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https://en.wikipedia.org/wiki/2003%E2%80%9304%20Austrian%20Football%20Bundesliga | Statistics of Austrian Football Bundesliga in the 2003–04 season.
Overview
It was contested by 10 teams, and Grazer AK won the championship.
League standings
Results
Teams played each other four times in the league. In the first half of the season each team played every other team twice (home and away), and then did the same in the second half of the season.
First half of season
Second half of season
Top goal scorers
External links
Austria - List of final tables (RSSSF)
Austrian Football Bundesliga seasons
Austria
1 |
https://en.wikipedia.org/wiki/2004%E2%80%9305%20Austrian%20Football%20Bundesliga | Statistics of Austrian Football Bundesliga in the 2004–05 season.
Overview
It was contested by 10 teams, and SK Rapid Wien won the championship.
League standings
Results
Teams played each other four times in the league. In the first half of the season each team played every other team twice (home and away), and then did the same in the second half of the season.
First half of season
Second half of season
Top goalscorers
External links
Austria - List of final tables (RSSSF)
Austrian Football Bundesliga seasons
Austria
1 |
https://en.wikipedia.org/wiki/2005%E2%80%9306%20Austrian%20Football%20Bundesliga | Statistics of Austrian Football Bundesliga in the 2005–06 season.
Overview
It was contested by 10 teams, and FK Austria Wien won the championship.
League standings
Results
Teams played each other four times in the league. In the first half of the season each team played every other team twice (home and away), and then did the same in the second half of the season.
First half of season
Second half of season
Top goalscorers
References
External links
Austria - List of final tables (RSSSF)
Austrian Football Bundesliga seasons
Austria
1 |
https://en.wikipedia.org/wiki/William%20Edge | William Edge may refer to:
William Edge (mathematician) (1904–1997), British mathematician most known for his work in finite geometry
Sir William Edge, 1st Baronet (1880–1948), British Liberal, later National Liberal politician and businessman
See also
Edge (disambiguation) |
https://en.wikipedia.org/wiki/J%C3%BCrgen%20Neukirch | Jürgen Neukirch (24 July 1937 – 5 February 1997) was a German mathematician known for his work on algebraic number theory.
Education and career
Neukirch received his diploma in mathematics in 1964 from the University of Bonn. For his Ph.D. thesis, written under the direction of Wolfgang Krull, he was awarded in 1965 the Felix-Hausdorff-Gedächtnis-Preis. He completed his habilitation one year later. From 1967 to 1969 he was guest professor at Queen's University in Kingston, Ontario and at the Massachusetts Institute of Technology in Cambridge, Massachusetts, after which he was a professor in Bonn. In 1971 he became a professor at the University of Regensburg.
Contributions
He is known for his work on the embedding problem in algebraic number theory, the Báyer–Neukirch theorem on special values of L-functions, arithmetic Riemann existence theorems and the Neukirch–Uchida theorem in birational anabelian geometry. He gave a simple description of the reciprocity maps in local and global class field theory.
Books
Neukirch wrote three books on class field theory, algebraic number theory, and the cohomology of number fields:
Notes
External links
On Neukirch's death (in German)
1937 births
1997 deaths
20th-century German mathematicians
Number theorists
University of Bonn alumni
Academic staff of the University of Bonn
Academic staff of the University of Regensburg
Scientists from Dortmund |
https://en.wikipedia.org/wiki/Jinsafut | Jinsafut () is a Palestinian village in the Qalqilya Governorate in the northeastern West Bank, located east of Qalqilya. According to the Palestinian Central Bureau of Statistics, the village had a population of 2,571 inhabitants in 2017.
Fatah's Secretary-General Farouk Kaddoumi was born in Jinsafut.
In 2012 it was decided that Jinsafut and Al-Funduq should be merged under one local council.
Location
Jinsafut (including Al-Funduq) is located east of Qalqiliya. It is bordered by Immatin to the east, Deir Istiya to the south, Wadi Qana (in Salfit Governorate) to the west and Hajja to the north.
History
A construction text, over the lintel to a shrine known both as az-Zawiyah, and al Kihlwah, informs us that it was built by Mubarak Ibn Salih Alusi in the Mamluk era, in the year 791 AH, that is 1389 CE.
Ottoman era
The place appeared in 1596 Ottoman tax registers as Jim Safut, being in the Nahiya of Bani Sa'b of the Liwa of Nablus. It had a population of 26 households, all Muslim. They paid a fixed tax-rate of 33.3% on agricultural products, including wheat barley, summer crops, olives, goats and beehives, and a press for olives or grapes; a total of 8,654 akçe.
In 1838, Robinson noted Jin Safut as a village in Beni Sa'ab district, west of Nablus.
In 1870 Victor Guérin noted it from Fara'ata, but did not visit it.
In 1870/1871 (1288 AH), an Ottoman census listed the village in the nahiya (sub-district) of Bani Sa'b.
In 1882, the PEF's Survey of Western Palestine described the village as "a small village on high ground, with wells to the north, and a few olives."
British Mandate era
In the 1922 census of Palestine conducted by the British Mandate authorities, Jensafut had a population of 267 inhabitants, all Muslims, increasing in the 1931 census to 315 Muslims, with 76 houses.
In the 1945 census the population was 450 Muslims, with 9,356 dunams of land, according to an official land and population survey. Of this, 1,410 dunams were for plantations or irrigated land, 2,208 for cereals, while 14 dunams were built-up (urban) land.
Jordanian era
In the wake of the 1948 Arab–Israeli War, and after the 1949 Armistice Agreements, Jinsafut came under Jordanian rule. It was annexed by Jordan in 1950.
The Jordanian census of 1961 found 729 inhabitants in Jinsafut.
1967-present
Since the Six-Day War in 1967, Jinsafut has been under Israeli occupation.
After the 1995 accords, 4.8% of Jinsafut and Al-Funduq land was classified as Area B, the remaining 95.2% is Area C.
Israel has expropriated 713 dunums of land from Jinsafut in order to establish two Israeli settlements; Karne Shomron and Neve Oramin.
Demographics
Some families of Jinsafut include al-Ayoub, al-Sukar, al-Saber, al-Allan, al-Nassar, al-Bashir and Eid. Prior to 1967, Jinsafut had a population of 700, which decreased to 550 after the 1967 Six-Day War; The drop was caused by residents fleeing the village to Jordan. According to a PCBS estimate, the village had grown to 2,1 |
https://en.wikipedia.org/wiki/2000%E2%80%9301%20Azerbaijan%20Top%20League | The 2000-01 Azerbaijan Top League was contested by 11 clubs and won by FK Shamkir.
Teams
Stadia and locations
League table
Results
Championship play-off
Season statistics
Top scorers
References
External links
Azerbaijan 2000-01 RSSSF
APL Stats
Azerbaijan Premier League seasons
Azer
1 |
https://en.wikipedia.org/wiki/John%20Benedetto | John Joseph Benedetto (born July 16, 1939) is a professor of Mathematics at the University of Maryland, College Park and is a leading researcher in wavelet analysis and Director of the Norbert Wiener Center for Harmonic Analysis and Applications. He was named Distinguished Scholar-Teacher by the University of Maryland in 1999 and has directed 63 Ph.D. students. The volume Harmonic Analysis and Applications: In Honor of John Benedetto, edited by Christopher Heil, describes his influence:
John J. Benedetto has had a profound influence not only on the direction of harmonic analysis and its applications, but also on the entire community of people involved in the field.
He was a Senior Fulbright-Hays Scholar (1973–1974), and was awarded the 2011 SPIE Wavelet Pioneer award. He is also a Fellow of the American Mathematical Society and a SIAM Fellow.
Education
Benedetto attended Boston College, graduating in 1960 with a B.A. in mathematics. He received an M.A. from Harvard University in 1962, and a Ph.D. from the University of Toronto in 1964. He was the first student to receive a Ph.D. from then 37-year-old Chandler Davis. His dissertation was The Laplace Transform of Generalized Functions.
