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" DME operation will continue and possibly expand as an alternate navigation source to space-based navigational systems such as GPS and Galileo.
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"= = = Feng Youlan = = =
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" Feng Youlan (; 4 December 1895 – 26 November 1990) was a Chinese philosopher, historian, and writer who was instrumental for reintroducing the study of Chinese philosophy in the modern era.
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" Feng Youlan was born on 4 December 1895 in Tanghe County, Nanyang, Henan, China, to a middle-class family. His younger sister was Feng Yuanjun, who would become a famous Chinese writer. He studied philosophy in the China Public School in Shanghai, between 1912–1915, a preparatory school for college, then studied in Chunghua University, Wuhan (later merged into Central China Normal University) and Peking University between 1915 and 1918, where he was able to study Western philosophy and logic as well as Chinese philosophy.
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" Upon his graduation in 1918, he traveled to the United States in 1919, where he studied at Columbia University on the Boxer Indemnity Scholarship Program. There he met, among many philosophers who were to influence his thought and career, John Dewey, the pragmatist, who became his teacher. Feng gained his PhD from Columbia in 1923. His PhD thesis was titled ""A Comparative Study of Life Ideals"".
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" He went on to teach at Chinese universities including Jinan University, Yenching University, and Tsinghua University in Beijing. From 1934 to 1938 (and again from 1946 to 1949) he was Chair of the Department of Philosophy at Tsinghua. It was while at Tsinghua that Feng published what was to be his best-known and most influential work, his ""History of Chinese Philosophy"" (1934, in two volumes). In it he presented and examined the history of Chinese philosophy from a viewpoint which was very much influenced by the Western philosophical fashions prevalent at the time, which resulted in what Peter J. King of Oxford describes as a distinctly positivist tinge to most of the philosophers he described. Nevertheless, the book became the standard work in its field, and had a huge effect in reigniting an interest in Chinese thought.
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" In 1935 Feng, on his way to a conference in Prague, stopped briefly in the Soviet Union and was impressed with the radical social changes and cultural ferment. His speeches extolling the utopian possibilities of communism, although also describing the mistakes he saw, drew attention from Chiang Kai-sheks's police. Feng was arrested and spent a short time in jail, but soon became a firm supporter of the government and its resistance to Japan. During the Sino-Japanese War he published works which supported the New Life Movement for revitalizing Confucian values.
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" In 1939, Feng brought out his ""Xin Lixue"" (""New Rational Philosophy"", or ""Neo-Lixue""). Lixue was a philosophical position of a small group of twelfth-century neo-Confucianists (including Cheng Hao, Cheng Yi, and Zhu Xi); Feng's book took certain metaphysical notions from their thought and from taoism (such as li and tao), analyzed and developed them in ways that owed much to the Western philosophical tradition, and produced a rationalistic neo-Confucian metaphysics. He also developed, in the same way, an account of the nature of morality and of the structure of human moral development.
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" When the Second Sino-Japanese War broke out, the students and staff of Beijing's Tsinghua and Peking Universities, together with Tianjin's Nankai University, fled their campuses. They went first to Hengshan, where they set up the Changsha Temporary University, and then to Kunming, where they set up Southwest Associated University.
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" When, in 1946 the three Universities returned to Beijing, Feng instead went to the U.S. again, this time to take up a post as visiting professor at the University of Pennsylvania. He spent the year 1948–1949 as a visiting professor at the University of Hawaii. He served as President of Tsinghua University from December 1948 to May 1949 because of Zhang Dongsun's refusal (it was known as National Tsinghua University until January 1949).
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" While he was at Pennsylvania, news from China made it clear that the communists were on their way to seizing power. Feng's friends tried to persuade him to stay, but he was determined to return; his political views were broadly socialist, and he thus felt optimistic about China's future under its new government.
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" Once back home, Feng began to study Marxist–Leninist thought, but he soon found that the political situation fell short of his hopes; by the mid-1950s his philosophical approach was being attacked by the authorities. He was forced to repudiate much of his earlier work, and to rewrite the rest – including his ""History"" – in order to fit in with the ideas of the Cultural revolution.
