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https://en.wikipedia.org/wiki/Algebraic%20Riccati%20equation | An algebraic Riccati equation is a type of nonlinear equation that arises in the context of infinite-horizon optimal control problems in continuous time or discrete time.
A typical algebraic Riccati equation is similar to one of the following:
the continuous time algebraic Riccati equation (CARE):
or the discrete time algebraic Riccati equation (DARE):
P is the unknown n by n symmetric matrix and A, B, Q, R are known real coefficient matrices.
Though generally this equation can have many solutions, it is usually specified that we want to obtain the unique stabilizing solution, if such a solution exists.
Origin of the name
The name Riccati is given to these equations because of their relation to the Riccati differential equation. Indeed, the CARE is verified by the time invariant solutions of the associated matrix valued Riccati differential equation. As for the DARE, it is verified by the time invariant solutions of the matrix valued Riccati difference equation (which is the analogue of the Riccati differential equation in the context of discrete time LQR).
Context of the discrete-time algebraic Riccati equation
In infinite-horizon optimal control problems, one cares about the value of some variable of interest arbitrarily far into the future, and one must optimally choose a value of a controlled variable right now, knowing that one will also behave optimally at all times in the future. The optimal current values of the problem's control variables at any time can be found using the solution of the Riccati equation and the current observations on evolving state variables. With multiple state variables and multiple control variables, the Riccati equation will be a matrix equation.
The algebraic Riccati equation determines the solution of the infinite-horizon time-invariant Linear-Quadratic Regulator problem (LQR) as well as that of the infinite horizon time-invariant Linear-Quadratic-Gaussian control problem (LQG). These are two of the most fundamental problems in control theory.
A typical specification of the discrete-time linear quadratic control problem is to minimize
subject to the state equation
where x is an n × 1 vector of state variables, u is a k × 1 vector of control variables, A is the n × n state transition matrix, B is the n × k matrix of control multipliers, Q (n × n) is a symmetric positive semi-definite state cost matrix, and R (k × k) is a symmetric positive definite control cost matrix.
Induction backwards in time can be used to obtain the optimal control solution at each time,
with the symmetric positive definite cost-to-go matrix P evolving backwards in time from according to
which is known as the discrete-time dynamic Riccati equation of this problem. The steady-state characterization of P, relevant for the infinite-horizon problem in which T goes to infinity, can be found by iterating the dynamic equation repeatedly until it converges; then P is characterized by removing the time subscripts from t |
https://en.wikipedia.org/wiki/Maitri%20%28missile%29 | The Maitri missile (Friendship) project was a cancelled proposal for a next-generation quick-reaction surface-to-air missile (QRSAM) with a lethal near-hundred per cent kill probability (according to manufacturer's claim) planned for development by India's Defence Research and Development Organisation. It is a short-range (strike range varies from 25–30 km) surface-to-air defense missile system.
The proposal was shelved and superseded by the QRSAM and VL-SRSAM missiles for the use of the Indian Army and Indian Navy respectively.
Introduction
The Maitri missile should not be confused with the similar Indian Army Low-Level Quick Reaction Missile system (LLQRM) requirement. The missile will fill the gap created by the Indian government's decision to wind up development of the Trishul point defense missile system. It is believed to be a blend of the French Mica and DRDO Trishul. Maitri will build on the work done by DRDO while developing the Trishul missile, using technology transfer from MBDA to fill the technological gaps that led to the failure of the Trishul project.
Development
On 15 July 2009, The Telegraph reported that the project was scrapped. But later, on June 4, 2010 Indian Express reported that, "After moving ahead with similar projects with Russia and Israel, India is set to finalise a missile co-development project with France to manufacture a new range of Short Range Surface to Air Missiles (SRSAM) for the armed forces." From 2007-2010, MBDA and DRDO finalised the design and performance parameters of the missile to suit the needs of the Indian armed forces. Besides providing the Indian armed forces with a modern air defence missile, the project will also add a new capability with France, which does not have a similar missile in production.
The Maitri missile project involved a technological collaboration between MBDA, India’s Defence Research and Development Organisation (DRDO) and defence public sector unit Bharat Dynamics Limited. Defence Research and Development Laboratory (DRDL), a premier missile laboratory of DRDO, will act as the main design centre in India.
The project, with a budget of US$500 million was said to have been signed in May 2007.
On 14 February 2013, India and France concluded negotiations on the Short Range Surface to Air Missile nearly worth of $6 billion during the talks between French President Francois Hollande and Prime Minister Manmohan Singh.
On 30 March 2015, it was reported that the project was revived specially by the request of Indian Navy for a point air defence system after stating that Akash missile defence system is not suitable for Indian warships defence. The DRDO with MBDA is planning to develop 9 short-range surface-to-air missile system (SRSAM) with 40 missiles each for Indian Navy. Development of the missile is expected to be completed within three years of the project go-ahead, when initial testing will commence.
As of 2020, The project was expected to be cancelled as DRDO has instead |
https://en.wikipedia.org/wiki/Estimating%20equations | In statistics, the method of estimating equations is a way of specifying how the parameters of a statistical model should be estimated. This can be thought of as a generalisation of many classical methods—the method of moments, least squares, and maximum likelihood—as well as some recent methods like M-estimators.