Garrett Birkhoff was the thesis advisor of Chandler Davis, and Birkhoff did not have a Ph.D. but was a member of the Society of Fellows at Harvard.
Publications
Benedetto is founding Editor-in-Chief of the Journal of Fourier Analysis and Applications, founded in 1994 and published by Springer-Birkhäuser. He is also founding and current editor of the Springer-Birkhäuser Applied and Numerical Harmonic Analysis book series. He has edited or authored 18 books and published over 185 research papers. Some of his books are the following.
Books
(1971) Harmonic Analysis on Totally Disconnected Sets, Springer Lecture Notes 202
(1975) Spectral Synthesis, Academic Press
(1976) Real Variable and Integration with Historical Notes, Teubner Publishers
(1977) A Mathematical Approach to Mathematics Appreciation, UMD
(1979) Euclidean Harmonic Analysis, editor, Springer Lecture Notes 779
(1994) Wavelets: Mathematics and Applications, co-edited with M. Frazier, CRC Press
(1997) Harmonic Analysis and Applications, CRC Press
(2001) Modern Sampling Theory: Mathematics and Applications, co-edited with P. Ferreira
(2004) Sampling, Wavelets, and Tomography, co-edited with A. Zayed
(2009) Integration and Modern Analysis, co-authored with Wojciech Czaja
References
External links
Speaker Bio from NIST
Norbert Wiener Center for Harmonic Analysis and Applications
Homepage
Mathematics genealogy project
Journal of Fourier Analysis and Applications
Applied and Numerical Harmonic Analysis
Harmonic Analysis and Applications, A volume in honor of John J. Benedetto (C. Heil, editor) Birkhäuser, Boston, 2006.
ICA Wavelet Pioneers
Mathematical Genealogy
Living people
1939 births
20th-century American mathematicians
21st-century American mathematicians
Morrissey College of Arts |
https://en.wikipedia.org/wiki/Norbert%20Wiener%20Center%20for%20Harmonic%20Analysis%20and%20Applications | The Norbert Wiener Center for Harmonic Analysis and Applications (NWC) is a division of the Mathematics Department in the University of Maryland College of Computer, Mathematical, and Natural Sciences devoted to research and education in pure and applied harmonic analysis. The center, named after acclaimed scientist Norbert Wiener was founded in 2004 and is based out of the Mathematics Building on the University of Maryland, College Park campus. It is supported by the University of Maryland, the National Science Foundation, and local industries with which it interacts.
Currently, the Norbert Wiener Center is actively involved in research project involved with waveform design, dimension reduction, geospatial terrain and image processing, data fusion, phase retrieval frames, and analysis on graphs.
February Fourier Talks
The Norbert Wiener Center hosts the annual conference, the February Fourier Talks (FFT). The first FFT was held in 2002 and 2003, and then annually since 2006. The aim of the annual FFT is to bring together researchers from academia, government, and industry, as a means to spur innovation and foster interaction in Harmonic Analysis and its Applications. The FFT lasts two days and consists of approximately 15 half-hour talks, a distinguished lecture, a colloquium, and a keynote lecture. The speakers are top researchers in pure and applied harmonic analysis in academia, government, and industry.
Current Personnel
The Director of the NWC is John Benedetto. The faculty members include: John Benedetto, Radu Balan, Wojciech Czaja, and Kasso Okoudjou. The current Scientific Development Officers include Michael Dellomo, Jeffrey Sieracki, and Alfredo Nava-Tudela. The current postdoctoral fellows include Xuemei Chen and Benjamin Manning. The associate director of the center is Matthew Begué. A list of all other members, including all graduate students, can be found on the center's official website.
External links
Official website of the Norbert Wiener Center
February Fourier Talks 2014
Mathematical institutes
Research institutes in Maryland
University of Maryland, College Park research centers |
https://en.wikipedia.org/wiki/2008%E2%80%9309%20Real%20Madrid%20CF%20season | The 2008–09 season was Real Madrid Club de Fútbol's 78th season in La Liga. This article lists all matches that the club played in the 2008–09 season and shows statistics of the club's players.
Players
Squad information
In
Total spending: €71.7 million
Out
Total income: €69.7 million
Club
Coaching staff
Kits
|
|
|
Other information
Competitions
La Liga
League table
Results by round
Matches
Copa del Rey
Champions League
Group H
Round of 16
Supercopa de España
Friendlies
Statistics
Players statistics
Long-term injury list
Last updated: 2009-06-01
Source: Realmadrid.com
Suspension list
Last updated: 2009-06-01
Source: Realmadrid.com
Disciplinary record
.
Start formations
It should be pointed out that Real is neither playing 4–3–3 nor 4–4–2, but a hybrid formation between both.
See also
2008–09 La Liga
2008–09 Copa del Rey
2008 Supercopa de España
2008–09 UEFA Champions League
References
Real Madrid
Real Madrid CF seasons |
https://en.wikipedia.org/wiki/SYZ%20conjecture | The SYZ conjecture is an attempt to understand the mirror symmetry conjecture, an issue in theoretical physics and mathematics. The original conjecture was proposed in a paper by Strominger, Yau, and Zaslow, entitled "Mirror Symmetry is T-duality".
Along with the homological mirror symmetry conjecture, it is one of the most explored tools applied to understand mirror symmetry in mathematical terms. While the homological mirror symmetry is based on homological algebra, the SYZ conjecture is a geometrical realization of mirror symmetry.
Formulation
In string theory, mirror symmetry relates type IIA and type IIB theories. It predicts that the effective field theory of type IIA and type IIB should be the same if the two theories are compactified on mirror pair manifolds.
The SYZ conjecture uses this fact to realize mirror symmetry. It starts from considering BPS states of type IIA theories compactified on X, especially 0-branes that have moduli space X. It is known that all of the BPS states of type IIB theories compactified on Y are 3-branes. Therefore, mirror symmetry will map 0-branes of type IIA theories into a subset of 3-branes of type IIB theories.
By considering supersymmetric conditions, it has been shown that these 3-branes should be special Lagrangian submanifolds. On the other hand, T-duality does the same transformation in this case, thus "mirror symmetry is T-duality".
Mathematical statement
The initial proposal of the SYZ conjecture by Strominger, Yau, and Zaslow, was not given as a precise mathematical statement. One part of the mathematical resolution of the SYZ conjecture is to, in some sense, correctly formulate the statement of the conjecture itself. There is no agreed upon precise statement of the conjecture within the mathematical literature, but there is a general statement that is expected to be close to the correct formulation of the conjecture, which is presented here. This statement emphasizes the topological picture of mirror symmetry, but does not precisely characterise the relationship between the complex and symplectic structures of the mirror pairs, or make reference to the associated Riemannian metrics involved.
SYZ Conjecture: Every 6-dimensional Calabi–Yau manifold has a mirror 6-dimensional Calabi–Yau manifold such that there are continuous surjections , to a compact topological manifold of dimension 3, such that
There exists a dense open subset on which the maps are fibrations by nonsingular special Lagrangian 3-tori. Furthermore for every point , the torus fibres and should be dual to each other in some sense, analogous to duality of Abelian varieties.
For each , the fibres and should be singular 3-dimensional special Lagrangian submanifolds of and respectively.
The situation in which so that there is no singular locus is called the semi-flat limit of the SYZ conjecture, and is often used as a model situation to describe torus fibrations. The SYZ conjecture can be shown to hold in some |
https://en.wikipedia.org/wiki/Quasi-maximum%20likelihood%20estimate | In statistics a quasi-maximum likelihood estimate (QMLE), also known as a pseudo-likelihood estimate or a composite likelihood estimate, is an estimate of a parameter θ in a statistical model that is formed by maximizing a function that is related to the logarithm of the likelihood function, but in discussing the consistency and (asymptotic) variance-covariance matrix, we assume some parts of the distribution may be mis-specified.
In contrast, the maximum likelihood estimate maximizes the actual log likelihood function for the data and model. The function that is maximized to form a QMLE is often a simplified form of the actual log likelihood function. A common way to form such a simplified function is to use the log-likelihood function of a misspecified model that treats certain data values as being independent, even when in actuality they may not be. This removes any parameters from the model that are used to characterize these dependencies. Doing this only makes sense if the dependency structure is a nuisance parameter with respect to the goals of the analysis.
