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https://en.wikipedia.org/wiki/2003%E2%80%9304%20Premier%20League%20of%20Bosnia%20and%20Herzegovina | Statistics of Premier League of Bosnia and Herzegovina in the 2003–2004 season.
Overview
It was contested by 16 teams, and NK Široki Brijeg won the championship.
Clubs and stadiums
League standings
Results
Top goalscorers
References
Bosnia-Herzegovina - List of final tables (RSSSF)
Premier League of Bosnia and Herzegovina seasons
1
Bosnia |
https://en.wikipedia.org/wiki/2004%E2%80%9305%20Premier%20League%20of%20Bosnia%20and%20Herzegovina | Statistics of Premier League of Bosnia and Herzegovina in the 2004–2005 season.
Overview
It was contested by 16 teams, and HŠK Zrinjski Mostar won the championship.
Clubs and stadiums
League standings
Results
Top goalscorers
References
Bosnia-Herzegovina - List of final tables (RSSSF)
Premier League of Bosnia and Herzegovina seasons
1
Bosnia |
https://en.wikipedia.org/wiki/2005%E2%80%9306%20Premier%20League%20of%20Bosnia%20and%20Herzegovina | Statistics of Premier League of Bosnia and Herzegovina in the 2005–2006 football season.
Overview
It was contested by 16 teams, and NK Široki Brijeg won the championship.
Clubs and stadiums
League standings
Results
Top goalscorers
References
Bosnia-Herzegovina - List of final tables (RSSSF)
Premier League of Bosnia and Herzegovina seasons
1
Bosnia |
https://en.wikipedia.org/wiki/2006%E2%80%9307%20Premier%20League%20of%20Bosnia%20and%20Herzegovina | Statistics of Premier League of Bosnia and Herzegovina in the 2006–2007 season.
Overview
It was contested by 16 teams, and FK Sarajevo won the championship.
Clubs and stadiums
League standings
Results
Top goalscorers
References
Bosnia-Herzegovina - List of final tables (RSSSF)
Premier League of Bosnia and Herzegovina seasons
1
Bosnia |
https://en.wikipedia.org/wiki/Pseudo-order | In constructive mathematics, pseudo-order is a name given to certain binary relations appropriate for modeling continuous orderings.
In classical mathematics, its axioms constitute a formulation of a strict total order (also called linear order), which in that context can also be defined in other, equivalent ways.
Examples
The constructive theory of the real numbers is the prototypical example where the pseudo-order formulation becomes crucial. A real number is less than another if there exists (one can construct) a rational number greater than the former and less than the latter. In other words, here x < y holds if there exists a rational number z such that x < z < y.
Notably, for the continuum in a constructive context, the usual trichotomy law does not hold, i.e. it is not automatically provable. The axioms in the characterization of orders like this are thus weaker (when working using just constructive logic) than alternative axioms of a strict total order, which are often employed in the classical context.
Definition
A pseudo-order is a binary relation satisfying the three conditions:
It is not possible for two elements to each be less than the other. That is, for all and ,
Every two elements for which neither one is less than the other must be equal. That is, for all and ,
For all , , and , if then either or . That is, for all , and ,
Auxiliary notation
There are common constructive reformulations making use of contrapositions and the valid equivalences as well as . The negation of the pseudo-order of two elements defines a reflexive partial order . In these terms, the first condition reads
and it really just expresses the asymmetry of . It implies irreflexivity, as familiar from the classical theory.
Classical equivalents to trichotomy
The second condition exactly expresses the anti-symmetry of the associated partial order,
With the above two reformulations, the negation signs may be hidden in the definition of a pseudo-order.
A natural apartness relation on a pseudo-ordered set is given by . With it, the second condition exactly states that this relation is tight,
Now the disjunctive syllogism may be expressed as . Such a logical implication can classically be reversed, and then this condition exactly expresses trichotomy. As such, it is also a formulation of connectedness.
Discussion
Asymmetry
The non-contradiction principle for the partial order states that or equivalently , for all elements. Constructively, the validity of the double-negation exactly means that there cannot be a refutation of any of the disjunctions in the classical claim , whether or not this proposition represents a decidable problem.
Using the asymmetry condition, the above also implies , the double-negated strong connectedness. In a classical logic context, "" thus constitutes a (non-strict) total order.
Co-transitivity
The contrapositive of the third condition exactly expresses that the associated relation (the partial order) is transi |
https://en.wikipedia.org/wiki/Coates%20graph | In mathematics, the Coates graph or Coates flow graph, named after C.L. Coates, is a graph associated with the Coates' method for the solution of a system of linear equations.
The Coates graph Gc(A) associated with an n × n matrix A is an n-node, weighted, labeled, directed graph. The nodes, labeled 1 through n, are each associated with the corresponding row/column of A. If entry aji ≠ 0 then there is a directed edge from node i to node j with weight aji. In other words, the Coates graph for matrix A is the one whose adjacency matrix is the transpose of A.
See also
Flow graph (mathematics)
Mason graph
References
Application-specific graphs
Linear algebra |
https://en.wikipedia.org/wiki/Fast%20Walsh%E2%80%93Hadamard%20transform | In computational mathematics, the Hadamard ordered fast Walsh–Hadamard transform (FWHTh) is an efficient algorithm to compute the Walsh–Hadamard transform (WHT). A naive implementation of the WHT of order would have a computational complexity of O(). The FWHTh requires only additions or subtractions.
The FWHTh is a divide-and-conquer algorithm that recursively breaks down a WHT of size into two smaller WHTs of size . This implementation follows the recursive definition of the Hadamard matrix :
The normalization factors for each stage may be grouped together or even omitted.
The sequency-ordered, also known as Walsh-ordered, fast Walsh–Hadamard transform, FWHTw, is obtained by computing the FWHTh as above, and then rearranging the outputs.
A simple fast nonrecursive implementation of the Walsh–Hadamard transform follows from decomposition of the Hadamard transform matrix as , where A is m-th root of .
Python example code
def fwht(a) -> None:
"""In-place Fast Walsh–Hadamard Transform of array a."""
h = 1
while h < len(a):
# perform FWHT
for i in range(0, len(a), h * 2):
for j in range(i, i + h):
x = a[j]
y = a[j + h]
a[j] = x + y
a[j + h] = x - y
# normalize and increment
a /= 2
h *= 2
See also
Fast Fourier transform
References
External links
Charles Constantine Gumas, A century old, the fast Hadamard transform proves useful in digital communications
Digital signal processing
Articles with example Python (programming language) code |
https://en.wikipedia.org/wiki/Ars%20Conjectandi | (Latin for "The Art of Conjecturing") is a book on combinatorics and mathematical probability written by Jacob Bernoulli and published in 1713, eight years after his death, by his nephew, Niklaus Bernoulli. The seminal work consolidated, apart from many combinatorial topics, many central ideas in probability theory, such as the very first version of the law of large numbers: indeed, it is widely regarded as the founding work of that subject. It also addressed problems that today are classified in the twelvefold way and added to the subjects; consequently, it has been dubbed an important historical landmark in not only probability but all combinatorics by a plethora of mathematical historians. The importance of this early work had a large impact on both contemporary and later mathematicians; for example, Abraham de Moivre.
Bernoulli wrote the text between 1684 and 1689, including the work of mathematicians such as Christiaan Huygens, Gerolamo Cardano, Pierre de Fermat, and Blaise Pascal. He incorporated fundamental combinatorial topics such as his theory of permutations and combinations (the aforementioned problems from the twelvefold way) as well as those more distantly connected to the burgeoning subject: the derivation and properties of the eponymous Bernoulli numbers, for instance. Core topics from probability, such as expected value, were also a significant portion of this important work.
Background
In Europe, the subject of probability was first formally developed in the 16th century with the work of Gerolamo Cardano, whose interest in the branch of mathematics was largely due to his habit of gambling. He formalized what is now called the classical definition of probability: if an event has a possible outcomes and we select any b of those such that b ≤ a, the probability of any of the b occurring is . However, his actual influence on mathematical scene was not great; he wrote only one light tome on the subject in 1525 titled Liber de ludo aleae (Book on Games of Chance), which was published posthumously in 1663.
The date which historians cite as the beginning of the development of modern probability theory is 1654, when two of the most well-known mathematicians of the time, Blaise Pascal and Pierre de Fermat, began a correspondence discussing the subject. The two initiated the communication because earlier that year, a gambler from Paris named Antoine Gombaud had sent Pascal and other mathematicians several questions on the practical applications of some of these theories; in particular he posed the problem of points, concerning a theoretical two-player game in which a prize must be divided between the players due to external circumstances halting the game. The fruits of Pascal and Fermat's correspondence interested other mathematicians, including Christiaan Huygens, whose De ratiociniis in aleae ludo (Calculations in Games of Chance) appeared in 1657 as the final chapter of Van Schooten's Exercitationes Matematicae. In 1665 Pascal posth |
https://en.wikipedia.org/wiki/1933%20Bulgarian%20State%20Football%20Championship | Statistics of Bulgarian State Football Championship in the 1933 season.
Overview
It was contested by 13 teams, and Levski Sofia won the championship.
First round
|}
Quarter-finals
|}
Semi-finals
|}
Final
References
Bulgaria - List of final tables (RSSSF)
Bulgarian State Football Championship seasons
1
1
Bul
Bul |
https://en.wikipedia.org/wiki/1934%20Bulgarian%20State%20Football%20Championship | Statistics of Bulgarian State Football Championship in the 1934 season.
Overview
It was contested by 14 teams, and Vladislav Varna won the championship.
First round
|}
Quarter-finals
|}
Semi-finals
Final
References
Bulgaria - List of final tables (RSSSF)
Bulgarian State Football Championship seasons
1
1
Bul
Bul |
https://en.wikipedia.org/wiki/1936%20Bulgarian%20State%20Football%20Championship | Statistics of Bulgarian State Football Championship in the 1936 season.
Overview
It was contested by 12 teams, and PFC Slavia Sofia won the championship.
First round
|}
Quarter-finals
|}
Semi-finals
|}
Final
References
Bulgaria - List of final tables (RSSSF)
Bulgarian State Football Championship seasons
1
1 |
https://en.wikipedia.org/wiki/1937%E2%80%9338%20Bulgarian%20National%20Football%20Division | Statistics of Bulgarian National Football Division in the 1937–38 season.
