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https://en.wikipedia.org/wiki/Dehn%20function | In the mathematical subject of geometric group theory, a Dehn function, named after Max Dehn, is an optimal function associated to a finite group presentation which bounds the area of a relation in that group (that is a freely reduced word in the generators representing the identity element of the group) in terms of the length of that relation (see pp. 79–80 in ). The growth type of the Dehn function is a quasi-isometry invariant of a finitely presented group. The Dehn function of a finitely presented group is also closely connected with non-deterministic algorithmic complexity of the word problem in groups. In particular, a finitely presented group has solvable word problem if and only if the Dehn function for a finite presentation of this group is recursive (see Theorem 2.1 in ). The notion of a Dehn function is motivated by isoperimetric problems in geometry, such as the classic isoperimetric inequality for the Euclidean plane and, more generally, the notion of a filling area function that estimates the area of a minimal surface in a Riemannian manifold in terms of the length of the boundary curve of that surface.
History
The idea of an isoperimetric function for a finitely presented group goes back to the work of Max Dehn in 1910s. Dehn proved that the word problem for the standard presentation of the fundamental group of a closed oriented surface of genus at least two is solvable by what is now called Dehn's algorithm. A direct consequence of this fact is that for this presentation the Dehn function satisfies Dehn(n) ≤ n. This result was extended in 1960s by Martin Greendlinger to finitely presented groups satisfying the C'(1/6) small cancellation condition. The formal notion of an isoperimetric function and a Dehn function as it is used today appeared in late 1980s – early 1990s together with the introduction and development of the theory of word-hyperbolic groups. In his 1987 monograph "Hyperbolic groups" Gromov proved that a finitely presented group is word-hyperbolic if and only if it satisfies a linear isoperimetric inequality, that is, if and only if the Dehn function of this group is equivalent to the function f(n) = n. Gromov's proof was in large part informed by analogy with filling area functions for compact Riemannian manifolds where the area of a minimal surface bounding a null-homotopic closed curve is bounded in terms of the length of that curve.
The study of isoperimetric and Dehn functions quickly developed into a separate major theme in geometric group theory, especially since the growth types of these functions are natural quasi-isometry invariants of finitely presented groups. One of the major results in the subject was obtained by Sapir, Birget and Rips who showed that most "reasonable" time complexity functions of Turing machines can be realized, up to natural equivalence, as Dehn functions of finitely presented groups.
Formal definition
Let
be a finite group presentation where the X is a finite alphabet and where |
https://en.wikipedia.org/wiki/ACM%20Transactions%20on%20Mathematical%20Software | ACM Transactions on Mathematical Software (TOMS) is a quarterly scientific journal that aims to disseminate the latest findings of note in the field of numeric, symbolic, algebraic, and geometric computing applications.
The journal publishes two kinds of articles: Regular research papers that advance the development of algorithms and software for mathematical computing, and "algorithms papers" that describe a specific implementation of an algorithm and that are accompanied by the source code for this algorithm.
Algorithms described in the transactions are generally published in the Collected Algorithms of the ACM (CALGO). Algorithms published since 1975 (and some earlier ones) are all still available.
Software that accompanies algorithm papers is accessible by anyone via the CALGO website.
History
ACM Transactions on Mathematical Software is one of the oldest scientific journals specifically dedicated to mathematical algorithms and their implementation in software, and has been published since March 1975 by the Association for Computing Machinery (ACM).
The journal is described as follows on the TOMS Homepage of the ACM Digital Library page:
The purpose of the journal was laid out by its founding editor, John Rice, in the inaugural issue. The decision to found the journal came out of the 1970 Mathematical Software Symposium at Purdue University, also organized by Rice, who then negotiated with both SIAM and the ACM regarding its publication.
References
External links
Journal home page
ACM Collected Algorithms
Transactions on Mathematical Software
Academic journals established in 1975 |
https://en.wikipedia.org/wiki/Bumbuta | Bumbuta is an administrative ward in the Kondoa district of the Dodoma Region of Tanzania. In 2016 the Tanzania National Bureau of Statistics report there were 9,349 people in the ward, from 8,602 in 2012.
References
Kondoa District
Wards of Dodoma Region |
https://en.wikipedia.org/wiki/Busi%20%28Tanzanian%20ward%29 | Busi is an administrative ward in the Kondoa district of the Dodoma Region of Tanzania. In 2016 the Tanzania National Bureau of Statistics report there were 8,459 people in the ward, from 18,724 in 2012.
References
Kondoa District
Wards of Dodoma Region |
https://en.wikipedia.org/wiki/Mondo%20%28Chemba%29 | Mondo is an administrative ward in the Chemba District of the Dodoma Region of Tanzania. In 2016 the Tanzania National Bureau of Statistics report there were 10,318 people in the ward, from 9,494 in 2012.
References
Wards of Dodoma Region |
https://en.wikipedia.org/wiki/Dalai%20%28Tanzanian%20ward%29 | Dalai is an administrative ward in the Chemba District of the Dodoma Region of Tanzania. In 2016 the Tanzania National Bureau of Statistics report there were 16,387 people in the ward, from 15,078 in 2012.
References
Wards of Dodoma Region |
https://en.wikipedia.org/wiki/Chemba | Chemba is an administrative ward in the Chemba district of the Dodoma Region of Tanzania. In 2016 the Tanzania National Bureau of Statistics report there were 5,341 people in the district, from 16,047 in 2012.
References
Wards of Dodoma Region |
https://en.wikipedia.org/wiki/Paranga%2C%20Tanzania | Paranga is an administrative ward in the Chemba District of the Dodoma Region of Tanzania. In 2016 the Tanzania National Bureau of Statistics report there were 13,365 people in the ward, from 12,297 in 2012.
References
Wards of Dodoma Region |
https://en.wikipedia.org/wiki/Mpendo | Mpendo is an administrative ward in the Chemba District of the Dodoma Region of Tanzania. In 2016 the Tanzania National Bureau of Statistics report there were 7,605 people in the ward, from 6,997 in 2012.
References
Wards of Dodoma Region |
https://en.wikipedia.org/wiki/Kingale | Kingale is an administrative ward in the Kondoa district of the Dodoma Region of Tanzania. In 2016 the Tanzania National Bureau of Statistics report there were 11,958 people in the ward, from 11,003 in 2012.
References
Kondoa District
Wards of Dodoma Region |
https://en.wikipedia.org/wiki/Changaa%20%28Tanzanian%20ward%29 | Changaa is an administrative ward in the Kondoa district of the Dodoma Region of Tanzania. In 2016 the Tanzania National Bureau of Statistics report there were 10,471 people in the ward, from 9,634 in 2012.
References
Kondoa District
Wards of Dodoma Region |
https://en.wikipedia.org/wiki/Thawi | Thawi is an administrative ward in the Kondoa District of the Dodoma Region of Tanzania. In 2016 the Tanzania National Bureau of Statistics report there were 11,737 people in the ward, from 10,799 in 2012.
References
Kondoa District
Wards of Dodoma Region |
https://en.wikipedia.org/wiki/Mnenia | Mnenia is an administrative ward in the Kondoa District of the Dodoma Region of Tanzania. In 2016 the Tanzania National Bureau of Statistics report there were 12,529 people in the ward, from 11,528 in 2012.
References
Kondoa District
Wards of Dodoma Region |
https://en.wikipedia.org/wiki/Kikilo | Kikilo is an administrative ward in the Kondoa district of the Dodoma Region of Tanzania. In 2016 the Tanzania National Bureau of Statistics report there were 10,127 people in the ward, from 9,318 in 2012.
References
Kondoa District
Wards of Dodoma Region |
https://en.wikipedia.org/wiki/Charles%20Sims%20%28mathematician%29 | Charles Coffin Sims (April 14, 1937 – October 23, 2017) was an American mathematician best known for his work in group theory. Together with Donald G. Higman he discovered the Higman–Sims group, one of the sporadic groups. The permutation group software developed by Sims also led to the proof of existence of the Lyons group (also known as the Lyons–Sims group) and the O'Nan group (also known as the O'Nan–Sims group).
Sims was born and raised in Elkhart, Indiana, and received his B.S. from the University of Michigan. He did his graduate studies at Harvard University, where he was a student of John G. Thompson and received his Ph.D. degree in 1963. In his thesis, he enumerated p-groups, giving sharp asymptotic upper and lower bounds. Sims is one of the founders of computational group theory and is the eponym of the Schreier–Sims algorithm. He was a faculty member at the Department of Mathematics at Rutgers University from 1965 to 2007. During that period he served, in particular, as Department Chair (1982–84) and Associate Provost for Computer Planning (1984–87). Sims retired from Rutgers in 2007 and moved to St. Petersburg, Florida.
In 2012, he became a fellow of the American Mathematical Society.
See also
Higman–Sims graph
Prevalence of p-groups
Sims conjecture
References
External links
Personal webpage
1937 births
2017 deaths
20th-century American mathematicians
21st-century American mathematicians
Group theorists
Computational group theory
Harvard University alumni
Rutgers University faculty
Fellows of the American Mathematical Society
Mathematicians from Indiana
University of Michigan alumni
People from Elkhart, Indiana |
https://en.wikipedia.org/wiki/Kengo%20Ishii | is a Japanese footballer who currently plays for Nankatsu SC.
Club statistics
Updated to 30 November 2017.
References
External links
Profile at Hokkaido Consadole Sapporo
1986 births
Living people
Association football people from Hokkaido
Japanese men's footballers
J1 League players
J2 League players
Hokkaido Consadole Sapporo players
Ehime FC players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Tomoki%20Suzuki%20%28footballer%29 | is a Japanese former professional footballer who played as a midfielder.
Career statistics
References
External links
Living people
1985 births
People from Iwamizawa, Hokkaido
Association football people from Hokkaido
Men's association football midfielders
Japanese men's footballers
J1 League players
J2 League players
Hokkaido Consadole Sapporo players |
https://en.wikipedia.org/wiki/Yasuaki%20Okamoto | is a former Japanese football player who featured for Roasso Kumamoto.
Club statistics
Updated to 2 February 2018.
References
External links
Profile at Roasso Kumamoto
Profile at Consadole Sapporo
1988 births
Living people
Japanese men's footballers
J1 League players
J2 League players
Hokkaido Consadole Sapporo players
Roasso Kumamoto players
Men's association football midfielders
Association football people from Kumamoto |
https://en.wikipedia.org/wiki/Hironobu%20Haga | is a former Japanese football player.
Club statistics
References
External links
1982 births
Living people
Sendai University alumni
Association football people from Miyagi Prefecture
Japanese men's footballers
J1 League players
J2 League players
JEF United Chiba players
Hokkaido Consadole Sapporo players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Kazumasa%20Uesato | is a Japanese football player who plays for FC Ryukyu.
Club statistics
Updated to 23 February 2018.
References
External links
Profile at Roasso Kumamoto
1986 births
Living people
Association football people from Okinawa Prefecture
Japanese men's footballers
J1 League players
J2 League players
Hokkaido Consadole Sapporo players
FC Tokyo players
Tokushima Vortis players
Roasso Kumamoto players
FC Ryukyu players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Yasuhiro%20Hiraoka | is a Japanese footballer who plays for Ehime FC from 2023.
Club career
On 18 December 2022, Hiraoka joined to J3 club, Ehime FC for upcoming 2023 season.
Career statistics
Updated to the end 2022 season.
References
External links
Profile at Vegalta Sendai
1986 births
Living people
People from Fujinomiya, Shizuoka
Association football people from Shizuoka Prefecture
Japanese men's footballers
J1 League players
J2 League players
J3 League players
Shimizu S-Pulse players
Hokkaido Consadole Sapporo players
Vegalta Sendai players
Ehime FC players
Men's association football defenders |
https://en.wikipedia.org/wiki/Split-pi%20topology | In electronics, a split-pi topology is a pattern of component interconnections used in a kind of power converter that can theoretically produce an arbitrary output voltage, either higher or lower than the input voltage. In practice the upper voltage output is limited to the voltage rating of components used. It is essentially a boost (step-up) converter followed by a buck (step-down) converter. The topology and use of MOSFETs make it inherently bi-directional which lends itself to applications requiring regenerative braking.
