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https://en.wikipedia.org/wiki/Multidimensional%20Chebyshev%27s%20inequality | In probability theory, the multidimensional Chebyshev's inequality is a generalization of Chebyshev's inequality, which puts a bound on the probability of the event that a random variable differs from its expected value by more than a specified amount.
Let be an -dimensional random vector with expected value and covariance matrix
If is a positive-definite matrix, for any real number :
Proof
Since is positive-definite, so is . Define the random variable
Since is positive, Markov's inequality holds:
Finally,
Infinite dimensions
There is a straightforward extension of the vector version of Chebyshev's inequality to infinite dimensional settings. Let be a random variable which takes values in a Fréchet space (equipped with seminorms ). This includes most common settings of vector-valued random variables, e.g., when is a Banach space (equipped with a single norm), a Hilbert space, or the finite-dimensional setting as described above.
Suppose that is of "strong order two", meaning that
for every seminorm . This is a generalization of the requirement that have finite variance, and is necessary for this strong form of Chebyshev's inequality in infinite dimensions. The terminology "strong order two" is due to Vakhania.
Let be the Pettis integral of (i.e., the vector generalization of the mean), and let
be the standard deviation with respect to the seminorm . In this setting we can state the following:
General version of Chebyshev's inequality.
Proof. The proof is straightforward, and essentially the same as the finitary version. If , then is constant (and equal to ) almost surely, so the inequality is trivial.
If
then , so we may safely divide by . The crucial trick in Chebyshev's inequality is to recognize that .
The following calculations complete the proof:
References
Probabilistic inequalities
Statistical inequalities |
https://en.wikipedia.org/wiki/John%20R.%20Stallings | John Robert Stallings Jr. (July 22, 1935 – November 24, 2008) was a mathematician known for his seminal contributions to geometric group theory and 3-manifold topology. Stallings was a Professor Emeritus in the Department of Mathematics at the University of California at Berkeley where he had been a faculty member since 1967. He published over 50 papers, predominantly in the areas of geometric group theory and the topology of 3-manifolds. Stallings' most important contributions include a proof, in a 1960 paper, of the Poincaré Conjecture in dimensions greater than six and a proof, in a 1971 paper, of the Stallings theorem about ends of groups.
Biography
John Stallings was born on July 22, 1935, in Morrilton, Arkansas.
Stallings received his B.Sc. from University of Arkansas in 1956 (where he was one of the first two graduates in the university's Honors program) and he received a Ph.D. in Mathematics from Princeton University in 1959 under the direction of Ralph Fox.
After completing his PhD, Stallings held a number of postdoctoral and faculty positions, including being an NSF postdoctoral fellow at the University of Oxford as well as an instructorship and a faculty appointment at Princeton. Stallings joined the University of California at Berkeley as a faculty member in 1967 where he remained until his retirement in 1994. Even after his retirement, Stallings continued supervising UC Berkeley graduate students until 2005. Stallings was an Alfred P. Sloan Research fellow from 1962 to 1965 and a Miller Institute fellow from 1972 to 1973.
Over the course of his career, Stallings had 22 doctoral students including Marc Culler, Stephen M. Gersten, and J. Hyam Rubinstein and 100 doctoral descendants. He published over 50 papers, predominantly in the areas of geometric group theory and the topology of 3-manifolds.
Stallings delivered an invited address as the International Congress of Mathematicians in Nice in 1970 and a James K. Whittemore Lecture at Yale University in 1969.
Stallings received the Frank Nelson Cole Prize in Algebra from the American Mathematical Society in 1970.
The conference "Geometric and Topological Aspects of Group Theory", held at the Mathematical Sciences Research Institute in Berkeley in May 2000, was dedicated to the 65th birthday of Stallings.
In 2002 a special issue of the journal Geometriae Dedicata was dedicated to Stallings on the occasion of his 65th birthday. Stallings died from prostate cancer on November 24, 2008.
Mathematical contributions
Most of Stallings' mathematical contributions are in the areas of geometric group theory and low-dimensional topology (particularly the topology of 3-manifolds) and on the interplay between these two areas.
An early significant result of Stallings is his 1960 proof of the Poincaré conjecture in dimensions greater than six. (Stallings' proof was obtained independently from and shortly after the different proof of Stephen Smale who established the same result in dimensions |
https://en.wikipedia.org/wiki/M.%20S.%20Raghunathan | Madabusi Santanam Raghunathan FRS is an Indian mathematician. He is currently Head of the National Centre for Mathematics, Indian Institute of Technology, Mumbai. Formerly Professor of eminence at TIFR in Homi Bhabha Chair. Raghunathan received his PhD in Mathematics from (TIFR), University of Mumbai; his advisor was M. S. Narasimhan. Raghunathan is a Fellow of the Royal Society, of the Third World Academy of Sciences, and of the American Mathematical Society and a recipient of the civilian honour of Padma Bhushan. He has also been on the Mathematical Sciences jury for the Infosys Prize from 2016.
Early life and education
Madabusi Santanam Raghunathan was born on 11 August 1941 at Anantapur, Andhra Pradesh, his maternal grandparents' place. The family lived in Chennai. His father Santanam continued the family's timber business and expanded it through exports to Europe and Japan. He had earlier joined the Indian Institute of Science, Bangalore, after a BSc in Physics, but had to leave his studies mid-way to take care of the family business. Raghunathan fondly recalls that his father had a feeling for science and used to talk about it, making it very interesting to the children. Raghunathan's mother came from a family with an academic tradition. Her father was an esteemed Professor of English, who had contributed articles to the Cornhill Magazine. He also wrote, and published on his own, a book on William Makepeace Thackeray, which was later found to have been reprinted in the United States, without his knowledge, indeed in violation of the copyright he held.
Raghunathan had his schooling in Chennai, in P.S. High School, Mylapore and the Madras Christian College High School. He passed his SSLC (Secondary School Leaving Certificate) examination in 1955. There is a rather interesting story about it: after the Sanskrit paper he absent-mindedly left the examination hall along with his answer paper, and was intercepted on his way home by a fellow student, following commotion at the examination hall on account of the missing answer paper. He narrowly escaped having to reappear for the entire examination, thanks to the headmaster vouching for his integrity.
The University of Madras had the curious restriction of not admitting anyone under the age of 14 years and six months, though after attaining that age it was possible to be admitted even in higher classes. Raghunathan therefore pursued his Intermediate at the St. Joseph's College, Bangalore during 1955–57. He then returned to Chennai and joined B.A.(Hons.) in mathematics, in Vivekananda College, which had a very good reputation.
Research
After initial training during 1960–62, he worked on a research problem suggested by Prof. M.S. Narasimhan, on "Deformations of linear connections and Riemannian metrics", and solved it by the summer of 1963.
He wrote his PhD thesis under the guidance of Professor Narasimhan and was awarded the degree by the University of Bombay in 1966. After completing his PhD, R |
https://en.wikipedia.org/wiki/Horrocks%20bundle | In algebraic geometry, Horrocks bundles are certain indecomposable rank 3 vector bundles (locally free sheaves) on 5-dimensional projective space, found by .
References
Algebraic geometry
Vector bundles |
https://en.wikipedia.org/wiki/Brun%20sieve | In the field of number theory, the Brun sieve (also called Brun's pure sieve) is a technique for estimating the size of "sifted sets" of positive integers which satisfy a set of conditions which are expressed by congruences. It was developed by Viggo Brun in 1915 and later generalized to the fundamental lemma of sieve theory by others.
Description
In terms of sieve theory the Brun sieve is of combinatorial type; that is, it derives from a careful use of the inclusion–exclusion principle.
Let be a finite set of positive integers.
Let be some set of prime numbers.
For each prime in , let denote the set of elements of that are divisible by .
This notation can be extended to other integers that are products of distinct primes in . In this case, define to be the intersection of the sets for the prime factors of .
Finally, define to be itself.
Let be an arbitrary positive real number.
The object of the sieve is to estimate:
where the notation denotes the cardinality of a set , which in this case is just its number of elements.
Suppose in addition that may be estimated by
where is some multiplicative function, and is some error function.
Let
Brun's pure sieve
This formulation is from Cojocaru & Murty, Theorem 6.1.2. With the notation as above, suppose that
for any squarefree composed of primes in ;
for all in ;
There exist constants such that, for any positive real number ,
Then
where is the cardinal of , is any positive integer and the invokes big O notation.
In particular, letting denote the maximum element in , if for a suitably small , then
Applications
Brun's theorem: the sum of the reciprocals of the twin primes converges;
Schnirelmann's theorem: every even number is a sum of at most primes (where can be taken to be 6);
There are infinitely many pairs of integers differing by 2, where each of the member of the pair is the product of at most 9 primes;
Every even number is the sum of two numbers each of which is the product of at most 9 primes.
The last two results were superseded by Chen's theorem, and the second by Goldbach's weak conjecture ().
References
.
Sieve theory |
https://en.wikipedia.org/wiki/Dynamic%20relaxation | Dynamic relaxation is a numerical method, which, among other things, can be used to do "form-finding" for cable and fabric structures. The aim is to find a geometry where all forces are in equilibrium. In the past this was done by direct modelling, using hanging chains and weights (see Gaudi), or by using soap films, which have the property of adjusting to find a "minimal surface".
The dynamic relaxation method is based on discretizing the continuum under consideration by lumping the mass at nodes and defining the relationship between nodes in terms of stiffness (see also the finite element method). The system oscillates about the equilibrium position under the influence of loads. An iterative process is followed by simulating a pseudo-dynamic process in time, with each iteration based on an update of the geometry, similar to Leapfrog integration and related to Velocity Verlet integration.
Main equations used
Considering Newton's second law of motion (force is mass multiplied by acceleration) in the direction at the th node at time :
Where:
is the residual force
is the nodal mass
is the nodal acceleration
Note that fictitious nodal masses may be chosen to speed up the process of form-finding.
The relationship between the speed , the geometry and the residuals can be obtained by performing a double numerical integration of the acceleration (here in central finite difference form), :
Where:
is the time interval between two updates.
By the principle of equilibrium of forces, the relationship between the residuals and the geometry can be obtained:
where:
is the applied load component
is the tension in link between nodes and
is the length of the link.