As long as the quasi-likelihood function that is maximized is not oversimplified, the QMLE (or composite likelihood estimate) is consistent and asymptotically normal. It is less efficient than the maximum likelihood estimate, but may only be slightly less efficient if the quasi-likelihood is constructed so as to minimize the loss of information relative to the actual likelihood. Standard approaches to statistical inference that are used with maximum likelihood estimates, such as the formation of confidence intervals, and statistics for model comparison, can be generalized to the quasi-maximum likelihood setting.
See also
Quasi-likelihood
Partial likelihood methods for panel data
References
Maximum likelihood estimation |
https://en.wikipedia.org/wiki/Link%20concordance | In mathematics, two links and are concordant if there exists an embedding such that and .
By its nature, link concordance is an equivalence relation. It is weaker than isotopy, and stronger than homotopy: isotopy implies concordance implies homotopy. A link is a slice link if it is concordant to the unlink.
Concordance invariants
A function of a link that is invariant under concordance is called a concordance invariant.
The linking number of any two components of a link is one of the most elementary concordance invariants. The signature of a knot is also a concordance invariant. A subtler concordance invariant are the Milnor invariants, and in fact all rational finite type concordance invariants are Milnor invariants and their products, though non-finite type concordance invariants exist.
Higher dimensions
One can analogously define concordance for any two submanifolds . In this case one considers two submanifolds concordant if there is a cobordism between them in i.e., if there is a manifold with boundary whose boundary consists of and
This higher-dimensional concordance is a relative form of cobordism – it requires two submanifolds to be not just abstractly cobordant, but "cobordant in N".
See also
Slice knot
References
Further reading
J. Hillman, Algebraic invariants of links. Series on Knots and everything. Vol 32. World Scientific.
Livingston, Charles, A survey of classical knot concordance, in: Handbook of knot theory, pp 319–347, Elsevier, Amsterdam, 2005.
Knot invariants
Manifolds |
https://en.wikipedia.org/wiki/1895%E2%80%9396%20Belgian%20First%20Division | Statistics of Belgian First Division in the 1895–96 season.
Overview
It was contested by 7 teams, and F.C. Liégeois won the championship.
League standings
Results
See also
1895–96 in Belgian football
References
1895
1895–96 in European association football leagues
1895–96 in Belgian football |
https://en.wikipedia.org/wiki/1896%E2%80%9397%20Belgian%20First%20Division | Statistics of Belgian First Division in the 1896–97 season.
Overview
It was contested by 6 teams, and Racing Club de Bruxelles won the championship.
League standings
Results
See also
1896–97 in Belgian football
References
1896
1896–97 in European association football leagues
1896–97 in Belgian football |
https://en.wikipedia.org/wiki/1898%E2%80%9399%20Belgian%20First%20Division | Statistics of Belgian First Division in the 1898–99 season.
Overview
This season saw a number of new clubs enter the Championship. along with a new format.
It was contested by 9 teams, and F.C. Liégeois won the championship.
League standings
Championship Group A
Championship Group B
Only the rankings are known.
Final
See also
1898–99 in Belgian football
References
External links
Belgian clubs history
1898
1898–99 in European association football leagues
1898–99 in Belgian football |
https://en.wikipedia.org/wiki/1899%E2%80%931900%20Belgian%20First%20Division | Statistics of Belgian First Division in the 1899–1900 season.
Overview
It was contested by 10 teams, and Racing Club de Bruxelles won the championship.
League standings
Championship Group A
Play-off
Racing Club de Bruxelles Qualified for the National Final.
Championship Group B
Only the rankings are known.
Final
See also
1899–1900 in Belgian football
References
External links
Belgian clubs history
1899
1899–1900 in European association football leagues
1899–1900 in Belgian football |
https://en.wikipedia.org/wiki/1900%E2%80%9301%20Belgian%20First%20Division | Statistics of Belgian First Division in the 1900–01 season.
Locations of teams
Overview
This season saw the two Groups of previous seasons merged back into one national Division.
It was contested by 9 teams, and Racing Club de Bruxelles won the championship.
League standings
Results
See also
1900–01 in Belgian football
References
1900
1900–01 in European association football leagues
1900–01 in Belgian football |
https://en.wikipedia.org/wiki/1901%E2%80%9302%20Belgian%20First%20Division | Statistics of Belgian First Division in the 1901–02 season.
Overview
This season saw another split, after just one season, into two Groups, this time with a Final Group to decide the champion.
It was contested by 11 teams, and Racing Club de Bruxelles won the championship.
League standings
Championship Cup A
Championship Cup B
Final round
Test match
See also
1901–02 in Belgian football
References
1901
1901–02 in Belgian football
Belgian First Division, 1913-14 |
https://en.wikipedia.org/wiki/1902%E2%80%9303%20Belgian%20First%20Division | Statistics of Belgian First Division in the 1902–03 season.
Overview
It was contested by 10 teams, and Racing Club de Bruxelles won the championship.
League standings
Championship Cup A
Championship Cup B
Final round
See also
1902–03 in Belgian football
References
1902
Belgian First Division, 1913-14
1902–03 in Belgian football |
https://en.wikipedia.org/wiki/1903%E2%80%9304%20Belgian%20First%20Division | Statistics of Belgian First Division in the 1903–04 season.
Overview
It was contested by 12 teams, and Union Saint-Gilloise won the championship.
League standings
Championship Cup A
Championship Cup B
Final round
See also
1903–04 in Belgian football
References
1903
Belgian First Division, 1913-14
1903–04 in Belgian football |
https://en.wikipedia.org/wiki/1908%E2%80%9309%20Belgian%20First%20Division | Statistics of Belgian First Division in the 1908–09 season.
Overview
It was contested by 12 teams, and Union Saint-Gilloise won the championship.
League standings
Results
See also
1908–09 in Belgian football
References
Belgian Pro League seasons
Belgian First Division, 1913-14
1908–09 in Belgian football |
https://en.wikipedia.org/wiki/1909%E2%80%9310%20Belgian%20First%20Division | Statistics of Belgian First Division in the 1909–10 season.
Overview
It was contested by 12 teams, and Union Saint-Gilloise won the championship.
League standings
Results
Play-off
See also
1909–10 in Belgian football
References
Belgian Pro League seasons
Belgian First Division, 1913-14
1909–10 in Belgian football |
https://en.wikipedia.org/wiki/1910%E2%80%9311%20Belgian%20First%20Division | Statistics of Belgian First Division in the 1910–11 season.
Overview
It was contested by 12 teams, and C.S. Brugeois won the championship.
League standings
Results
See also
1910–11 in Belgian football
References
Belgian Pro League seasons
Belgian First Division, 1913-14
1910–11 in Belgian football |
https://en.wikipedia.org/wiki/1911%E2%80%9312%20Belgian%20First%20Division | Statistics of Belgian First Division in the 1911–12 season.
Overview
It was contested by 12 teams, and Daring Club de Bruxelles won the championship.
League standings
Results
See also
1911–12 in Belgian football
References
Belgian Pro League seasons
Belgian First Division, 1913-14
1911–12 in Belgian football |
https://en.wikipedia.org/wiki/1912%E2%80%9313%20Belgian%20First%20Division | Statistics of Belgian First Division in the 1912–13 season.
Overview
It was contested by 12 teams, and Union Saint-Gilloise won the championship.
League standings
Results
Championship play-off
See also
1912–13 in Belgian football
References
Belgian Pro League seasons
Belgian First Division, 1913-14
1912–13 in Belgian football |
https://en.wikipedia.org/wiki/1913%E2%80%9314%20Belgian%20First%20Division | Statistics of Belgian First Division in the 1913–14 season.
Overview
It was contested by 12 teams, and Daring Club won the championship.