The split-pi converter is a type of DC-to-DC converter that has an output voltage magnitude either greater than or less than the input voltage magnitude. It is a switched-mode power supply with a similar circuit configuration to a boost converter followed by a buck converter. Split-pi gets its name from the pi circuit due to the use of two pi filters in series and split with the switching MOSFET bridges.
Other DC–DC converter topologies that can produce output voltage magnitude either greater than or less than the input voltage magnitude include the boost-buck converter topologies (the split-pi, the Ćuk converter, the SEPIC, etc.) and the buck–boost converter topologies.
Principle of operation
In typical operation where a source voltage is located at the left-hand side input terminals, the left-hand bridge operates as a boost converter and the right-hand bridge operates as a buck converter. In regenerative mode, the reverse is true with the left-hand bridge operating as a buck converter and the right as the boost converter.
Only one bridge switches at any time to provide voltage conversion, with the unswitched bridge's top switch always switched on. A straight through 1:1 voltage output is achieved with the top switch of each bridge switch on and the bottom switches off. The output voltage is adjustable based on the duty cycle of the switching MOSFET bridge.
Applications
Electric drivetrain
Motor control
Battery balancing
Regenerative braking
References
British Patent GB2376357B - Power converter and method for power conversion
DC-to-DC converters
Voltage regulation |
https://en.wikipedia.org/wiki/Hiroki%20Miyazawa | is a Japanese football player currently playing for Hokkaido Consadole Sapporo.
Career statistics
Club
Updated to the start of 2023 season.
National team career statistics
Appearances in major competitions
References
External links
Profile at Consadole Sapporo
1989 births
Living people
Association football people from Hokkaido
Japanese men's footballers
J1 League players
J2 League players
Hokkaido Consadole Sapporo players
Men's association football midfielders
People from Date, Hokkaido |
https://en.wikipedia.org/wiki/Junki%20Yokono | is a Japanese football player.
Club statistics
Updated to 8 March 2018.
References
External links
1989 births
Living people
Association football people from Hokkaido
Japanese men's footballers
J1 League players
J2 League players
J3 League players
Japan Football League players
Hokkaido Consadole Sapporo players
Zweigen Kanazawa players
Fukushima United FC players
ReinMeer Aomori players
Nara Club players
Expatriate men's footballers in Thailand
Men's association football forwards |
https://en.wikipedia.org/wiki/Toshiyasu%20Takahara | is a former Japanese football player.
Club statistics
Updated to 31 December 2018.
1Includes J2/J3 Playoffs.
References
External links
Profile at FC Machida Zelvia
1980 births
Living people
Aichi Gakuin University alumni
Association football people from Gifu Prefecture
Japanese men's footballers
J1 League players
J2 League players
J3 League players
Júbilo Iwata players
Hokkaido Consadole Sapporo players
Shimizu S-Pulse players
FC Machida Zelvia players
Men's association football goalkeepers
Sportspeople from Gifu |
https://en.wikipedia.org/wiki/Shingo%20Shibata | is a former Japanese football player.
Club statistics
References
External links
1985 births
Living people
Tokoha University alumni
Association football people from Tokyo
Japanese men's footballers
J1 League players
J2 League players
Hokkaido Consadole Sapporo players
Thespakusatsu Gunma players
Men's association football defenders
People from Ōme, Tokyo |
https://en.wikipedia.org/wiki/Hiroyuki%20Omichi | is a former Japanese football player.
Club statistics
References
External links
1987 births
Living people
Association football people from Ibaraki Prefecture
Japanese men's footballers
J1 League players
J2 League players
J3 League players
Japan Football League players
Kashima Antlers players
Fagiano Okayama players
AC Nagano Parceiro players
Iwate Grulla Morioka players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Kenta%20Kasai | is a former Japanese football player.
Club statistics
References
1985 births
Living people
Association football people from Shizuoka Prefecture
Japanese men's footballers
Japanese expatriate men's footballers
J1 League players
Paulista Futebol Clube players
Kashima Antlers players
Men's association football defenders |
https://en.wikipedia.org/wiki/Stratified%20Morse%20theory | In mathematics, stratified Morse theory is an analogue to Morse theory for general stratified spaces, originally developed by Mark Goresky and Robert MacPherson. The main point of the theory is to consider functions and consider how the stratified space changes as the real number changes. Morse theory of stratified spaces has uses everywhere from pure mathematics topics such as braid groups and representations to robot motion planning and potential theory. A popular application in pure mathematics is Morse theory on manifolds with boundary, and manifolds with corners.
See also
Digital Morse theory
Discrete Morse theory
Level-set method
References
DJVU file on Goresky's page
Generalized manifolds
Morse theory
Singularity theory
Stratifications |
https://en.wikipedia.org/wiki/The%20Story%20of%20Maths | The Story of Maths is a four-part British television series outlining aspects of the history of mathematics. It was a co-production between the Open University and the BBC and aired in October 2008 on BBC Four. The material was written and presented by University of Oxford professor Marcus du Sautoy. The consultants were the Open University academics Robin Wilson, professor Jeremy Gray and June Barrow-Green. Kim Duke is credited as series producer.
The series comprised four programmes respectively titled: The Language of the Universe; The Genius of the East; The Frontiers of Space; and To Infinity and Beyond. Du Sautoy documents the development of mathematics covering subjects such as the invention of zero and the unproven Riemann hypothesis, a 150-year-old problem for whose solution the Clay Mathematics Institute has offered a $1,000,000 prize. He escorts viewers through the subject's history and geography. He examines the development of key mathematical ideas and shows how mathematical ideas underpin the world's science, technology, and culture.
He starts his journey in ancient Egypt and finishes it by looking at current mathematics. Between he travels through Babylon, Greece, India, China, and the medieval Middle East. He also looks at mathematics in Europe and then in America and takes the viewers inside the lives of many of the greatest mathematicians.
"The Language of the Universe"
In this opening programme Marcus du Sautoy looks at how important and fundamental mathematics is to our lives before looking at the mathematics of ancient Egypt, Mesopotamia, and Greece.
Du Sautoy commences in Egypt where recording the patterns of the seasons and in particular the flooding of the Nile was essential to their economy. There was a need to solve practical problems such as land area for taxation purposes. Du Sautoy discovers the use of a decimal system based on the fingers on the hands, the unusual method for multiplication and division. He examines the Rhind Papyrus, the Moscow Papyrus and explores their understanding of binary numbers, fractions and solid shapes.
He then travels to Babylon and discovered that the way we tell the time today is based on the Babylonian 60 base number system. So because of the Babylonians we have 60 seconds in a minute, and 60 minutes in an hour. He then shows how the Babylonians used quadratic equations to measure their land. He deals briefly with Plimpton 322.
In Greece, the home of ancient Greek mathematics, he looks at the contributions of some of its greatest and well known mathematicians including Pythagoras, Plato, Euclid, and Archimedes, who are some of the people who are credited with beginning the transformation of mathematics from a tool for counting into the analytical subject we know today. A controversial figure, Pythagoras' teachings were considered suspect and his followers seen as social outcasts and a little be strange and not in the norm. There is a legend going around that one of his followers, |
https://en.wikipedia.org/wiki/Yasushi%20Endo | is a Japanese footballer who plays for Vegalta Sendai.
Career statistics
.
International career
On 7 May 2015, Japan's coach Vahid Halilhodžić called him for a two-days training camp.
Honours
Club
Kashima Antlers
J. League Division 1 (4) : 2007, 2008, 2009, 2016
Emperor's Cup (3) : 2007, 2010, 2016
J. League Cup (3) : 2011, 2012, 2015
Japanese Super Cup (3) : 2009, 2010, 2017
Suruga Bank Championship (2) : 2012, 2013
AFC Champions League (1): 2018
References
External links
official instagram
Profile at Kashima Antlers
1988 births
Living people
Association football people from Miyagi Prefecture
Japanese men's footballers
J1 League players
Kashima Antlers players
J2 League players
Vegalta Sendai players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Naoya%20Ishigami | is a Japanese footballer who is currently playing for FC Tiamo Hirakata.
Career statistics
Updated to 23 February 2020.
1Includes Promotion Playoffs to J1.
Team honors
Kashima Antlers
J1 League (2): 2007, 2008
References
External links
Profile at Giravanz Kitakyushu
1985 births
Living people
Kanagawa University alumni
Association football people from Ibaraki Prefecture
Japanese men's footballers
J1 League players
J2 League players
Japan Football League players
Kashima Antlers players
Cerezo Osaka players
Shonan Bellmare players
Oita Trinita players
Tokyo Verdy players
V-Varen Nagasaki players
Giravanz Kitakyushu players
FC Maruyasu Okazaki players
FC Tiamo Hirakata players
Men's association football defenders |
https://en.wikipedia.org/wiki/Masaki%20Chugo | is a former Japanese football player.
Club statistics
Team honors
J1 League - 2007, 2008
Emperor's Cup - 2007
References
External links
1982 births
Living people
Komazawa University alumni
Japanese men's footballers
J1 League players
J2 League players
Kashima Antlers players
JEF United Chiba players
Cerezo Osaka players
Tokyo Verdy players
FISU World University Games gold medalists for Japan
Universiade medalists in football
Men's association football midfielders
Association football people from Chiba (city) |
https://en.wikipedia.org/wiki/Taishi%20Tsukamoto | is a former Japanese football player.
Club statistics
Personal life
On 28 February 2010 was announced that the 24-year-old Japanese is injured with the Osteosarcoma at the knee. Whether the defender can continue his career is still uncertain.
References
External links
1985 births
Living people
Komazawa University alumni
Association football people from Saitama Prefecture
Japanese men's footballers
J1 League players
Omiya Ardija players
Men's association football defenders |
https://en.wikipedia.org/wiki/Hayato%20Hashimoto | is a former Japanese football player.
Club statistics
References
External links
1981 births
Living people
Komazawa University alumni
Association football people from Fukui Prefecture
Japanese men's footballers
J1 League players
J2 League players
Omiya Ardija players
Expatriate men's footballers in Thailand
Men's association football midfielders |
https://en.wikipedia.org/wiki/Masahiko%20Ichikawa | is a former Japanese football player.
Club statistics
References
External links
1985 births
Living people
Hosei University alumni
Association football people from Tokyo
Japanese men's footballers
J1 League players
J2 League players
Omiya Ardija players
Tokyo Verdy players
Men's association football forwards |
https://en.wikipedia.org/wiki/Tatsuya%20Kawahara | is a former Japanese football player.
Club statistics
References
External links
1985 births
Living people
Toyo University alumni
Association football people from Ibaraki Prefecture
Japanese men's footballers
J1 League players
J2 League players
Omiya Ardija players
Thespakusatsu Gunma players
Men's association football defenders |
https://en.wikipedia.org/wiki/Takuya%20Aoki | is a Japanese professional footballer who plays as a defensive midfielder for J1 League club FC Tokyo.
Career statistics
Club
Updated to 19 July 2022.
1Includes Japanese Super Cup, J. League Championship, FIFA Club World Cup.
Honours
Club
Urawa Red Diamonds
AFC Champions League: 2017
J.League Cup: 2016
References
External links
Profile at FC Tokyo
1989 births
Living people
Association football people from Gunma Prefecture
Japanese men's footballers
J1 League players
Omiya Ardija players
Urawa Red Diamonds players
FC Tokyo players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Mitsuki%20Ichihara | is a former Japanese football player.
Club statistics
References
External links
1986 births
Living people
Japanese men's footballers
J1 League players
Singapore Premier League players
JEF United Chiba players
Albirex Niigata Singapore FC players
Briobecca Urayasu players
Men's association football defenders
Japanese expatriate men's footballers
Association football people from Chiba (city) |
https://en.wikipedia.org/wiki/Atsushi%20Ito%20%28footballer%29 | is a former Japanese football player.