The sum must cover the forces in all the connections between the node and other nodes.
By repeating the use of the relationship between the residuals and the geometry, and the relationship between the geometry and the residual, the pseudo-dynamic process is simulated.
Iteration Steps
1. Set the initial kinetic energy and all nodal velocity components to zero:
2. Compute the geometry set and the applied load component:
3. Compute the residual:
4. Reset the residuals of constrained nodes to zero
5. Update velocity and coordinates:
6. Return to step 3 until the structure is in static equilibrium
Damping
It is possible to make dynamic relaxation more computationally efficient (reducing the number of iterations) by using damping.
There are two methods of damping:
Viscous damping, which assumes that connection between the nodes has a viscous force component.
Kinetic energy damping, where the coordinates at peak kinetic energy are calculated (the equilibrium position), then updates the geometry to this position and resets the velocity to zero.
The advantage of viscous damping is that it represents the reality of a cable with viscous properties. Moreover, it is easy to realize because the speed is already computed.
The kinetic energy damping is an artificial damping which is not a real |
https://en.wikipedia.org/wiki/X-ray%20transform | In mathematics, the X-ray transform (also called ray transform or John transform) is an integral transform introduced by Fritz John in 1938 that is one of the cornerstones of modern integral geometry. It is very closely related to the Radon transform, and coincides with it in two dimensions. In higher dimensions, the X-ray transform of a function is defined by integrating over lines rather than over hyperplanes as in the Radon transform. The X-ray transform derives its name from X-ray tomography (used in CT scans) because the X-ray transform of a function ƒ represents the attenuation data of a tomographic scan through an inhomogeneous medium whose density is represented by the function ƒ. Inversion of the X-ray transform is therefore of practical importance because it allows one to reconstruct an unknown density ƒ from its known attenuation data.
In detail, if ƒ is a compactly supported continuous function on the Euclidean space Rn, then the X-ray transform of ƒ is the function Xƒ defined on the set of all lines in Rn by
where x0 is an initial point on the line and θ is a unit vector in Rn giving the direction of the line L. The latter integral is not regarded in the oriented sense: it is the integral with respect to the 1-dimensional Lebesgue measure on the Euclidean line L.
The X-ray transform satisfies an ultrahyperbolic wave equation called John's equation.
The Gauss hypergeometric function can be written as an X-ray transform .
References
.
Integral geometry
Integral transforms
X-ray computed tomography |
https://en.wikipedia.org/wiki/Ramachandran%20Balasubramanian | Ramachandran Balasubramanian (born 15 March 1951) is an Indian mathematician and was Director of the Institute of Mathematical Sciences in Chennai, India. He is known for his work in number theory, which includes settling the final g(4) case of Waring's problem in 1986.
His works on moments of Riemann zeta function is highly appreciated and he was a plenary speaker from India at ICM in 2010. He was a visiting scholar at the Institute for Advanced Study in 1980-81.
Awards and honours
He has received the following awards:
The Shanti Swarup Bhatnagar Prize for Science and Technology in 1990.
The French government's Ordre National du Mérite for "furthering Indo-French cooperation in the field of mathematics" in 2003.
The Padma Shri, the fourth highest civilian award in India, in 2006.
Fellow of the American Mathematical Society, 2012.
The Lifetime Achievement Award, 2013 awarded by Manmohan Singh, the Prime Minister of India.
Fellow of the Indian National Science Academy (1988)
References
External links
R. Balasubramian's homepage
His CV
20th-century Indian mathematicians
Recipients of the Padma Shri in science & engineering
Living people
Fellows of the Indian National Science Academy
Tata Institute of Fundamental Research alumni
Institute for Advanced Study visiting scholars
Fellows of the American Mathematical Society
Fellows of the Indian Academy of Sciences
1951 births
Recipients of the Shanti Swarup Bhatnagar Award in Mathematical Science |
https://en.wikipedia.org/wiki/Jeffery%E2%80%93Williams%20Prize | The Jeffery–Williams Prize is a mathematics award presented annually by the Canadian Mathematical Society. The award is presented to individuals in recognition of outstanding contributions to mathematical research. The first award was presented in 1968. The prize was named in honor of the mathematicians Ralph Lent Jeffery and Lloyd Williams.
Recipients of the Jeffery–Williams Prize
Source: Canadian Mathematical Society
See also
List of mathematics awards
References
External links
Canadian Mathematical Society
Awards of the Canadian Mathematical Society
Awards established in 1968
1968 establishments in Canada |
https://en.wikipedia.org/wiki/Coxeter%E2%80%93James%20Prize | The Coxeter-James Prize is a mathematics award given by the Canadian Mathematical Society (CMS) to recognize outstanding contributions to mathematics by young mathematicians in Canada. First presented in 1978, the prize is named after two renowned Canadian mathematicians, Donald Coxeter and Ralph James.
The prize is awarded annually to a young Canadian mathematician who has made significant contributions to the field of mathematics. It is intended to recognize and encourage young mathematicians in Canada and to promote the development of mathematics in the country.
Recipients of the Coxeter-James Prize are selected by the CMS Research Committee and are typically honored at the Society's annual meeting.
The Coxeter-James Prize is one of several awards given by the Canadian Mathematical Society to recognize and encourage excellence in mathematics. Other awards given by the Society include the Jeffery–Williams Prize, the Krieger–Nelson Prize, and the Blair Spearman Doctoral Prize.
Recipients of the Coxeter–James Prize
The Canadian Mathematical Society has awarded the Coxeter–James prize to the following recipients:
See also
List of mathematics awards
References
External links
Canadian Mathematical Society
Awards of the Canadian Mathematical Society
Awards established in 1978
1978 establishments in Canada |
https://en.wikipedia.org/wiki/Milagros%20D.%20Ibe | Milagros Dimal Ibe (born 1931) is a teacher of mathematics. Dr. Ibe devised teacher-training programs and research studies that led to the development of policies in basic and higher education in the Philippines. According to the Science Education Institute of the Philippines, "she has left a legacy of teaching with compassion to the young generation of math and science teachers" and "her ability to simplify esoteric concepts into lessons easily understood by young minds significantly helped in demystifying mathematics".
Educational background
Milagros Dimal Ibe was born in Lubao, Pampanga in 1931, but moved to Manila to study. She graduated summa cum laude from the now defunct Quezon College in Manila, with a BA in English and BSc major in mathematics. She taught for a few years in her hometown before she transferred to teach at the University of the Philippines Rural High School at Los Baños, Laguna. Eventually, she moved to the University of the Philippines Diliman, where she finished her Master of Arts major in curriculum and instruction. Later on, she got her PhD from the University of Toronto in Canada. She almost became Dean of the College of Education in 1990, but instead she became Vice Chancellor of the University of the Philippines Diliman.
Awards and achievements
In 1993 Ibe was appointed Director of the University of the Philippines - Institute for Science and Mathematics Education Development (UP-ISMED). The Dolores Hernandez Lecture Series in science education was started by her during the start of her term, to be a monthly Friday afternoon event as part of the Institution's extension activities. The series continued through the years of her directorship and long after her term, though much less frequently. In December 1995, Dr. Ibe represented the Philippines in the Third International Mathematics and Science Study (TIMSS).
Retired life
Ibe retired from UP-ISMED in November 1996 on her sixty-fifth birthday, following the practice of those in government service, but she continued to work as consultant to various educational institutions and to the Professional Regulation Commission. Presently, Dr. Ibe, already in her mid-70s, is the Dean of Graduate School of Miriam College in Quezon City and concurrently professor emeritus in the College of Education of the University of the Philippines, where she is still active in promoting, among other things, mathematics education.
References
External links
Saidi.edu.ph
Sito.org
Cell07boardexaminees.multiply.com
Ca.supremecourt.gov
Diwa.ph
Living people
Kapampangan people
People from Pampanga
1931 births
Filipino educators
Mathematics educators
University of the Philippines Diliman alumni
University of Toronto alumni
Academic staff of the University of the Philippines |
https://en.wikipedia.org/wiki/Nassif%20Ghoussoub | Nassif A. Ghoussoub is a Canadian mathematician working in the fields of non-linear analysis and partial differential equations. He is a Professor of Mathematics and a Distinguished University Scholar at the University of British Columbia.
Early life and education
Ghoussoub was born to Lebanese parents in Western Africa (now Mali).
He completed his doctorat 3ème cycle (PhD) in 1975, and a Doctorat d'Etat in 1979 at the Pierre and Marie Curie University, where his advisors were Gustave Choquet and Antoine Brunel.
Career
Ghoussoub completed his post-doctoral fellowship at the Ohio State University during 1976–77. He then joined the University of British Columbia, where he currently holds a position of Professor of Mathematics and a Distinguished University Scholar. Ghoussoub is known for his work in functional analysis, non-linear analysis, and partial differential equations.
He was vice-president of the Canadian Mathematical Society from 1994 to 1996, the founding director of the Pacific Institute for the Mathematical Sciences (PIMS) for the period 1996–2003, the co-editor-in-chief of the Canadian Journal of Mathematics during 1993–2002, a co-founder of the MITACS Network of Centres of Excellence, and is the founder and current scientific director of the Banff International Research Station (BIRS). In 1994, Ghoussoub became a fellow of the Royal Society of Canada, and in 2012, a fellow of the American Mathematical Society.
Ghoussoub has been awarded multiple awards and distinctions, including the Coxeter-James prize in 1990, and the Jeffrey-Williams prize in 2007. He holds honorary doctorates from the Université Paris-Dauphine (France), and the University of Victoria (Canada). He was awarded the Queen Elizabeth II Diamond Jubilee Medal in 2012, and appointed to the Order of Canada in 2015, with the grade of officer for contributions to mathematics, research, and education.
In 2018, Ghoussoub was elected a faculty representative on the University of British Columbia's Board of Governors. He will serve until February 29, 2020. Ghoussoub has previously served two consecutive terms in this role from 2008 to 2014.
Ghoussoub's scholarly work has been cited over 5,900 times and has an h-index of 40.
