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±1-sequence
In mathematics, a sign sequence, or ±1–sequence or bipolar sequence, is a sequence of numbers, each of which is either 1 or −1. One example is the sequence (1, −1, 1, −1, ...). Such sequences are commonly studied in discrepancy theory. ErdÅ‘s discrepancy problem Around 1932, mathematician Paul ErdÅ‘s conjectured that for any infinite ±1-sequence (x_1, x_2, \ldots) and any integer ''C'', there exist integers ''k'' and ''d'' such that : \left, \sum_^k x_ \ > C. The ErdÅ‘s discrepancy problem asks for a proof or disproof of this conjecture. In February 2014, Alexei Lisitsa and Boris Konev of the University of Liverpool showed that every sequence of 1161 or more elements satisfies the conjecture in the special case ''C'' = 2, which proves the conjecture for ''C'' ≤ 2. This was the best such bound available at the time. Their proof relied on a SAT-solver computer algorithm whose output takes up 13 gigabytes of data, more than the entire te ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sequence
In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters. Like a set, it contains members (also called ''elements'', or ''terms''). The number of elements (possibly infinite) is called the ''length'' of the sequence. Unlike a set, the same elements can appear multiple times at different positions in a sequence, and unlike a set, the order does matter. Formally, a sequence can be defined as a function from natural numbers (the positions of elements in the sequence) to the elements at each position. The notion of a sequence can be generalized to an indexed family, defined as a function from an ''arbitrary'' index set. For example, (M, A, R, Y) is a sequence of letters with the letter 'M' first and 'Y' last. This sequence differs from (A, R, M, Y). Also, the sequence (1, 1, 2, 3, 5, 8), which contains the number 1 at two different positions, is a valid sequence. Sequences can be '' finite'', as in these examples, or '' i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Erdős Discrepancy Problem
In mathematics, a sign sequence, or ±1–sequence or bipolar sequence, is a sequence of numbers, each of which is either 1 or −1. One example is the sequence (1, −1, 1, −1, ...). Such sequences are commonly studied in discrepancy theory. ErdÅ‘s discrepancy problem Around 1932, mathematician Paul ErdÅ‘s conjectured that for any infinite ±1-sequence (x_1, x_2, \ldots) and any integer ''C'', there exist integers ''k'' and ''d'' such that : \left, \sum_^k x_ \ > C. The ErdÅ‘s discrepancy problem asks for a proof or disproof of this conjecture. In February 2014, Alexei Lisitsa and Boris Konev of the University of Liverpool showed that every sequence of 1161 or more elements satisfies the conjecture in the special case ''C'' = 2, which proves the conjecture for ''C'' ≤ 2. This was the best such bound available at the time. Their proof relied on a SAT-solver computer algorithm whose output takes up 13 gigabytes of data, more than the entire tex ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting poin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Crowdsourcing
Crowdsourcing involves a large group of dispersed participants contributing or producing goods or services—including ideas, votes, micro-tasks, and finances—for payment or as volunteers. Contemporary crowdsourcing often involves digital platforms to attract and divide work between participants to achieve a cumulative result. Crowdsourcing is not limited to online activity, however, and there are various historical examples of crowdsourcing. The word crowdsourcing is a portmanteau of " crowd" and "outsourcing". In contrast to outsourcing, crowdsourcing usually involves less specific and more public groups of participants. Advantages of using crowdsourcing include lowered costs, improved speed, improved quality, increased flexibility, and/or increased scalability of the work, as well as promoting diversity. Crowdsourcing methods include competitions, virtual labor markets, open online collaboration and data donation. Some forms of crowdsourcing, such as in "idea compe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Independent
''The Independent'' is a British online newspaper. It was established in 1986 as a national morning printed paper. Nicknamed the ''Indy'', it began as a broadsheet and changed to tabloid format in 2003. The last printed edition was published on Saturday 26 March 2016, leaving only the online edition. The newspaper was controlled by Tony O'Reilly's Irish Independent News & Media from 1997 until it was sold to the Russian oligarch and former KGB Officer Alexander Lebedev in 2010. In 2017, Sultan Muhammad Abuljadayel bought a 30% stake in it. The daily edition was named National Newspaper of the Year at the 2004 British Press Awards. The website and mobile app had a combined monthly reach of 19,826,000 in 2021. History 1986 to 1990 Launched in 1986, the first issue of ''The Independent'' was published on 7 October in broadsheet format.Dennis Griffiths (ed.) ''The Encyclopedia of the British Press, 1422–1992'', London & Basingstoke: Macmillan, 1992, p. 330 It was prod ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
