|
Kazuoki Azuma
(born 1939) is a Japanese mathematician. Azuma's inequality in probability theory is named after him. Publications * References External links * , archived at the Internet Archive Partial Bibliographyat CiNii CiNii () is a bibliographic database service for material in Japanese academic libraries, especially focusing on Japanese works and English works published in Japan. The database was founded in April 2005 and is maintained by the National Inst ... (alshere and perhaps at other slightly variant names) 1939 births Living people 20th-century Japanese mathematicians 21st-century Japanese mathematicians {{Japan-scientist-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematical model, models, and mathematics#Calculus and analysis, change. History One of the earliest known mathematicians were Thales of Miletus (c. 624–c.546 BC); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. The number of known mathematicians grew when Pythagoras of Samos (c. 582–c. 507 BC) established the Pythagoreans, Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathemat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Azuma's Inequality
In probability theory, the Azuma–Hoeffding inequality (named after Kazuoki Azuma and Wassily Hoeffding) gives a concentration result for the values of martingales that have bounded differences. Suppose \ is a martingale (or super-martingale) and :, X_k - X_, \leq c_k, \, almost surely. Then for all positive integers ''N'' and all positive reals ''\epsilon'', :\text(X_N - X_0 \geq \epsilon) \leq \exp\left ( \right). And symmetrically (when ''X''''k'' is a sub-martingale): :\text(X_N - X_0 \leq -\epsilon) \leq \exp\left ( \right). If ''X'' is a martingale, using both inequalities above and applying the union bound allows one to obtain a two-sided bound: :\text(, X_N - X_0, \geq \epsilon) \leq 2\exp\left ( \right). Proof The proof shares similar idea of the proof for the general form of Azuma's inequality listed below. Actually, this can be viewed as a direct corollary of the general form of Azuma's inequality. A general form of Azuma's inequality Limitation of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability Theory
Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms of probability, axioms. Typically these axioms formalise probability in terms of a probability space, which assigns a measure (mathematics), measure taking values between 0 and 1, termed the probability measure, to a set of outcomes called the sample space. Any specified subset of the sample space is called an event (probability theory), event. Central subjects in probability theory include discrete and continuous random variables, probability distributions, and stochastic processes (which provide mathematical abstractions of determinism, non-deterministic or uncertain processes or measured Quantity, quantities that may either be single occurrences or evolve over time in a random fashion). Although it is not possible to perfectly p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Miyagi University Of Education
, is a national university A national university is mainly a university created or managed by a government, but which may also at the same time operate autonomously without direct control by the state. Some national universities are associated with national cultural or po ... at Sendai, Miyagi, Japan. The predecessor of the school was founded in 1873, and it was chartered as a university in 1965., Florida State University website (sister university). It is accredited by the Japanese Ministry of Education (MEXT) , Japanese Ministry of Education. as a public co-educational institute and is ranked in Japan's first tier of leading schools. With four academic divisions, MUE offers degrees in Education and in the disciplines of Language and Social Science, Science, Math and Life, and Art and Physical Education. Their Development and Education division ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Internet Archive
The Internet Archive is an American digital library with the stated mission of "universal access to all knowledge". It provides free public access to collections of digitized materials, including websites, software applications/games, music, movies/videos, moving images, and millions of books. In addition to its archiving function, the Archive is an activist organization, advocating a free and open Internet. , the Internet Archive holds over 35 million books and texts, 8.5 million movies, videos and TV shows, 894 thousand software programs, 14 million audio files, 4.4 million images, 2.4 million TV clips, 241 thousand concerts, and over 734 billion web pages in the Wayback Machine. The Internet Archive allows the public to upload and download digital material to its data cluster, but the bulk of its data is collected automatically by its web crawlers, which work to preserve as much of the public web as possible. Its web archive, the Wayback Machine, contains hundreds of b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zasshi Kiji Sakuin
Zasshi Kiji Sakuin (雑誌記事索引, "Japanese Periodicals Index"), often called Zassaku in short, is a searchable database of scholarly articles in Japanese. The database, produced by the National Diet Library (NDL) in 1948, catalogs selected articles from NDL's extensive collection of periodicals. The database was created for the purpose of facilitating scholastic research in providing citation information. Scholarly journals, specialized magazines, institutional periodical publications and general-interest magazines are included in the database from all areas of academic interest: humanities, social sciences, science and technology, and medical sciences, including pharmacology. Approximately 10,000 periodicals and more than 6,660,000 articles are currently registered in Zasshi Kiji Sakuin. It is updated every two weeks. Zasshi Kiji Sakuin's extensive coverage of periodicals provides an excellent bibliography of research and publications in Japan, which may not necessarily appear ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1939 Births
This year also marks the start of the Second World War, the largest and deadliest conflict in human history. Events Below, the events of World War II have the "WWII" prefix. January * January 1 ** Third Reich *** Jews are forbidden to work with Germans. *** The Youth Protection Act was passed on April 30, 1938 and the Working Hours Regulations came into effect. *** The Jews name change decree has gone into effect. ** The rest of the world *** In Spain, it becomes a duty of all young women under 25 to complete compulsory work service for one year. *** First edition of the Vienna New Year's Concert. *** The company of technology and manufacturing scientific instruments Hewlett-Packard, was founded in a garage in Palo Alto, California, by William (Bill) Hewlett and David Packard. This garage is now considered the birthplace of Silicon Valley. *** Sydney, in Australia, records temperature of 45 ˚C, the highest record for the city. *** Philipp Etter took over ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Living People
Related categories * :Year of birth missing (living people) / :Year of birth unknown * :Date of birth missing (living people) / :Date of birth unknown * :Place of birth missing (living people) / :Place of birth unknown * :Year of death missing / :Year of death unknown * :Date of death missing / :Date of death unknown * :Place of death missing / :Place of death unknown * :Missing middle or first names See also * :Dead people * :Template:L, which generates this category or death years, and birth year and sort keys. : {{DEFAULTSORT:Living people 21st-century people People by status ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
.svg "Click for more on -> Probability Theory")
.jpg "Click for more on -> 1939 Births")