Awards
Coxeter-James Prize, Canadian Mathematical Society (1990)
Killam Senior Research Fellowship, UBC (1992)
Fellow of the Royal Society of Canada (1994)
Distinguished University Scholar, UBC (2003)
Doctorat Honoris Causa, Paris Dauphine University
Jeffery–Williams Prize, Canadian mathematical Society (2007)
Faculty of Science Achievement Award for outstanding service and leadership, UBC (2007)
David Borwein Distinguished Career Award, Canadian Mathematical Society (2010)
Fellow of the American Mathematical Society (2012)
Queen Elizabeth II Diamond Jubilee Medal (2012)
Honorary Doctor of Science-University of Victoria (June 2015)
Officer of the Order of Canada (December 2015)
Inaugural fellow of the Canadian Mathematical Society |
https://en.wikipedia.org/wiki/Selberg%20sieve | In number theory, the Selberg sieve is a technique for estimating the size of "sifted sets" of positive integers which satisfy a set of conditions which are expressed by congruences. It was developed by Atle Selberg in the 1940s.
Description
In terms of sieve theory the Selberg sieve is of combinatorial type: that is, derives from a careful use of the inclusion–exclusion principle. Selberg replaced the values of the Möbius function which arise in this by a system of weights which are then optimised to fit the given problem. The result gives an upper bound for the size of the sifted set.
Let be a set of positive integers and let be a set of primes. Let denote the set of elements of divisible by when is a product of distinct primes from . Further let denote itself. Let be a positive real number and denote the product of the primes in which are . The object of the sieve is to estimate
We assume that |Ad| may be estimated by
where f is a multiplicative function and X = |A|. Let the function g be obtained from f by Möbius inversion, that is
where μ is the Möbius function.
Put
Then
where denotes the least common multiple of and . It is often useful to estimate by the bound
Applications
The Brun–Titchmarsh theorem on the number of primes in arithmetic progression;
The number of n ≤ x such that n is coprime to φ(n) is asymptotic to e−γ x / log log log (x) .
References
Sieve theory |
https://en.wikipedia.org/wiki/Free%20loop | In the mathematical field of topology, a free loop is a variant of the mathematical notion of a loop. Whereas a loop has a distinguished point on it, called a basepoint, a free loop lacks such a distinguished point. Formally, let be a topological space. Then a free loop in is an equivalence class of continuous functions from the circle to . Two loops are equivalent if they differ by a reparameterization of the circle. That is, if there exists a homeomorphism such that .
Thus, a free loop, as opposed to a based loop used in the definition of the fundamental group, is a map from the circle to the space without the basepoint-preserving restriction. Assuming the space is path-connected, free homotopy classes of free loops correspond to conjugacy classes in the fundamental group.
Recently, interest in the space of all free loops has grown with the advent of string topology, i.e. the study of new algebraic structures on the homology of the free loop space.
See also
Loop space
Loop (topology)
Quasigroup
Further reading
Brylinski, Jean-Luc: Loop spaces, characteristic classes and geometric quantization. Reprint of the 1993 edition. Modern Birkhäuser Classics. Birkhäuser Boston, Inc., Boston, MA, 2008.
Cohen and Voronov: Notes on String Topology
Knot theory
Topology |
https://en.wikipedia.org/wiki/Afghans%20in%20the%20United%20Kingdom | British Afghans are British citizens and non-citizen residents born in or with ancestors from, Afghanistan, part of worldwide Afghan diaspora. The Office for National Statistics (ONS) estimates that there were 79,000 people born in Afghanistan living in the UK in 2019.
History
Historical migration
The first Afghan immigrants to the British capital were students, businesspeople and Afghan government officials. It wasn't until years later that significant numbers came in the form of refugees. The first large wave of Afghan immigrants to the UK were political refugees fleeing the 1980s communist regime and numerous others came in the early 1990s escaping Mujahideen. The number skyrocketed later that decade due to the rise of the Taliban in Afghanistan.
Refugees of war and asylum policies
As stated earlier, one of the large flows of Afghans to the UK was caused by refugees fleeing Afghanistan after the Taliban came to power. The country has been in a state of political unrest ever since. Despite the flow of immigrants and refugees remaining fairly stable over the new millennium period, the number of Afghans coming to the UK since the mid-2000s has completely eclipsed the recorded number of Afghans in the 2001 census, as more and more are fleeing the threat of violence and even death in their homeland during the War in Afghanistan. In 2003, the British government announced that they would begin enforced repatriation of failed asylum-seekers in April. This marked a break from the previous policy, observed continuously since 1978, of not returning any Afghans to their country of origin whether or not they were deemed to be economic migrants. At the time, roughly 700 Afghans applied for asylum in the United Kingdom each month, making them one of the largest group of asylum-seekers along with Iraqis.
Between 1994 and 2006, around 36,000 Afghans claimed asylum in the UK. Many whose claims were refused have not returned to Afghanistan, although the International Organization for Migration has helped some voluntarily return. 5,540 Afghan nationals were granted British citizenship in 2008, down from 10,555 in 2007.
Following the completion of the withdrawal of United States troops from Afghanistan in August 2021, the UK government launched the Afghan Citizens Resettlement Scheme (ACRS) in January 2022, to provide resettlement in the UK for Afghans who had worked for or were linked to the British government's presence in the country. In early December 2022, it was revealed that no Afghan had yet been resettled under the ACRS.
Afghan asylum seekers in the UK are facing homelessness as they are evicted from Home Office hotels without alternative housing. The government's plan to relocate 8,000 Afghans by August has raised concerns due to a housing shortage and long waiting lists. The Local Government Association has expressed difficulties in securing accommodation, while the Home Office emphasizes that hotels are not meant for long-term stays. The Illega |
https://en.wikipedia.org/wiki/Analysis%20on%20fractals | Analysis on fractals or calculus on fractals is a generalization of calculus on smooth manifolds to calculus on fractals.
The theory describes dynamical phenomena which occur on objects modelled by fractals.
It studies questions such as "how does heat diffuse in a fractal?" and "How does a fractal vibrate?"
In the smooth case the operator that occurs most often in the equations modelling these questions is the Laplacian, so the starting point for the theory of analysis on fractals is to define a Laplacian on fractals. This turns out not to be a full differential operator in the usual sense but has many of the desired properties. There are a number of approaches to defining the Laplacian: probabilistic, analytical or measure theoretic.
See also
Time scale calculus for dynamic equations on a cantor set.
Differential geometry
Discrete differential geometry
Abstract differential geometry
References
External links
Analysis on Fractals, Robert S. Strichartz - Article in Notices of the AMS
University of Connecticut - Analysis on fractals Research projects
Calculus on fractal subsets of real line - I: formulation
Fractals |
https://en.wikipedia.org/wiki/Kosuke%20Suda | is a former Japanese football player.
Club statistics
References
External links
1980 births
Living people
Nippon Sport Science University alumni
Association football people from Ibaraki Prefecture
Japanese men's footballers
J2 League players
Mito HollyHock players
Shonan Bellmare players
Montedio Yamagata players
Men's association football defenders |
https://en.wikipedia.org/wiki/Kei%20Uemura | is a former Japanese football player.
Club statistics
References
External links
1981 births
Living people
Chuo University alumni
Association football people from Kanagawa Prefecture
Japanese men's footballers
J1 League players
J2 League players
J3 League players
Shonan Bellmare players
Júbilo Iwata players
Fukushima United FC players
Men's association football goalkeepers |
https://en.wikipedia.org/wiki/Toshitaka%20Tsurumi | is a Japanese football player. He plays for Maruyasu Okazaki.
Tsurumi previously played for Shonan Bellmare in the J2 League.
Club statistics
References
External links
1986 births
Living people
Association football people from Kanagawa Prefecture
Japanese men's footballers
J2 League players
Japan Football League players
Shonan Bellmare players
Gainare Tottori players
Nara Club players
FC Maruyasu Okazaki players
People from Fujisawa, Kanagawa
Men's association football midfielders |
https://en.wikipedia.org/wiki/Tatsuyuki%20Tomiyama | is a former Japanese football player.
Tomiyama previously played for Shonan Bellmare in the J2 League.
Club statistics
References
External links
1982 births
Living people
Ryutsu Keizai University alumni
Association football people from Chiba Prefecture
Japanese men's footballers
J2 League players
Japan Football League players
Shonan Bellmare players
Gainare Tottori players
Men's association football defenders |
https://en.wikipedia.org/wiki/Normal%20order%20of%20an%20arithmetic%20function | In number theory, a normal order of an arithmetic function is some simpler or better-understood function which "usually" takes the same or closely approximate values.
Let f be a function on the natural numbers. We say that g is a normal order of f if for every ε > 0, the inequalities
hold for almost all n: that is, if the proportion of n ≤ x for which this does not hold tends to 0 as x tends to infinity.
It is conventional to assume that the approximating function g is continuous and monotone.
Examples
The Hardy–Ramanujan theorem: the normal order of ω(n), the number of distinct prime factors of n, is log(log(n));
The normal order of Ω(n), the number of prime factors of n counted with multiplicity, is log(log(n));
The normal order of log(d(n)), where d(n) is the number of divisors of n, is log(2) log(log(n)).
See also
Average order of an arithmetic function
Divisor function
Extremal orders of an arithmetic function
Turán–Kubilius inequality
References
. p. 473
External links
Arithmetic functions |
https://en.wikipedia.org/wiki/Tur%C3%A1n%20sieve | In number theory, the Turán sieve is a technique for estimating the size of "sifted sets" of positive integers which satisfy a set of conditions which are expressed by congruences. It was developed by Pál Turán in 1934.
Description
In terms of sieve theory the Turán sieve is of combinatorial type: deriving from a rudimentary form of the inclusion–exclusion principle. The result gives an upper bound for the size of the sifted set.
Let A be a set of positive integers ≤ x and let P be a set of primes. For each p in P, let Ap denote the set of elements of A divisible by p and extend this to let Ad be the intersection of the Ap for p dividing d, when d is a product of distinct primes from P. Further let A1 denote A itself. Let z be a positive real number and P(z) denote the product of the primes in P which are ≤ z. The object of the sieve is to estimate
We assume that |Ad| may be estimated, when d is a prime p by
and when d is a product of two distinct primes d = p q by
where X = |A| and f is a function with the property that 0 ≤ f(d) ≤ 1. Put
Then
Applications
The Hardy–Ramanujan theorem that the normal order of ω(n), the number of distinct prime factors of a number n, is log(log(n));
Almost all integer polynomials (taken in order of height) are irreducible.