Club statistics
References
External links
1983 births
Living people
Association football people from Yamaguchi Prefecture
Japanese men's footballers
J1 League players
J2 League players
JEF United Chiba players
Tochigi SC players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Geir%20Axelsen | Geir Axelsen (born 15 May 1965) is a Norwegian economist, civil servant and politician for the Norwegian Labour Party. From 2018 he was appointed director general of Statistics Norway.
Early life
Born in Oslo, he has a cand.oecon. degree from the University of Oslo in 1994 and a Master of Public Administration from John F. Kennedy School of Government in 2004.
Career
He started his political career in the Workers' Youth League, and chaired that organization's chapter in Oslo from 1987 to 1988. He worked as party secretary for the Labour Party in Oslo from 1994 to 1997, when he was hired in the Ministry of Finance. In 2005 he became counsellor of the Norwegian embassy in Brussels.
When the second cabinet Stoltenberg assumed office following the 2005 election, he was appointed State Secretary in the Ministry of Finance.
References
Biography at Government.no
1965 births
Living people
Labour Party (Norway) politicians
Norwegian state secretaries
Politicians from Oslo
University of Oslo alumni
Harvard Kennedy School alumni
Norwegian civil servants
Norwegian expatriates in the United States |
https://en.wikipedia.org/wiki/Jiro%20Kamata | is a Japanese footballer who currently plays for Kashiwa Reysol.
Club career statistics
Updated to 28 February 2019.
References
External links
Profile at Kashiwa Reysol
Twitter
1985 births
Living people
Ryutsu Keizai University alumni
Association football people from Tokyo
Japanese men's footballers
J1 League players
J2 League players
J3 League players
Kashiwa Reysol players
Vegalta Sendai players
SC Sagamihara players
Men's association football defenders |
https://en.wikipedia.org/wiki/Chunyu%20%28ward%29 | Chunyu is an administrative ward in the Mpwapwa district of the Dodoma Region of Tanzania. In 2016 the Tanzania National Bureau of Statistics report there were 12,600 people in the ward, from 11,593 in 2012.
References
Wards of Dodoma Region |
https://en.wikipedia.org/wiki/Godegode | Gode Gode is an administrative ward in the Mpwapwa district of the Dodoma Region of Tanzania. In 2016 the Tanzania National Bureau of Statistics report there were 8,569 people in the ward, from 7,884 in 2012.
References
Wards of Dodoma Region |
https://en.wikipedia.org/wiki/Ipera | Ipera is an administrative ward in the Mpwapwa district of the Dodoma Region of Tanzania. In 2016 the Tanzania National Bureau of Statistics report there were 8,362 people in the ward, from 12,870 in 2012.
References
Wards of Dodoma Region |
https://en.wikipedia.org/wiki/Kimagai | Kimagai is an administrative ward in the Mpwapwa district of the Dodoma Region of Tanzania. In 2016 the Tanzania National Bureau of Statistics report there were 7,977 people in the ward, from 7,340 in 2012.
References
Wards of Dodoma Region |
https://en.wikipedia.org/wiki/Luhundwa | Luhundwa is an administrative ward in the Mpwapwa district of the Dodoma Region of Tanzania. In 2016 the Tanzania National Bureau of Statistics report there were 13,217 people in the ward, from 12,161 in 2012.
References
Wards of Dodoma Region |
https://en.wikipedia.org/wiki/Slovan%20Bratislava%20statistics%20and%20records | Several players for the Slovak football team ŠK Slovan Bratislava have been outstanding, in terms of goalscoring or in terms of appearances for the Slovak or Czechoslovak national teams.
Most goals
Jozef Adamec 170
Emil Pažický 123
Anton Moravčík 109
Marián Masný 103
Ján Čapkovič 100
Best scorers
Emil Pažický 19 (1954/55)
Ján Čapkovič 19 (1971/72)
Marián Masný 16 (1980/81)
Peter Dubovský 22 (1991/92), 23 (1992/93)
Pavol Masaryk 15 (2008/09)
Most matches in national team
Marián Masný 75
Róbert Vittek 74
Ján Popluhár 62
Szilárd Németh 59
Anton Ondruš 58
ŠK Slovan Bratislava |
https://en.wikipedia.org/wiki/Mazae | Mazae is an administrative ward in the Mpwapwa district of the Dodoma Region of Tanzania. In 2016 the Tanzania National Bureau of Statistics reported 8,717 people in the ward, from 8,021 in 2012.
References
Wards of Dodoma Region |
https://en.wikipedia.org/wiki/Mbuga | Mbuga is an administrative ward in the Mpwapwa district of the Dodoma Region of Tanzania. In 2016 the Tanzania National Bureau of Statistics report there were 6,318 people in the ward, from 5,813 in 2012.
References
Wards of Dodoma Region |
https://en.wikipedia.org/wiki/Mpwapwa%20Mjini | Mpwapwa Mjini is an administrative ward in the Mpwapwa district of the Dodoma Region of Tanzania. In 2016 the Tanzania National Bureau of Statistics report there were 23,190 people in the ward, from 21,337 in 2012.
References
Wards of Dodoma Region |
https://en.wikipedia.org/wiki/Ving%27hawe | Ving'hawe is an administrative ward in the Mpwapwa district of the Dodoma Region of Tanzania. In 2016 the Tanzania National Bureau of Statistics report there were 12,712 people in the ward, from 12,277 in 2012.
References
Wards of Dodoma Region |
https://en.wikipedia.org/wiki/H%20square | In mathematics and control theory, H2, or H-square is a Hardy space with square norm. It is a subspace of L2 space, and is thus a Hilbert space. In particular, it is a reproducing kernel Hilbert space.
On the unit circle
In general, elements of L2 on the unit circle are given by
whereas elements of H2 are given by
The projection from L2 to H2 (by setting an = 0 when n < 0) is orthogonal.
On the half-plane
The Laplace transform given by
can be understood as a linear operator
where is the set of square-integrable functions on the positive real number line, and is the right half of the complex plane. It is more; it is an isomorphism, in that it is invertible, and it isometric, in that it satisfies
The Laplace transform is "half" of a Fourier transform; from the decomposition
one then obtains an orthogonal decomposition of into two Hardy spaces
This is essentially the Paley-Wiener theorem.
See also
H∞
References
Jonathan R. Partington, "Linear Operators and Linear Systems, An Analytical Approach to Control Theory", London Mathematical Society Student Texts 60, (2004) Cambridge University Press, .
Control theory
Mathematical analysis |
https://en.wikipedia.org/wiki/Pawe%C5%82%20Wojciechowski%20%28economist%29 | Paweł Wojciechowski (born 3 January 1960) is a Polish economist.
Life
He graduated from the Foreign Trade Faculty of the Main School of Planning and Statistics in 1983. In 1986 he graduated with a bachelor's degree in Economics from John Carroll University, Ohio in the United States.
Paweł Wojciechowski has academic, corporate and government experiences. While staying in Cleveland between 1983 and 1991, he worked as an analyst at the Center for Regional Economic Issues and lectured in statistics at John Carroll University.
After returning to Warsaw, from 1992 to 1995, he advised the Polish government on privatisation and capital market development, including work for UNDP, the Polish Ministry of Privatisation and KPMG/USAID.
From 1995 to 2005, he worked as CEO of three financial institutions: Polish Fund Management Group Sp. z o.o. – Polish Development Bank S.A. division (1995–1996); PBK ATUT TFI S.A. – Investment Fund Company (1996–1999); and PTE Allianz Poland S.A. – Allianz Pension Fund (1999–2005).
In June 2006 Paweł Wojciechowski was entrusted with the position of Minister of Finance of Poland, earlier serving as economic advisor to the Prime Minister Kazimierz Marcinkiewicz. After the change of government, he became Chief Economist of the Polish Institute of Directors, and then he headed the Polish Information and Foreign Investment Agency for two years.
From March 2009, until his nomination as Permanent Representative of Poland to the OECD, Paweł Wojciechowski was Undersecretary of State at the Ministry of Foreign Affairs in Poland, responsible for economic cooperation and development.
On 11 August 2010, Paweł Wojciechowski took up his duties as Ambassador, Permanent Representative of Poland to the Organisation for Economic Co-operation and Development.
In 2014, after his tenure as an Ambassador, Paweł Wojciechowski became the Chief Economist of the Polish Social Insurance Institution (ZUS). He is also the European Coordinator for the TEN-T Rhine-Alpine Corridor, since May 2015.
References
1960 births
Living people
Writers from Warsaw
John Carroll University alumni
John Carroll University faculty
Finance Ministers of Poland
Polish economists
Ambassadors of Poland to the Organisation for Economic Co-operation and Development
SGH Warsaw School of Economics alumni
Politicians from Warsaw |
https://en.wikipedia.org/wiki/Pharmaceutical%20Statistics%20%28journal%29 | Pharmaceutical Statistics is a peer-reviewed scientific journal that publishes papers related to pharmaceutical statistics. It is the official journal of Statisticians in the Pharmaceutical Industry and is published by John Wiley & Sons.
Abstracting and indexing
Pharmaceutical Statistics is indexed in the following services:
Current Index to Statistics
MEDLINE
Science Citation Index
Science Citation Index Expanded
Scopus
External links
http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1539-1612
Biostatistics journals |
https://en.wikipedia.org/wiki/Regiomontanus%27%20angle%20maximization%20problem | In mathematics, the Regiomontanus's angle maximization problem, is a famous optimization problem posed by the 15th-century German mathematician Johannes Müller (also known as Regiomontanus). The problem is as follows:
A painting hangs from a wall. Given the heights of the top and bottom of the painting above the viewer's eye level, how far from the wall should the viewer stand in order to maximize the angle subtended by the painting and whose vertex is at the viewer's eye?
If the viewer stands too close to the wall or too far from the wall, the angle is small; somewhere in between it is as large as possible.
The same approach applies to finding the optimal place from which to kick a ball in rugby. For that matter, it is not necessary that the alignment of the picture be at right angles: we might be looking at a window of the Leaning Tower of Pisa or a realtor showing off the advantages of a sky-light in a sloping attic roof.
Solution by elementary geometry
There is a unique circle passing through the top and bottom of the painting and tangent to the eye-level line. By elementary geometry, if the viewer's position were to move along the circle, the angle subtended by the painting would remain constant. All positions on the eye-level line except the point of tangency are outside of the circle, and therefore the angle subtended by the painting from those points is smaller.
Let
a = the height of the painting´s bottom above eye level;
b = the height of the painting´s top above eye level;
A right triangle is formed from the centre of the circle, the centre of the picture and the bottom of the picture. The hypotenuse has the length of the circle´s radius a+(b-a)/2, the length of the two legs are the distance from the wall to the point of tangency and (b-a)/2 respectively. According to the Pythagorean theorem, the distance from the wall to the point of tangency is therefore , i. e. the geometric mean of the heights of the top and bottom of the painting.
Solution by calculus
In the present day, this problem is widely known because it appears as an exercise in many first-year calculus textbooks (for example that of Stewart ).
Let
a = the height of the bottom of the painting above eye level;
b = the height of the top of the painting above eye level;
x = the viewer's distance from the wall;
α = the angle of elevation of the bottom of the painting, seen from the viewer's position;
β = the angle of elevation of the top of the painting, seen from the viewer's position.
The angle we seek to maximize is β − α. The tangent of the angle increases as the angle increases; therefore it suffices to maximize
Since b − a is a positive constant, we only need to maximize the fraction that follows it. Differentiating, we get
Therefore the angle increases as x goes from 0 to and decreases as x increases from . The angle is therefore as large as possible precisely when x = , the geometric mean of a and b.
Solution by algebra
We have s |
https://en.wikipedia.org/wiki/Shu%20Abe | is a former Japanese football player.