Because they finished level on points in 10th/11th place, A.A. La Gantoise and Standard Club Liégeois played a Test Match to decide who would stay up: this was won by La Gantoise, thus relegating Liégeois to the Promotion Division.
League standings
Results
See also
1913–14 in Belgian football
References
Belgian Pro League seasons
Belgian First Division, 1913-14
1913–14 in Belgian football |
https://en.wikipedia.org/wiki/1919%E2%80%9320%20Belgian%20First%20Division | Statistics of Belgian First Division in the 1919–20 season.
Overview
It was contested by 12 teams, and FC Bruges won the championship: however, for reasons unknown, La Gantoise were not relegated to the Promotion Division.
League standings
Results
References
Belgian Pro League seasons
Belgian
Belgian First Division |
https://en.wikipedia.org/wiki/1920%E2%80%9321%20Belgian%20First%20Division | Statistics of Belgian First Division in the 1920–21 season.
Overview
It was contested by 12 teams, and Daring Club won the championship.
As the number of clubs was to be increased from 12 to 14, only one club was relegated to the Promotion Division, with three clubs promoted.
League standings
Results
References
Belgian Pro League seasons
Belgian
Belgian First Division |
https://en.wikipedia.org/wiki/1921%E2%80%9322%20Belgian%20First%20Division | Statistics of Belgian First Division in the 1921–22 season.
Overview
It was contested by 14 teams, and Beerschot won the championship.
League standings
Results
References
Belgian Pro League seasons
Belgian
Belgian First Division |
https://en.wikipedia.org/wiki/1922%E2%80%9323%20Belgian%20First%20Division | Statistics of Belgian First Division in the 1922–23 season.
Overview
It was contested by 14 teams, and Royale Union Saint-Gilloise won the championship.
League standings
Results
References
Belgian Pro League seasons
Belgian
Belgian First Division |
https://en.wikipedia.org/wiki/1923%E2%80%9324%20Belgian%20First%20Division | Statistics of Belgian First Division in the 1923–24 season.
Overview
It was contested by 14 teams, and Beerschot won the championship.
League standings
Results
References
Belgian Pro League seasons
Belgian
Belgian First Division |
https://en.wikipedia.org/wiki/1924%E2%80%9325%20Belgian%20First%20Division | Statistics of Belgian First Division in the 1924–25 season.
Overview
It was contested by 14 teams, and Beerschot won the championship.
League standings
Results
References
Belgian Pro League seasons
Belgian
Belgian First Division |
https://en.wikipedia.org/wiki/1925%E2%80%9326%20Belgian%20First%20Division | Statistics of Belgian First Division in the 1925–26 season.
Overview
It was contested by 14 teams, and Beerschot won the championship.
League standings
Results
References
Belgian Pro League seasons
Belgian
Belgian First Division |
https://en.wikipedia.org/wiki/1926%E2%80%9327%20Belgian%20First%20Division | Statistics of Belgian First Division in the 1926–27 season.
Overview
It was contested by 14 teams, and Cercle Brugge K.S.V. won the championship.
League standings
Results
References
Belgian Pro League seasons
Belgian First Division, 1926-27
1 |
https://en.wikipedia.org/wiki/1927%E2%80%9328%20Belgian%20First%20Division | Statistics of Belgian First Division in the 1927–28 season.
Overview
It was contested by 14 teams, and Beerschot won the championship.
League standings
Results
Relegation play-offs
References
Belgian Pro League seasons
Belgian First Division, 1927-28
1927–28 in Belgian football |
https://en.wikipedia.org/wiki/1928%E2%80%9329%20Belgian%20First%20Division | Statistics of Belgian First Division in the 1928–29 season.
Overview
It was contested by 14 teams, and Royal Antwerp FC won the championship.
League standings
Results
Championship play-off
References
Belgian Pro League seasons
Belgian First Division, 1928-29
1928–29 in Belgian football |
https://en.wikipedia.org/wiki/1929%E2%80%9330%20Belgian%20First%20Division | Statistics of Belgian First Division in the 1929–30 season.
Overview
It was contested by 14 teams, and Cercle Brugge K.S.V. won the championship.
League standings
Results
References
Belgian Pro League seasons
Belgian First Division, 1929-30
1 |
https://en.wikipedia.org/wiki/1930%E2%80%9331%20Belgian%20First%20Division | Statistics of Belgian First Division in the 1930–31 season.
Overview
It was contested by 14 teams, and Royal Antwerp FC won the championship.
League standings
Results
References
Belgian Pro League seasons
Belgian First Division, 1930-31
1930–31 in Belgian football |
https://en.wikipedia.org/wiki/1931%E2%80%9332%20Belgian%20First%20Division | Statistics of Belgian First Division in the 1931–32 season.
Overview
It was contested by 14 teams, and Lierse S.K. won the championship.
League standings
Results
References
Belgian Pro League seasons
Belgian First Division, 1931-32
1931–32 in Belgian football |
https://en.wikipedia.org/wiki/1932%E2%80%9333%20Belgian%20First%20Division | Statistics of Belgian First Division in the 1932–33 season.
Overview
It was contested by 14 teams, and Royale Union Saint-Gilloise won the championship.
League standings
Results
References
Belgian Pro League seasons
Belgian First Division, 1932-33
1932–33 in Belgian football |
https://en.wikipedia.org/wiki/1933%E2%80%9334%20Belgian%20First%20Division | Statistics of Belgian First Division in the 1933–34 season.
Overview
It was contested by 14 teams, and Royale Union Saint-Gilloise won the championship.
League standings
Results
References
Belgian Pro League seasons
Belgian First Division, 1933-34
1933–34 in Belgian football |
https://en.wikipedia.org/wiki/1934%E2%80%9335%20Belgian%20First%20Division | Statistics of Belgian First Division in the 1934–35 season.
Overview
It was contested by 14 teams, and Royale Union Saint-Gilloise won the championship.
League standings
Results
References
Belgian Pro League seasons
Belgian First Division, 1934-35
1934–35 in Belgian football |
https://en.wikipedia.org/wiki/1935%E2%80%9336%20Belgian%20First%20Division | Statistics of Belgian First Division in the 1935–36 season.
Overview
It was contested by 14 teams, and Daring Club won the championship.
League standings
Results
References
Belgian Pro League seasons
Belgian First Division, 1935-36
1935–36 in Belgian football |
https://en.wikipedia.org/wiki/1936%E2%80%9337%20Belgian%20First%20Division | Statistics of Belgian First Division in the 1936–37 season.
Overview
It was contested by 14 teams, and Daring Club won the championship.
League standings
Results
References
Belgian Pro League seasons
Belgian First Division, 1936-37
1936–37 in Belgian football |
https://en.wikipedia.org/wiki/1937%E2%80%9338%20Belgian%20First%20Division | Statistics of Belgian First Division in the 1937–38 season.
Overview
It was contested by 14 teams, and Beerschot won the championship.
League standings
Results
References
Belgian Pro League seasons
Belgian First Division, 1937-38
1937–38 in Belgian football |
https://en.wikipedia.org/wiki/1938%E2%80%9339%20Belgian%20First%20Division | Statistics of Belgian First Division in the 1938–39 season.
Overview
It was contested by 14 teams, and Beerschot won the championship.
Owing to the outbreak of World War II, the 1939-40 Belgian League season was suspended after 9 matches, and was not restarted until 1941-42 (although an unofficial 1940-41 Championship took place).
League standings
Results
References
Belgian Pro League seasons
Belgian First Division, 1938-39
1938–39 in Belgian football |
https://en.wikipedia.org/wiki/1941%E2%80%9342%20Belgian%20First%20Division | Statistics of Belgian First Division in the 1941–42 season.
Overview
It was contested by 14 teams, and Lierse S.K. won the championship.
No clubs were relegated owing to the expansion of the Premier Division the following season from 14 clubs to 16.
League standings
Results
References
Belgian Pro League seasons
1941–42 in Belgian football
Belgian |
https://en.wikipedia.org/wiki/1942%E2%80%9343%20Belgian%20First%20Division | Statistics of Belgian First Division in the 1942–43 season.
