records after she was found to be 14 at the time of the Olympics. *Khorkina withdrew from the final so that her teammate Elena Zamolodchikova, who finished ninth in qualification, would take her place as she had more chances to win a gold medal. Note: In April 2010, the results of Dong Fangxiao from this event were struck from the records after she was found to be 14 at the time of the Olympics. Note: In April 2010, the results of Dong Fangxiao from this event were struck from the records.

Official Olympic Report