He generally plays from a central position as a defensively minded midfielder.
Club statistics
References
External links
1984 births
Living people
Ryutsu Keizai University alumni
Association football people from Osaka Prefecture
Japanese men's footballers
J1 League players
J2 League players
Japan Football League players
Kashiwa Reysol players
Avispa Fukuoka players
Zweigen Kanazawa players
FC Machida Zelvia players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Jun%20Yanagisawa | is a Japanese football player. He plays for MIO Biwako Shiga.
Club statistics
References
External links
1987 births
Living people
Association football people from Ibaraki Prefecture
Japanese men's footballers
J1 League players
J2 League players
Japan Football League players
Kashiwa Reysol players
Sagan Tosu players
Azul Claro Numazu players
Reilac Shiga FC players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Ryoichi%20Kurisawa | is a Japanese football manager and former player. He is currently assistant coach for J1 League club Kashiwa Reysol.
Club statistics
Updated to 23 February 2019.
1Includes Japanese Super Cup and FIFA Club World Cup.
References
External links
Profile at Kashiwa Reysol
1982 births
Living people
Ryutsu Keizai University alumni
Association football people from Chiba Prefecture
Japanese men's footballers
J1 League players
J2 League players
FC Tokyo players
Kashiwa Reysol players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Hitoshi%20Shiota | is a Japanese football player who plays for Tochigi SC.
Club statistics
Updated to 23 February 2018.
1Includes Japanese Super Cup.
References
External links
1981 births
Living people
Ryutsu Keizai University alumni
Association football people from Ibaraki Prefecture
Japanese men's footballers
J1 League players
J2 League players
FC Tokyo players
Omiya Ardija players
Tochigi SC players
Men's association football goalkeepers
FISU World University Games gold medalists for Japan
Universiade medalists in football |
https://en.wikipedia.org/wiki/Kota%20Morimura | is a Japanese football player currently playing for FC Machida Zelvia.
Career statistics
Updated to end of 2018 season.
National team career statistics
Appearances in major competitions
References
External links
Profile at Machida Zelvia
1988 births
Living people
Association football people from Tokyo Metropolis
People from Kodaira, Tokyo
Japanese men's footballers
J1 League players
J2 League players
J3 League players
FC Tokyo players
Mito HollyHock players
Giravanz Kitakyushu players
Avispa Fukuoka players
FC Machida Zelvia players
Men's association football midfielders |
https://en.wikipedia.org/wiki/M%C3%A1ria%20Bal%C3%A1%C5%BEov%C3%A1 | Mária Balážová (born 31 August 1956) is a contemporary Slovak artist. Her practise as an artist is usually associated with new geometry, post-geometry and postmodern.
Life and work
Balážová studied at the Academy of Muse Arts, Bratislava and Magister of Arts degree received in 1984. Since 1997, Balážová is also known as a teacher at the University of Trnava. Her husband is Blažej Baláž, Slovak painter.
Immediately at the beginning, Mária Balážová, created her own „personal mythology“, emphasizing a snake motif in the geometrically stylised form of a cobra. This animal, which occupies an important position in world mythologies and religions, became the main motif of cycles of paintings, to which the artist gave the name Serpent Geometry. Balážová distinguished herself from classic Neo-Constructivism, outlined on subjectless combinations of shapes and colours, put together into geometric structures. Art theorists appreciate the „new significance“ she achieved by creating radically reductive forms (Jiří Valoch, 2002). "
In her latest works, fear of violence, power and hegemony are projected in the intimate family background, where the dominant men´s element is systematically planned in the painting area and it culminates in the series of drawings and paintings called Domestic Violence. A distinctly expressive handwriting used in some places refers very straightforwardly to Balážová´s personal story and moves the general criticism of an androcentric society to a more intimate position. Here, the key role is played by the figure of a despotic father who permanently and demonically comes back in acrylic canvases and large-format drawings – destructively and aggressively . In the latest works, Mária Balážová bet on a straightforward expression of her personal story associated with a therapeutic character. This approach in her works represents a new dimension not only for her herself, but also for geometric painting in general. (Roman Gajdoš)
Her works are held in the collections of Slovak National Gallery, Bratislava, National Gallery, Prague (CZ), Wannieck Gallery Brno (CZ), Jan Koniarek Gallery , Trnava.
The artist has been a member of the revived Club of Concrete Artists 2 and the artist's group East of Eden. She lives and works in Trnava.
Awards
1990 Honorable Mention, Drawing 1990, Provo (USA)
1995 Prize of Masaryk's Academy, Prague (CZ)
2019 Honorary Mention Award, International Drawing Biennale India 2018-19, New Delhi (India)
Selected solo exhibitions
Maria Balazova, Jan Koniarek Gallery, Trnava, 26 June – 30 July 1991 (catalogue)
Maria Balazova, Gallery Arpex, Bratislava, 28 January – 17 February 1993
Serpent Geometry, Cyprian Majernik Gallery, Bratislava, 19 April – 8 May 1995
Serpent Geometry 2, Jan Koniarek Gallery, Trnava, 23 May – 23 June 1996 (catalogue)
Dozen 1988-2000, The Central Slovakian Gallery, Banská Bystrica, 5 May – 30 June 2000
Dozen 1988-2000, The East Slovak Gallery, Košice, 14 September – 15 October 200 |
https://en.wikipedia.org/wiki/SORT%20%28journal%29 | SORT or Statistics and Operations Research Transactions is a peer-reviewed open access scientific journal that publishes papers related to statistics. It is published by the Institut d'Estadística de Catalunya, the statistical office of Catalonia, in English with a brief summary in Catalan.
The journal was established in 2003, when it replaced the journal Qüestiió (Quaderns d'Estadística i Investigació Operativa, 1977–2002). It publishes two issues each year, and is available online as open access.
Abstracting and indexing
SORT is indexed in the Current Index to Statistics, Science Citation Index Expanded, and Journal Citation Reports.
External links
Academic journals established in 1977
Open access journals
Statistics journals
Biannual journals
English-language journals |
https://en.wikipedia.org/wiki/REVSTAT | REVSTAT is a peer-reviewed open access scientific journal that publishes papers related to statistics. It is published in English by the Instituto Nacional de Estatística, the national statistical office of Portugal. The journal was established in 2003, when it replaced the journal Revista de Estatística. It publishes two issues each year, both in print (subscription) and online as open access.
Abstracting and indexing
REVSTAT is abstracted and indexed in Current Index to Statistics, Science Citation Index Expanded, MathSciNet, Statistical Theory and Method Abstracts, and Zentralblatt MATH.
External links
Statistics journals
Academic journals established in 2003
Open access journals
English-language journals
Biannual journals |
https://en.wikipedia.org/wiki/Armadillo%20%28C%2B%2B%20library%29 | Armadillo is a linear algebra software library for the C++ programming language. It aims to provide efficient and streamlined base calculations, while at the same time having a straightforward and easy-to-use interface. Its intended target users are scientists and engineers.
It supports integer, floating point (single and double precision), complex numbers, and a subset of trigonometric and statistics functions. Dense and sparse matrices are supported. Various matrix decompositions are provided through optional integration with Linear Algebra PACKage (LAPACK), Automatically Tuned Linear Algebra Software (ATLAS), and ARPACK. High-performance BLAS/LAPACK replacement libraries such as OpenBLAS and Intel MKL can also be used.
The library employs a delayed-evaluation approach (during compile time) to combine several operations into one and reduce (or eliminate) the need for temporaries. Where applicable, the order of operations is optimised. Delayed evaluation and optimisation are achieved through template metaprogramming.
Armadillo is related to the Boost Basic Linear Algebra Subprograms (uBLAS) library, which also uses template metaprogramming. However, Armadillo builds upon ATLAS and LAPACK libraries, thereby providing machine-dependent optimisations and functions not present in uBLAS.
It is open-source software distributed under the permissive Apache License, making it applicable for the development of both open source and proprietary software. The project is supported by the NICTA research centre in Australia.
An interface to the Python language is available through the PyArmadillo package,
which facilitates prototyping of algorithms in Python followed by relatively straightforward conversion to C++.
Armadillo is a core dependency of the mlpack machine learning library and the ensmallen C++ library for numerical optimization.
Example in C++ 11
Here is a trivial example demonstrating Armadillo functionality:
// Compile with:
// $ g++ -std=c++11 main.cpp -o file_name -O2 -larmadillo
#include <iostream>
#include <armadillo>
#include <cmath>
int main()
{
// ^
// Position of a particle // |
arma::vec Pos = {{0}, // | (0,1)
{1}}; // +---x-->
// Rotation matrix
double phi = -3.1416/2;
arma::mat RotM = {{+cos(phi), -sin(phi)},
{+sin(phi), +cos(phi)}};
Pos.print("Current position of the particle:");
std::cout << "Rotating the point " << phi*180/3.1416 << " deg" << std::endl;
Pos = RotM*Pos;
Pos.print("New position of the particle:"); // ^
// x (1,0)
// |
// +------>
return 0;
}
Example in C++ 98
Here is another trivial example in C++ 98:
#include <iostream>
#include <armadillo>
int main()
{
ar |
https://en.wikipedia.org/wiki/Yohei%20Otake | is a Japanese football player currently playing for V-Varen Nagasaki.
Club statistics
Updated to 1 March 2019.
References
External links
1989 births
Living people
Association football people from Saitama Prefecture
Japanese men's footballers
J1 League players
J2 League players
FC Tokyo players
Cerezo Osaka players
Shonan Bellmare players
Fagiano Okayama players
V-Varen Nagasaki players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Kenta%20Mukuhara | is a Japanese former football player.
Career
After three seasons playing for Fagiano Okayama in J2 League, Mukuhara retired in December 2020.
Career statistics
Club
Updated to end of 2018 season.
1Includes Emperor's Cup.
2Includes J. League Cup.
3Includes AFC Champions League.
4Includes Suruga Bank Championship and Japanese Super Cup.
Honours
Club
F.C. Tokyo
J. League Division 2 (1) : 2011
Emperor's Cup (1) : 2011
J. League Cup (1) : 2009
Suruga Bank Championship (1) : 2010
References
External links
Profile at Cerezo Osaka
1989 births
Living people
Association football people from Tokyo
Japanese men's footballers
J1 League players
J2 League players
J3 League players
FC Tokyo players
Cerezo Osaka players
Cerezo Osaka U-23 players
Sanfrecce Hiroshima players
Fagiano Okayama players
Men's association football defenders |
https://en.wikipedia.org/wiki/Kohei%20Shimoda | is a former Japanese football player who last played for Blaublitz Akita.
Club statistics
Updated to 2 February 2018.
Honours
FC Tokyo
J2 League (1): 2011
Emperor's Cup (1): 2011
Blaublitz Akita
J3 League (1): 2017
References
External links
Profile at Blaublitz Akita
1989 births
Living people
Association football people from Akita Prefecture
Japanese men's footballers
J1 League players
J2 League players
J3 League players
FC Tokyo players
Mito HollyHock players
FC Machida Zelvia players
V-Varen Nagasaki players
Blaublitz Akita players
Men's association football defenders
People from Akita (city) |
https://en.wikipedia.org/wiki/Tatsuya%20Suzuki%20%28footballer%2C%20born%201982%29 | is a former Japanese football player.
Club statistics
References
External links
1982 births
Living people
University of Tsukuba alumni
Association football people from Kanagawa Prefecture
Japanese men's footballers
J1 League players
J2 League players
Kashiwa Reysol players
FC Tokyo players
Tokushima Vortis players
Men's association football forwards |
https://en.wikipedia.org/wiki/Taira%20Inoue | is a Japanese footballer.