Overview
It was contested by 10 teams, and Ticha Varna won the championship.
League standings
Results
References
Bulgaria - List of final tables (RSSSF)
Bulgarian State Football Championship seasons
Bul
1937–38 in Bulgarian football |
https://en.wikipedia.org/wiki/1938%E2%80%9339%20Bulgarian%20National%20Football%20Division | Statistics of Bulgarian National Football Division in the 1938–39 season.
Overview
It was contested by 10 teams, and PFC Slavia Sofia won the championship.
League standings
Results
References
Bulgaria - List of final tables (RSSSF)
Bulgarian State Football Championship seasons
Bulgaria
1938–39 in Bulgarian football |
https://en.wikipedia.org/wiki/1939%E2%80%9340%20Bulgarian%20National%20Football%20Division | Statistics of Bulgarian National Football Division in the 1939–40 season.
Overview
It was contested by 10 teams, and ZhSK Sofia won the championship.
League standings
Results
References
Bulgaria - List of final tables (RSSSF)
Bulgarian State Football Championship seasons
Bulgaria
1939–40 in Bulgarian football |
https://en.wikipedia.org/wiki/1941%20Bulgarian%20State%20Football%20Championship | Statistics of Bulgarian State Football Championship in the 1941 season.
Overview
It was contested by 11 teams, and PFC Slavia Sofia won the championship. The 1941 season was the first A PFG season to include teams from Vardar Macedonia, Western Thrace or the parts of Greek Macedonia under Bulgarian administration during much of World War II.
First round
|}
Quarter-finals
|}
1The replay was originally finished 1–1.
Semi-finals
|}
Final
First game
Second game
References
Bulgaria - List of final tables (RSSSF)
Bulgarian State Football Championship seasons
1
1 |
https://en.wikipedia.org/wiki/1943%20Bulgarian%20State%20Football%20Championship | Statistics of Bulgarian State Football Championship in the 1943 season.
Overview
It was contested by 26 teams, and PFC Slavia Sofia won the championship. Besides teams from the present borders of Bulgaria, the 1943 season also involved teams from the areas under Bulgarian administration during much of World War II. Football clubs from Bitola and Skopje in Vardar Macedonia and Kavala in Greek Macedonia took part in the competition.
Teams
The teams that participated in the competition were the winners of their local sport districts. According to the format of the competition - Sofia is having five seeds and Varna and Plovdiv two seeds each. Note that Makedonia Skopie was competing in the Sofia sport district during that season of the championship.
First round
|}
Second round
|}
Quarter-finals
|}
Semi-finals
|}
Final
First game
Second game
Slavia Sofia won 2–0 on aggregate.
References
Bulgaria - List of final tables (RSSSF)
Bulgarian State Football Championship seasons
1
1 |
https://en.wikipedia.org/wiki/1944%20Bulgarian%20State%20Football%20Championship | Statistics of Bulgarian State Football Championship in the 1944 season.
Overview
It was contested by 26 teams. The championship was not finished. Besides teams from the present borders of Bulgaria, the 1944 season was the last season to involve teams from the areas under Bulgarian administration during much of World War II. Football clubs from Skopje in Vardar Macedonia and Kavala in Greek Macedonia took part in the competition.
First round
|}
1Orel-Chegan 30 Vratsa were originally qualified to the second round because Knyaz Simeon Tarnovski Pavlikeni were withdraw from the competition, but they were also withdraw.
2ZhSK Stara Zagora were qualified to the second round because Botev Yambol were withdraw from the competition.
3Bulgaria Haskovo were qualified to the second round because Momchil yunak Kavala were withdraw from the competition.
Second round
|}
1Shipchenski sokol Varna were qualified to the quarter-finals because Levski Dobrich were rejected participation in the replay match.
Quarter-finals
|}
References
Bulgaria - List of final tables (RSSSF)
Bulgarian State Football Championship seasons
1
1 |
https://en.wikipedia.org/wiki/1945%20Bulgarian%20Republic%20Football%20Championship | Statistics of Bulgarian Republic Football Championship in the 1945 season.
Overview
It was contested by 24 teams, and Lokomotiv Sofia won the championship. As Bulgaria had lost the territories of Vardar Macedonia, Western Thrace and parts of Greek Macedonia that it administered during most of World War II, teams from those regions no longer took part in the Bulgarian championships, beginning in 1945.
First round
|-
!colspan="3" style="background-color:#D0F0C0; text-align:left;" |Replay
|}
Second round
|}
Quarter-finals
|-
!colspan="3" style="background-color:#D0F0C0; text-align:left;" |Replay
|}
Semi-finals
|}
Final
First game
Second game
Lokomotiv Sofia won 4–2 on aggregate.
References
Bulgaria - List of final tables (RSSSF)
Bulgarian Republic Football Championship seasons
1
1 |
https://en.wikipedia.org/wiki/1946%20Bulgarian%20Republic%20Football%20Championship | Statistics of Bulgarian Republic Football Championship in the 1946 season.
Overview
It was contested by 16 teams, and Levski Sofia won the championship.
First round
|-
!colspan="3" style="background-color:#D0F0C0; text-align:left;" |Replay
|}
Quarter-finals
|}
Semi-finals
|}
Final
First game
Second game
Levski Sofia won 2–0 on aggregate.
References
Bulgaria - List of final tables (RSSSF)
Bulgarian Republic Football Championship seasons
1
1 |
https://en.wikipedia.org/wiki/1947%20Bulgarian%20Republic%20Football%20Championship | Statistics of Bulgarian Republic Football Championship in the 1947 season.
Overview
It was contested by 16 teams, and Levski Sofia won the championship.
First round
|-
!colspan="3" style="background-color:#D0F0C0; text-align:left;" |Replay
|}
Quarter-finals
|}
Semi-finals
|}
Final
First game
Second game
Levski Sofia won 2–1 on aggregate.
References
Bulgaria - List of final tables (RSSSF)
Bulgarian Republic Football Championship seasons
1
1 |
https://en.wikipedia.org/wiki/1948%20Bulgarian%20Republic%20Football%20Championship | Statistics of Bulgarian Republic Football Championship in the 1948 season.
Overview
It was contested by 16 teams, and Septemvri pri CDV Sofia won the championship.
First round
|}
Quarter-finals
|}
Semi-finals
|}
Final
First game
Second game
Septemvri pri CDV Sofia won 4–3 on aggregate.
References
Bulgaria - List of final tables (RSSSF)
Bulgarian Republic Football Championship seasons
1
1 |
https://en.wikipedia.org/wiki/Mikko%20Kaasalainen | Mikko K.J. Kaasalainen (1965 – 12 April 2020) was a Finnish applied mathematician and mathematical physicist. He was professor of mathematics at the department of mathematics at Tampere University of Technology. Kaasalainen mostly worked on inverse problems and their applications especially in astrophysics, as well as on dynamical systems.
Education and career
Kaasalainen received an MSc in theoretical physics at the University of Helsinki in 1990, moving shortly afterwards to Merton College, Oxford where he completed his DPhil in theoretical physics in 1994, supervised by James Binney. After a series of post-doctoral and senior positions in Europe, he moved to the University of Helsinki and to his present institute in 2009. He led a research group in the Finnish Centre of Excellence in Inverse Problems Research.
Kaasalainen was awarded the first Pertti Lindfors prize of the Finnish Inverse Problems Society in 2001. The asteroid 16007 Kaasalainen, discovered by ODAS in 1999, was named in his honour. The official was published by the Minor Planet Center on 7 January 2004 ().
Research
Kaasalainen's research interests mostly focused on mathematical modelling in various fields ranging from remote sensing and space research to planetary and galactic dynamics. Typically, the models and mathematical methods Kaasalainen developed with his colleagues are connected with inverse problems. Two such topics featured prominently in Kaasalainen's research:
Asteroid lightcurve inversion, i.e., the reconstruction of the shapes and spin states of asteroids from their brightness measurements (lightcurves), based on mathematical results and uniqueness and stability theorems that have been transformed into modelling algorithms with which a multitude of otherwise unresolvable asteroids can now be mapped. This method has also been used in the direct verification of the Yarkovsky–O'Keefe–Radzievskii–Paddack effect in our solar system.
Analysis of large dynamical systems, where torus construction methods in phase space allow a compact representation or approximation of the dynamics of the observed system (such as a galaxy).
References
External links
Mikko Kaasalainen's homepage at the University of Helsinki
Asteroid model website at the Charles University in Prague
Finnish Centre of Excellence in Inverse Problems Research
1965 births
2020 deaths
Alumni of Merton College, Oxford
20th-century Finnish mathematicians
21st-century Finnish mathematicians |
https://en.wikipedia.org/wiki/2001%20Djurg%C3%A5rdens%20IF%20season | Djurgårdens IF was promoted from Superettan and finished second. This was the beginning of a new era.
Player statistics
Appearances for competitive matches only
|}
Topscorers
Allsvenskan
Svenska Cupen
Friendlies
Competitions
Overall
Allsvenskan
League table
Matches
Svenska Cupen
Friendlies
References
Djurgårdens IF Fotboll seasons
Djurgarden |
https://en.wikipedia.org/wiki/Parthasarathy%27s%20theorem | In mathematics – and in particular the study of games on the unit square – Parthasarathy's theorem is a generalization of Von Neumann's minimax theorem. It states that a particular class of games has a mixed value, provided that at least one of the players has a strategy that is restricted to absolutely continuous distributions with respect to the Lebesgue measure (in other words, one of the players is forbidden to use a pure strategy).
The theorem is attributed to the Indian mathematician Thiruvenkatachari Parthasarathy.
Theorem
Let and stand for the unit interval ; denote the set of probability distributions on (with defined similarly); and denote the set of absolutely continuous distributions on (with defined similarly).
Suppose that is bounded on the unit square and that is continuous except possibly on a finite number of curves of the form (with ) where the are continuous functions. For , define
Then
This is equivalent to the statement that the game induced by has a value. Note that one player (WLOG ) is forbidden from using a pure strategy.
Parthasarathy goes on to exhibit a game in which
which thus has no value. There is no contradiction because in this case neither player is restricted to absolutely continuous distributions (and the demonstration that the game has no value requires both players to use pure strategies).