References
Sieve theory |
https://en.wikipedia.org/wiki/Complex%20analytic%20variety | In mathematics, and in particular differential geometry and complex geometry, a complex analytic variety or complex analytic space is a generalization of a complex manifold which allows the presence of singularities. Complex analytic varieties are locally ringed spaces which are locally isomorphic to local model spaces, where a local model space is an open subset of the vanishing locus of a finite set of holomorphic functions.
Definition
Denote the constant sheaf on a topological space with value by . A -space is a locally ringed space , whose structure sheaf is an algebra over .
Choose an open subset of some complex affine space , and fix finitely many holomorphic functions in . Let be the common vanishing locus of these holomorphic functions, that is, . Define a sheaf of rings on by letting be the restriction to of , where is the sheaf of holomorphic functions on . Then the locally ringed -space is a local model space.
A complex analytic variety is a locally ringed -space which is locally isomorphic to a local model space.
Morphisms of complex analytic varieties are defined to be morphisms of the underlying locally ringed spaces, they are also called holomorphic maps. A structure sheaf may have nilpotent element,
and also, when the complex analytic space whose structure sheaf is reduced, then the complex analytic space is reduced, that is, the complex analytic space may not be reduced.
An associated complex analytic space (variety) is such that;
Let X be schemes finite type over , and cover X with open affine subset () (Spectrum of a ring). Then each is an algebra of finite type over , and . Where are polynomial in , which can be regarded as a holomorphic function on . Therefore, their common zero of the set is the complex analytic subspace . Here, scheme X obtained by glueing the data of the set , and then the same data can be used to glueing the complex analytic space into an complex analytic space , so we call a associated complex analytic space with X. The complex analytic space X is reduced if and only if the associated complex analytic space reduced.
See also
Algebraic variety - Roughly speaking, an (complex) analytic variety is a zero locus of a set of an (complex) analytic function, while an algebraic variety is a zero locus of a set of a polynomial function and allowing singular point.
Analytic space
Complex algebraic variety
GAGA
Rigid analytic space
Note
Annotation
References
(no.10-13)
Future reading
External links
Kiran Kedlaya. 18.726 Algebraic Geometry (LEC # 30 - 33 GAGA)Spring 2009. Massachusetts Institute of Technology: MIT OpenCourseWare Creative Commons BY-NC-SA.
Tasty Bits of Several Complex Variables (p. 137) open source book by Jiří Lebl BY-NC-SA.
Algebraic geometry
Several complex variables
Complex geometry |
https://en.wikipedia.org/wiki/Semialgebraic%20space | In mathematics, especially in real algebraic geometry, a semialgebraic space is a space which is locally isomorphic to a semialgebraic set.
Definition
Let U be an open subset of Rn for some n. A semialgebraic function on U is defined to be a continuous real-valued function on U whose restriction to any semialgebraic set contained in U has a graph which is a semialgebraic subset of the product space Rn×R. This endows Rn with a sheaf of semialgebraic functions.
(For example, any polynomial mapping between semialgebraic sets is a semialgebraic function, as is the maximum of two semialgebraic functions.)
A semialgebraic space is a locally ringed space which is locally isomorphic to Rn with its sheaf of semialgebraic functions.
See also
Semialgebraic set
Real algebraic geometry
Real closed ring
Real algebraic geometry |
https://en.wikipedia.org/wiki/1921%20Polish%20census | The Polish census of 1921 or First General Census in Poland () was the first census in the Second Polish Republic, performed on September 30, 1921 by the Main Bureau of Statistics (Główny Urząd Statystyczny). It was followed by the Polish census of 1931.
Content
Due to war, not all of interwar Poland was enumerated. Upper Silesia was formally assigned to Poland by the League of Nations after the census was conducted elsewhere. Meanwhile, the conditions in eastern Galicia were still unstable and chaotic, and the census data had to be adjusted after the fact, wrote Joseph Marcus, thus leading to more questions than answers. The army and personnel under military jurisdiction were not included in the results. Also, specific areas of considerable size lacked complete returns due to absence of war refugees.
Entire categories considered essential today were absent from the questionnaires, subject to historic interpretation at any given time. For example, the Ukrainians were lumped with the Rusyns (as Ruthenes) with the only distinguishing factor possible being religion. Within a single total number of Ruthenes (narodowość rusińska), separate categories existed only for Greek Catholics (68.4 percent or 2,667,840 of them) and Orthodox Christians (31 percent or 1,207,739 of the total),[page 80] but did not address language in the same way as the next Polish census of 1931. Neither the Ukrainians, Carpatho-Rusyns (or Rusnaks), nor Polesians were defined by their name. The categories listed in the census included verbatim: Narodowość: polska (polonais), rusińska (ruthènes), żydowska (juifs), białoruska (biėlorusses), niemiecka (allemands), litewska (lithuaniens), rosyjska (russes), tutejsza (indigène), czeska (tchèques), inna (autre), niewiadoma (inconnue).
Some scholars claim that minorities had been undercounted, with some claiming as much as 40% of Poland's population was a minority, 18 percent Ukrainian, 10 percent Jewish, 6 percent Byelorussian, and 5 percent German.
Results
Nationality
Religion
Source:
References
External links
Partial results
Partial results when searching for the following keyword: Spis powszechny - Polska 1921 r
Nationalities (page 56, polish-french version) at Stat.gov.pl.
1921
1921 in Poland
Poland |
https://en.wikipedia.org/wiki/Euler%27s%20theorem%20%28differential%20geometry%29 | In the mathematical field of differential geometry, Euler's theorem is a result on the curvature of curves on a surface. The theorem establishes the existence of principal curvatures and associated principal directions which give the directions in which the surface curves the most and the least. The theorem is named for Leonhard Euler who proved the theorem in .
More precisely, let M be a surface in three-dimensional Euclidean space, and p a point on M. A normal plane through p is a plane passing through the point p containing the normal vector to M. Through each (unit) tangent vector to M at p, there passes a normal plane PX which cuts out a curve in M. That curve has a certain curvature κX when regarded as a curve inside PX. Provided not all κX are equal, there is some unit vector X1 for which k1 = κX1 is as large as possible, and another unit vector X2 for which k2 = κX2 is as small as possible. Euler's theorem asserts that X1 and X2 are perpendicular and that, moreover, if X is any vector making an angle θ with X1, then
The quantities k1 and k2 are called the principal curvatures, and X1 and X2 are the corresponding principal directions. Equation () is sometimes called Euler's equation .
See also
Differential geometry of surfaces
Dupin indicatrix
References
Full 1909 text (now out of copyright)
.
Differential geometry of surfaces
Theorems in differential geometry
Leonhard Euler |
https://en.wikipedia.org/wiki/Schild%27s%20ladder | In the theory of general relativity, and differential geometry more generally, Schild's ladder is a first-order method for approximating parallel transport of a vector along a curve using only affinely parametrized geodesics. The method is named for Alfred Schild, who introduced the method during lectures at Princeton University.
Construction
The idea is to identify a tangent vector x at a point with a geodesic segment of unit length , and to construct an approximate parallelogram with approximately parallel sides and as an approximation of the Levi-Civita parallelogramoid; the new segment thus corresponds to an approximately parallel translated tangent vector at
Formally, consider a curve γ through a point A0 in a Riemannian manifold M, and let x be a tangent vector at A0. Then x can be identified with a geodesic segment A0X0 via the exponential map. This geodesic σ satisfies
The steps of the Schild's ladder construction are:
Let X0 = σ(1), so the geodesic segment has unit length.
Now let A1 be a point on γ close to A0, and construct the geodesic X0A1.
Let P1 be the midpoint of X0A1 in the sense that the segments X0P1 and P1A1 take an equal affine parameter to traverse.
Construct the geodesic A0P1, and extend it to a point X1 so that the parameter length of A0X1 is double that of A0P1.
Finally construct the geodesic A1X1. The tangent to this geodesic x1 is then the parallel transport of X0 to A1, at least to first order.
Approximation
This is a discrete approximation of the continuous process of parallel transport. If the ambient space is flat, this is exactly parallel transport, and the steps define parallelograms, which agree with the Levi-Civita parallelogramoid.
In a curved space, the error is given by holonomy around the triangle which is equal to the integral of the curvature over the interior of the triangle, by the Ambrose-Singer theorem; this is a form of Green's theorem (integral around a curve related to integral over interior), and in the case of Levi-Civita connections on surfaces, of Gauss–Bonnet theorem.
Notes
Schild's ladder requires not only geodesics but also relative distance along geodesics. Relative distance may be provided by affine parametrization of geodesics, from which the required midpoints may be determined.
The parallel transport which is constructed by Schild's ladder is necessarily torsion-free.
A Riemannian metric is not required to generate the geodesics. But if the geodesics are generated from a Riemannian metric, the parallel transport which is constructed in the limit by Schild's ladder is the same as the Levi-Civita connection because this connection is defined to be torsion-free.
References
.
Connection (mathematics)
First order methods |
https://en.wikipedia.org/wiki/Maharam%27s%20theorem | In mathematics, Maharam's theorem is a deep result about the decomposability of measure spaces, which plays an important role in the theory of Banach spaces. In brief, it states that every complete measure space is decomposable into "non-atomic parts" (copies of products of the unit interval [0,1] on the reals), and "purely atomic parts", using the counting measure on some discrete space. The theorem is due to Dorothy Maharam.
It was extended to localizable measure spaces by Irving Segal.
The result is important to classical Banach space theory, in that, when considering the Banach space given as an Lp space of measurable functions over a general measurable space, it is sufficient to understand it in terms of its decomposition into non-atomic and atomic parts.
Maharam's theorem can also be translated into the language of abelian von Neumann algebras. Every abelian von Neumann algebra is isomorphic to a product of σ-finite abelian von Neumann algebras, and every σ-finite abelian von Neumann algebra is isomorphic to a spatial tensor product of discrete abelian von Neumann algebras; that is, algebras of bounded functions on a discrete set.
A similar theorem was given by Kazimierz Kuratowski for Polish spaces, stating that they are isomorphic, as Borel spaces, to either the reals, the integers, or a finite set.