Club career statistics
References
External links
1983 births
Living people
Hosei University alumni
Association football people from Tokyo
People from Hachiōji, Tokyo
Japanese men's footballers
J1 League players
J2 League players
J3 League players
Tokyo Verdy players
FC Gifu players
SC Sagamihara players
Men's association football forwards |
https://en.wikipedia.org/wiki/Brazilian%20Journal%20of%20Probability%20and%20Statistics | The Brazilian Journal of Probability and Statistics () is a peer-reviewed scientific journal that publishes papers related to statistics. It is published four times a year by the Brazilian Statistical Association with the support of the Institute of Mathematical Statistics. The journal was established in 1987.
Abstracting and indexing
The Brazilian Journal of Probability and Statistics is indexed in the Current Index to Statistics and Zentralblatt MATH.
Probability journals
Statistics journals
Academic journals established in 1987
English-language journals
Quarterly journals
Academic journals published by learned and professional societies |
https://en.wikipedia.org/wiki/Z88%20FEM%20software | Z88 is a software package for the finite element method (FEM) and topology optimization. A team led by Frank Rieg at the University of Bayreuth started development in 1985 and now the software is used by several universities, as well as small and medium-sized enterprises. Z88 is capable of calculating two and three dimensional element types with a linear approach. The software package contains several solvers and two post-processors and is available for Microsoft Windows, Mac OS X and Unix/Linux computers in 32-bit and 64-bit versions. Benchmark tests conducted in 2007 showed a performance on par with commercial software.
History and functionalities
Overview
The software was developed by Frank Rieg, a professor for engineering design and CAD at the University of Bayreuth. Originally written in FORTRAN 77, the program was ported to the programming language C in the early 1990s.
There are two programs for finite element analysis:
Z88OS (current version 15.0) is available as free software including the source code under the GNU General Public License. Due to the modular structure of the program and the open availability of the source code it is possible to develop customized extensions and add-ons and several special case 2D and 3D continuum elements (e.g. anisotropic shell element) were developed by users.
Z88Aurora (current version 5.0) originally described the user interface of the Z88 finite element analysis program. After several additions and further development it now comprises a significantly larger range of functionalities than Z88OS. Z88Aurora is freeware, however the source code is not publicly available.
Since 2014 two Android Apps are also available:
Z88Tina is a freeware FEA program for Android smartphones and tablets. Using Z88Tina it is not only possible to compute trusses and beams, but also continuum elements like plane stress elements, plates and tori.
Z88Mobile is free, like all Z88 products. This app offers two different modes (basic and advanced) and has a touch interface.
The product family is supported by a software for topology optimization since 2016:
Z88Arion is a free program for topology optimization and provides three separate algorithms for computation (OC: Optimality Criteria, SKO: Soft Kill Option, TOSS: Topology Optimization for Stiffness and Stress).
Functionalities of Z88Aurora
Z88Aurora's current version contains several computation modules:
In the case of linear static analyses it is assumed that the result is proportional to the applied forces.
Nonlinear analyses are used for nonlinear geometries and nonlinear materials.
Using thermal and thermomechanical analyses it is possible to not only compute results about temperature or heat currents, but also thermomechanical displacements and stresses.
By utilizing natural frequency simulation natural frequencies and the resulting oscillations can be determined.
A contact module makes it possible to simulate interacting parts and assemblies. An integra |
https://en.wikipedia.org/wiki/Moderation%20%28statistics%29 | In statistics and regression analysis, moderation (also known as effect modification) occurs when the relationship between two variables depends on a third variable. The third variable is referred to as the moderator variable (or effect modifier) or simply the moderator (or modifier). The effect of a moderating variable is characterized statistically as an interaction; that is, a categorical (e.g., sex, ethnicity, class) or continuous (e.g., age, level of reward) variable that is associated with the direction and/or magnitude of the relation between dependent and independent variables. Specifically within a correlational analysis framework, a moderator is a third variable that affects the zero-order correlation between two other variables, or the value of the slope of the dependent variable on the independent variable. In analysis of variance (ANOVA) terms, a basic moderator effect can be represented as an interaction between a focal independent variable and a factor that specifies the appropriate conditions for its operation.
Example
Moderation analysis in the behavioral sciences involves the use of linear multiple regression analysis or causal modelling. To quantify the effect of a moderating variable in multiple regression analyses, regressing random variable Y on X, an additional term is added to the model. This term is the interaction between X and the proposed moderating variable.
Thus, for a response Y and two variables x1 and moderating variable x2,:
In this case, the role of x2 as a moderating variable is accomplished by evaluating b3, the parameter estimate for the interaction term. See linear regression for discussion of statistical evaluation of parameter estimates in regression analyses.
Multicollinearity in moderated regression
In moderated regression analysis, a new interaction predictor () is calculated. However, the new interaction term may be correlated with the two main effects terms used to calculate it. This is the problem of multicollinearity in moderated regression. Multicollinearity tends to cause coefficients to be estimated with higher standard errors and hence greater uncertainty.
Mean-centering (subtracting raw scores from the mean) may reduce multicollinearity, resulting in more interpretable regression coefficients. However, it does not affect the overall model fit.
Post-hoc probing of interactions
Like simple main effect analysis in ANOVA, in post-hoc probing of interactions in regression, we are examining the simple slope of one independent variable at the specific values of the other independent variable. Below is an example of probing two-way interactions.
In what follows the regression equation with two variables A and B and an interaction term A*B,
will be considered.
Two categorical independent variables
If both of the independent variables are categorical variables, we can analyze the results of the regression for one independent variable at a specific level of the other independent varia |
https://en.wikipedia.org/wiki/Pseudoreflection | In mathematics, a pseudoreflection is an invertible linear transformation of a finite-dimensional vector space such that it is not the identity transformation, has a finite (multiplicative) order, and fixes a hyperplane. The concept of pseudoreflection generalizes the concepts of reflection and complex reflection and is simply called reflection by some mathematicians. It plays an important role in Invariant theory of finite groups, including the Chevalley-Shephard-Todd theorem.
Formal definition
Suppose that V is vector space over a field K, whose dimension is a finite number n. A pseudoreflection is an invertible linear transformation such that the order of g is finite and the fixed subspace of all vectors in V fixed by g has dimension n-1.
Eigenvalues
A pseudoreflection g has an eigenvalue 1 of multiplicity n-1 and another eigenvalue r of multiplicity 1. Since g has finite order, the eigenvalue r must be a root of unity in the field K. It is possible that r = 1 (see Transvections).
Diagonalizable pseudoreflections
Let p be the characteristic of the field K. If the order of g is coprime to p then g is diagonalizable and represented by a diagonal matrix
diag(1, ... , 1, r ) =
where r is a root of unity not equal to 1. This includes the case when K is a field of characteristic zero, such as the field of real numbers and the field of complex numbers.
A diagonalizable pseudoreflection is sometimes called a semisimple reflection.
Real reflections
When K is the field of real numbers, a pseudoreflection has matrix form diag(1, ... , 1, -1). A pseudoreflection with such matrix form is called a real reflection. If the space on which this transformation acts admits a symmetric bilinear form so that orthogonality of vectors can be defined, then the transformation is a true reflection.
Complex reflections
When K is the field of complex numbers, a pseudoreflection is called a complex reflection, which can be represented by a diagonal matrix diag(1, ... , 1, r) where r is a complex root of unity unequal to 1.
Transvections
If the pseudoreflection g is not diagonalizable then r = 1 and g has Jordan normal form
In such case g is called a transvection. A pseudoreflection g is a transvection if and only if the characteristic p of the field K is positive and the order of g is p. Transvections are useful in the study of finite geometries and the classification of their groups of motions.
References
Functions and mappings |
https://en.wikipedia.org/wiki/Nehemiah%20Strong | Rev. Nehemiah Strong (24 February 1729 (N.S.) – 13 August 1807) was an American astronomer and meteorologist who was the first Professor of Mathematics and Natural Philosophy at Yale College from 1770 and produced a series of annual ephemerides, the astronomical element in almanacs, which were printed in Hartford, Connecticut, and in New Haven.
Strong was born in Northampton, Massachusetts, eldest of three children of Nehemiah and Hannah Strong and the grandson of Samuel and Esther (Clapp) Strong, of Northampton, Massachusetts.
Nehemiah Strong graduated from Yale College in 1755. He entered on a tutorship at Yale in November 1757 and was soon licensed to preach and was settled Congregationalist minister at Turkey Hill, now part of East Granby, Connecticut, 1761-67.
His marriage to Lydia Smith proved to be an embarrassment, when after she had been granted a divorce in February 1759 on grounds of abandonment, her husband, Andrew Burr Jr of New Haven, having gone to the West Indies in January 1755, Burr reappeared and her marriage to Nehemiah Strong was necessarily annulled, and as a result of entanglements he was dismissed from his pastorate at Turkey Hill, 23 June 1767. He married Mrs Mary Thomas, the widow of Dr Lemuel Thomas of Newtown, 15 June 1778.
Thereafter he resided in Newtown, in New Milford, where he kept an academy for boys, and, from 1803 in Bridgeport, giving occasional sermons and teaching to the time of his death. He resigned his chair at Yale in 1781, in a dispute over his salary, exacerbated by the sense on the part of the Corporation that he was not a sufficiently ardent Patriot. He represented Newtown in the Connecticut General Assembly, May 1784. His portrait by Ralph Earl, painted in 1789-90, was presented to Yale by the artist and remains in the University's collection.
His treatise on astronomy won him such a wide reputation that anonymous almanacs were attributed to him. His first essay at compiling an almanac was anonymous, for Watson's Register for 1775, printed at Hartford; his second essay was The Connecticut Almanack for 1778, which identified his Yale title only. From 1782 he published almanacs under his own name at Hartford and as "Hosea Stafford" in New Haven (1776–1804). In addition, finding that he was publicly assumed to be the "Isaac Bickerstaff", having disclaimed authorship in a letter to the Connecticut Journal, New Haven, 27 October 1784, he apparently decided to take up the slack and issue almanacs as "Bickerstaff" himself: they appeared at Hartford for several years after 1785.
In a letter of 6 May 1803 to Elisha Babcock, Strong remarks that the calculations for the forthcoming year will be his last:
He recommended his pupil David Sanford of Newtown, Connecticut.
Notes
American astronomers
Almanac compilers
1729 births
1807 deaths
People from Northampton, Massachusetts
Yale College alumni |
https://en.wikipedia.org/wiki/Bures%20metric | In mathematics, in the area of quantum information geometry, the Bures metric (named after Donald Bures) or Helstrom metric (named after Carl W. Helstrom) defines an infinitesimal distance between density matrix operators defining quantum states. It is a quantum generalization of the Fisher information metric, and is identical to the Fubini–Study metric when restricted to the pure states alone.
Definition
The Bures metric may be defined as
where is Hermitian 1-form operator implicitly given by
which is a special case of a continuous Lyapunov equation.
Some of the applications of the Bures metric include that given a target error, it allows the calculation of the minimum number of measurements to distinguish two different states and the use of the volume element as a candidate for the Jeffreys prior probability density for mixed quantum states.
Bures distance
The Bures distance is the finite version of the infinitesimal square distance described above and is given
by
where the fidelity function is defined
as
Another associated function is the Bures arc also known as Bures angle, Bures length or quantum angle, defined as
which is a measure of the statistical distance
between quantum states.
Wootters distance
When both density operators are diagonal (so that they are just classical probability distributions), then let and similarly , then the fidelity iswith the Bures length becoming the Wootters distance . The Wootters distance is the geodesic distance between the probability distributions under the chi-squared metric .
Perform a change of variables with , then the chi-squared metric becomes . Since , the points are restricted to move on the positive quadrant of a unit hypersphere. So, the geodesics are just the great circles on the hypersphere, and we also obtain the Wootters distance formula.
If both density operators are pure states, , then the fidelity is , and we obtain the quantum version of Wootters distance
.
In particular, the Bures distance between any two orthogonal states is .