References
T. Parthasarathy 1970. On Games over the unit square, SIAM, volume 19, number 2.
Game theory
Theorems in discrete mathematics
Theorems in measure theory |
https://en.wikipedia.org/wiki/Mohamed%20Badache | Mohamed Badache born 15 October 1976 in Hussein Dey, Alger) is an Algerian footballer. He last played as a forward for ES Sétif in the Algerian Championnat National.
National team statistics
Honours
Won the Algerian Cup twice with MC Alger in 2006 and 2007
Won the Algerian Super Cup twice with MC Alger in 2006 and 2007
Won the Arab Champions League once with ES Sétif in 2008
References
External links
1976 births
Algerian men's footballers
Living people
Footballers from Algiers
Algeria men's international footballers
USM Blida players
MC Alger players
ES Sétif players
Kabyle people
Men's association football forwards
21st-century Algerian people |
https://en.wikipedia.org/wiki/Chris%20Haviland | Christopher Douglas Haviland (born 27 February 1952) is an Australian politician. Born in Sydney, he has worked as a public servant with the Commonwealth Department of Health, a teacher, a maths tutor and an umpire for Sydney Grade Cricket. He was district cricketer in Sydney and Perth. He is a leading activist for party democratisation and is an active member of the progressive Left faction. He is the New South Wales State Convenor of grassroots party reform organisation Local Labor.
Since 2014, Chris Haviland has been an active member of the New South Wales Labor Party Administrative Committee and is currently the President of the Hawkesbury Branch of the Australian Labor Party.
Local government
In 1987, Haviland was elected to Campbelltown City Council.
In 1991, he was elected to the Executive of the NSW Local Government Association.
Federal politics
In 1993, Haviland was elected to the Australian House of Representatives as the Labor member for Macarthur, succeeding Stephen Martin, who contested Cunningham instead. In 1996, however, he lost his Labor endorsement and retired from politics.
Haviland was also a two-time Labor candidate for the safe Liberal seat of Bradfield. In the 2019 Australian federal election Haviland achieved 33.4% on the two-party preferred vote and a 4.5% swing which was notably the highest swing to the Australian Labor Party in any electorate within NSW.
References
Australian Labor Party members of the Parliament of Australia
Members of the Australian House of Representatives for Macarthur
Members of the Australian House of Representatives
1952 births
Living people
Australian cricket umpires
Australian public servants
Australian schoolteachers
Mathematics educators
20th-century Australian politicians
Labor Left politicians |
https://en.wikipedia.org/wiki/Modal%20matrix | In linear algebra, the modal matrix is used in the diagonalization process involving eigenvalues and eigenvectors.
Specifically the modal matrix for the matrix is the n × n matrix formed with the eigenvectors of as columns in . It is utilized in the similarity transformation
where is an n × n diagonal matrix with the eigenvalues of on the main diagonal of and zeros elsewhere. The matrix is called the spectral matrix for . The eigenvalues must appear left to right, top to bottom in the same order as their corresponding eigenvectors are arranged left to right in .
Example
The matrix
has eigenvalues and corresponding eigenvectors
A diagonal matrix , similar to is
One possible choice for an invertible matrix such that is
Note that since eigenvectors themselves are not unique, and since the columns of both and may be interchanged, it follows that both and are not unique.
Generalized modal matrix
Let be an n × n matrix. A generalized modal matrix for is an n × n matrix whose columns, considered as vectors, form a canonical basis for and appear in according to the following rules:
All Jordan chains consisting of one vector (that is, one vector in length) appear in the first columns of .
All vectors of one chain appear together in adjacent columns of .
Each chain appears in in order of increasing rank (that is, the generalized eigenvector of rank 1 appears before the generalized eigenvector of rank 2 of the same chain, which appears before the generalized eigenvector of rank 3 of the same chain, etc.).
One can show that
where is a matrix in Jordan normal form. By premultiplying by , we obtain
Note that when computing these matrices, equation () is the easiest of the two equations to verify, since it does not require inverting a matrix.
Example
This example illustrates a generalized modal matrix with four Jordan chains. Unfortunately, it is a little difficult to construct an interesting example of low order.
The matrix
has a single eigenvalue with algebraic multiplicity . A canonical basis for will consist of one linearly independent generalized eigenvector of rank 3 (generalized eigenvector rank; see generalized eigenvector), two of rank 2 and four of rank 1; or equivalently, one chain of three vectors , one chain of two vectors , and two chains of one vector , .
An "almost diagonal" matrix in Jordan normal form, similar to is obtained as follows:
where is a generalized modal matrix for , the columns of are a canonical basis for , and . Note that since generalized eigenvectors themselves are not unique, and since some of the columns of both and may be interchanged, it follows that both and are not unique.
Notes
References
Matrices |
https://en.wikipedia.org/wiki/Lassi%20P%C3%A4iv%C3%A4rinta | Lassi Päivärinta is a Finnish mathematician, one-time professor of applied mathematics at the department of mathematics and statistics at the University of Helsinki. Päivärinta's research is mostly in the fields of inverse problems and partial differential equations.
Education and career
Päivärinta received an MSc in mathematics at the University of Helsinki in 1976, and a PhD in mathematics in 1980. He has spent several periods at the University of Delaware and Washington University in St. Louis as visiting and adjunct professor. He became professor of mathematics at the University of Oulu in 1992, and started his professorship at the University of Helsinki in 2003. He was the leader of the Finnish Centre of Excellence in Inverse Problems Research and the director of the Rolf Nevanlinna Institute and the section of applied mathematics at the University of Helsinki. He is the editor-in-chief of the journal Inverse Problem and Imaging.
Päivärinta was awarded the Magnus Ehrnrooth Foundation Prize in mathematics by the Finnish Society of Sciences and Letters in 2006. He is a member of the Finnish Academy of Sciences.
In 2011, Päivärinta was awarded one of the ERC Advanced Grants 2010 of the European Research Council for mathematical research in inverse problems.
Research
Since the late 1980s, inverse problems have attracted rapidly growing research interest, mostly in applied but also in pure mathematics. Päivärinta is one of the leading figures in this development from an early stage, and his research interests range from mathematical theory to practical applications. An example of this is Alberto Calderon's inverse problem, studied by several mathematicians and solved in the plane by Astala and Päivärinta. The problem has immediate application in electrical impedance tomography (EIT), a means of imaging the interior of the human body. In addition to his theoretical work, Päivärinta has worked on several similar topics related with biomedical and industrial imaging. He is a founding member of the Finnish Inverse Problems Society, the world's first scientific society for inverse problems.
References
External links
Finnish Centre of Excellence in Inverse Problems Research
Finnish Inverse Problems Society
1954 births
Living people
Scientists from Helsinki
20th-century Finnish mathematicians
21st-century Finnish mathematicians
Academic staff of the University of Helsinki
University of Delaware faculty
Academic staff of the University of Oulu
Washington University in St. Louis faculty |
https://en.wikipedia.org/wiki/2000%20Djurg%C3%A5rdens%20IF%20season | 1999 was Djurgården remoted from Allsvenskan.
2000 was the first season of the new second division Superettan. Djurgården finished first.
Player statistics
Appearances for competitive matches only
|}
Topscorers
Total
Superettan
Svenska Cupen
Friendlies
Competitions
Overall
Superettan
League table
Results summary
Matches
Kickoff times are in CEST.
2000–01 Svenska Cupen
Friendlies
References
2000
Swedish football clubs 2000 season |
https://en.wikipedia.org/wiki/Charles%20Graves%20%28bishop%29 | Charles Graves (6 December 1812 – 17 July 1899) was an Irish mathematician, academic, and clergyman. He was Erasmus Smith's Professor of Mathematics at Trinity College Dublin (1843–1862), and was president of the Royal Irish Academy (1861–1866). He served as dean of the Chapel Royal at Dublin Castle, and later as Bishop of Limerick, Ardfert and Aghadoe. He was the brother of both the jurist and mathematician John Graves, and the writer and clergyman Robert Perceval Graves.
Early life
Born at 12 Fitzwilliam Square, Dublin, the son of John Crosbie Graves (1776–1835), Chief Police Magistrate for Dublin, by his wife Helena Perceval, the daughter and co-heiress of the Revd Charles Perceval (1751–1795) of Bruhenny, County Cork. Helena enjoyed the patronage of John Freeman-Mitford, 1st Baron Redesdale, who married her second cousin, a daughter of John Perceval, 2nd Earl of Egmont.
Educated at Trinity College Dublin, he was elected a Scholar in classics in 1832, and in 1834 graduated BA as Senior Moderator in mathematics, getting his MA in 1838. He played cricket for Trinity, and later in his life did much boating and fly-fishing. He was a founder member of the Dublin University Choral Society, with its first meeting held in his rooms in Trinity. It was intended that he should join the 18th (Royal Irish) Regiment of Foot under his uncle, Major-General James William Graves (1774–1845), and in preparation he had become an expert swordsman and rider.
Career
Charles Graves was appointed a fellow of Trinity College in 1836, and in 1843 became Erasmus Smith's Professor of Mathematics, a position he held until 1862, when he became a senior fellow. In 1841, he published the book Two Geometrical Memoirs on the General Properties of Cones of the Second Degree and on the Spherical Conics, a translation of Aperçu historique sur l'origine et le développement des méthodes en géométrie (1837) by Michel Chasles, but including many new results of his own. His version was admired by James Sylvester.
Graves published over 30 mathematical papers, some of those later in life, after he had left TCD for the life of a clergyman. His post-TCD mathematical output includes, "On a Theorem Relating to the Binomial Coefficients" (1665), "On the Focal Circles of Plane and Spherical Conics" (1888), "The Focal Circles of Spherical Conics" (1889) and "On the Plane Circular Sections of the Surfaces of the Second Order" (1890) (all published in either the Proceedings or the Transactions of the Royal Irish Academy).
After leaving Trinity College, Graves followed in the footsteps of his grandfather, Thomas Graves, (appointed Dean of Ardfert in 1785 and Dean of Connor in 1802) and his great uncle, Richard Graves.