References
Banach spaces
Theorems in measure theory |
https://en.wikipedia.org/wiki/Average%20order%20of%20an%20arithmetic%20function | In number theory, an average order of an arithmetic function is some simpler or better-understood function which takes the same values "on average".
Let be an arithmetic function. We say that an average order of is if
as tends to infinity.
It is conventional to choose an approximating function that is continuous and monotone. But even so an average order is of course not unique.
In cases where the limit
exists, it is said that has a mean value (average value) .
Examples
An average order of , the number of divisors of , is ;
An average order of , the sum of divisors of , is ;
An average order of , Euler's totient function of , is ;
An average order of , the number of ways of expressing as a sum of two squares, is ;
The average order of representations of a natural number as a sum of three squares is ;
The average number of decompositions of a natural number into a sum of one or more consecutive prime numbers is ;
An average order of , the number of distinct prime factors of , is ;
An average order of , the number of prime factors of , is ;
The prime number theorem is equivalent to the statement that the von Mangoldt function has average order 1;
An average value of , the Möbius function, is zero; this is again equivalent to the prime number theorem.
Calculating mean values using Dirichlet series
In case is of the form
for some arithmetic function , one has,
Generalized identities of the previous form are found here. This identity often provides a practical way to calculate the mean value in terms of the Riemann zeta function. This is illustrated in the following example.
The density of the k-th power free integers in
For an integer the set of k-th-power-free integers is
We calculate the natural density of these numbers in , that is, the average value of , denoted by , in terms of the zeta function.
The function is multiplicative, and since it is bounded by 1, its Dirichlet series converges absolutely in the half-plane , and there has Euler product
By the Möbius inversion formula, we get
where stands for the Möbius function. Equivalently,
where
and hence,
By comparing the coefficients, we get
Using , we get
We conclude that,
where for this we used the relation
which follows from the Möbius inversion formula.
In particular, the density of the square-free integers is .
Visibility of lattice points
We say that two lattice points are visible from one another if there is no lattice point on the open line segment joining them.
Now, if , then writing a = da2, b = db2 one observes that the point (a2, b2) is on the line segment which joins (0,0) to (a, b) and hence (a, b) is not visible from the origin. Thus (a, b) is visible from the origin implies that (a, b) = 1. Conversely, it is also easy to see that gcd(a, b) = 1 implies that there is no other integer lattice point in the segment joining (0,0) to (a,b).
Thus, (a, b) is visible from (0,0) if and only if gcd(a, b) = 1.
Notice that is the probability of a |
https://en.wikipedia.org/wiki/Bertrand%E2%80%93Diguet%E2%80%93Puiseux%20theorem | In the mathematical study of the differential geometry of surfaces, the Bertrand–Diguet–Puiseux theorem expresses the Gaussian curvature of a surface in terms of the circumference of a geodesic circle, or the area of a geodesic disc. The theorem is named for Joseph Bertrand, Victor Puiseux, and Charles François Diguet.
Let p be a point on a smooth surface M. The geodesic circle of radius r centered at p is the set of all points whose geodesic distance from p is equal to r. Let C(r) denote the circumference of this circle, and A(r) denote the area of the disc contained within the circle. The Bertrand–Diguet–Puiseux theorem asserts that
The theorem is closely related to the Gauss–Bonnet theorem.
References
Differential geometry of surfaces
Theorems in differential geometry |
https://en.wikipedia.org/wiki/Shape%20theory%20%28mathematics%29 | Shape theory is a branch of topology that provides a more global view of the topological spaces than homotopy theory. The two coincide on compacta dominated homotopically by finite polyhedra. Shape theory associates with the Čech homology theory while homotopy theory associates with the singular homology theory.
Background
Shape theory was reinvented, further developed and promoted by the Polish mathematician Karol Borsuk in 1968. Actually, the name shape theory was coined by Borsuk.
Warsaw circle
Borsuk lived and worked in Warsaw, hence the name of one of the fundamental examples of the area, the Warsaw circle. It is a compact subset of the plane produced by "closing up" a topologist's sine curve (also called a Warsaw sine curve) with an arc. The homotopy groups of the Warsaw circle are all trivial, just like those of a point, and so any map between the Warsaw circle and a point induces a weak homotopy equivalence. However these two spaces are not homotopy equivalent. So by the Whitehead theorem, the Warsaw circle does not have the homotopy type of a CW complex.
Development
Borsuk's shape theory was generalized onto arbitrary (non-metric) compact spaces, and even onto general categories, by Włodzimierz Holsztyński in year 1968/1969, and published in Fund. Math. 70 , 157–168, y.1971 (see Jean-Marc Cordier, Tim Porter, (1989) below). This was done in a continuous style, characteristic for the Čech homology rendered by Samuel Eilenberg and Norman Steenrod in their monograph Foundations of Algebraic Topology. Due to the circumstance, Holsztyński's paper was hardly noticed, and instead a great popularity in the field was gained by a later paper by Sibe Mardešić and Jack Segal, Fund. Math. 72, 61–68, y.1971. Further developments are reflected by the references below, and by their contents.
For some purposes, like dynamical systems, more sophisticated invariants were developed under the name strong shape. Generalizations to noncommutative geometry, e.g. the shape theory for operator algebras have been found.
See also
List of topologies
References
Jean-Marc Cordier and Tim Porter, (1989), Shape Theory: Categorical Methods of Approximation, Mathematics and its Applications, Ellis Horwood. Reprinted Dover (2008)
Aristide Deleanu and Peter John Hilton, On the categorical shape of a functor, Fundamenta Mathematicae 97 (1977) 157 - 176.
Aristide Deleanu and Peter John Hilton, Borsuk's shape and Grothendieck categories of pro-objects, Mathematical Proceedings of the Cambridge Philosophical Society 79 (1976) 473–482.
Sibe Mardešić and Jack Segal, Shapes of compacta and ANR-systems, Fundamenta Mathematicae 72 (1971) 41–59
Karol Borsuk, Concerning homotopy properties of compacta, Fundamenta Mathematicae 62 (1968) 223-254
Karol Borsuk, Theory of Shape, Monografie Matematyczne Tom 59, Warszawa 1975.
D. A. Edwards and H. M. Hastings, Čech Theory: its Past, Present, and Future, Rocky Mountain Journal of Mathematics, Volume 10, Number 3, Summ |
https://en.wikipedia.org/wiki/Levi-Civita%20parallelogramoid | In the mathematical field of differential geometry, the Levi-Civita parallelogramoid is a quadrilateral in a curved space whose construction generalizes that of a parallelogram in the Euclidean plane. It is named for its discoverer, Tullio Levi-Civita. Like a parallelogram, two opposite sides AA′ and BB′ of a parallelogramoid are parallel (via parallel transport side AB) and the same length as each other, but the fourth side A′B′ will not in general be parallel to or the same length as the side AB, although it will be straight (a geodesic).
Construction
A parallelogram in Euclidean geometry can be constructed as follows:
Start with a straight line segment AB and another straight line segment AA′.
Slide the segment AA′ along AB to the endpoint B, keeping the angle with AB constant, and remaining in the same plane as the points A, A′, and B.
Label the endpoint of the resulting segment B′ so that the segment is BB′.
Draw a straight line A′B′.
In a curved space, such as a Riemannian manifold or more generally any manifold equipped with an affine connection, the notion of "straight line" generalizes to that of a geodesic. In a suitable neighborhood (such as a ball in a normal coordinate system), any two points can be joined by a geodesic. The idea of sliding the one straight line along the other gives way to the more general notion of parallel transport. Thus, assuming either that the manifold is complete, or that the construction is taking place in a suitable neighborhood, the steps to producing a Levi-Civita parallelogram are:
Start with a geodesic AB and another geodesic AA′. These geodesics are assumed to be parameterized by their arclength in the case of a Riemannian manifold, or to carry a choice of affine parameter in the general case of an affine connection.
"Slide" (parallel transport) the tangent vector of AA′ from A to B.
The resulting tangent vector at B generates a geodesic via the exponential map. Label the endpoint of this geodesic by B′, and the geodesic itself BB′.
Connect the points A′ and B′ by the geodesic A′B′.
Quantifying the difference from a parallelogram
The length of this last geodesic constructed connecting the remaining points A′B′ may in general be different than the length of the base AB. This difference is measured by the Riemann curvature tensor. To state the relationship precisely, let AA′ be the exponential of a tangent vector X at A, and AB the exponential of a tangent vector Y at A. Then
where terms of higher order in the length of the sides of the parallelogram have been suppressed.
Discrete approximation
Parallel transport can be discretely approximated by Schild's ladder, which approximates Levi-Civita parallelogramoids by approximate parallelograms.
Notes
References
Curvature (mathematics)
Differential geometry
Types of quadrilaterals |
https://en.wikipedia.org/wiki/Discover%20Science%20%26%20Engineering | Discover Science & Engineering (DSE) is an Irish Government initiative that aims to increase interest in science, technology, engineering and mathematics (STEM) among students, teachers and members of the public in Ireland.
DSE’s mission is to contribute to Ireland's continued growth and development as a society that has an active and informed interest and involvement in science, engineering and technology.
Overall DSE objectives are to increase the numbers of students studying the physical sciences, promote a positive attitude to careers in science, technology, engineering and mathematics and to foster a greater understanding of science and its value to Irish society.
In September 2009, Discover Science & Engineering launched a redeveloped corporate website built on the open source CMS, WordPress.
DSE runs numerous initiatives, including:
My Science Career
Project Blogger
Science.ie
Science Week Ireland
Greenwave
Discover Primary Science
Discover sensors
See also
Sentinus, equivalent in Northern Ireland
References
External links
Discover-Science.ie – official website of Discover Science & Engineering (DSE)
My Science Career - resources for finding out more about a career in science, technology, engineering or mathematics (STEM)
Follow Science.ie on Twitter
MyScience.ie - DSE blog about Irish science
I Love Science Bebo page
DSE YouTube channel - videos from the Science Week Lecture Series and the BT Young Scientist
Science education in Ireland
Science and technology in the Republic of Ireland
Learning programs in Europe |
https://en.wikipedia.org/wiki/Nicholas%20Manton | Nicholas Stephen Manton (born 2 October 1952 in the City of Westminster) is a British mathematical physicist. He is a Professor of Mathematical Physics at the Department of Applied Mathematics and Theoretical Physics of the University of Cambridge and a fellow of St John's College.