Quantum Fisher information
The Bures metric can be seen as the quantum equivalent of the Fisher information metric and can be rewritten in terms of the variation of coordinate parameters as
which holds as long as and have the same rank. In cases where they do not have the same rank, there is an additional term on the right hand side.
is the Symmetric logarithmic derivative operator (SLD) defined from
In this way, one has
where the quantum Fisher metric (tensor components) is identified as
The definition of the SLD implies that the quantum Fisher metric is 4 times the Bures metric. In other words, given that are components of the Bures metric tensor, one has
As it happens with the classical Fisher information metric, the quantum Fisher metric can be used to find the Cramér–Rao bound of the covariance.
Explicit formulas
The actual computation of the Bures metric is not evident from the definition, so, some formulas were developed f |
https://en.wikipedia.org/wiki/Statistical%20Applications%20in%20Genetics%20and%20Molecular%20Biology | Statistical Applications in Genetics and Molecular Biology is a bimonthly peer-reviewed scientific journal covering the application of statistics to problems in computational biology. It was established in 2002 and is published by de Gruyter. The editor-in-chief is Guido Sanguinetti. According to the Journal Citation Reports, the journal has a 2012 impact factor of 1.717.
Abstracting and indexing
The journal is abstracted and indexed in:
Current Index to Statistics
MEDLINE
Science Citation Index Expanded
Zentralblatt MATH
References
External links
Biostatistics journals
Statistics journals
Academic journals established in 2002
Delayed open access journals
English-language journals
Bioinformatics and computational biology journals
De Gruyter academic journals |
https://en.wikipedia.org/wiki/L%C3%A9vy%20family%20of%20graphs | In graph theory, a branch of mathematics, a Lévy family of graphs is a family of graphs Gn, n = 1, 2, 3, ..., which possess a certain type of "compactness" or "tangledness". Many naturally occurring families of graphs are Lévy families. Many mathematicians have noted this fact and have expressed surprise that it does not appear to have a ready explanation.
Formally, a family of graphs Gn, n = 1, 2, 3, ..., is a Lévy family if, for any
where
Here D is the graph diameter of G, and A(n) is the n-graph neighborhood of A. Note that the maximization ranges over subsets A of G, subject to A being over half the size of G
In words, this means that one can take a subset of size at least half of G, and blow it up by only of the graph diameter, and end up with nearly all the set.
Long "stringy" (i.e. not "compact") families of graphs such as the cycle graph of order n clearly don't have such a property: one could consider a subset comprising the n/2 neighborhood of a point (midnight to six o'clock, say). The graph has graph diameter D of about n/2. So the -neighborhood of the subset is only of size about n/2. A Levy family would have this neighborhood covering almost all the set. It should be clear that a Levy family must have a very special type of compact structure.
Hypercube graphs of order n are known to be a Lévy family.
If Sn is the graph with points that are elements of the permutation group of n elements, with edges joining points that differ by a transposition, then the series Si, i=1,2,..., is a Lévy family.
References
Bollobás (editor). Probabilistic combinatorics and its applications. American Mathematical Society, 1991 (p63)
Graph families |
https://en.wikipedia.org/wiki/Journal%20of%20Statistical%20Computation%20and%20Simulation | The Journal of Statistical Computation and Simulation is a peer-reviewed scientific journal that covers computational statistics. It is published by Taylor & Francis and was established in 1972. The editors-in-chief are Richard Krutchkoff (Virginia Polytechnic Institute and State University, Blacksburg) and Andrei Volodin (University of Regina).
Abstracting and indexing
The journal is abstracted and indexed in:
Current Index to Statistics
Science Citation Index Expanded
Zentralblatt MATH
According to the Journal Citation Reports, the journal has a 2018 impact factor of 0.767.
References
External links
Computational statistics journals
Statistics journals
Academic journals established in 1972 |
https://en.wikipedia.org/wiki/Gompertz%20distribution | In probability and statistics, the Gompertz distribution is a continuous probability distribution, named after Benjamin Gompertz. The Gompertz distribution is often applied to describe the distribution of adult lifespans by demographers and actuaries. Related fields of science such as biology and gerontology also considered the Gompertz distribution for the analysis of survival. More recently, computer scientists have also started to model the failure rates of computer code by the Gompertz distribution. In Marketing Science, it has been used as an individual-level simulation for customer lifetime value modeling. In network theory, particularly the Erdős–Rényi model, the walk length of a random self-avoiding walk (SAW) is distributed according to the Gompertz distribution.
Specification
Probability density function
The probability density function of the Gompertz distribution is:
where is the scale parameter and is the shape parameter of the Gompertz distribution. In the actuarial and biological sciences and in demography, the Gompertz distribution is parametrized slightly differently (Gompertz–Makeham law of mortality).
Cumulative distribution function
The cumulative distribution function of the Gompertz distribution is:
where and
Moment generating function
The moment generating function is:
where
Properties
The Gompertz distribution is a flexible distribution that can be skewed to the right and to the left. Its hazard function is a convex function of . The model can be fitted into the innovation-imitation paradigm with
as the coefficient of innovation and as the coefficient of imitation. When becomes large, approaches . The model can also belong to the propensity-to-adopt paradigm with
as the propensity to adopt and as the overall appeal of the new offering.
Shapes
The Gompertz density function can take on different shapes depending on the values of the shape parameter :
When the probability density function has its mode at 0.
When the probability density function has its mode at
Kullback-Leibler divergence
If and are the probability density functions of two Gompertz distributions, then their Kullback-Leibler divergence is given by
where denotes the exponential integral and is the upper incomplete gamma function.
Related distributions
If X is defined to be the result of sampling from a Gumbel distribution until a negative value Y is produced, and setting X=−Y, then X has a Gompertz distribution.
The gamma distribution is a natural conjugate prior to a Gompertz likelihood with known scale parameter
When varies according to a gamma distribution with shape parameter and scale parameter (mean = ), the distribution of is Gamma/Gompertz.
If , then , and hence .
Applications
In hydrology the Gompertz distribution is applied to extreme events such as annual maximum one-day rainfalls and river discharges. The blue picture illustrates an example of fitting the Gompertz distribution to ranked annually maximum |
https://en.wikipedia.org/wiki/Ethernet%20Ring%20Protection%20Switching | Ethernet Ring Protection Switching, or ERPS, is an effort at ITU-T under G.8032 Recommendation to provide sub-50ms protection and recovery switching for Ethernet traffic in a ring topology and at the same time ensuring that there are no loops formed at the Ethernet layer. This ITU-T specification is directly based on and derived from the Ethernet Automatic Protection Switching technology developed and patented by Extreme Networks. G.8032v1 supported a single ring topology and G.8032v2 supports multiple rings/ladder topology.
Overview
ERPS specifies protection switching mechanisms and a protocol for Ethernet layer network (ETH) rings. Ethernet Rings can provide wide-area multipoint connectivity more economically due to their reduced number of links. The mechanisms and protocol defined in this Recommendation achieve highly reliable and stable protection; and never form loops, which would fatally affect network operation and service availability.
Each Ethernet Ring Node is connected to adjacent Ethernet Ring Nodes participating in the same Ethernet Ring, using two independent links. A ring link is bounded by two adjacent Ethernet Ring Nodes, and a port for a ring link is called a ring port. The minimum number of Ethernet Ring Nodes in an Ethernet Ring is three.
The fundamentals of this ring protection switching architecture are:
a) The principle of loop avoidance.
b) The utilization of learning, forwarding, and Filtering Database (FDB) mechanisms defined in the Ethernet flow forwarding function (ETH_FF).
Loop avoidance in an Ethernet Ring is achieved by guaranteeing that, at any time, traffic may flow on all but one of the ring links. This particular link is called the Ring Protection Link (RPL), and under normal conditions this ring link is blocked, i.e. not used for service traffic. One designated Ethernet Ring Node, the RPL Owner Node, is responsible for blocking traffic at one end of the RPL.
Under an Ethernet ring failure condition, the RPL Owner Node is responsible for unblocking its end of the RPL (unless the RPL has failed) allowing the RPL to be used for traffic. The other Ethernet Ring
Node adjacent to the RPL, the RPL Neighbour Node, may also participate in blocking or unblocking its end of the RPL.
The event of an Ethernet Ring failure results in protection switching of the traffic. This is achieved under the control of the ETH_FF functions on all Ethernet Ring Nodes.
An APS protocol is used to coordinate the protection actions over the ring.
G.8032v2
Version 2 of G.8032 introduced many additional features, such as:
Multi-ring/ladder network support
Revertive/ Non-revertive mode after the condition that is causing the switch has been cleared
Administrative commands: Forced Switch (FS), Manual Switch (MS) for blocking a particular ring port
Flush FDB (Filtering database) Logic, which significantly reduces amount of flush FDB operations in the ring
Support of multiple ERP instances on a single ring
Principle of operation
G. |
https://en.wikipedia.org/wiki/Koreans%20in%20Spain | Koreans in Spain form one of the country's smaller Asian populations.
Demography and distribution
2006 statistics from Spain's Instituto Nacional de Estadística showed 2,873 registered residents of Spain born in South Korea, of whom 514 held Spanish nationality, while 2,359 held other nationalities. Among Spanish nationals, men outnumbered women by a ratio of 1.3:1, which was almost exactly reversed among non-Spanish nationals. Between 1980 and 2004, a total of 696 people originally holding South Korean nationality became Spanish citizens. South Korea's Ministry of Foreign Affairs and Trade, whose statistics are based largely on registrations with consulates and count locally born persons of Korean descent as well as South Korean-born individuals, recorded a somewhat higher count of 3,769 individuals in 2005; of those, 2,538 resided in, with another 1,231 in Las Palmas. This made Koreans in Spain the fifth-largest Korean diaspora population in Western Europe, behind Koreans in the United Kingdom, Koreans in Germany, Koreans in France, and Koreans in Italy.
The most recent statistics of the South Korean government, issued in July 2011, show only slight growth compared to the 2005 statistics. Of the 4,080 Koreans recorded as living in Spain, 929 had Spanish citizenship, 2,108 had permanent residence, 216 were on student visas, and the remaining 727 had other kinds of visas.
Las Palmas
Koreans in Las Palmas form a community distinct from that on the Spanish mainland. Theirs is the only concentration of Koreans in Spain whose presence has resulted in a recognisable Koreatown. They trace their origins to South Korean migrant workers who worked on deep-ocean fishing boats based on the island starting in the 1960s. Fishing, along with construction, was one of the main sources of overseas employment for South Koreans for decades; by the 1970s, nearly 15,000 Koreans resided in Las Palmas, making them about 4% of the city's population of 350,000. Many brought their families over and became rooted in Spain, sending their children to local schools. However, with the decline of South Korea's ocean fisheries industries in the 1990s, their population shrank, from 2,283 individuals in 1997 to just 1,292 by 1999, a number which decreased at a slower rate over the following decade to reach 1,197 by 2011. Most of the remaining Korean population have shifted away from the fishing industry, and their children have largely entered professional fields, achieving relative affluence.
Mainland Spain
The Korean community on the Spanish mainland consists mainly of two groups: primarily male small business owners and executives of South Korean companies along with their spouses and children, and primarily female international students at Spanish universities. Korean martial artists, though a smaller group, are also well represented; they either run their own dojang, or work for private security companies. They do not trace their origins exclusively to South Korea; some m |
https://en.wikipedia.org/wiki/Mark%20Ronan | Mark Andrew Ronan (born 1947) is Emeritus Professor of Mathematics at the University of Illinois at Chicago and Honorary Professor of Mathematics at University College London. He has lived and taught in: Germany (at the University of Braunschweig and the Free University of Berlin); in England, where from 1989 to 1992 he was Mason Professor of Mathematics at the University of Birmingham; and America at the University of Illinois at Chicago, where his teaching included courses on ancient literature from Mesopotamia, and on the history of the calendar, as well as mathematics.
In addition to his research papers, Ronan's popular account of the quest to discover and classify all the finite building blocks for symmetry (the finite simple groups) was published in 2006. In 2008 it formed the basis for a series of BBC radio broadcasts. In his research work he is an expert on the theory of buildings, with a standard text on the subject, now being reissued in paperback. Apart from his professional work, he has acted in many operas at the Lyric Opera of Chicago, danced in the Nutcracker, and maintains a blog on opera, ballet and theatre reviews.