Overview
It was contested by 16 teams, and KV Mechelen won the championship.
League standings
Results
References
Belgian Pro League seasons
1942–43 in Belgian football
Belgian |
https://en.wikipedia.org/wiki/1943%E2%80%9344%20Belgian%20First%20Division | Statistics of Belgian First Division in the 1943–44 season.
Overview
It was contested by 16 teams, and Royal Antwerp FC won the championship.
League standings
Results
References
Belgian Pro League seasons
1943–44 in Belgian football
Belgian |
https://en.wikipedia.org/wiki/1946%E2%80%9347%20Belgian%20First%20Division | Statistics of Belgian First Division in the 1946–47 season.
Overview
It was contested by 19 teams, and R.S.C. Anderlecht won the championship.
At the end of the season, the number of clubs was reduced from 19 back to 16 for the following season.
League standings
Results
References
Belgian Pro League seasons
1946–47 in Belgian football
Belgian |
https://en.wikipedia.org/wiki/1947%E2%80%9348%20Belgian%20First%20Division | Statistics of Belgian First Division in the 1947–48 season.
Overview
It was contested by 16 teams, and KV Mechelen won the championship.
League standings
Results
References
Belgian Pro League seasons
1947–48 in Belgian football
Belgian |
https://en.wikipedia.org/wiki/1948%E2%80%9349%20Belgian%20First%20Division | Statistics of Belgian First Division in the 1948–49 season.
Overview
It was contested by 16 teams, and R.S.C. Anderlecht won the championship.
League standings
Results
References
Belgian Pro League seasons
1948–49 in Belgian football
Belgian |
https://en.wikipedia.org/wiki/1949%E2%80%9350%20Belgian%20First%20Division | Statistics of Belgian First Division in the 1949–50 season.
Overview
It was contested by 16 teams, and R.S.C. Anderlecht won the championship.
League standings
Results
References
Belgian Pro League seasons
1949–50 in Belgian football
Belgian |
https://en.wikipedia.org/wiki/1950%E2%80%9351%20Belgian%20First%20Division | Statistics of Belgian First Division in the 1950–51 season.
Overview
It was contested by 16 teams, and R.S.C. Anderlecht won the championship.
League standings
Results
References
Belgian Pro League seasons
1950–51 in Belgian football
Belgian |
https://en.wikipedia.org/wiki/1951%E2%80%9352%20Belgian%20First%20Division | Statistics of Belgian First Division in the 1951–52 season.
Overview
It was contested by 16 teams, and R.F.C. de Liège won the championship.
As part of the re-organisation of Belgian football for the following season, this division was renamed Division I.
League standings
Results
References
Belgian Pro League seasons
1951–52 in Belgian football
Belgian |
https://en.wikipedia.org/wiki/1952%E2%80%9353%20Belgian%20First%20Division | Statistics of Belgian First Division in the 1952–53 season.
Overview
It was contested by 16 teams, and R.F.C. de Liège won the championship.
League standings
Results
References
Belgian Pro League seasons
1952–53 in Belgian football
Belgian |
https://en.wikipedia.org/wiki/1953%E2%80%9354%20Belgian%20First%20Division | Statistics of Belgian First Division in the 1953–54 season.
Overview
It was contested by 16 teams, and R.S.C. Anderlecht won the championship.
League standings
Results
References
Belgian Pro League seasons
1953–54 in Belgian football
Belgian |
https://en.wikipedia.org/wiki/1954%E2%80%9355%20Belgian%20First%20Division | Statistics of Belgian First Division in the 1954–55 season.
Overview
It was contested by 16 teams, and R.S.C. Anderlecht won the championship.
League standings
Results
References
Belgian Pro League seasons
1954–55 in Belgian football
Belgian |
https://en.wikipedia.org/wiki/1956%E2%80%9357%20Belgian%20First%20Division | Statistics of Belgian First Division in the 1956–57 season.
Overview
It was contested by 16 teams, and Royal Antwerp FC won the championship.
League standings
Results
References
Belgian Pro League seasons
1956–57 in Belgian football
Belgian |
https://en.wikipedia.org/wiki/1957%E2%80%9358%20Belgian%20First%20Division | Statistics of Belgian First Division in the 1957–58 season.
Overview
It was contested by 16 teams, and Standard Liège won the championship.
League standings
Results
References
Belgian Pro League seasons
1957–58 in Belgian football
Belgian |
https://en.wikipedia.org/wiki/1958%E2%80%9359%20Belgian%20First%20Division | Statistics of Belgian First Division in the 1958–59 season.
Overview
It was contested by 16 teams, and R.S.C. Anderlecht won the championship.
League standings
Results
References
Belgian Pro League seasons
1958–59 in Belgian football
Belgian |
https://en.wikipedia.org/wiki/1959%E2%80%9360%20Belgian%20First%20Division | Statistics of Belgian First Division in the 1959–60 season.
Overview
It was contested by 16 teams, and Lierse S.K. won the championship.
League standings
Results
Belgian Pro League seasons
Belgian
1959–60 in Belgian football |
https://en.wikipedia.org/wiki/1960%E2%80%9361%20Belgian%20First%20Division | Statistics of Belgian First Division in the 1960–61 season.
Overview
It was contested by 16 teams, and Standard Liège won the championship.
League standings
Results
References
Belgian Pro League seasons
Belgian
1960–61 in Belgian football |
https://en.wikipedia.org/wiki/1961%E2%80%9362%20Belgian%20First%20Division | Statistics of Belgian First Division in the 1961–62 season.
Overview
It was contested by 16 teams, and R.S.C. Anderlecht won the championship.
League standings
Results
References
Belgian Pro League seasons
Belgian
1961–62 in Belgian football |
https://en.wikipedia.org/wiki/1962%E2%80%9363%20Belgian%20First%20Division | Statistics of Belgian First Division in the 1962–63 season.
Overview
It was contested by 16 teams, and Standard Liège won the championship.
League standings
Results
References
Belgian Pro League seasons
Belgian
1962–63 in Belgian football |
https://en.wikipedia.org/wiki/1963%E2%80%9364%20Belgian%20First%20Division | Statistics of Belgian First Division in the 1963–64 season.
Overview
It was contested by 16 teams, and R.S.C. Anderlecht won the championship.
League standings
Results
References
External links
wildstat.com
Belgian Pro League seasons
Belgian
1 |
https://en.wikipedia.org/wiki/1964%E2%80%9365%20Belgian%20First%20Division | Statistics of Belgian First Division in the 1964–65 season.
Overview
It was contested by 16 teams, and R.S.C. Anderlecht won the championship.
League standings
Results
References
Belgian Pro League seasons
Belgian
1964–65 in Belgian football |
https://en.wikipedia.org/wiki/1965%E2%80%9366%20Belgian%20First%20Division | Statistics of Belgian First Division in the 1965–66 season.
Overview
It was contested by 16 teams, and R.S.C. Anderlecht won the championship.
League standings
Results
References
Belgian Pro League seasons
Belgian
1965–66 in Belgian football |
https://en.wikipedia.org/wiki/1966%E2%80%9367%20Belgian%20First%20Division | Statistics of Belgian First Division in the 1966–67 season.
Overview
It was contested by 16 teams, and R.S.C. Anderlecht won the championship.
League standings
Results
References
Belgian Pro League seasons
Belgian
1966–67 in Belgian football |
https://en.wikipedia.org/wiki/1967%E2%80%9368%20Belgian%20First%20Division | Statistics of Belgian First Division in the 1967–68 season.
Overview
It was contested by 16 teams, and R.S.C. Anderlecht won the championship.
League standings
Results
References
Belgian Pro League seasons
Belgian
1967–68 in Belgian football |
https://en.wikipedia.org/wiki/1968%E2%80%9369%20Belgian%20First%20Division | Statistics of Belgian First Division in the 1968–69 season.
Overview
It was contested by 16 teams, and Standard Liège won the championship.
League standings
Results
References
Belgian Pro League seasons
Belgian
1968–69 in Belgian football |
https://en.wikipedia.org/wiki/1969%E2%80%9370%20Belgian%20First%20Division | Statistics of Belgian First Division in the 1969–70 season.