Education
Manton earned his PhD from the University of Cambridge in 1978, under the supervision of Peter Goddard. His thesis was entitled Magnetic Monopoles and Other Extended Objects in Field Theory.
Research
Manton has made contributions to the theory of soliton-like particles in two and three dimensions. He calculated the forces between static and moving monopoles and vortices in gauge theories, leading to the geometrical idea of moduli space dynamics. This has been applied to the classical, quantum and statistical mechanics of solitons. He has also developed the theory of skyrmions as a soliton model of atomic nuclei.
He discovered the unstable sphaleron solution in the electroweak sector of the Standard Model of particle physics. The Higgs field is topologically twisted within a sphaleron. The sphaleron defines an energy scale for baryon and lepton number violation in the early universe — an energy scale within the range of the Large Hadron Collider. His other work includes the construction of a 10-dimensional theory containing supergravity and Yang–Mills theory, which is a low-energy limit of superstring theory.
Awards and honours
Manton was elected a Fellow of the Royal Society (FRS) in 1996.
Publications
Topological Solitons (Cambridge Monographs on Mathematical Physics), by N. Manton and P. Sutcliffe (Cambridge University Press, 2004) .
The Physical World: An Inspirational Tour of Fundamental Physics, by M. Manton and N. Mee (Oxford University Press, 2017) .
Skyrmions - A Theory Of Nuclei, by N. Manton (World Scientific, 2022) .
References
1952 births
Living people
20th-century British mathematicians
21st-century British mathematicians
Fellows of the Royal Society
Fellows of St John's College, Cambridge |
https://en.wikipedia.org/wiki/Inherent%20zero | In statistics, an inherent zero is a reference point used to describe data sets which are indicative of magnitude of an absolute or relative nature. Inherent zeros are used in the "ratio level" of "levels of measurement" and imply "none".
References
Statistical data types |
https://en.wikipedia.org/wiki/Ariel%20Ag%C3%BCero | Antonio Ariel Agüero (born 18 August 1980) is a football centre back.
External links
Ariel Agüero – Argentine Primera statistics at Fútbol XXI
1980 births
Living people
Sportspeople from San Juan Province, Argentina
Argentine men's footballers
Men's association football defenders
Argentine Primera División players
Club de Gimnasia y Esgrima La Plata footballers
San Martín de San Juan footballers
Juventud Alianza players
Quilmes Atlético Club footballers
Independiente Rivadavia footballers
Sportivo Desamparados footballers |
https://en.wikipedia.org/wiki/Esteban%20Gonz%C3%A1lez%20%28footballer%2C%20born%201978%29 | Esteban Nicolás González (born 16 September 1978 in Córdoba, Argentina) is a former Argentine footballer and current coach.
References
External links
Argentine Primera statistics
1978 births
Living people
Footballers from Córdoba, Argentina
Argentine men's footballers
Men's association football midfielders
Club Atlético Belgrano footballers
Club de Gimnasia y Esgrima La Plata footballers
SS Lazio players
Club Atlético Colón footballers
UD Las Palmas players
Club Atlético Tigre footballers
Argentine expatriate men's footballers
Expatriate men's footballers in Italy
Expatriate men's footballers in Spain
Serie A players
Argentine Primera División players
Argentine expatriate sportspeople in Italy
Argentine expatriate sportspeople in Spain
Club Atlético Belgrano managers
Argentine football managers |
https://en.wikipedia.org/wiki/El%C5%BCbieta%20Pleszczy%C5%84ska | Elżbieta Pleszczyńska (born 20 March 1933) is a Polish full professor of statistics, activist of disability rights movement.
Biography
She gained an M.Sc. in mathematics at University of Warsaw, Faculty of Mathematics, Physics and Chemistry in 1956. She held position at Institute of Mathematics PAS until 1972. She received her Ph.D. in 1965 in the area of discriminant analysis ("Power of Test, and Separability of Hypothesis in Statistical Design of Experiments"). Her habilitation thesis, titled "Trend Estimation Problems in Time Series Analysis", was accepted in 1973.
In 1967/8 she was visiting researcher in University of Wales (Great Britain), and in 1971/2 in University of Montreal. In 1973 she moved to the Institute of Computer Science, PAS. In 1977, 1979 and 1989 she was awarded by the Polish Academy of Science. In 1981 she visited Italy invited by CNR. In the 1990s she started (together with her team) so called grade data analysis, a science of applying copula and rank methods to problems of correspondence and cluster analysis together with outlier detection. (The adjective grade here honors statisticians of the first half of the 20th century, who called cumulative distribution functions in this way.) In 1993 the President of the Republic of Poland awarded Elżbieta Pleszczyńska with the Full Professor title in the area of mathematics. In 2000 she was an invited consultant of the Cambridge University.
In the Institute of Computer Science PAS, she had been leader of the Statistical Data Analysis division for many years. According to the Polish law, professors in PAS must retire at the age of 70. Retirement in 2003, although a bit confusing, didn't stop her scientific and social activity.
Scientific views
Prof. Pleszczyńska is known for her criticism of the classic statistical approach. Classic parametric methods, like Pearson correlation coefficient, or least squares method produce comparable results only for comparable distribution types (in practice multivariate normal distribution is being assumed). Parametric statistical tests are derived from distribution assumptions. Classic methods fail if the input data contain strong outliers, and interpretation of their results should be different for different distribution types. In practice, the underlying assumptions are often not checked, moreover they are always violated – there is no normal distribution in the real world, because every real variable is limited (for example people cannot be –170 cm or +2 km tall), and the normal distribution implies positive probability density for every real number. In most cases the real distribution is skewed or discrete, which does not prevent people from using normal distribution methods. The extent of this violation can be measured, but its maximum accepted level is just a convention, not mathematics. The parametric methods always work out of their conditions of use. However, their results are often considered valid, which leads to "scientific" valid |
https://en.wikipedia.org/wiki/1932%E2%80%9333%20Allsvenskan | Statistics of Allsvenskan in season 1932/1933.
Overview
The league was contested by 12 teams, with Hälsingborgs IF winning the championship.
League table
Results
Footnotes
References
Allsvenskan seasons
1932–33 in Swedish association football leagues
Sweden |
https://en.wikipedia.org/wiki/1933%E2%80%9334%20Allsvenskan | Statistics of Allsvenskan in season 1933/1934.
Overview
The league was contested by 12 teams, with Hälsingborgs IF winning the championship.
Malmö FF was disqualified after 13 rounds. The reason for this was that rivals IFK Malmö had learned that Malmö FF had given their players watches for Christmas, which was a violation of the amateur rules of the time. As a result, all nine of Malmö FF's matches during the spring were cancelled. As of 2023, this is the lowest points total a team has recorded in the Allsvenskan.
League table
Results
Footnotes
References
Allsvenskan seasons
1933–34 in Swedish association football leagues
Sweden |
https://en.wikipedia.org/wiki/1934%E2%80%9335%20Allsvenskan | Statistics of Allsvenskan in season 1934/1935.
Overview
The league was contested by 12 teams, with IFK Göteborg winning the championship.
League table
Results
Footnotes
References
Allsvenskan seasons
1934–35 in Swedish association football leagues
Sweden |
https://en.wikipedia.org/wiki/1935%E2%80%9336%20Allsvenskan | Statistics of Allsvenskan in season 1935/1936.
Overview
The league was contested by 12 teams, with IF Elfsborg winning the championship.
League table
Results
Footnotes
References
Allsvenskan seasons
1935–36 in Swedish association football leagues
Sweden |
https://en.wikipedia.org/wiki/1936%E2%80%9337%20Allsvenskan | Statistics of Allsvenskan in season 1936/1937.
Overview
The league was contested by 12 teams, with AIK winning the championship.
League table
Results
Footnotes
References
Allsvenskan seasons
1936–37 in Swedish association football leagues
Sweden |
https://en.wikipedia.org/wiki/1937%E2%80%9338%20Allsvenskan | Statistics of Allsvenskan in season 1937/1938.
Overview
The league was contested by 12 teams, with IK Sleipner winning the championship. Following Sleipner in the table were three clubs all with the same points, thus leaving goal ratio as the tie breaker (as was the case until the 1940–41 season).
League table
Results
Footnotes
References
Allsvenskan seasons
1937–38 in Swedish association football leagues
Sweden |
https://en.wikipedia.org/wiki/1938%E2%80%9339%20Allsvenskan | Statistics of Allsvenskan in season 1938/1939.
Overview
The league was contested by 12 teams, with IF Elfsborg winning the championship.
League table
Results
Footnotes
References
Allsvenskan seasons
1938–39 in Swedish association football leagues
Sweden |
https://en.wikipedia.org/wiki/1939%E2%80%9340%20Allsvenskan | Statistics of Allsvenskan in season 1939/1940.
Overview
The league was contested by 12 teams, with IF Elfsborg winning the championship.
League table
Results
Footnotes
References
Allsvenskan seasons
1939–40 in Swedish association football leagues
Sweden |
https://en.wikipedia.org/wiki/1940%E2%80%9341%20Allsvenskan | Statistics of Allsvenskan in season 1940/1941.
Overview
The league was contested by 12 teams, with Hälsingborgs IF winning the championship.
League table
Results
Footnotes
References
Allsvenskan seasons
1940–41 in Swedish association football leagues
Sweden |
https://en.wikipedia.org/wiki/1941%E2%80%9342%20Allsvenskan | Statistics of Allsvenskan in season 1941/1942.
Overview
The league was contested by 12 teams, with IFK Göteborg winning the championship.
League table
Results
Footnotes
References
Allsvenskan seasons
1941–42 in Swedish association football leagues
Sweden |
https://en.wikipedia.org/wiki/1942%E2%80%9343%20Allsvenskan | Statistics of Allsvenskan in season 1942/1943.
Overview
The league was contested by 12 teams, with IFK Norrköping winning the championship.