In 1860 he was appointed Dean of the Chapel Royal and, from 1864 to 1866, he was the dean of Clonfert before being consecrated as Bishop of Limerick, Ardfert and Aghadoe, a position he held for 33 years until his death in 1899. He had been elected a member of the Royal Iris |
https://en.wikipedia.org/wiki/Arithmetic%20dynamics | Arithmetic dynamics is a field that amalgamates two areas of mathematics, dynamical systems and number theory. Part of the inspiration comes from complex dynamics, the study of the iteration of self-maps of the complex plane or other complex algebraic varieties. Arithmetic dynamics is the study of the number-theoretic properties of integer, rational, -adic, or algebraic points under repeated application of a polynomial or rational function. A fundamental goal is to describe arithmetic properties in terms of underlying geometric structures.
Global arithmetic dynamics is the study of analogues of classical diophantine geometry in the setting of discrete dynamical systems, while local arithmetic dynamics, also called p-adic or nonarchimedean dynamics, is an analogue of complex dynamics in which one replaces the complex numbers by a -adic field such as or and studies chaotic behavior and the Fatou and Julia sets.
The following table describes a rough correspondence between Diophantine equations, especially abelian varieties, and dynamical systems:
Definitions and notation from discrete dynamics
Let be a set and let be a map from to itself. The iterate of with itself times is denoted
A point is periodic if for some .
The point is preperiodic if is periodic for some .
The (forward) orbit of is the set
Thus is preperiodic if and only if its orbit is finite.
Number theoretic properties of preperiodic points
Let be a rational function of degree at least two with coefficients in . A theorem of Douglas Northcott says that has only finitely many -rational preperiodic points, i.e., has only finitely many preperiodic points in . The uniform boundedness conjecture for preperiodic points of Patrick Morton and Joseph Silverman says that the number of preperiodic points of in is bounded by a constant that depends only on the degree of .
More generally, let be a morphism of degree at least two defined over a number field . Northcott's theorem says that has only finitely many preperiodic points in
, and the general Uniform Boundedness Conjecture says that the number of preperiodic points in
may be bounded solely in terms of , the degree of , and the degree of over .
The Uniform Boundedness Conjecture is not known even for quadratic polynomials over the rational numbers . It is known in this case that cannot have periodic points of period four, five, or six, although the result for period six is contingent on the validity of the conjecture of Birch and Swinnerton-Dyer. Bjorn Poonen has conjectured that cannot have rational periodic points of any period strictly larger than three.
Integer points in orbits
The orbit of a rational map may contain infinitely many integers. For example, if is a polynomial with integer coefficients and if is an integer, then it is clear that the entire orbit consists of integers. Similarly, if is a rational map and some iterate is a polynomial with integer coefficients, then every -th entry in th |
https://en.wikipedia.org/wiki/Collaboration%20graph | In mathematics and social science, a collaboration graph is a graph modeling some social network where the vertices represent participants of that network (usually individual people) and where two distinct participants are joined by an edge whenever there is a collaborative relationship between them of a particular kind. Collaboration graphs are used to measure the closeness of collaborative relationships between the participants of the network.
Types considered in the literature
The most well-studied collaboration graphs include:
Collaboration graph of mathematicians also known as the Erdős collaboration graph, where two mathematicians are joined by an edge whenever they co-authored a paper together (with possibly other co-authors present).
Collaboration graph of movie actors, also known as the Hollywood graph or co-stardom network, where two movie actors are joined by an edge whenever they appeared in a movie together.
Collaborations graphs in other social networks, such as sports, including the "NBA graph" whose vertices are players where two players are joined by an edge if they have ever played together on the same team.
Co-authorship graphs in published articles, where individual nodes may be assigned either at the level of the author, institution, or country. These types of graphs are useful in establishing and evaluating research networks.
Features
By construction, the collaboration graph is a simple graph, since it has no loop-edges and no multiple edges.
The collaboration graph need not be connected. Thus each person who never co-authored a joint paper represents an isolated vertex in the collaboration graph of mathematicians.
Both the collaboration graph of mathematicians and movie actors were shown to have "small world topology": they have a very large number of vertices, most of small degree, that are highly clustered, and a "giant" connected component with small average distances between vertices.
Collaboration distance
The distance between two people/nodes in a collaboration graph is called the collaboration distance. Thus the collaboration distance between two distinct nodes is equal to the smallest number of edges in an edge-path connecting them. If no path connecting two nodes in a collaboration graph exists, the collaboration distance between them is said to be infinite.
The collaboration distance may be used, for instance, for evaluating the citations of an author, a group of authors or a journal.
In the collaboration graph of mathematicians, the collaboration distance from a particular person to Paul Erdős is called the Erdős number of that person. MathSciNet has a free online tool for computing the collaboration distance between any two mathematicians as well as the Erdős number of a mathematician. This tool also shows the actual chain of co-authors that realizes the collaboration distance.
For the Hollywood graph, an analog of the Erdős number, called the Bacon number, has also been considered, which measures the co |
https://en.wikipedia.org/wiki/Weber%20function | In mathematics, Weber function can refer to several different families of functions, mostly named after the physicist H. F. Weber or the mathematician H. M. Weber:
Weber's modular functions named after the mathematician H. M. Weber
Weber functions Eν are solutions of an inhomogeneous Bessel equation, and are linear combinations of Anger functions if ν is not an integer, or linear combinations of Struve functions if ν is an integer
Weber–Hermite function is another name for parabolic cylinder functions, which are solutions of Weber's (differential) equation |
https://en.wikipedia.org/wiki/Nathan%20Mendelsohn | Nathan Saul Mendelsohn, (April 14, 1917 – July 4, 2006) was an American-born mathematician who lived and worked in Canada. Mendelsohn was a researcher in several areas of discrete mathematics, including group theory and combinatorics.
Early life and education
Mendelsohn was born in 1917 in Brooklyn, New York City, the eldest of four children of Samuel Mendelsohn (1880–1959) and Sylvia, née Kirschenbaum (1895–1984). His paternal grandparents, Hyman Mendelsohn (1853-1928) and Hinda, née Silverstone (1859–1942) had originally immigrated to Montreal from Romania in 1898. In 1918, he and his family moved to Toronto, Ontario, Canada, after a fire destroyed the tenement they were living in. Mendelsohn and his family lived in a house at 13 Euclid Avenue.
Mendelsohn completed all his education at the University of Toronto. He would have been unable to attend university had he not won a four years' tuition and books scholarship. In 1938, he was on the University of Toronto team for the first Putnam Competition, along with Irving Kaplansky and John Coleman. The team placed first and each of the three team members won fifty dollars. Mendelsohn was a junior, the other two were seniors. The subsequent year Mendelsohn was barred from competition as at that time the winning university set the examination for the next year and its students were barred from competition. Mendelsohn completed his Ph.D. dissertation in 1941. It was titled "A Group-Theoretic Characterization of the General Projective Collineation Group", and summarized in the Proceedings of the National Academy of Sciences in 1944. His supervisor was Gilbert de Beauregard Robinson.
Mendelsohn also began practising magic tricks in high school as a means of steadying a tremor in his hands. He placed second in the 1953 International Brotherhood of Magicians contest, behind Johnny Carson. He could memorize a shuffled deck of cards seeing each card only once briefly, or a list of fifty objects called out in any order. He could identify the position of each card or name the card in any position.
Career
During the Second World War, Mendelsohn worked on simulations of artillery and
code breaking. As with much of the mathematical work for military purposes during the time, it was classified. Although others related after fifty years what their exact role was, Nathan Mendelsohn strictly followed the Official Secrets Act and never revealed exact details of what he had done. We now know that When Norway fell to the Nazi’s,he worked on a team recomputing ballistics tables for Canadian wood as TNT is made from wood.
Then he went on to break code at Canada’s Camp X , which was Canada’s equivalent of Bletchley Park
From 1945 to 1947, Mendelsohn was a professor at Queen's University in Kingston, Ontario, Canada. Mendelsohn's son later remarked that Mendelsohn "understood that, as a Jew, he would never get a permanent position" at Queen's, as the university "already had a Jewish professor in the department." |
https://en.wikipedia.org/wiki/Optional%20stopping%20theorem | In probability theory, the optional stopping theorem (or sometimes Doob's optional sampling theorem, for American probabilist Joseph Doob) says that, under certain conditions, the expected value of a martingale at a stopping time is equal to its initial expected value. Since martingales can be used to model the wealth of a gambler participating in a fair game, the optional stopping theorem says that, on average, nothing can be gained by stopping play based on the information obtainable so far (i.e., without looking into the future). Certain conditions are necessary for this result to hold true. In particular, the theorem applies to doubling strategies.
The optional stopping theorem is an important tool of mathematical finance in the context of the fundamental theorem of asset pricing.
Statement
A discrete-time version of the theorem is given below, with denoting the set of natural integers, including zero.
Let be a discrete-time martingale and a stopping time with values in }, both with respect to a filtration . Assume that one of the following three conditions holds:
() The stopping time is almost surely bounded, i.e., there exists a constant such that a.s.
() The stopping time has finite expectation and the conditional expectations of the absolute value of the martingale increments are almost surely bounded, more precisely, and there exists a constant such that almost surely on the event } for all .
() There exists a constant such that a.s. for all where denotes the minimum operator.
Then is an almost surely well defined random variable and
Similarly, if the stochastic process is a submartingale or a supermartingale and one of the above conditions holds, then
for a submartingale, and
for a supermartingale.
Remark
Under condition () it is possible that happens with positive probability. On this event is defined as the almost surely existing pointwise limit of , see the proof below for details.
Applications
The optional stopping theorem can be used to prove the impossibility of successful betting strategies for a gambler with a finite lifetime (which gives condition ()) or a house limit on bets (condition ()). Suppose that the gambler can wager up to c dollars on a fair coin flip at times 1, 2, 3, etc., winning his wager if the coin comes up heads and losing it if the coin comes up tails. Suppose further that he can quit whenever he likes, but cannot predict the outcome of gambles that haven't happened yet. Then the gambler's fortune over time is a martingale, and the time at which he decides to quit (or goes broke and is forced to quit) is a stopping time. So the theorem says that . In other words, the gambler leaves with the same amount of money on average as when he started. (The same result holds if the gambler, instead of having a house limit on individual bets, has a finite limit on his line of credit or how far in debt he may go, though this is easier to show with another version of the theorem.)