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" Despite all this, Feng refused to leave China, and after enduring much hardship he finally saw a relaxation of censorship, and was able to write with a certain degree of freedom. He died on 26 November 1990 in Beijing.
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"= = = Boyer–Moore string-search algorithm = = =
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" In computer science, the Boyer–Moore string-search algorithm is an efficient string-searching algorithm that is the standard benchmark for practical string-search literature. It was developed by Robert S. Boyer and J Strother Moore in 1977. The algorithm preprocesses the string being searched for (the pattern), but not the string being searched in (the text). It is thus well-suited for applications in which the pattern is much shorter than the text or where it persists across multiple searches. The Boyer-Moore algorithm uses information gathered during the preprocess step to skip sections of the text, resulting in a lower constant factor than many other string search algorithms. In general, the algorithm runs faster as the pattern length increases. The key features of the algorithm are to match on the tail of the pattern rather than the head, and to skip along the text in jumps of multiple characters rather than searching every single character in the text.
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" The Boyer-Moore algorithm searches for occurrences of in by performing explicit character comparisons at different alignments. Instead of a brute-force search of all alignments (of which there are ), Boyer-Moore uses information gained by preprocessing to skip as many alignments as possible.
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" Previous to the introduction of this algorithm, the usual way to search within text was to examine each character of the text for the first character of the pattern. Once that was found the subsequent characters of the text would be compared to the characters of the pattern. If no match occurred then the text would again be checked character by character in an effort to find a match. Thus almost every character in the text needs to be examined.
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" The key insight in this algorithm is that if the end of the pattern is compared to the text, then jumps along the text can be made rather than checking every character of the text. The reason that this works is that in lining up the pattern against the text, the last character of the pattern is compared to the character in the text. If the characters do not match, there is no need to continue searching backwards along the text. If the character in the text does not match any of the characters in the pattern, then the next character in the text to check is located characters farther along the text, where is the length of the pattern. If the character in the text ""is"" in the pattern, then a partial shift of the pattern along the text is done to line up along the matching character and the process is repeated. Jumping along the text to make comparisons rather than checking every character in the text decreases the number of comparisons that have to be made, which is the key to the efficiency of the algorithm.
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" More formally, the algorithm begins at alignment , so the start of is aligned with the start of . Characters in and are then compared starting at index in and in , moving backward. The strings are matched from the end of to the start of . The comparisons continue until either the beginning of is reached (which means there is a match) or a mismatch occurs upon which the alignment is shifted forward (to the right) according to the maximum value permitted by a number of rules. The comparisons are performed again at the new alignment, and the process repeats until the alignment is shifted past the end of , which means no further matches will be found.
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" The shift rules are implemented as constant-time table lookups, using tables generated during the preprocessing of .
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" A shift is calculated by applying two rules: the bad character rule and the good suffix rule. The actual shifting offset is the maximum of the shifts calculated by these rules.
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" The bad-character rule considers the character in at which the comparison process failed (assuming such a failure occurred). The next occurrence of that character to the left in is found, and a shift which brings that occurrence in line with the mismatched occurrence in is proposed. If the mismatched character does not occur to the left in , a shift is proposed that moves the entirety of past the point of mismatch.
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" Methods vary on the exact form the table for the bad character rule should take, but a simple constant-time lookup solution is as follows: create a 2D table which is indexed first by the index of the character in the alphabet and second by the index in the pattern. This lookup will return the occurrence of in with the next-highest index or -1 if there is no such occurrence. The proposed shift will then be , with lookup time and space, assuming a finite alphabet of length .
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" The C and Java implementations below have a space complexity (make_delta1, makeCharTable). This is the same as the original delta1 and the BMH bad character table. This table maps a character at position to shift by , with the last instance -- the least shift amount -- taking precedence. All unused characters are set as as a sentinel value.