League table
Results
Footnotes
References
Allsvenskan seasons
1942–43 in Swedish association football leagues
Sweden |
https://en.wikipedia.org/wiki/1943%E2%80%9344%20Allsvenskan | Statistics of Allsvenskan in season 1943/1944.
Overview
The league was contested by 12 teams, with Malmö FF winning the championship.
League table
Results
References
Allsvenskan seasons
1943–44 in Swedish association football leagues
Sweden |
https://en.wikipedia.org/wiki/1944%E2%80%9345%20Allsvenskan | Statistics of Allsvenskan in season 1944/1945.
Overview
The league was contested by 12 teams, with IFK Norrköping winning the championship.
League table
Results
Footnotes
References
Allsvenskan seasons
1944–45 in Swedish association football leagues
Sweden |
https://en.wikipedia.org/wiki/1945%E2%80%9346%20Allsvenskan | Statistics of Allsvenskan in season 1945/1946.
Overview
The league was contested by 12 teams, with IFK Norrköping winning the championship.
League table
Results
Footnotes
References
Allsvenskan seasons
1945–46 in Swedish association football leagues
Sweden |
https://en.wikipedia.org/wiki/1946%E2%80%9347%20Allsvenskan | Statistics of Allsvenskan in season 1946/1947.
Overview
The league was contested by 12 teams, with IFK Norrköping winning the championship.
League table
Results
Footnotes
References
Allsvenskan seasons
1946–47 in Swedish association football leagues
Sweden |
https://en.wikipedia.org/wiki/1947%E2%80%9348%20Allsvenskan | Statistics of Allsvenskan in season 1947/1948.
Overview
The league was contested by 12 teams, with IFK Norrköping winning the championship.
League table
Results
Footnotes
References
Allsvenskan seasons
1947–48 in Swedish association football leagues
Sweden |
https://en.wikipedia.org/wiki/1948%E2%80%9349%20Allsvenskan | Statistics of Allsvenskan in season 1948/1949.
Overview
The league was contested by 12 teams, with Malmö FF winning the championship.
League table
Results
Footnotes
References
Allsvenskan seasons
1948–49 in Swedish association football leagues
Sweden |
https://en.wikipedia.org/wiki/1949%E2%80%9350%20Allsvenskan | Statistics of Allsvenskan in season 1949/1950.
Overview
The league was contested by 12 teams, with Malmö FF winning the championship unbeaten.
League table
Results
Footnotes
References
Allsvenskan seasons
1949–50 in Swedish association football leagues
Sweden |
https://en.wikipedia.org/wiki/1950%E2%80%9351%20Allsvenskan | Statistics of Allsvenskan in season 1950/1951.
Overview
The league was contested by 12 teams, with Malmö FF winning the championship.
League table
Results
Footnotes
References
Allsvenskan seasons
1950–51 in Swedish association football leagues
Sweden |
https://en.wikipedia.org/wiki/1951%E2%80%9352%20Allsvenskan | Statistics of Allsvenskan in season 1951/1952.
Overview
The league was contested by 12 teams, with IFK Norrköping winning the championship.
League table
Results
Footnotes
References
Allsvenskan seasons
1951–52 in Swedish association football leagues
Sweden |
https://en.wikipedia.org/wiki/1952%E2%80%9353%20Allsvenskan | Statistics of Allsvenskan in season 1952/1953.
Overview
The league was contested by 12 teams, with Malmö FF winning the championship.
League table
Results
Footnotes
References
Allsvenskan seasons
1952–53 in Swedish association football leagues
Sweden |
https://en.wikipedia.org/wiki/1953%E2%80%9354%20Allsvenskan | Statistics of Allsvenskan in season 1953–54.
Overview
The league was contested by 12 teams, with GAIS winning the championship.
League table
Results
Footnotes
References
Allsvenskan seasons
1953–54 in Swedish association football leagues
Sweden |
https://en.wikipedia.org/wiki/1954%E2%80%9355%20Allsvenskan | Statistics of Allsvenskan in season 1954/1955.
Overview
The league was contested by 12 teams, with Djurgårdens IF winning the championship.
League table
Results
Footnotes
References
Allsvenskan seasons
1954–55 in Swedish association football leagues
Sweden |
https://en.wikipedia.org/wiki/1955%E2%80%9356%20Allsvenskan | Statistics of Allsvenskan in season 1955/1956.
Overview
The league was contested by 12 teams, with IFK Norrköping winning the championship.
League table
Results
Footnotes
References
Allsvenskan seasons
1955–56 in Swedish association football leagues
Sweden |
https://en.wikipedia.org/wiki/1956%E2%80%9357%20Allsvenskan | Statistics of Allsvenskan in season 1956/1957.
Overview
The league was contested by 12 teams, with IFK Norrköping winning the championship.
League table
Results
Footnotes
References
Allsvenskan seasons
1956–57 in Swedish association football leagues
Sweden |
https://en.wikipedia.org/wiki/1957%E2%80%9358%20Allsvenskan | Statistics of Allsvenskan in season 1957/1958.
Overview
The league was contested by 12 teams, with IFK Göteborg winning the championship. This season began in the summer of 1957, but didn't finish until the autumn of 1958. In this unusually long season, the teams met each other three times instead of twice, resulting in a season consisting of 33 rounds instead of 22. For this reason, it was referred to as the "Marathon Allsvenskan".
League table
Results
Rounds 1–22
Rounds 23–33
Footnotes
References
Allsvenskan seasons
1957–58 in Swedish association football leagues
Sweden |
https://en.wikipedia.org/wiki/1959%20Allsvenskan | Statistics of Allsvenskan in season 1959.
Overview
The league was contested by 12 teams, with Djurgårdens IF winning the championship.
League table
Results
Footnotes
References
Allsvenskan seasons
1
Sweden
Sweden |
https://en.wikipedia.org/wiki/1960%20Allsvenskan | Statistics of Allsvenskan in season 1960.
Overview
The league was contested by 12 teams, with IFK Norrköping winning the championship.
League table
Results
Footnotes
References
Allsvenskan seasons
Sweden
Sweden
1 |
https://en.wikipedia.org/wiki/1961%20Allsvenskan | Statistics of Allsvenskan in season 1961.
Overview
The league was contested by 12 teams, with IF Elfsborg winning the championship.
League table
Results
Footnotes
References
Allsvenskan seasons
1
Sweden
Sweden |
https://en.wikipedia.org/wiki/1962%20Allsvenskan | Statistics of Allsvenskan in season 1962.
Overview
The league was contested by 12 teams, with IFK Norrköping winning the championship.
League table
Results
Footnotes
References
Allsvenskan seasons
1
Sweden
Sweden |
https://en.wikipedia.org/wiki/1963%20Allsvenskan | Statistics of Allsvenskan in season 1963.
Overview
The league was contested by 12 teams, with IFK Norrköping winning the championship. It started on 15 April and ended on 20 October.
League table
Results
Footnotes
References
Allsvenskan seasons
1
Sweden
Sweden |
https://en.wikipedia.org/wiki/1964%20Allsvenskan | Statistics of Allsvenskan in season 1964.
Overview
The league was contested by 12 teams, with Djurgårdens IF winning the championship. Three top teams finished all with same points, but Djurgården was declared the champion because it had the largest goal difference.
The tournament started on 12 April and ended on 25 October.
League table
Results
Footnotes
References
External links
http://wildstat.com/p/8401/ch/SWE_1_1964/stg/all/tour/all
Allsvenskan seasons
1
Sweden
Sweden |
https://en.wikipedia.org/wiki/1965%20Allsvenskan | Statistics of Allsvenskan in season 1965.
Overview
The league was contested by 12 teams, with Malmö FF winning the championship.
League table
Results
Footnotes
References
Allsvenskan seasons
1
Sweden
Sweden |
https://en.wikipedia.org/wiki/1966%20Allsvenskan | Statistics of Allsvenskan in season 1966.
Overview
The league was contested by 12 teams, with Djurgårdens IF Fotboll winning the championship.
League table
Results
Footnotes
References
Allsvenskan seasons
1
Sweden
Sweden |
https://en.wikipedia.org/wiki/1967%20Allsvenskan | Statistics of Allsvenskan in season 1967.
Overview
The league was contested by 12 teams, with Malmö FF winning the championship.
League table
Results
Footnotes
References
Allsvenskan seasons
1
Sweden
Sweden |
https://en.wikipedia.org/wiki/1968%20Allsvenskan | Statistics of Allsvenskan in season 1968.
Overview
The league was contested by 12 teams, with Östers IF winning the championship.
League table
Results
Footnotes
References
Allsvenskan seasons
1
Sweden
Sweden |
https://en.wikipedia.org/wiki/1969%20Allsvenskan | Statistics of Allsvenskan in season 1969.
Overview
The league was contested by 12 teams, with IFK Göteborg winning the championship.
League table
Results
Season statistics
Top scorers
Footnotes
References
Allsvenskan seasons
1
Sweden
Sweden |
https://en.wikipedia.org/wiki/1970%20Allsvenskan | Statistics of Allsvenskan in season 1970.
Overview
The league was contested by 12 teams, with Malmö FF winning the championship.
In August, young Hammarby IF supporters began to stand and sing songs with own-written lyrics. This is seen as the beginning of modern organized soccer chants in Sweden. Inspirationens came from England through Tipsextra in SVT.
Örebro SK defeated defending champions IFK Göteborg, 1-0, at home at Eyravallen in the final game, leading to IFK Göteborg being relegated. Riots began when IFK Göteborg supporters stormed the pitch in an attempt to tear down the goal in order to make sure the game would be replayed. The game was cancelled with circa eight minutes left, and IFK Göteborg was relegated.
League table
Results
Footnotes
References
Allsvenskan seasons
Swed
Swed
1 |
https://en.wikipedia.org/wiki/1971%20Allsvenskan | Statistics of Allsvenskan in season 1971.
Overview
The league was contested by 12 teams, with Malmö FF winning the championship.
League table
Results
Footnotes
References
Allsvenskan seasons
Swed
Swed
1 |
https://en.wikipedia.org/wiki/1972%20Allsvenskan | Statistics of Allsvenskan in season 1972.
Overview
The league was contested by 12 teams, with Åtvidabergs FF winning the championship.