Bibliography
Lectures on Buildings, original edition, Academic Press 1989; paperback edition, updated and revised, University of Chicago Press 2009.
Symmetry and the Monster, Oxford University Press 2006.
References
External links
Mark Ronan's Homepage
Mark Ronan's Theatre Reviews
20th-century British mathematicians
21st-century British mathematicians
20th-century American mathematicians
21st-century American mathematicians
Group theorists
Academics of University College London
University of Illinois Chicago faculty
Living people
Academic staff of the Technical University of Braunschweig
1947 births |
https://en.wikipedia.org/wiki/Hate%20My%20Life | "Hate My Life" is a song by Canadian rock group Theory of a Deadman. It was released in October 2008 as the fourth overall single (third American single and fifth Canadian single) from their third studio album Scars & Souvenirs. The track was selected as BBC Radio One's Track of the Week for the week ending March 20, 2009.
Background and writing
According to Tyler Connolly, the band's lead singer, this song enables people to feel that no matter how bad their own life is going, that there is always someone out there who feels just as bad.
Music video
According to Theory's site, the video was shot on November 15, 2008. It was asked on the site, as a contest, for forty fans to star in the music video. It was filmed at the Warner Brothers Studio in Burbank, California. It was released January 9, 2009, on Yahoo! Music. It was directed by Bill Fishman.
At the beginning of the video, Tyler sees a hobo, and then he starts singing the song, the lyrics matching everything that is happening in the video. He complains about how he hates hobos ("So sick of the hobos always begging for change, I don't like how I gotta work and they just sit around and get paid"), he almost gets hit by a car ("I hate all of the people, who can't drive their cars...), we meet his wife, played by his real wife Christine Danielle Connolly ("I hate how my wife; is always up my ass...), a girl drops her bag of lingerie (Tyler looking at it interestingly), a construction worker's boss telling him off ("I still hate my job, my boss is a dick...), and when he sings the chorus, a sign comes down from a building reading "I Hate My Life." Then, Tyler jumps onto a parade float with the rest of the band, performing the rest of the song. Behind them travels a huge group of people, which include the hobo, the construction workers, and the others Tyler ran into.
Charts
Weekly charts
Year-end charts
Certifications
References
Theory of a Deadman songs
2008 singles
604 Records singles
Songs written by Tyler Connolly
Song recordings produced by Howard Benson
2008 songs |
https://en.wikipedia.org/wiki/Not%20Meant%20to%20Be | "Not Meant to Be" is a song recorded by Canadian rock group Theory of a Deadman for their third studio album, Scars & Souvenirs (2008). Band members Tyler Connolly, Dave Brenner, and Dean Back composed the song, while Connolly co-wrote the lyrics with songwriter and producer Kara DioGuardi. The song was released November 18, 2008 as the album's fifth overall radio single. It was the first song from the album to impact mainstream radio in the United States, concurrent with the release of "Hate My Life" to rock formats. In 2009, "Not Meant to Me" was included on the soundtrack to the science fiction action film, Transformers: Revenge of the Fallen.
"Not Meant to Be" became the group's highest-charting entry in the United States, peaking at number 55 on the Billboard Hot 100 as well as their first top ten hit on the Billboard Adult Top 40 airplay chart. The song has been certified Platinum by both Music Canada and the Recording Industry Association of America (RIAA).
Content
"Not Meant to Be" is a ballad with influences of pop and rock music composed in the key of A minor and set in common time to a "slow" tempo of 120 BPM. The vocals range over two octaves from D to G. The song is written from the point of view of a man who wants to be with his ex-girlfriend so much after their relationship ends, but she is never satisfied with him and keeps pushing him away, leaving him thinking that their relationship is "not meant to be." Lead vocalist Tyler Connolly co-wrote the lyrics with Kara DioGuardi at the latter's house. "We wrote 'Not Meant To Be' in 5 minutes," Connolly said in a 2009 interview with The Gauntlet. "Our writing styles fit together so perfectly it was almost like it was 'meant to be.'" In the same interview, DioGuardi stated that "the best part about my job is that you never know who you are going to meet, and who's going to inspire you. Although I'd never worked with Tyler, when he started singing the song, I knew we were onto something special." The song's mid-tempo composition has been compared to the work of labelmates Nickelback.
Critical reception
In a review of the album Scars & Souvenirs for AllMusic, Katherine Fulton identified "Not Meant to Be" as an example of the album's "derivative" sound, writing that its "melody and chorus bear more than a passing resemblance to" Nickelback's 2006 single "Rockstar".
Music video
The band filmed the music video with Tony Petrossian in February 2009. It features Kara DioGuardi (the song's co-writer) as the love interest. It was released on March 25, 2009. The video begins when Kara walks out on Tyler, breaks up with him and drives away. By the first chorus in the song, all of the non-singing scenes start running backwards: all the objects in the house (including a fish tank, a wine rack, a mirror, a table, two chairs and more) change from broken to unbroken and Kara's car is also shown travelling backwards, implying that the whole timeline of the main story is running in reverse. At the en |
https://en.wikipedia.org/wiki/Foster%27s%20theorem | In probability theory, Foster's theorem, named after Gordon Foster, is used to draw conclusions about the positive recurrence of Markov chains with countable state spaces. It uses the fact that positive recurrent Markov chains exhibit a notion of "Lyapunov stability" in terms of returning to any state while starting from it within a finite time interval.
Theorem
Consider an irreducible discrete-time Markov chain on a countable state space having a transition probability matrix with elements for pairs , in . Foster's theorem states that the Markov chain is positive recurrent if and only if there exists a Lyapunov function , such that and
for
for all
for some finite set and strictly positive .
Related links
Lyapunov optimization
References
Theorems regarding stochastic processes
Markov processes |
https://en.wikipedia.org/wiki/2008%E2%80%9309%20Guam%20Men%27s%20Soccer%20League | Statistics of Guam League for the 2008–09 season.
Final standings
References
Guam 2008/09 (RSSSF)
Guam Soccer League seasons
Guam
Mens |
https://en.wikipedia.org/wiki/Edmund%20F.%20Robertson | Edmund Frederick Robertson (born 1 June 1943) is a professor emeritus of pure mathematics at the University of St Andrews.
Work
Robertson is one of the creators of the MacTutor History of Mathematics archive, along with John J. O'Connor. Robertson has written over 100 research articles, mainly on the theory of groups and semigroups. He is also the author or co-author of 17 textbooks.
Robertson obtained a Bachelor of Science degree at the University of St Andrews in 1965. He then went to the University of Warwick, where he received a Master of Science degree in 1966 and a Doctor of Philosophy degree in 1968.
In 1998, he was elected a Fellow of the Royal Society of Edinburgh.
In 2015, he received together with his colleague O'Connor, the Hirst Prize of the London Mathematical Society for his work on the MacTutor History of Mathematics archive. His thesis on "Classes of Generalised Nilpotent Groups" was done with Stewart E. Stonehewer.
Personal life
He is with his wife, Helena, and his two sons.
Bibliography
Algebra Through Practice: A Collection of Problems in Algebra with Solutions: Books 4-6 - with T.S.Blyth,
Rings, Fields and Modules - with T.S.Blyth, 1985,
Sets and mappings - with T.S.Blyth, 1986,
Linear Algebra - with T.S.Blyth, 1986,
Essential Student Algebra: Groups - with T.S.Blyth, 1986,
Basic Linear Algebra - with T.S.Blyth, 1998,
Colin MacLaurin (1698-1746): Argyllshire's Mathematician, 2000,
Further Linear Algebra - with T.S.Blyth, 2002,
References
External links
Group theorists
20th-century Scottish mathematicians
Fellows of the Royal Society of Edinburgh
Academics of the University of St Andrews
1943 births
Living people
21st-century Scottish mathematicians
People from St Andrews |
https://en.wikipedia.org/wiki/StatXact | StatXact is a statistical software package for analyzing data using exact statistics. It calculates exact p-values and confidence intervals for contingency tables and non-parametric procedures. It is marketed by Cytel Inc.
References
External links
StatXact homepage at Cytel Inc.
Statistical software
Windows-only proprietary software |
https://en.wikipedia.org/wiki/Georges%20Reeb | Georges Henri Reeb (12 November 1920 – 6 November 1993) was a French mathematician. He worked in differential topology, differential geometry, differential equations, topological dynamical systems theory and non-standard analysis.
Biography
Reeb was born in Saverne, Bas-Rhin, Alsace, to Theobald Reeb and Caroline Engel. He started studying mathematics at University of Strasbourg, but in 1939 the entire university was evacuated to Clermont-Ferrand due to the German occupation of France.
After the war, he completed his studies and in 1948 he defended his PhD thesis, entitled Propriétés topologiques des variétés feuilletées [Topological properties of foliated manifolds] and supervised by Charles Ehresmann.
In 1952 Reeb was appointed professor at Université Joseph Fourier in Grenoble and in 1954 he visited the Institute for Advanced Study. From 1963 he worked at Université Louis Pasteur in Strasbourg.
There, in 1965 he created with Jean Leray and Pierre Lelong the series of meeting Rencontres entre Mathématiciens et Physiciens Théoriciens. in 1966 Reeb and Jean Frenkel founded the Institute de Recherche mathématique Avancée, the first university laboratory associated to the Centre National de la Recherche Scientifique, which he directed between 1967 and 1972.
In 1967 he was President of the Société Mathématique de France and in 1971 he was awarded the .
In 1991 Reeb received an honorary doctorate from Albert-Ludwigs-Universität Freiburg and from Université de Neuchâtel. He died in 1993 in Strasbourg when he was 72 years old.
Research
Reeb was the founder of the topological theory of foliations, a geometric structure on smooth manifolds which partition them in smaller pieces. In particular, he described what is now called the Reeb foliation, a foliation of the 3-sphere, whose leaves are all diffeomorphic to , except one, which is a 2-torus.
One of its first significant result, Reeb stability theorem, describes the local structure foliations around a compact leaf with finite holonomy group.
His works on foliations had also applications in Morse theory. In particular, the Reeb sphere theorem says that a compact manifold with a function with exactly two critical points is homeomorphic to the sphere. In turn, in 1956 this was used to prove that the Milnor spheres, although not diffeomorphic, are homeomorphic to the sphere .
Other important geometric concepts named after him include the Reeb graph and the Reeb vector field associated to a contact form.
Towards the end of his career, Reeb become a supporter of the theory of non-standard analysis by Abraham Robinson, coining the slogan "The naïve integers don't fill up " and working on its applications to dynamical systems.
Selected works
Books
with Wu Wen-Tsün: Sur les espaces fibrés et les variétés feuilletées, 1952
with A. Fuchs: Statistiques commentées, 1967
with J. Klein: Formules commentées de mathématiques: Programme P.C., 1971
Feuilletages: résultats anciens et nouveaux (Painlevé, Hect |
https://en.wikipedia.org/wiki/Avner%20Friedman | Avner Friedman (; born November 19, 1932) is Distinguished Professor of Mathematics and Physical Sciences at Ohio State University. His primary field of research is partial differential equations, with interests in stochastic processes, mathematical modeling, free boundary problems, and control theory.
Friedman received his Ph.D. degree in 1956 from the Hebrew University. He was a professor of mathematics at Northwestern University (1962–1985), a Duncan Distinguished Professor of Mathematics at Purdue University (1985–1987), and a professor of mathematics (Regents' Professor from 1996) at the University of Minnesota (1987–2001). He was director of the Institute for Mathematics and its Applications from 1987 to 1997. He was the founding director of Minnesota Center for Industrial Mathematics (1994-2001). He was the founding Director of the Mathematical Biosciences Institute at Ohio State University, serving as its first director from 2002–2008.