Overview
It was contested by 16 teams, and Standard Liège won the championship.
League standings
Results
References
Belgian Pro League seasons
Belgian
1969–70 in Belgian football |
https://en.wikipedia.org/wiki/1970%E2%80%9371%20Belgian%20First%20Division | Statistics of Belgian First Division in the 1970–71 season.
Overview
It was contested by 16 teams, and Standard Liège won the championship.
League standings
Results
References
Belgian Pro League seasons
Belgian
1970–71 in Belgian football |
https://en.wikipedia.org/wiki/1971%E2%80%9372%20Belgian%20First%20Division | Statistics of Belgian First Division in the 1971–72 season.
Overview
It was contested by 16 teams, and R.S.C. Anderlecht won the championship.
League standings
Results
References
Belgian Pro League seasons
Belgian
1971–72 in Belgian football |
https://en.wikipedia.org/wiki/1972%E2%80%9373%20Belgian%20First%20Division | Statistics of Belgian First Division in the 1972–73 season for association football clubs in Belgium.
Overview
It was contested by 16 teams, and Club Brugge K.V. won the championship.
League standings
Results
References
Belgian Pro League seasons
Belgian
1972–73 in Belgian football |
https://en.wikipedia.org/wiki/1973%E2%80%9374%20Belgian%20First%20Division | Statistics of Belgian First Division in the 1973–74 season.
Overview
It was contested by 16 teams, and R.S.C. Anderlecht won the championship.
League standings
Results
Play-off
References
Belgian Pro League seasons
Belgian
1973–74 in Belgian football |
https://en.wikipedia.org/wiki/1974%E2%80%9375%20Belgian%20First%20Division | Statistics of Belgian First Division in the 1974–75 season.
Overview
It was contested by 20 teams, and R.W.D. Molenbeek won the championship.
At the end of the season the division was reduced in size from 20 to 19 clubs, so three clubs were relegated with two clubs promoted from Division II to replace them.
League standings
Results
References
Belgian Pro League seasons
Belgian
1974–75 in Belgian football |
https://en.wikipedia.org/wiki/1975%E2%80%9376%20Belgian%20First%20Division | Statistics of Belgian First Division in the 1975–76 season.
Overview
It was contested by 19 teams, and Club Brugge K.V. won the championship.
At the end of the season the division was reduced in size from 19 to 18 clubs, so three clubs were relegated to Division II to be replaced by two promoted clubs.
League standings
Results
References
Belgian Pro League seasons
Belgian
1975–76 in Belgian football |
https://en.wikipedia.org/wiki/1976%E2%80%9377%20Belgian%20First%20Division | Statistics of Belgian First Division in the 1976–77 season.
Overview
It was contested by 18 teams, and Club Brugge K.V. won the championship.
League standings
Results
References
Belgian Pro League seasons
Belgian
1976–77 in Belgian football |
https://en.wikipedia.org/wiki/1977%E2%80%9378%20Belgian%20First%20Division | Statistics of Belgian First Division in the 1977–78 season.
Overview
It was contested by 18 teams, and Club Brugge K.V. won the championship.
League standings
Results
References
Belgian Pro League seasons
Belgian
1977–78 in Belgian football |
https://en.wikipedia.org/wiki/1978%E2%80%9379%20Belgian%20First%20Division | Statistics of Belgian First Division in the 1978–79 season.
Overview
It was contested by 18 teams, and K.S.K. Beveren won the championship for the first time in club history.
League standings
Results
References
Belgian Pro League seasons
Belgian
1978–79 in Belgian football |
https://en.wikipedia.org/wiki/1979%E2%80%9380%20Belgian%20First%20Division | Statistics of Belgian First Division in the 1979–80 season.
Overview
It was contested by 18 teams, and Club Brugge K.V. won the championship.
League standings
Results
References
Belgian Pro League seasons
Belgian
1979–80 in Belgian football |
https://en.wikipedia.org/wiki/1980%E2%80%9381%20Belgian%20First%20Division | Statistics of Belgian First Division in the 1980–81 season.
Overview
It was contested by 18 teams, and Anderlecht won the championship.
League standings
Results
References
Belgian Pro League seasons
Belgian
1980–81 in Belgian football |
https://en.wikipedia.org/wiki/1981%E2%80%9382%20Belgian%20First%20Division | Statistics of Belgian First Division in the 1981–82 season.
Overview
It was contested by 18 teams, and Standard Liège won the championship.
League standings
Results
References
Belgian Pro League seasons
Belgian
1981–82 in Belgian football |
https://en.wikipedia.org/wiki/1982%E2%80%9383%20Belgian%20First%20Division | Statistics of Belgian First Division in the 1982–83 season.
Overview
It was contested by 18 teams, and Standard Liège won the championship.
League standings
Results
References
Belgian Pro League seasons
Belgian
1 |
https://en.wikipedia.org/wiki/Christoph%20Zenger | Christoph Zenger (born 10 August 1940) is a German mathematician.
Career
Born in Lindau, Zenger studied physics at the Ludwig Maximilian University of Munich and did a doctorate in mathematics (theory of normed vector spaces) in 1967. In 1973 he did his habilitation in mathematics and in 1977 he became professor of mathematics at Technical University of Munich. In 1980 he accepted an offer of a full professorship from the Bundeswehr University of Munich. In 1982 he returned to TU Munich to fill a chair in computer science. In 2000 Zenger was selected as a member of the Bavarian Academy of Sciences and Humanities. He retired in 2005, but is still active in research.
The most important of Zenger's scientific achievements is the discovery of how to harness approximation on sparse grids for the efficient solution of elliptic partial differential equations in higher dimensions.
Beside his substantial scientific work, Zenger will be remembered for his contributions to contemporary wisdom, the most notable of which have been collected in the volume Löwenzähnchen am Bachesrand.
Selected publications
A cache-oblivious self-adaptive full multigrid method (2006)
Der Fluch der Dimension in der numerischen Simulation (2004)
with Hans-Joachim Bungartz and Michael Griebel: Einführung in die Computergraphik. Vieweg, Braunschweig 2002,
with Sascha Hilgenfeldt and Robert Balder: Sparse Grids. SFB, München 1995.
with Michael Griebel and Michael Schneider: A combination technique for the solution of sparse grid problems. SFB, München 1990
References
External links
Löwenzähnchen am Bachesrand
1940 births
Living people
20th-century German mathematicians
People from Lindau
Academic staff of the Technical University of Munich
Recipients of the Cross of the Order of Merit of the Federal Republic of Germany
21st-century German mathematicians |
https://en.wikipedia.org/wiki/Sion%27s%20minimax%20theorem | In mathematics, and in particular game theory, Sion's minimax theorem is a generalization of John von Neumann's minimax theorem, named after Maurice Sion.
It states:
Let be a compact convex subset of a linear topological space and a convex subset of a linear topological space. If is a real-valued function on with
upper semicontinuous and quasi-concave on , , and
lower semicontinuous and quasi-convex on ,
then,
See also
Parthasarathy's theorem
Saddle point
References
Game theory
Mathematical optimization
Mathematical theorems |
https://en.wikipedia.org/wiki/Football%20records%20and%20statistics%20in%20Thailand | This page details football records in Thailand.
Most successful teams
Top-performing clubs - league structures
Thai League 1
The Invincibles
Unbeatable champions:
Muangthong United in 2012
Buriram United in 2013
Buriram United in 2015
Thai League 2
Thai League 3
Thai League 4
Provincial League
Futsal League
Top-performing clubs - cup competitions
Asian Club Championship and AFC Champions League
Thailand FA Cup
Thailand League Cup
Thailand Champions Cup (2017 - Present)
Kor Royal Cup - 1996-2016
Queen's Cup
Super Cup
National team top caps goalscorers
Thai League 1 records
All-time Thai League 1 table
The all-time Thai League 1 table is a cumulative record of all match results, points, and goals of every team that has played in the Thai League 1 since its inception in 1996. The table that follows is accurate as of the end of the 2022–23 season. Teams in bold are part of the 2023–24 Thai League 1.