League table
Results
Footnotes
References
Allsvenskan seasons
Swed
Swed
1 |
https://en.wikipedia.org/wiki/1973%20Allsvenskan | Statistics of Allsvenskan in season 1973.
Overview
The league was contested by 14 teams, with Åtvidabergs FF winning the championship.
League table
Results
Footnotes
References
Allsvenskan seasons
Swed
Swed
1 |
https://en.wikipedia.org/wiki/1974%20Allsvenskan | Statistics of Allsvenskan in season 1974.
Overview
The league was contested by 14 teams, with Malmö FF winning the championship.
League table
Results
Footnotes
References
Allsvenskan seasons
Swed
Swed
1 |
https://en.wikipedia.org/wiki/1975%20Allsvenskan | Statistics of Allsvenskan in season 1975.
Overview
The league was contested by 14 teams, with Malmö FF winning the championship.
League table
Results
Footnotes
References
Allsvenskan seasons
Swed
Swed
1 |
https://en.wikipedia.org/wiki/1976%20Allsvenskan | Statistics of Allsvenskan in season 1976.
Overview
The league was contested by 14 teams, with Halmstads BK winning the championship.
League table
Results
Footnotes
References
Allsvenskan seasons
Swed
Swed
1 |
https://en.wikipedia.org/wiki/1977%20Allsvenskan | Statistics of Allsvenskan in season 1977.
Overview
The league was contested by 14 teams, with Malmö FF winning the championship.
League table
Results
Footnotes
References
Allsvenskan seasons
Swed
Swed
1 |
https://en.wikipedia.org/wiki/1978%20Allsvenskan | Statistics of Allsvenskan in season 1978.
Overview
The league was contested by 14 teams, with Östers IF winning the championship.
League table
Results
Footnotes
References
Allsvenskan seasons
Swed
Swed
1 |
https://en.wikipedia.org/wiki/1979%20Allsvenskan | Statistics of Allsvenskan in season 1979.
Overview
The league was contested by 14 teams, with Halmstads BK winning the championship.
League table
Results
References
Allsvenskan seasons
Swed
Swed
1 |
https://en.wikipedia.org/wiki/1980%20Allsvenskan | Statistics of Allsvenskan in season 1980.
Overview
The league was contested by 14 teams, with Östers IF winning the championship.
League table
Results
Footnotes
References
Allsvenskan seasons
Swed
Swed
1 |
https://en.wikipedia.org/wiki/1981%20Allsvenskan | Statistics of Allsvenskan in season 1981.
Overview
The league was contested by 14 teams, with Östers IF winning the championship.
League table
Results
Relegation play-offs
Elfsborg won 2–1 on aggregate.
Kalmar FF won 4–2 on aggregate.
Footnotes
References
Allsvenskan seasons
Swed
Swed
1 |
https://en.wikipedia.org/wiki/1982%20Allsvenskan | Statistics of Allsvenskan in season 1982.
Overview
The league was contested by 12 teams, with IFK Göteborg winning the league and the Swedish championship after the playoffs.
League table
Results
Allsvenskan play-offs
The 1982 Allsvenskan play-offs was the first edition of the competition. The eight best placed teams from Allsvenskan qualified to the competition. Allsvenskan champions IFK Göteborg won the competition and the Swedish championship after defeating league runners-up Hammarby IF.
Quarter-finals
First leg
Second leg
Semi-finals
First leg
Second leg
Final
Relegation play-offs
Season statistics
Top scorers
Footnotes
References
Allsvenskan seasons
Swed
Swed
1 |
https://en.wikipedia.org/wiki/1983%20Allsvenskan | Statistics of Allsvenskan in season 1983.
Overview
The league was contested by 12 teams, with AIK winning the league and IFK Göteborg winning the Swedish championship after the play-offs.
League table
Results
Allsvenskan play-offs
The 1983 Allsvenskan play-offs was the second edition of the competition. The eight best placed teams from Allsvenskan qualified to the competition. IFK Göteborg who finished third in the league won the competition and the Swedish championship after defeating Öster who finished fourth in the league.
Quarter-finals
First leg
Second leg
Semi-finals
First leg
Second leg
Final
Season statistics
Top scorers
Footnotes
References
Allsvenskan seasons
Swed
Swed
1 |
https://en.wikipedia.org/wiki/1984%20Allsvenskan | Statistics of Allsvenskan in season 1984.
Overview
The league was contested by 12 teams, with IFK Göteborg winning the league and the Swedish championship after the play-offs.
League table
Results
Allsvenskan play-offs
The 1984 Allsvenskan play-offs was the third edition of the competition. The eight best placed teams from Allsvenskan qualified to the competition. Allsvenskan champions IFK Göteborg won the competition and the Swedish championship after defeating IFK Norrköping who finished fifth in the league.
Quarter-finals
First leg
Second leg
Semi-finals
First leg
Second leg
Final
Season statistics
Top scorers
Footnotes
References
Allsvenskan seasons
Swed
Swed
1 |
https://en.wikipedia.org/wiki/1985%20Allsvenskan | Statistics of Allsvenskan in season 1985.
Overview
The league was contested by 12 teams, with Malmö FF winning the league and Örgryte IS winning the Swedish championship after the play-offs.
League table
Results
Allsvenskan play-offs
The 1985 Allsvenskan play-offs was the fourth edition of the competition. The four best placed teams from Allsvenskan qualified to the competition. Örgryte who placed third in the league won the competition and the Swedish championship after defeating IFK Göteborg who finished fourth in the league.
Semi-finals
First leg
Second leg
Final
Season statistics
Top scorers
Footnotes
References
Allsvenskan seasons
Swed
Swed
1 |
https://en.wikipedia.org/wiki/1986%20Allsvenskan | Statistics of Allsvenskan in season 1986.
Overview
The league was contested by 12 teams, with Malmö FF winning the league and the Swedish championship after the play-offs.
League table
Results
Allsvenskan play-offs
The 1986 Allsvenskan play-offs was the fifth edition of the competition. The four best placed teams from Allsvenskan qualified to the competition. Allsvenskan champions Malmö FF won the competition and the Swedish championship after defeating AIK who finished third in the league.
Semi-finals
First leg
Second leg
Final
Season statistics
Top scorers
Footnotes
References
Allsvenskan seasons
Swed
Swed
1 |
https://en.wikipedia.org/wiki/1987%20Allsvenskan | Statistics of Allsvenskan in season 1987.
Overview
Allsvenskan 1987 was played between 12 April and 4 October 1987 and was won by Malmö FF. The championship play-off finals were played from 10 to 31 October 1987 and was won by IFK Göteborg, who defeated Malmö FF in the final and thus became Swedish champions.
League table
Results
Allsvenskan play-offs
The 1987 Allsvenskan play-offs was the sixth edition of the competition. The four best placed teams from Allsvenskan qualified to the competition. IFK Göteborg who finished third in the league won the competition and the Swedish championship after defeating Allsvenskan champions Malmö FF.
Semi-finals
First leg
Second leg
Final
Season statistics
Top scorers
Footnotes
References
Allsvenskan seasons
Swed
Swed
1 |
https://en.wikipedia.org/wiki/1988%20Allsvenskan | Statistics of Allsvenskan in season 1988.
Overview
The league was contested by 12 teams, with Malmö FF winning the league and the Swedish championship after the play-offs.
League table
Results
Allsvenskan play-offs
The 1988 Allsvenskan play-offs was the seventh edition of the competition. The four best placed teams from Allsvenskan qualified to the competition. Allsvenskan champions Malmö FF won the competition and the Swedish championship after defeating Djurgården who finished third in the league.
Semi-finals
First leg
Second leg
Final
Season statistics
Top scorers
Footnotes
References
Allsvenskan seasons
Swed
Swed
1 |
https://en.wikipedia.org/wiki/1989%20Allsvenskan | Statistics of Allsvenskan in season 1989.
Overview
The league was contested by 12 teams, with Malmö FF winning the league and IFK Norrköping winning the Swedish championship after the play-offs.
League table
Results
Allsvenskan play-offs
The 1989 Allsvenskan play-offs was the eight edition of the competition. The four best placed teams from Allsvenskan qualified to the competition. League runners-up IFK Norrköping won the competition and the Swedish championship after defeating Allsvenskan champions Malmö FF. The champion was determined by a final in best of three matches in contrast to previous years.
Semi-finals
First leg
Second leg
Final
IFK Norrköping won 2–1 in matches.
Season statistics
Top scorers
Footnotes
References
Allsvenskan seasons
Swed
Swed
1 |
https://en.wikipedia.org/wiki/1965%E2%80%9366%201.Lig | Statistics of the Turkish First Football League for the 1965–66 season.
Overview
It was contested by 16 teams, and Beşiktaş J.K. won the championship.
League table
Results
References
Turkey - List of final tables (RSSSF)
Süper Lig seasons
1965–66 in Turkish football
Turkey |
https://en.wikipedia.org/wiki/1966%E2%80%9367%201.Lig | Statistics of the Turkish First Football League for the 1966–67 season.
Overview
It was contested by 17 teams, and Beşiktaş J.K. won the championship.
League table
Results
References
Turkey - List of final tables (RSSSF)
Süper Lig seasons
1966–67 in Turkish football
Turkey |
https://en.wikipedia.org/wiki/1967%E2%80%9368%201.Lig | Statistics of the Turkish First Football League for the 1967–68 season.
Overview
It was contested by 17 teams, and Fenerbahçe S.K. won the championship.
League table
Results
References
Turkey - List of final tables (RSSSF)
Süper Lig seasons
1967–68 in Turkish football
Turkey |
https://en.wikipedia.org/wiki/1968%E2%80%9369%201.Lig | Statistics of the Turkish First Football League for the 1968–69 season.
Overview
It was contested by 16 teams, and Galatasaray S.K. won the championship.
League table
Results
References
Turkey - List of final tables (RSSSF)
Süper Lig seasons
1968–69 in Turkish football
Turkey |
https://en.wikipedia.org/wiki/1969%E2%80%9370%201.Lig | Statistics of the Turkish First Football League for the 1969–70 season.
Overview
It was contested by 16 teams, and Fenerbahçe S.K. won the championship.
League table
Results
References
Turkey - List of final tables (RSSSF)
Süper Lig seasons
1969–70 in Turkish football
Turkey |
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