Suppos |
https://en.wikipedia.org/wiki/Point-free | Point-free may refer to:
Pointless topology, an approach to topology that avoids mentioning points
Point-free style in programming, called also tacit programming
Whitehead's point-free geometry, a geometry whose primitive ontological notion is region rather than point. Two axiomatic systems are set out below, one grounded in mereology, the other in mereotopology and known as connection theory. A point can mark a space or objects |
https://en.wikipedia.org/wiki/Generalized%20semi-infinite%20programming | In mathematics, a semi-infinite programming (SIP) problem is an optimization problem with a finite number of variables and an infinite number of constraints. The constraints are typically parameterized. In a generalized semi-infinite programming (GSIP) problem, the feasible set of the parameters depends on the variables.
Mathematical formulation of the problem
The problem can be stated simply as:
where
In the special case that the set : is nonempty for all GSIP can be cast as bilevel programs (Multilevel programming).
Methods for solving the problem
Examples
See also
optimization
Semi-Infinite Programming (SIP)
References
External links
Mathematical Programming Glossary
Optimization in vector spaces |
https://en.wikipedia.org/wiki/Clique-sum | In graph theory, a branch of mathematics, a clique sum (or clique-sum) is a way of combining two graphs by gluing them together at a clique, analogous to the connected sum operation in topology. If two graphs G and H each contain cliques of equal size, the clique-sum of G and H is formed from their disjoint union by identifying pairs of vertices in these two cliques to form a single shared clique, and then deleting all the clique edges (the original definition, based on the notion of set sum) or possibly deleting some of the clique edges (a loosening of the definition). A k-clique-sum is a clique-sum in which both cliques have exactly (or sometimes, at most) k vertices. One may also form clique-sums and k-clique-sums of more than two graphs, by repeated application of the clique-sum operation.
Different sources disagree on which edges should be removed as part of a clique-sum operation. In some contexts, such as the decomposition of chordal graphs or strangulated graphs, no edges should be removed. In other contexts, such as the SPQR-tree decomposition of graphs into their 3-vertex-connected components, all edges should be removed. And in yet other contexts, such as the graph structure theorem for minor-closed families of simple graphs, it is natural to allow the set of removed edges to be specified as part of the operation.
Related concepts
Clique-sums have a close connection with treewidth: If two graphs have treewidth at most k, so does their k-clique-sum. Every tree is the 1-clique-sum of its edges. Every series–parallel graph, or more generally every graph with treewidth at most two, may be formed as a 2-clique-sum of triangles. The same type of result extends to larger values of k: every graph with treewidth at most k may be formed as a clique-sum of graphs with at most k + 1 vertices; this is necessarily a k-clique-sum.
There is also a close connection between clique-sums and graph connectivity: if a graph is not (k + 1)-vertex-connected (so that there exists a set of k vertices the removal of which disconnects the graph) then it may be represented as a k-clique-sum of smaller graphs. For instance, the SPQR tree of a biconnected graph is a representation of the graph as a 2-clique-sum of its triconnected components.
Application in graph structure theory
Clique-sums are important in graph structure theory, where they are used to characterize certain families of graphs as the graphs formed by clique-sums of simpler graphs. The first result of this type was a theorem of , who proved that the graphs that do not have a five-vertex complete graph as a minor are the 3-clique-sums of planar graphs with the eight-vertex Wagner graph; this structure theorem can be used to show that the four color theorem is equivalent to the case k = 5 of the Hadwiger conjecture. The chordal graphs are exactly the graphs that can be formed by clique-sums of cliques without deleting any edges, and the strangulated graphs are the graphs that can be formed by cli |
https://en.wikipedia.org/wiki/Dura%20al-Qar%27 | Dura al-Qar' () or Dura al-Qari'a is a Palestinian town in the central West Bank, part of the Ramallah and al-Bireh Governorate. According to the Palestinian Central Bureau of Statistics, Dura al-Qar' had a population of 3,032 inhabitants in 2017.
The town's total land area is 4,016 dunams, of which 2,891 dunams have been appropriated by Israel mostly for the purpose of building a by-pass road. According to Dura al-Qar's village council, 142 families have been directly affected by the confiscations and 58% of the town's population depend on those lands as main sources of income.
Location
Dura el Qar' is located north-east of Ramallah. It is bordered by Ein Yabrud to the east, Ein Siniya to the north, Jifna, Al-Jalazun Camp and Surda to the west, and Al Bireh to the south.
History
Potsherds from the Roman and Roman/Byzantine era have been found in the village.
Ottoman era
Potsherds from the early Ottoman era have been found here.
In 1838, it was noted as a Muslim village, Durah, in the Beni Harit district, north of Jerusalem.
In 1863 Victor Guérin found the village to have 250 inhabitants. He further described that old oaks shaded for ancient springs, which were used to irrigate the fields. Several houses in the village were built, at least in part, with ancient stones. An Ottoman village list from about 1870 found that the village had a population of 120, in 22 houses, though the population count only included men.
In 1882, the PEF's Survey of Western Palestine (SWP) described Durah as "a small village on the side of a valley, with springs on the south, and olives".
In 1907, it was described as "a small, healthfully located Moslem village. Its inhabitants have a good reputation for peaceful relations with the Jifna Christians. The Durah people raise many vegetables."
In 1896 the population of Dura el-kara was estimated to be about 246 persons.
British Mandate era
In the 1922 census of Palestine, conducted by the British Mandate authorities, Dura el Qare''' had a population of 191, all Muslims, increasing in the 1931 census to 303, still all Muslims, in a total of 71 houses.
In the 1945 statistics the population was 370, all Muslims, while the total land area was 4,166 dunams, according to an official land and population survey. Of this, 1,762 were allocated for plantations and irrigable land, 1,253 for cereals, while 18 dunams were classified as built-up areas.
Jordanian era
In the wake of the 1948 Arab–Israeli War, and after the 1949 Armistice Agreements, Dura al-Qar' came under Jordanian rule.
The Jordanian census of 1961 found 576 inhabitants in Dura Qar'''.
1967 and after
Since the Six-Day War in 1967, Dura al-Qar' has been under Israeli occupation.
After the 1995 accords, 23.3% of the village‟s total area has been classified as Area B land, while the remaining 76.7% is classified as Area C. Israel has “confiscated” 680 dunum of village land for constructing the Israeli settlement of Beit El.
On August 14, 1995, Khe |
https://en.wikipedia.org/wiki/1925%20Czechoslovak%20First%20League | Statistics of Czechoslovak First League in the 1925 season. Jan Vaník was the league's top scorer with 13 goals.
Overview
It was contested by 10 teams, and Slavia Prague won the championship.
League standings
Results
Top goalscorers
References
Czechoslovakia - List of final tables (RSSSF)
Czechoslovak First League seasons
1
Czech |
https://en.wikipedia.org/wiki/1925%E2%80%9326%20Czechoslovak%20First%20League | Statistics of Czechoslovak First League in the 1925–26 season.
Overview
It was contested by 12 teams, and Sparta Prague won the championship. Jan Dvořáček was the league's top scorer with 32 goals.
League standings
Results
Top goalscorers
References
Czechoslovakia - List of final tables (RSSSF)
Czechoslovak First League seasons
1925–26 in Czechoslovak football
Czech |
https://en.wikipedia.org/wiki/1927%20Czechoslovak%20First%20League | Statistics of Czechoslovak First League in the 1927 season. Antonín Puč was the league's top scorers with 13 goals.
Overview
It was contested by 9 teams, and Sparta Prague won the championship.
League standings
Results
Top goalscorers
References
Czechoslovakia - List of final tables (RSSSF)
Czechoslovak First League seasons
1
Czech |
https://en.wikipedia.org/wiki/1927%E2%80%9328%20Czechoslovak%20First%20League | Statistics of Czechoslovak First League in the 1927–28 season. Karel Meduna was the league's top scorer with 12 goals.
Overview
It was contested by 7 teams, and FK Viktoria Žižkov won the championship.
League standings
Results
Top goalscorers
References
Czechoslovakia - List of final tables (RSSSF)
Czechoslovak First League seasons
1927–28 in Czechoslovak football
Czech |
https://en.wikipedia.org/wiki/1928%E2%80%9329%20Czechoslovak%20First%20League | Statistics of Czechoslovak First League in the 1928–29 season. Antonín Puč was the league's top scorer with 13 goals.
Overview
It was contested by 7 teams, and Slavia Prague won the championship.
League standings
Results
Top goalscorers
References
Czechoslovakia - List of final tables (RSSSF)
Czechoslovak First League seasons
1928–29 in Czechoslovak football
Czech |
https://en.wikipedia.org/wiki/1929%E2%80%9330%20Czechoslovak%20First%20League | Statistics of Czechoslovak First League in the 1929–30 season.
Overview
It was contested by eight teams, and Slavia Prague won the championship. František Kloz was the league's top scorer with 15 goals.
League standings
Results
Top goalscorers
References
Czechoslovakia - List of final tables (RSSSF)
Czechoslovak First League seasons
1929–30 in Czechoslovak football
Czech |
https://en.wikipedia.org/wiki/1930%E2%80%9331%20Czechoslovak%20First%20League | Statistics of Czechoslovak First League in the 1930–31 season. Josef Silný was the league's top scorer with 18 goals.
Overview
It was contested by 8 teams, and Slavia Prague won the championship.
League standings
Results
Relegation play-off
|}
Top goalscorers
References
Notes
Sources
Czechoslovakia - List of final tables (RSSSF)
Czechoslovak First League seasons
1930–31 in Czechoslovak football
Czech |
https://en.wikipedia.org/wiki/1931%E2%80%9332%20Czechoslovak%20First%20League | Statistics of Czechoslovak First League in the 1931–32 season. Raymond Braine was the league's top scorer with 16 goals.
Overview
It was contested by 9 teams, and Sparta Prague won the championship.
League standings
Results
Top goalscorers
References
Czechoslovakia - List of final tables (RSSSF)
Czechoslovak First League seasons
1931–32 in Czechoslovak football
Czech |
https://en.wikipedia.org/wiki/1932%E2%80%9333%20Czechoslovak%20First%20League | Statistics of Czechoslovak First League in the 1932–33 season. Gejza Kocsis was the league's top scorer with 23 goals.
Overview
It was contested by 10 teams, and Slavia Prague won the championship.