Friedman has been the Chair of the Board of Mathematical Sciences (1994–1997) and the President of the Society for Industrial and Applied Mathematics (1993–1994). He has been awarded the Sloan Fellowship (1962–65), the Guggenheim Fellowship (1966–7), the Stampacchia Prize (1982), the National Science Foundation Special Creativity Award (1983–85; 1991–93). He is a Fellow of the American Academy of Arts and Sciences (since 1987) and a member of the National Academy of Sciences (since 1993). In 2009 he became a Fellow of the Society for Industrial and Applied Mathematics. In 2012 he became a fellow of the American Mathematical Society.
He has been adviser to 27 doctoral students and has published 25 books and over 500 papers.
Works
Generalized Functions and Partial Differential Equations. Prentice-Hall (1963). Dover Publications 2005 ; 2011 Dover reprint
Partial Differential Equations of Parabolic Type. Prentice-Hall (1964). 2008 Dover Publications; 2013 Dover reprint
Partial Differential Equations. Holt, Rinehart, and Winston, New York (1969). reprint Dover Books 2008
Foundations of Modern Analysis. Holt, Rinehart, and Winston, New York (1970). (hbk); 1982 Dover reprint; Dover Publications on Mathematics 2010.
Advanced Calculus. Holt, Rinehart, and Winston, New York (1971). Dover Publications 2007
Differential Games. John Wiley, Interscience Publishers (1971). Dover Publications 2006 2013 Dover reprint
Stochastic Differential Equations and Applications. Vol. 1, Academic Press (1975). Dover Books 2006.
Stochastic Differential Equations and Applications. Vol. 2, Academic Press (1976).
Variational Principles and Free Boundary Problems, Wiley & Sons (1983). Dover Publications on Mathematics 2010 ; 2012 pbk reprint, Springer
Mathematics in Industrial Problems, IMA Volume 16, Springer-Verlag (1988).
Mathematics in Industrial Problems, Part 2, IMA Volume 24, Springer-Verlag (1989); 2012 pbk reprint
Mathematics in Industrial Problems, Part 3, IMA Volume 31, Springer-Verlag (1990).
Ma |
https://en.wikipedia.org/wiki/Quartic%20reciprocity | Quartic or biquadratic reciprocity is a collection of theorems in elementary and algebraic number theory that state conditions under which the congruence x4 ≡ p (mod q) is solvable; the word "reciprocity" comes from the form of some of these theorems, in that they relate the solvability of the congruence x4 ≡ p (mod q) to that of x4 ≡ q (mod p).
History
Euler made the first conjectures about biquadratic reciprocity. Gauss published two monographs on biquadratic reciprocity. In the first one (1828) he proved Euler's conjecture about the biquadratic character of 2. In the second one (1832) he stated the biquadratic reciprocity law for the Gaussian integers and proved the supplementary formulas. He said that a third monograph would be forthcoming with the proof of the general theorem, but it never appeared. Jacobi presented proofs in his Königsberg lectures of 1836–37. The first published proofs were by Eisenstein.
Since then a number of other proofs of the classical (Gaussian) version have been found, as well as alternate statements. Lemmermeyer states that there has been an explosion of interest in the rational reciprocity laws since the 1970s.
Integers
A quartic or biquadratic residue (mod p) is any number congruent to the fourth power of an integer (mod p). If x4 ≡ a (mod p) does not have an integer solution, a is a quartic or biquadratic nonresidue (mod p).
As is often the case in number theory, it is easiest to work modulo prime numbers, so in this section all moduli p, q, etc., are assumed to positive, odd primes.
Gauss
The first thing to notice when working within the ring Z of integers is that if the prime number q is ≡ 3 (mod 4) then a residue r is a quadratic residue (mod q) if and only if it is a biquadratic residue (mod q). Indeed, the first supplement of quadratic reciprocity states that −1 is a quadratic nonresidue (mod q), so that for any integer x, one of x and −x is a quadratic residue and the other one is a nonresidue. Thus, if r ≡ a2 (mod q) is a quadratic residue, then if a ≡ b2 is a residue, r ≡ a2 ≡ b4 (mod q) is a biquadratic residue, and if a is a nonresidue, −a is a residue, −a ≡ b2, and again, r ≡ (−a)2 ≡ b4 (mod q) is a biquadratic residue.
Therefore, the only interesting case is when the modulus p ≡ 1 (mod 4).
Gauss proved that if p ≡ 1 (mod 4) then the nonzero residue classes (mod p) can be divided into four sets, each containing (p−1)/4 numbers. Let e be a quadratic nonresidue. The first set is the quartic residues; the second one is e times the numbers in the first set, the third is e2 times the numbers in the first set, and the fourth one is e3 times the numbers in the first set. Another way to describe this division is to let g be a primitive root (mod p); then the first set is all the numbers whose indices with respect to this root are ≡ 0 (mod 4), the second set is all those whose indices are ≡ 1 (mod 4), etc. In the vocabulary of group theory, the first set is a subgroup of index 4 (of the multiplica |
https://en.wikipedia.org/wiki/Sho%20Asuke | is a former Japanese football player.
Club statistics
References
External links
1985 births
Living people
Kokushikan University alumni
Association football people from Tokyo
Japanese men's footballers
J1 League players
J2 League players
Tokyo Verdy players
Kataller Toyama players
Men's association football defenders |
https://en.wikipedia.org/wiki/Masaki%20Iida | is a Japanese football player for Nara Club.
Club statistics
Updated to 24 February 2019.
References
External links
Profile at Matsumoto Yamaga
1985 births
Living people
Ryutsu Keizai University alumni
Association football people from Ibaraki Prefecture
Japanese men's footballers
J1 League players
J2 League players
Japan Football League players
Tokyo Verdy players
Matsumoto Yamaga FC players
FC Maruyasu Okazaki players
Nara Club players
Men's association football defenders |
https://en.wikipedia.org/wiki/Kosuke%20Kikuchi | is a Japanese football player currently playing for Renofa Yamaguchi FC.
Career statistics
Updated to 19 July 2022.
Notes
References
External links
Profile at Omiya Ardija
Profile at Kawasaki Frontale
1985 births
Living people
Komazawa University alumni
Association football people from Saitama Prefecture
Japanese men's footballers
J1 League players
J2 League players
Kawasaki Frontale players
Omiya Ardija players
Renofa Yamaguchi FC players
Men's association football defenders |
https://en.wikipedia.org/wiki/Tomonobu%20Yokoyama | is a retired Japanese footballer.
Career
On 5 February 2020, FC Gifu confirmed that 34-year old Yokoyama had decided to retire.
Club statistics
Updated to 2 January 2020.
References
External links
Profile at Kawasaki Frontale
Profile at Omiya Ardija
Profile at Hokkaido Consadole Sapporo
1985 births
Living people
Waseda University alumni
Association football people from Tokyo
Japanese men's footballers
J1 League players
J2 League players
Kawasaki Frontale players
Cerezo Osaka players
Omiya Ardija players
Hokkaido Consadole Sapporo players
Roasso Kumamoto players
FC Gifu players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Yuji%20Yabu | is a Japanese former football player.
Career
Yabu retired at the end of the 2019 season.
Club statistics
Updated to 23 February 2020.
References
External links
Profile at V-Varen Nagasaki
Profile at Kawasaki Frontale
1984 births
Living people
Kokushikan University alumni
People from Isehara, Kanagawa
Association football people from Kanagawa Prefecture
Japanese men's footballers
J1 League players
J2 League players
J3 League players
Kawasaki Frontale players
Ventforet Kofu players
Roasso Kumamoto players
V-Varen Nagasaki players
Fujieda MYFC players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Quartic%20surface | In mathematics, especially in algebraic geometry, a quartic surface is a surface defined by an equation of degree 4.
More specifically there are two closely related types of quartic surface: affine and projective. An affine quartic surface is the solution set of an equation of the form
where is a polynomial of degree 4, such as . This is a surface in affine space .
On the other hand, a projective quartic surface is a surface in projective space of the same form, but now is a homogeneous polynomial of 4 variables of degree 4, so for example .
If the base field is or the surface is said to be real or complex respectively. One must be careful to distinguish between algebraic Riemann surfaces, which are in fact quartic curves over , and quartic surfaces over . For instance, the Klein quartic is a real surface given as a quartic curve over . If on the other hand the base field is finite, then it is said to be an arithmetic quartic surface.
Special quartic surfaces
Dupin cyclides
The Fermat quartic, given by x4 + y4 + z4 + w4 =0 (an example of a K3 surface).
More generally, certain K3 surfaces are examples of quartic surfaces.
Kummer surface
Plücker surface
Weddle surface
See also
Quadric surface (The union of two quadric surfaces is a special case of a quartic surface)
Cubic surface (The union of a cubic surface and a plane is another particular type of quartic surface)
References
Complex surfaces
Algebraic surfaces |
https://en.wikipedia.org/wiki/William%20Shaw%20%28mathematician%29 | William Shaw (born 14 May 1958) is a British mathematician, and formerly professor of the mathematics and computation of risk at University College London. He is a consultant on financial derivatives, an author of a primary book on using Mathematica to model financial derivatives, formerly co-Editor-in-Chief of the journal Applied Mathematical Finance.
Shaw studied at King's College, Cambridge, where he studied mathematics; he was Wrangler and earned a B.A. in 1980. In 1981 he won the Mayhew Prize for his performance on the Cambridge Mathematical Tripos. In 1984 he received a D.Phil. (PhD) in mathematical physics from Wolfson College, Oxford. From 1984 to 1987 he was a research fellow at Clare College, Cambridge and C.L.E. Moore Instructor at the Massachusetts Institute of Technology. From 1987 to 1990, he worked for Smith Associates in Guildford, and ECL in Henley-on Thames. From 1991 to 2002 he was a lecturer in mathematics at Balliol College, Oxford. In 2002 he moved to St Catherine's College, Oxford, where he was University Lecturer in financial mathematics. In 2006 he moved to a Professorship at King's College London and in 2011 to a Professorship at UCL. He returned to the financial industry in 2012 and remained a visiting professor at UCL until 2017.
Books
Applied Mathematica: Getting Started, Getting it Done by W.T. Shaw and J. Tigg. Addison-Wesley, 1993.
Modelling Financial Derivatives with Mathematica by W.T. Shaw, Cambridge University Press, 1998.
Complex Analysis with Mathematica by W.T. Shaw, Cambridge University Press, 2006.
References
External links
William Shaw's former UCL web-page
Entry in Mathematics Genealogy Project
LinkedIn profile
1958 births
Living people
Alumni of King's College, Cambridge
Academics of King's College London
Academics of University College London
English mathematicians
Mathematical finance
Massachusetts Institute of Technology School of Science faculty |
https://en.wikipedia.org/wiki/Federico%20Laurito | Federico Raúl Laurito (born 18 May 1990) is an Argentine professional footballer.
External links
Gazzetta profile
Primera División statistics
Federico Laurito at Soccerway
1990 births
Living people
Argentine men's footballers
Argentina men's youth international footballers
Argentina men's under-20 international footballers
Argentine expatriate men's footballers
Argentine Primera División players
Primera B de Chile players
Serie B players
Ecuadorian Serie A players
Categoría Primera A players
Newell's Old Boys footballers
Udinese Calcio players
US Livorno 1915 players
Venezia FC players
Club Atlético Huracán footballers
C.D. Cuenca footballers
Everton de Viña del Mar footballers
Barcelona S.C. footballers
Arsenal de Sarandí footballers
Fuerza Amarilla S.C. footballers
L.D.U. Portoviejo footballers
Independiente Medellín footballers
Men's association football forwards
Footballers from Rosario, Santa Fe
Expatriate men's footballers in Chile
Expatriate men's footballers in Italy
Expatriate men's footballers in Ecuador
Expatriate men's footballers in Colombia
Argentine expatriate sportspeople in Chile
Argentine expatriate sportspeople in Italy
Argentine expatriate sportspeople in Ecuador
Argentine expatriate sportspeople in Colombia |
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