League or status at 2023:
Notes
Asian Champions League
Participations
Q: Qualifying stage, GS: Group Stage, R16: Round of 16, QF: Quarterfinals, SF: Semifinal, RU: Runner-up, W: Winner
Asian Club Championship
Participations
A total of seven clubs represented Thailand in the AFC Asian Club Championship which became defunct in 2002 (see: AFC Champions League).
W: Winner
AFC Cup
Participations
Thai clubs history of playing in the AFC Cup, Osotsapa were the first side to take part since the competition started in 2004. After the revamping of the Champions League in 2009, Thai clubs once again entered.
G: Group round, Q: Quarterfinals, S: Semifinal, R: Runner-up, W: Winner
Asian Cup Winners Cup
Participations
The Asian Cup Winner Cup started in 1991, although Thai clubs did not enter until 1995. There was no Thai entrant in 1997. The competition became defunct in 2002. Thai clubs generally entered at the 2nd round.
2: 2nd round, Q: Quarterfinals, S: Semifinal, R: Runner-up, W: Winner
References
The Football History Association of Thailand
Thai Premier League FAT
External links
Football Association of Thailand
The Football History Association of Thailand
Thai Premier League FIFA
Thailand - List of Champions RSSSF
Thai football blog
ผลบอลสด บ้านผลบอล ผลบอลวันนี้ 7m 888 Livescore
Football in Thailand
records and statistics
Association football records and statistics by country
Football
All-time football league tables |
https://en.wikipedia.org/wiki/Consumer%20price%20index%20by%20country | This page lists details of the consumer price index by country
Argentina
The CPI is calculated and posted monthly by the National Institute of Statistics and Census of Argentina.
Austria
Statistik Austria publishes the CPI for Austria.
Australia
The CPI is calculated and posted quarterly by the Australian Bureau of Statistics. Historical figures are available at the Reserve Bank of Australia website.
Belgium
In Belgium, wages, pensions, house rent, insurance premiums, unemployment benefits, health insurance payments, etc. are by law tied to a consumer price index.
Canada
Canada's CPI is published by Statistics Canada. The index is calculated and published monthly. It is used to escalate a given dollar value, over time, to preserve the purchasing power of that value. Thus, the CPI is widely used to adjust contracted payments, such as wages, rents, leases and child or spousal support allowances. Private and public pension programs (Old Age Security and the Canada Pension Plan), personal income tax deductions, and some government social payments are also escalated using the CPI. It is also used to set and monitor the implementation of economic policy. The Bank of Canada, for example, uses the CPI, and special aggregates of the CPI, to monitor its monetary policies.
Chile
Chile's CPI is published by the Instituto Nacional de Estadística de Chile.
China
China's CPI is published by National Bureau of Statistics of China.
Hong Kong
Hong Kong's CPI is published by the Census and Statistics Department.
Colombia
The IPC, which stands for Indice de Precios al Consumidor (Consumer Price Index), is calculated and published on a monthly basis by Banco de la República de Colombia, the National Central Bank.
Croatia
Croatian CPI, (Croatian: Indeks potrošačkih cijena) is issued by Central Bureau of Statistics (Croatia).
Eurozone
The European Central Bank publishes the Harmonized Index of Consumer Prices (HICP). It is a weighted average of price indices of member states. It is a seasonally adjusted chained index in which goods are split by final consumption.
Finland
The index (kuluttajahintaindeksi) is calculated and published by Statistics Finland
Finnish food prices have been increasing almost fastest in European Union. In the current year, consumer prices for food are forecast to increase by 4.5 per cent on average.
Most shopping centers have expensive underground car parking places that are often in practice free of charge. The high construction prices are included in the price of food and goods. The two biggest food retailers Kesko and S-Market (HOK Elanto) cover over 80% of the markets. Most often the town planning has ignored to plan new independent small shops. Satu Hassi (Green) has made a questionary for the EU Commission of the retail industry.
Germany
The index is calculated and published by the Federal Statistical Office of Germany (Statistisches Bundesamt), yearly and monthly results are available from 1991 onwards.
Greece
Th |
https://en.wikipedia.org/wiki/Virtual%20manipulatives%20for%20mathematics | Virtual math manipulatives are visual representations of concrete math manipulatives. They are accessed through a variety of websites and apps. Virtual math manipulatives are modeled after concrete math manipulatives that are commonly used in classrooms to physically represent mathematical concepts and support student understanding of mathematical concepts.
The most common manipulatives include: base ten blocks, coins, blocks, tangrams, rulers, fraction bars, algebra tiles, geoboards, geometric plane, and solids figures.
Advantages and Disadvantages
Classroom studies were conducted which investigated virtual manipulatives. The studies compare virtual manipulatives to concrete manipulatives and discuss some of its implications.
Advantages
The observed learning benefits of virtual manipulatives includes providing detailed instruction and prompt evaluation for assigned tasks. Students were seen to apprehend concepts better, since this style of learning appeals to digital natives. Virtual manipulatives can often provide explicit connections between visual and symbolic representations. Moreover, it signals to students when they’ve made a mistake, which encourages them to reflect and revisit answers accordingly. Lastly, virtual manipulatives prove to be more convenient because they are likely more accessible at home than concrete manipulatives.
Disadvantages
In comparison to concrete manipulatives, virtual manipulatives lack opportunities for learners and educators to physically touch objects, which is an immense disadvantage for kinesthetic learners. Educators are unable to follow the learners thought process, making it difficult to understand their comprehension levels. Moreover, virtual manipulatives are a form of digital learning. One of the drawbacks of digital learning is an increase in computer dependence as it limits students learning abilities. It does not encourage learners to independently find answers and locate their mistakes. Teaching preferences often include guiding students through answers only when they are unable to grasp content or find difficulty comprehending questions. Lastly, Hunts et al. states that learning mathematics through the use of virtual manipulatives feels more like a "do" experience rather than learn and explore learning experience.
Special Education
Although relatively new, virtual manipulatives can support learning mathematics for all students, which include those with learning disabilities and ELL learners. If they are used wisely, virtual manipulatives can provide students with opportunities for guided discovery, which can help them to build a better understanding of mathematical concepts and ultimately exhibit measurable learning skills. Virtual manipulatives can be included into the general academic curriculum as assistive technology and should not just be used for its novelty.
Studies on the use of virtual manipulatives in mathematics for students with learning disabilities advocate the use of virtu |
https://en.wikipedia.org/wiki/Equal%20incircles%20theorem | In geometry, the equal incircles theorem derives from a Japanese Sangaku, and pertains to the following construction: a series of rays are drawn from a given point to a given line such that the inscribed circles of the triangles formed by adjacent rays and the base line are equal. In the illustration the equal blue circles define the spacing between the rays, as described.
The theorem states that the incircles of the triangles formed (starting from any given ray) by every other ray, every third ray, etc. and the base line are also equal. The case of every other ray is illustrated above by the green circles, which are all equal.
From the fact that the theorem does not depend on the angle of the initial ray, it can be seen that the theorem properly belongs to analysis, rather than geometry, and must relate to a continuous scaling function which defines the spacing of the rays. In fact, this function is the hyperbolic sine.
The theorem is a direct corollary of the following lemma:
Suppose that the nth ray makes an angle with the normal to the baseline. If is parameterized according to the equation, , then values of , where and are real constants, define a sequence of rays that satisfy the condition of equal incircles, and furthermore any sequence of rays satisfying the condition can be produced by suitable choice of the constants and .
Proof of the lemma
In the diagram, lines PS and PT are adjacent rays making angles and with line PR, which is perpendicular to the baseline, RST.
Line QXOY is parallel to the baseline and passes through O, the center of the incircle of PST, which is tangent to the rays at W and Z. Also, line PQ has length , and line QR has length , the radius of the incircle.
Then OWX is similar to PQX and OZY is similar to PQY, and from XY = XO + OY we get
This relation on a set of angles, , expresses the condition of equal incircles.