League standings
Results
Top goalscorers
References
Czechoslovakia - List of final tables (RSSSF)
Czechoslovak First League seasons
1932–33 in Czechoslovak football
Czech |
https://en.wikipedia.org/wiki/1933%E2%80%9334%20Czechoslovak%20First%20League | Statistics of Czechoslovak First League in the 1933–34 season.
Overview
It was contested by 10 teams, and Slavia Prague won the championship. Raymond Braine and Jiří Sobotka were the league's top scorers with 18 goals each.
League standings
Results
Top goalscorers
References
Czechoslovakia - List of final tables (RSSSF)
Czechoslovak First League seasons
1933–34 in Czechoslovak football
Czech |
https://en.wikipedia.org/wiki/1934%E2%80%9335%20Czechoslovak%20First%20League | Statistics of Czechoslovak First League in the 1934–35 season.
Overview
It was contested by 12 teams, and Slavia Prague won the championship. František Svoboda was the league's top scorer with 27 goals.
League standings
Results
Top goalscorers
References
Czechoslovakia - List of final tables (RSSSF)
Czechoslovak First League seasons
1934–35 in Czechoslovak football
Czech |
https://en.wikipedia.org/wiki/1935%E2%80%9336%20Czechoslovak%20First%20League | Statistics of Czechoslovak First League in the 1935–36 season.
Overview
It was contested by 14 teams, and Sparta Prague won the championship. Vojtěch Bradáč was the league's top scorer with 42 goals.
League standings
Results
Top goalscorers
References
Czechoslovakia - List of final tables (RSSSF)
Czechoslovak First League seasons
1935–36 in Czechoslovak football
Czech |
https://en.wikipedia.org/wiki/1936%E2%80%9337%20Czechoslovak%20First%20League | Statistics of Czechoslovak First League in the 1936–37 season.
Overview
It was contested by 12 teams, and Slavia Prague won the championship. František Kloz was the league's top scorer with 28 goals.
League standings
Results
Top goalscorers
References
Czechoslovakia - List of final tables (RSSSF)
Czechoslovak First League seasons
1936–37 in Czechoslovak football
Czech |
https://en.wikipedia.org/wiki/1937%E2%80%9338%20Czechoslovak%20First%20League | Statistics of Czechoslovak First League in the 1937–38 season.
Overview
It was contested by 12 teams, and Sparta Prague won the championship. Josef Bican was the league's top scorer with 22 goals.
League standings
Results
Top goalscorers
References
Czechoslovakia League of the Whole State 1934-1938 - List of final tables (RSSSF)
Czechoslovak First League seasons
1937–38 in Czechoslovak football
Czech |
https://en.wikipedia.org/wiki/1945%E2%80%9346%20Czechoslovak%20First%20League | Statistics of Czechoslovak First League in the 1945–46 season.
Overview
It was contested by 20 teams, and Sparta Prague won the championship. Josef Bican was the league's top scorer with 31 goals.
Stadia and locations
Group A
Table
Results
Group B
Table
Results
Championship playoff
Sparta Prague 4–2 Slavia Prague
Slavia Prague 0–5 Sparta Prague
Top goalscorers
References
Czechoslovakia - List of final tables (RSSSF)
Czechoslovak First League seasons
Czechoslovak First League, 1945-46
1945–46 in Czechoslovak football |
https://en.wikipedia.org/wiki/1946%E2%80%9347%20Czechoslovak%20First%20League | Statistics of Czechoslovak First League in the 1946–47 season.
Overview
It was contested by 14 teams, and Slavia Prague won the championship. Josef Bican was the league's top scorer with 43 goals.
AC Sparta toured Great Britain opening with a 2 – 2 draw against Arsenal on 2 October 1946.
Stadia and locations
League standings
Results
Top goalscorers
References
Czechoslovakia - List of final tables (RSSSF)
Czechoslovak First League seasons
Czechoslovak First League, 1946-47
1946–47 in Czechoslovak football |
https://en.wikipedia.org/wiki/1947%E2%80%9348%20Czechoslovak%20First%20League | Statistics of Czechoslovak First League in the 1947–48 season.
Overview
It was contested by 11 teams, and Sparta Prague won the championship. Jaroslav Cejp was the league's top scorer with 21 goals.
Stadia and locations
League standings
Results
Top goalscorers
References
Czechoslovakia - List of final tables (RSSSF)
Czechoslovak First League seasons
Czechoslovak First League, 1947-48
1947–48 in Czechoslovak football |
https://en.wikipedia.org/wiki/1949%20Czechoslovak%20First%20League | Statistics of Czechoslovak First League in the 1949 season.
Overview
It was contested by 14 teams, and NV Bratislava won the championship. Ladislav Hlaváček was the league's top scorer with 28 goals.
Stadia and locations
League standings
Results
Top goalscorers
References
Czechoslovakia - List of final tables (RSSSF)
Czechoslovak First League seasons
Czech
Czech
1948–49 in Czechoslovak football
1949–50 in Czechoslovak football |
https://en.wikipedia.org/wiki/1950%20Czechoslovak%20First%20League | Statistics of Czechoslovak First League in the 1950 season.
Overview
It was contested by 14 teams, and NV Bratislava won the championship. Josef Bican was the league's top scorer with 22 goals.
Stadia and locations
League standings
Results
Top goalscorers
References
Czechoslovakia - List of final tables (RSSSF)
Czechoslovak First League seasons
Czech
Czech
1
1 |
https://en.wikipedia.org/wiki/1951%20Czechoslovak%20First%20League | Statistics of Czechoslovak First League in the 1951 season.
Overview
It was contested by 14 teams, and NV Bratislava won the championship. Alois Jaroš was the league's top scorer with 16 goals.
Stadia and locations
League standings
Results
Top goalscorers
References
Czechoslovakia - List of final tables (RSSSF)
Czechoslovak First League seasons
Czech
Czech
1
1 |
https://en.wikipedia.org/wiki/1952%20Czechoslovak%20First%20League | Statistics of Czechoslovak First League in the 1952 season.
Overview
It was contested by 14 teams, and Sparta ČKD Sokolovo won the championship. Miroslav Wiecek was the league's top scorer with 20 goals.
Stadia and locations
League standings
Results
Top goalscorers
References
Czechoslovakia - List of final tables (RSSSF)
Czechoslovak First League seasons
Czech
Czech
1
1 |
https://en.wikipedia.org/wiki/1953%20Czechoslovak%20First%20League | Statistics of Czechoslovak First League in the 1953 season.
Overview
It was contested by 14 teams, and ÚDA Praha won the championship. Josef Majer was the league's top scorer with 13 goals.
Stadia and locations
League standings
Results
Top goalscorers
References
Czechoslovakia - List of final tables (RSSSF)
Czechoslovak First League seasons
Czech
Czech
1
1 |
https://en.wikipedia.org/wiki/1954%20Czechoslovak%20First%20League | Statistics of Czechoslovak First League in the 1954 season.
Overview
It was contested by 12 teams, and Spartak Praha Sokolovo won the championship. Jiří Pešek was the league's top scorer with 15 goals.
Stadia and locations
League standings
Results
Top goalscorers
References
Czechoslovakia - List of final tables (RSSSF)
Czechoslovak First League seasons
Czech
Czech
1
1 |
https://en.wikipedia.org/wiki/1955%20Czechoslovak%20First%20League | Statistics of Czechoslovak First League in the 1955 season.
Overview
It was contested by 12 teams, and Slovan Bratislava won the championship. Emil Pažický was the league's top scorer with nineteen goals.
Stadia and locations
League standings
Results
Top goalscorers
References
Czechoslovakia - List of final tables (RSSSF)
Czechoslovak First League seasons
Czech
Czech
1
1 |
https://en.wikipedia.org/wiki/1956%20Czechoslovak%20First%20League | Statistics of Czechoslovak First League in the 1956 season.
Overview
It was contested by 12 teams, and Dukla Prague won the championship. Milan Dvořák and Miroslav Wiecek were the league's top scorers with 15 goals each.
Stadia and locations
League standings
Results
Top goalscorers
References
Czechoslovakia - List of final tables (RSSSF)
Czechoslovak First League seasons
Czech
Czech
1
1 |
https://en.wikipedia.org/wiki/1957%E2%80%9358%20Czechoslovak%20First%20League | Statistics of Czechoslovak First League in the 1957–58 season.
Overview
It was contested by 12 teams, and Dukla Prague won the championship. Miroslav Wiecek was the league's top scorer with 25 goals.
Stadia and locations
League standings
Results
First and second round
Third round
Top goalscorers
References
Czechoslovakia - List of final tables (RSSSF)
Czechoslovak First League seasons
Czech
1957–58 in Czechoslovak football |
https://en.wikipedia.org/wiki/1958%E2%80%9359%20Czechoslovak%20First%20League | Statistics of Czechoslovak First League in the 1958–59 season.
Overview
It was contested by 14 teams, and CH Bratislava won the championship. Miroslav Wiecek was the league's top scorer with 20 goals.
Stadia and locations
League standings
Results
Top goalscorers
References
Czechoslovakia - List of final tables (RSSSF)
Czechoslovak First League seasons
Czech
1958–59 in Czechoslovak football |
https://en.wikipedia.org/wiki/1959%E2%80%9360%20Czechoslovak%20First%20League | Statistics of Czechoslovak First League in the 1959–60 season.
Overview
It was contested by 14 teams, and Spartak Hradec Králové won the championship. Michal Pucher was the league's top scorer with 18 goals.
Stadia and locations
League standings
Results
Top goalscorers
References
Czechoslovakia - List of final tables (RSSSF)
Czechoslovak First League seasons
Czech
1959–60 in Czechoslovak football |
https://en.wikipedia.org/wiki/1960%E2%80%9361%20Czechoslovak%20First%20League | Statistics of Czechoslovak First League in the 1960–61 season.
Overview
It was contested by 14 teams, and Dukla Prague won the championship. Rudolf Kučera and Ladislav Pavlovič were the league's top scorers with 17 goals each.
Stadia and locations
League standings
Dynamo Žilina qualified for the Cup Winners' Cup as Czechoslovak Cup runners-up from a lower division.Spartak Brno KPS invited for the Inter-Cities Fairs Cup from a lower division.