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" The good suffix rule is markedly more complex in both concept and implementation than the bad character rule. It is the reason comparisons begin at the end of the pattern rather than the start, and is formally stated thus:
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" Suppose for a given alignment of P and T, a substring t of T matches a suffix of P, but a mismatch occurs at the next comparison to the left. Then find, if it exists, the right-most copy t' of t in P such that t' is not a suffix of P and the character to the left of t' in P differs from the character to the left of t in P. Shift P to the right so that substring t' in P aligns with substring t in T. If t' does not exist, then shift the left end of P past the left end of t in T by the least amount so that a prefix of the shifted pattern matches a suffix of t in T. If no such shift is possible, then shift P by n places to the right. If an occurrence of P is found, then shift P by the least amount so that a ""proper"" prefix of the shifted P matches a suffix of the occurrence of P in T. If no such shift is possible, then shift P by n places, that is, shift P past t.
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" The good suffix rule requires two tables: one for use in the general case, and another for use when either the general case returns no meaningful result or a match occurs. These tables will be designated and respectively. Their definitions are as follows:
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" For each , is the largest position less than such that string matches a suffix of and such that the character preceding that suffix is not equal to . is defined to be zero if there is no position satisfying the condition.
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" Let denote the length of the largest suffix of that is also a prefix of , if one exists. If none exists, let be zero.
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" Both of these tables are constructible in time and use space. The alignment shift for index in is given by or . should only be used if is zero or a match has been found.
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" A simple but important optimization of Boyer-Moore was put forth by Galil in 1979.
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" As opposed to shifting, the Galil rule deals with speeding up the actual comparisons done at each alignment by skipping sections that are known to match. Suppose that at an alignment , is compared with down to character of . Then if is shifted to such that its left end is between and , in the next comparison phase a prefix of must match the substring . Thus if the comparisons get down to position of , an occurrence of can be recorded without explicitly comparing past . In addition to increasing the efficiency of Boyer-Moore, the Galil rule is required for proving linear-time execution in the worst case.
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" The Galil rule, in its original version, is only effective for versions that output multiple matches. It updates the substring range only on , i.e. a full match. A generalized version for dealing with submatches was reported in 1985 as the Apostolico–Giancarlo algorithm.
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" The Boyer-Moore algorithm as presented in the original paper has worst-case running time of only if the pattern does ""not"" appear in the text. This was first proved by Knuth, Morris, and Pratt in 1977,
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" followed by Guibas and Odlyzko in 1980 with an upper bound of comparisons in the worst case. Richard Cole gave a proof with an upper bound of comparisons in the worst case in 1991.
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" When the pattern ""does"" occur in the text, running time of the original algorithm is in the worst case. This is easy to see when both pattern and text consist solely of the same repeated character. However, inclusion of the Galil rule results in linear runtime across all cases.
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" Various implementations exist in different programming languages. In C++ it is part of the Standard Library since C++17, also Boost provides the generic Boyer–Moore search implementation under the ""Algorithm"" library. In Go (programming language) there is an implementation in search.go. D (programming language) uses a BoyerMooreFinder for predicate based matching within ranges as a part of the Phobos Runtime Library.
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" The Boyer-Moore algorithm is also used in GNU's grep.
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" Below are a few simple implementations.
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" The Boyer–Moore–Horspool algorithm is a simplification of the Boyer–Moore algorithm using only the bad character rule.
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" The Apostolico–Giancarlo algorithm speeds up the process of checking whether a match has occurred at the given alignment by skipping explicit character comparisons. This uses information gleaned during the pre-processing of the pattern in conjunction with suffix match lengths recorded at each match attempt. Storing suffix match lengths requires an additional table equal in size to the text being searched.
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" The Raita algorithm improves the performance of Boyer-Moore-Horspool algorithm. The searching pattern of particular sub-string in a given string is different from Boyer-Moore-Horspool algorithm.
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"= = = Snooker world rankings 1990/1991 = = =
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" Snooker world rankings 1990/1991: The professional world rankings for the top 32 snooker players and five others from the top 64 in the 1990/1991 season are listed below.