To prove the lemma, we set , which gives .
Using , we apply the addition rules for and , and verify that the equal incircles relation is satisfied by setting
This gives an expression for the parameter in terms of the geometric measures, and . With this definition of we then obtain an expression for the radii, , of the incircles formed by taking every Nth ray as the sides of the triangles
See also
Hyperbolic function
Japanese theorem for cyclic polygons
Japanese theorem for cyclic quadrilaterals
Tangent lines to circles
References
Equal Incircles Theorem at cut-the-knot
J. Tabov. A note on the five-circle theorem. Mathematics Magazine 63 (1989), 2, 92–94.
Euclidean geometry
Japanese mathematics
Theorems about triangles and circles |
https://en.wikipedia.org/wiki/1994%E2%80%9395%20First%20League%20of%20Bosnia%20and%20Herzegovina | Statistics of the First League of Bosnia and Herzegovina in the 1994–95 season.
Overview
It was contested by 22 teams, divided in 3 groups with 6 teams, while the last group consisted of 4 teams. After the group stage, the best 2 teams from each group would go to a preliminary knockout playoff round. The 4 winners of those matches were once again grouped in a single group, and the team which placed first in that group would be declared as the overall winner of that session. The winner in the end was NK Čelik Zenica.
This was the first and only time that the league was played in this format.
First round
Group Sarajevo
Group Jablanica
Group Tuzla
Group Zenica
Play-off
Played in Zenica.
Preliminary round
Played on 4 and 5 August 1994.
Final
References
Bosnia-Herzegovina - List of final tables (RSSSF)
SportSport.ba forum
First League of Bosnia and Herzegovina seasons
1994–95 in Bosnia and Herzegovina football
Bosnia |
https://en.wikipedia.org/wiki/1995%E2%80%9396%20First%20League%20of%20Bosnia%20and%20Herzegovina | Statistics of First League of Bosnia and Herzegovina in the 1995–96 season. It was contested only by Bosniak clubs. Serbian clubs played in the 1995–96 First League of the Republika Srpska and the Croatian clubs in the 1995–96 First League of Herzeg-Bosnia.
Overview
It was contested by 16 teams, and NK Čelik Zenica won the championship.
Final table
Results
Top goalscorers
Source: SportSport.ba forum
References
Bosnia-Herzegovina - List of final tables (RSSSF)
First League of Bosnia and Herzegovina seasons
1995–96 in Bosnia and Herzegovina football
Bosnia |
https://en.wikipedia.org/wiki/1996%E2%80%9397%20First%20League%20of%20Bosnia%20and%20Herzegovina | Statistics of First League of Bosnia and Herzegovina in the 1996–97 season. It was contested only by Bosniak clubs. Serbian clubs played in the 1996–97 First League of the Republika Srpska and the Croatian clubs in the 1996–97 First League of Herzeg-Bosnia.
Overview
It was contested by 16 teams, and NK Čelik Zenica won the championship.
Final table
Results
Top goalscorers
Source: SportSport.ba forum
References
Bosnia-Herzegovina - List of final tables (RSSSF)
First League of Bosnia and Herzegovina seasons
1996–97 in Bosnia and Herzegovina football
Bosnia |
https://en.wikipedia.org/wiki/1997%E2%80%9398%20First%20League%20of%20Bosnia%20and%20Herzegovina | Statistics of First League of Bosnia and Herzegovina in the 1997–98 season. It was contested only by Bosniak and Croatian clubs. Serbian clubs played in the 1997–98 First League of the Republika Srpska.
Overview
It was contested by 6 teams. Željezničar have won the championship.
First round
Bosniaks First League
League standings
Results
Top goalscorers
Source: SportSport.ba forum
First League of Herzeg-Bosnia
Clubs and stadiums
League standings
Play-offs
Group stage
Group Sarajevo
Group Mostar
Final
Both clubs qualified for 1998–99 UEFA Cup.
See also
1997–98 First League of the Republika Srpska
References
Bosnia-Herzegovina - List of final tables (RSSSF)
First League of Bosnia and Herzegovina seasons
1997–98 in Bosnia and Herzegovina football
Bosnia |
https://en.wikipedia.org/wiki/1998%E2%80%9399%20First%20League%20of%20Bosnia%20and%20Herzegovina | This article includes the statistics of the First League of Bosnia and Herzegovina in the 1998–99 season. It was contested only by Bosniak and Croatian clubs. Serbian clubs played in the 1998–99 First League of the Republika Srpska.
Overview
It was contested by 16 teams (Bosniak Group) and 14 teams (Croat Group).
Originally playoff between Croat and Bosniak Group was scheduled, but due to stadium reason, the playoff was canceled. The title was awarded to FK Sarajevo, but neither clubs were qualified for European competition.(Only Jedinstvo Bihac)
Bosniak First League
League standings
Results
First League of Herzeg-Bosnia
League standings
See also
1998–99 First League of the Republika Srpska
References
Bosnia-Herzegovina - List of final tables (RSSSF)
First League of Bosnia and Herzegovina seasons
1998–99 in Bosnia and Herzegovina football
Bosnia |
https://en.wikipedia.org/wiki/1999%E2%80%932000%20First%20League%20of%20Bosnia%20and%20Herzegovina | Statistics of First League of Bosnia and Herzegovina in the 1999–2000 season. It was contested only by Bosniak and Croatian clubs. Serbian clubs played in the 1999–2000 First League of the Republika Srpska.
Overview
It was contested by 8 teams, and Brotnjo won the championship.
First round
First League of Football Association of Bosnia and Herzegovina
League standings
Results
First League of Herzeg-Bosnia
League standings
Play-offs
Group stage
Group A
Group B
Brotnjo - Jedinstvo Bihać 3–0
Jedinstvo Bihać - Brotnjo 3–1
Final
First leg
Second leg
Brotnjo 1–1 Budućnost Banovići on aggregate. Brotnjo won on away goals rule and qualified for 2000–01 UEFA Champions League (first qualifying round), while Budućnost qualified for 2000–01 UEFA Cup (qualifying round).
Intertoto Cup play-off
Zrinjski was qualified for 2000 UEFA Intertoto Cup (first round).
See also
1999–2000 First League of the Republika Srpska
References
Bosnia-Herzegovina - List of final tables (RSSSF)
First League of Bosnia and Herzegovina seasons
1999–2000 in Bosnia and Herzegovina football
Bosnia |
https://en.wikipedia.org/wiki/2000%E2%80%9301%20Premier%20League%20of%20Bosnia%20and%20Herzegovina | Statistics of Premier League of Bosnia and Herzegovina in the 2000–01 season. It was contested by Bosniak and Croatian clubs. Serbian clubs played in the 2000–01 First League of the Republika Srpska.
Overview
It was contested by 22 teams, and FK Željezničar Sarajevo won the championship. The season was the first season all team from Federation of Bosnia and Herzegovina, either Bosniaks and Croats played in the same league, unlike 2 stages league in previous seasons. Đerzelez conceded a record 198 goals in the league even to this day. At the end, six clubs were relegated and Željezničar striker Dželaludin Muharemović became top goalscorer with 31.
Clubs and stadiums
League standings
Results
References
Bosnia-Herzegovina - List of final tables (RSSSF)
See also
2000–01 First League of the Republika Srpska
Premier League of Bosnia and Herzegovina seasons
1
Bosnia |
https://en.wikipedia.org/wiki/2001%E2%80%9302%20Premier%20League%20of%20Bosnia%20and%20Herzegovina | Statistics of Premier League of Bosnia and Herzegovina in the 2001–02 season. It was contested by Bosniak and Croatian clubs. Serbian clubs played in the 2001–02 First League of the Republika Srpska.
Overview
It was contested by 16 teams, and FK Željezničar Sarajevo won the championship.
Clubs and stadiums
League standings
Results
References
Bosnia-Herzegovina - List of final tables (RSSSF)
See also
2001–02 First League of the Republika Srpska
Premier League of Bosnia and Herzegovina seasons
1
Bosnia |
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