Results
Top goalscorers
References
Czechoslovakia - List of final tables (RSSSF)
Czechoslovak First League seasons
Czech
1960–61 in Czechoslovak football |
https://en.wikipedia.org/wiki/1961%E2%80%9362%20Czechoslovak%20First%20League | Statistics of Czechoslovak First League in the 1961–62 season.
Overview
It was contested by 14 teams, and Dukla Prague won the championship. Adolf Scherer was the league's top scorer with 24 goals.
Stadia and locations
League standings
Spartak ZJŠ Brno invited for the Inter-Cities Fairs Cup from a lower division.
Results
Relegation play-off
Dynamo Žilina were relegated to the Czechoslovak Second League.
Top goalscorers
References
Czechoslovakia - List of final tables (RSSSF)
Czechoslovak First League seasons
Czech
1961–62 in Czechoslovak football |
https://en.wikipedia.org/wiki/1962%E2%80%9363%20Czechoslovak%20First%20League | Statistics of Czechoslovak First League in the 1962–63 season.
Overview
It was contested by 14 teams, and Dukla Prague won the championship. Karel Petroš was the league's top scorer with 19 goals.
Stadia and locations
League standings
Results
Top goalscorers
References
Czechoslovakia - List of final tables (RSSSF)
Czechoslovak First League seasons
Czech
1962–63 in Czechoslovak football |
https://en.wikipedia.org/wiki/1963%E2%80%9364%20Czechoslovak%20First%20League | Statistics of Czechoslovak First League in the 1963–64 season.
Overview
It was contested by 14 teams, and Dukla Prague won the championship. Ladislav Pavlovič was the league's top scorer with 21 goals.
Stadia and locations
League standings
Results
Top goalscorers
References
Czechoslovakia - List of final tables (RSSSF)
Czechoslovak First League seasons
Czech
1963–64 in Czechoslovak football |
https://en.wikipedia.org/wiki/1964%E2%80%9365%20Czechoslovak%20First%20League | Statistics of Czechoslovak First League in the 1964–65 season.
Overview
It was contested by 14 teams, and Sparta Prague won the championship. Pavol Bencz was the league's top scorer with 21 goals.
Stadia and locations
League standings
Results
Top goalscorers
References
Czechoslovakia - List of final tables (RSSSF)
Czechoslovak First League seasons
Czech
1964–65 in Czechoslovak football |
https://en.wikipedia.org/wiki/1965%E2%80%9366%20Czechoslovak%20First%20League | Statistics of Czechoslovak First League in the 1965–66 season.
Overview
It was contested by 14 teams, and Dukla Prague won the championship. Ladislav Michalík was the league's top scorer with 15 goals. The match between Sparta Prague and Slavia Prague had an attendance of 50,105 - setting a league record.
Stadia and locations
League standings
Results
Top goalscorers
References
Czechoslovakia - List of final tables (RSSSF)
Czechoslovak First League seasons
Czech
1965–66 in Czechoslovak football |
https://en.wikipedia.org/wiki/1966%E2%80%9367%20Czechoslovak%20First%20League | Statistics of Czechoslovak First League in the 1966–67 season.
Overview
It was contested by 14 teams, and Sparta Prague won the championship. Jozef Adamec was the league's top scorer with 21 goals.
Stadia and locations
League standings
Results
Top goalscorers
References
Czechoslovakia - List of final tables (RSSSF)
Czechoslovak First League seasons
Czech
1966–67 in Czechoslovak football |
https://en.wikipedia.org/wiki/1967%E2%80%9368%20Czechoslovak%20First%20League | Statistics of Czechoslovak First League in the 1967–68 season.
Overview
It was contested by 14 teams, and FC Spartak Trnava won the championship. Jozef Adamec was the league's top scorer with 18 goals.
Stadia and locations
League standings
Results
Top goalscorers
References
Czechoslovakia - List of final tables (RSSSF)
Czechoslovak First League seasons
Czech
1967–68 in Czechoslovak football |
https://en.wikipedia.org/wiki/1968%E2%80%9369%20Czechoslovak%20First%20League | Statistics of Czechoslovak First League in the 1968–69 season.
Overview
It was contested by 14 teams, and Spartak Trnava won the championship. Ladislav Petráš was the league's top scorer with 20 goals.
Stadia and locations
League standings
Results
Top goalscorers
References
Czechoslovakia - List of final tables (RSSSF)
Czechoslovak First League seasons
Czech
1968–69 in Czechoslovak football |
https://en.wikipedia.org/wiki/1969%E2%80%9370%20Czechoslovak%20First%20League | Statistics of Czechoslovak First League in the 1969–70 season.
Overview
It was contested by 16 teams, and ŠK Slovan Bratislava won the championship. Jozef Adamec was the league's top scorer with 18 goals.
Stadia and locations
League standings
Results
Top goalscorers
References
Czechoslovakia - List of final tables (RSSSF)
Czechoslovak First League seasons
Czech
1969–70 in Czechoslovak football |
https://en.wikipedia.org/wiki/1970%E2%80%9371%20Czechoslovak%20First%20League | Statistics of Czechoslovak First League in the 1970–71 season.
Overview
It was contested by 16 teams, and FC Spartak Trnava won the championship. Jozef Adamec and Zdeněk Nehoda were the league's top scorers with 16 goals each.
Stadia and locations
League standings
Results
Top goalscorers
References
Czechoslovakia - List of final tables (RSSSF)
Czechoslovak First League seasons
Czech
1 |
https://en.wikipedia.org/wiki/1971%E2%80%9372%20Czechoslovak%20First%20League | Statistics of Czechoslovak First League in the 1971–72 season.
Overview
It was contested by 16 teams, and Spartak Trnava won the championship. Ján Čapkovič was the league's top scorer with 19 goals.
Stadia and locations
League standings
Results
Top goalscorers
References
Czechoslovakia - List of final tables (RSSSF)
Czechoslovak First League seasons
Czech
1971–72 in Czechoslovak football |
https://en.wikipedia.org/wiki/1972%E2%80%9373%20Czechoslovak%20First%20League | Statistics of Czechoslovak First League in the 1972–73 season.
Overview
It was contested by 16 teams, and FC Spartak Trnava won the championship. Ladislav Józsa was the league's top scorer with 21 goals.
Stadia and locations
Table
Results
Top goalscorers
References
Czechoslovak First League seasons
Czech
1972–73 in Czechoslovak football |
https://en.wikipedia.org/wiki/1973%E2%80%9374%20Czechoslovak%20First%20League | Statistics of Czechoslovak First League in the 1973–74 season.
Overview
It was contested by 16 teams, and ŠK Slovan Bratislava won the championship. Ladislav Józsa and Přemysl Bičovský were the league's top scorers with 17 goals each.
Stadia and locations
League standings
Results
Top goalscorers
References
External links
Czechoslovakia - List of final tables (RSSSF)
Czechoslovak First League seasons
Czech
1973–74 in Czechoslovak football |
https://en.wikipedia.org/wiki/1974%E2%80%9375%20Czechoslovak%20First%20League | Statistics of Czechoslovak First League in the 1974–1975 season.
Overview
It was contested by 16 teams, and ŠK Slovan Bratislava won the championship. Ladislav Petráš was the league's top scorer with 20 goals.
Stadia and locations
League standings
Results
Top goalscorers
References
Czechoslovakia - List of final tables (RSSSF)
Czechoslovak First League seasons
Czech
1974–75 in Czechoslovak football |
https://en.wikipedia.org/wiki/1975%E2%80%9376%20Czechoslovak%20First%20League | Statistics of Czechoslovak First League in the 1975–76 season.
Overview
It was contested by 16 teams, and FC Baník Ostrava won the championship. Dušan Galis was the league's top scorer with 21 goals.
Stadia and locations
League standings
Sparta Prague qualified for the Cup Winners' Cup as Czechoslovak Cup winners from a lower division.
Results
Squad of the champions Baník Ostrava
Coach: Jiří Rubáš
Milan Albrecht
Josef Foks
Jiří Hudeček
František Huml
Jiří Klement
Lubomír Knapp
Josef Kolečko
Arnošt Kvasnica
Verner Lička
Zdeněk Lorenc
Pavol Michalík
Miroslav Mička
Lumír Mochel
Libor Radimec
Jiří Ruš
Zdeněk Rygel
František Schmucker
Rostislav Sionko
Vladimír Šišma
Petr Slaný
Miroslav Smetana
Zdeněk Svatonský
Josef Tondra
Rostislav Vojáček
Miroslav Vojkůvka
Ladislav Zetocha
Top goalscorers
References
Czechoslovakia - List of final tables (RSSSF)
Czechoslovak First League seasons
Czech
1975–76 in Czechoslovak football |
https://en.wikipedia.org/wiki/1976%E2%80%9377%20Czechoslovak%20First%20League | Statistics of Czechoslovak First League in the 1976–77 season.
Overview
It was contested by 16 teams, and Dukla Prague won the championship. Ladislav Józsa was the league's top scorer with 18 goals.
Stadia and locations
League standings
Results
Top goalscorers
References
Czechoslovakia - List of final tables (RSSSF)
Czechoslovak First League seasons
Czech
1976–77 in Czechoslovak football |
https://en.wikipedia.org/wiki/1977%E2%80%9378%20Czechoslovak%20First%20League | Statistics of Czechoslovak First League in the 1977–78 season.
Overview
It was contested by 16 teams, and Zbrojovka Brno won the championship. Karel Kroupa was the league's top scorer with 20 goals.
Stadia and locations
League standings
Results
Top goalscorers
References
Czechoslovakia - List of final tables (RSSSF)
Czechoslovak First League seasons
Czech
1977–78 in Czechoslovak football |
https://en.wikipedia.org/wiki/1978%E2%80%9379%20Czechoslovak%20First%20League | Statistics of Czechoslovak First League in the 1978–79 season.
Overview
It was contested by 16 teams, and Dukla Prague won the championship. Karel Kroupa and Zdeněk Nehoda were the league's top scorers with 17 goals each.
Stadia and locations
League standings
Results
Top goalscorers
References
Czechoslovakia - List of final tables (RSSSF)
Czechoslovak First League seasons
Czech
1978–79 in Czechoslovak football |
https://en.wikipedia.org/wiki/1979%E2%80%9380%20Czechoslovak%20First%20League | Statistics of Czechoslovak First League in the 1979–80 season.
Overview
It was contested by 16 teams, and FC Baník Ostrava won the championship. Werner Lička was the league's top scorer with 18 goals.
Stadia and locations
League standings
Results
Squad of the champions Baník Ostrava
Coach: Evžen Hadamczik
Milan Albrecht
Augustín Antalík
Václav Daněk
František Kadlček
Lubomír Knapp
Verner Lička
Zdeněk Lorenc
Pavel Mačák
Jozef Marchevský
Jan Matuštík
Pavol Michalík
Petr Němec
Václav Pěcháček
Libor Radimec
Zdeněk Rygel
Lubomír Šrámek
Zdeněk Šreiner
Dušan Šrubař
Rostislav Vojáček
Top goalscorers
References
Czechoslovakia - List of final tables (RSSSF)
Czechoslovak First League seasons
Czech
1979–80 in Czechoslovak football |
https://en.wikipedia.org/wiki/1980%E2%80%9381%20Czechoslovak%20First%20League | Statistics of Czechoslovak First League in the 1980–81 season.
Overview
It was contested by 16 teams, and FC Baník Ostrava won the championship. Marián Masný was the league's top scorer with 16 goals.
Stadia and locations
League standings
Results
Top goalscorers
References
Czechoslovak First League seasons
Czech
1980–81 in Czechoslovak football |
https://en.wikipedia.org/wiki/1982%E2%80%9383%20Czechoslovak%20First%20League | Statistics of Czechoslovak First League in the 1982–83 season.
Overview
It was contested by 16 teams, and Bohemians Prague won the championship. Pavel Chaloupka was the league's top scorer with 17 goals.
Stadia and locations
League standings
Results
Top goalscorers
References
Czechoslovakia - List of final tables (RSSSF)
Czechoslovak First League seasons
Czech
1982–83 in Czechoslovak football |
https://en.wikipedia.org/wiki/1983%E2%80%9384%20Czechoslovak%20First%20League | Statistics of Czechoslovak First League in the 1983–84 season.
Overview
It was contested by 16 teams, and Sparta Prague won the championship. Werner Lička was the league's top scorer with 20 goals.
Stadia and locations
League standings
Results
Top goalscorers
References
Czechoslovakia - List of final tables (RSSSF)
Czechoslovak First League seasons
Czech
1983–84 in Czechoslovak football |
https://en.wikipedia.org/wiki/1984%E2%80%9385%20Czechoslovak%20First%20League | Statistics of Czechoslovak First League in the 1984–85 season.
Overview
It was contested by 16 teams, and Sparta Prague won the championship. Ivo Knoflíček was the league's top scorer with 21 goals.
Stadia and locations
League standings
Results
Top goalscorers
References
Czechoslovakia - List of final tables (RSSSF)
Czechoslovak First League seasons
Czech
1984–85 in Czechoslovak football |
https://en.wikipedia.org/wiki/1985%E2%80%9386%20Czechoslovak%20First%20League | Statistics of Czechoslovak First League in the 1985–86 season.
Overview
It was contested by 16 teams, and FC Vítkovice won the championship. Stanislav Griga was the league's top scorer with 19 goals.
Stadia and locations
League standings
Results
Top goalscorers
References
Czechoslovakia - List of final tables (RSSSF)
Czechoslovak First League seasons
Czech
1985–86 in Czechoslovak football |
https://en.wikipedia.org/wiki/1986%E2%80%9387%20Czechoslovak%20First%20League | Statistics of Czechoslovak First League in the 1986–87 season.
Overview
It was contested by 16 teams, and Sparta Prague won the championship. Václav Daněk was the league's top scorer with 24 goals.
Stadia and locations
League standings
Results
Top goalscorers
References
Czechoslovakia - List of final tables (RSSSF)
Czechoslovak First League seasons
Czech
1986–87 in Czechoslovak football |
https://en.wikipedia.org/wiki/1987%E2%80%9388%20Czechoslovak%20First%20League | Statistics of Czechoslovak First League in the 1987–88 season. Milan Luhový was the league's top scorer with 24 goals.
Overview
It was contested by 16 teams, and Sparta Prague won the championship.
Stadia and locations
League standings
Results
Top goalscorers
References
Czechoslovakia - List of final tables (RSSSF)
Czechoslovak First League seasons
Czech
1987–88 in Czechoslovak football |
https://en.wikipedia.org/wiki/1988%E2%80%9389%20Czechoslovak%20First%20League | Statistics of Czechoslovak First League in the 1988–89 season. Milan Luhový was the league's top scorer with 25 goals.
Overview
It was contested by 16 teams, and Sparta Prague won the championship.
Stadia and locations
League standings
Results
Top goalscorers
References
Czechoslovakia - List of final tables (RSSSF)
Czechoslovak First League seasons
Czech
1988–89 in Czechoslovak football |
https://en.wikipedia.org/wiki/1989%E2%80%9390%20Czechoslovak%20First%20League | Statistics of Czechoslovak First League in the 1989–90 season. Ľubomír Luhový was the league's top scorer with 20 goals.
Overview
It was contested by 16 teams, and Sparta Prague won the championship.
Stadia and locations
League standings
Results
Top goalscorers
References
Czechoslovakia - List of final tables (RSSSF)
Czechoslovak First League seasons
Czech
1989–90 in Czechoslovak football |
https://en.wikipedia.org/wiki/1990%E2%80%9391%20Czechoslovak%20First%20League | Statistics of Czechoslovak First League in the 1990–91 season. Roman Kukleta was the league's top scorer with 17 goals.
Overview
It was contested by 16 teams, and Sparta Prague won the championship.
Stadia and locations
League standings
Results
Top goalscorers
References
Czechoslovakia - List of final tables (RSSSF)
Czechoslovak First League seasons
Czech
1990–91 in Czechoslovak football |
https://en.wikipedia.org/wiki/1991%E2%80%9392%20Czechoslovak%20First%20League | Statistics of Czechoslovak First League in the 1991–92 season. Peter Dubovský was the league's top scorer with 27 goals.
Overview
It was contested by 16 teams, and ŠK Slovan Bratislava won the championship.
Stadia and locations
League standings
Results
Top goalscorers
References
Czechoslovakia - List of final tables (RSSSF)
Czechoslovak First League seasons
Czech
1991–92 in Czechoslovak football |
https://en.wikipedia.org/wiki/Qatanna | Qatanna () is a Palestinian town in the central West Bank part of the Jerusalem Governorate, located 12 km. northwest of Jerusalem. According to the Palestinian Central Bureau of Statistics, the town had a population of 6,981 inhabitants in 2017. Primary health care for the town is level 2.
Geography and land
Qatanna has an elevation of 650 meters above sea level. Nearby towns and villages include Biddu to the east and Beit Liqya to the north. Khirbet Kefireh is located just north of Qatanna.
History
In the Roman and Byzantine periods, Qatanna was home to extensive settlement including agricultural institutions, roads, and many burial caves.
Both Mordechai Nisan and Tsvi Misinai cite stories that claim that although the people of Qatanna practice Islam today, they are originally of Jewish ancestry.
Ottoman era
Incorporated into the Ottoman Empire in 1517 with all of Palestine, Qatanna appeared in the 1596 Ottoman tax registers as being in the Nahiya of Quds of the Liwa of Quds. It had a population of 12 households, all Muslim, and paid taxes on wheat, barley, olives, occasional revenues, goats and/or beehives.
In 1838 Katunneh was noted as a Muslim village, part of Beni Malik district, located west of Jerusalem.
In 1863, the French explorer Victor Guérin found the village to have 250 inhabitants, while an Ottoman village list of about 1870 showed that Kattane had a population of 300, in 57 houses, though the population count included only men. It was also noted that it was located north of Abu Ghosh, in the Beni Malik district.
In 1883, the PEF's Survey of Western Palestine described it as a "small village in a deep, narrow, rocky valley, surrounded by fine groves of olives and vegetable gardens."
In 1896 the population of Katanne was estimated to be about 351 persons.
British Mandate era
In the 1922 census of Palestine conducted by the British Mandate authorities, Qatanneh had a population 633, all Muslims. In the 1931 census it was counted with Nitaf, together they had 875 Muslim inhabitants, in 233 houses.
In the 1945 statistics Qatanna had a population of 1,150, all Muslims, with 9,464 dunams of land, according to an official land and population survey. Of this, 1,829 dunams were plantations and irrigable land, 1,603 used for cereals, while 32 dunams were built-up (urban) land.
Jordanian era
In the wake of the 1948 Arab–Israeli War, and after the 1949 Armistice Agreements, Qatanna came under Jordanian rule.
After the 1948 war, much of Qatanna's land area was designated as "no-man's land" forming a part of the Demilitarized Zone between the armistice lines of Israeli and Jordanian territory.
In 1961, the population of Qatanna was 1,897.
Post-1967
Since the Six-Day War in 1967, Qatanna has been under Israeli occupation. The population in the 1967 census conducted by the Israeli authorities was 1,594, of whom 151 were refugees.
Currently, the town has a total land area of 3,555 dunams, of which 677 dunams are designated a |
https://en.wikipedia.org/wiki/Vic%20Elias | Vic Elias (1948–2006) was a poet who was born in Chicago, Illinois, and emigrated to Canada in 1979. Settling in London, Ontario, he was a Professor of Applied Mathematics at the University of Western Ontario. He was also an Affiliate Member of the Perimeter Institute for Theoretical Physics in Waterloo, Ontario. In 1997 he received the Edward G. Pleva Award for Excellence in Teaching, UWO's highest teaching award. In addition to his work in mathematics and physics, Vic Elias was an accomplished poet whose work appeared in a number of literary publications including Parchment, Tabula Rasa, and Afterthoughts. He is the author of three full-length collections and one chapbook of poetry. His poems have dealt with his Jewish identity and spiritual themes, humorous anecdotes, and in his final works, his struggle with cancer, which took his life in May 2006.
Books
1991: Reflected Scenery from Where My Eyes Should Be, Moonstone Press
2004: Drinking with Old Men, South Western Ontario Poetry,
2006: A Game of Jeopardy, South Western Ontario Poetry,
Chapbooks
2006: The Cataracts of Troy, South Western Ontario Poetry
References
External links
Vic Elias: Publisher Site
American male poets
Poets from Chicago
1948 births
2006 deaths
Chapbook writers
20th-century American poets
20th-century American male writers |
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