The basis of the method is to have, or to find, a set of simultaneous equations involving both the sample data and the unknown model parameters which are to be solved in order to define the estimates of the parameters. Various components of the equations are defined in terms of the set of observed data on which the estimates are to be based.
Important examples of estimating equations are the likelihood equations.
Examples
Consider the problem of estimating the rate parameter, λ of the exponential distribution which has the probability density function:
Suppose that a sample of data is available from which either the sample mean, , or the sample median, m, can be calculated. Then an estimating equation based on the mean is
while the estimating equation based on the median is
Each of these equations is derived by equating a sample value (sample statistic) to a theoretical (population) value. In each case the sample statistic is a consistent estimator of the population value, and this provides an intuitive justification for this type of approach to estimation.
See also
Generalized estimating equations
Method of moments (statistics)
Generalized method of moments
Maximum likelihood
Empirical likelihood
References
Estimation methods |
https://en.wikipedia.org/wiki/Index%20of%20dispersion | In probability theory and statistics, the index of dispersion, dispersion index, coefficient of dispersion, relative variance, or variance-to-mean ratio (VMR), like the coefficient of variation, is a normalized measure of the dispersion of a probability distribution: it is a measure used to quantify whether a set of observed occurrences are clustered or dispersed compared to a standard statistical model.
It is defined as the ratio of the variance to the mean ,It is also known as the Fano factor, though this term is sometimes reserved for windowed data (the mean and variance are computed over a subpopulation), where the index of dispersion is used in the special case where the window is infinite. Windowing data is frequently done: the VMR is frequently computed over various intervals in time or small regions in space, which may be called "windows", and the resulting statistic called the Fano factor.
It is only defined when the mean is non-zero, and is generally only used for positive statistics, such as count data or time between events, or where the underlying distribution is assumed to be the exponential distribution or Poisson distribution.
Terminology
In this context, the observed dataset may consist of the times of occurrence of predefined events, such as earthquakes in a given region over a given magnitude, or of the locations in geographical space of plants of a given species. Details of such occurrences are first converted into counts of the numbers of events or occurrences in each of a set of equal-sized time- or space-regions.
The above defines a dispersion index for counts. A different definition applies for a dispersion index for intervals, where the quantities treated are the lengths of the time-intervals between the events. Common usage is that "index of dispersion" means the dispersion index for counts.
Interpretation
Some distributions, most notably the Poisson distribution, have equal variance and mean, giving them a VMR = 1. The geometric distribution and the negative binomial distribution have VMR > 1, while the binomial distribution has VMR < 1, and the constant random variable has VMR = 0. This yields the following table:
This can be considered analogous to the classification of conic sections by eccentricity; see Cumulants of particular probability distributions for details.
The relevance of the index of dispersion is that it has a value of 1 when the probability distribution of the number of occurrences in an interval is a Poisson distribution. Thus the measure can be used to assess whether observed data can be modeled using a Poisson process. When the coefficient of dispersion is less than 1, a dataset is said to be "under-dispersed": this condition can relate to patterns of occurrence that are more regular than the randomness associated with a Poisson process. For instance, regular, periodic events will be under-dispersed. If the index of dispersion is larger than 1, a dataset is said to be over-dispersed.
A |
https://en.wikipedia.org/wiki/Binomial%20differential%20equation | In mathematics, the binomial differential equation is an ordinary differential equation containing one or more functions of one independent variable and the derivatives of those functions.
For example:
when is a natural number (i.e., a positive integer), and is a polynomial in two variables (i.e., a bivariate polynomial).
The Solution
Let be a polynomial in two variables of order ; where is a positive integer. The binomial differential equation becomes
using the substitution , we get that , therefore
or we can write , which is a separable ordinary differential equation, hence
Special cases:
- If , we have the differential equation and the solution is , where is a constant.
- If , i.e., divides so that there is a positive integer such that , then the solution has the form . From the tables book of Gradshteyn and Ryzhik we found that
and
See also
Examples of differential equations
References
Zwillinger, Daniel Handbook of Differential Equations, 3rd ed. Boston, MA: Academic Press, p. 120, 1997.
Differential calculus
Ordinary differential equations |
https://en.wikipedia.org/wiki/Benjamin%E2%80%93Ono%20equation | In mathematics, the Benjamin–Ono equation is a nonlinear partial integro-differential equation that
describes one-dimensional internal waves in deep water.
It was introduced by and .
The Benjamin–Ono equation is
where H is the Hilbert transform.
It possesses infinitely many conserved densities and symmetries; thus it is a completely integrable system.
See also
Bretherton equation
References
Sources
External links
Benjamin-Ono equations: Solitons and Shock Waves
Nonlinear partial differential equations
Integrable systems |
https://en.wikipedia.org/wiki/Reza%20Khaleghifar | Reza Khaleghifar () is an Iranian football player who is playing for Sanat Naft Abadan in the Persian Gulf Pro League.
Club career statistics
Assist Goals
Statistics accurate as of match played 31 July 2014
References
Iranian men's footballers
Iran men's international footballers
1983 births
Living people
Persian Gulf Pro League players
Fajr Sepasi Shiraz F.C. players
Saipa F.C. players
Sanat Naft Abadan F.C. players
Rah Ahan Tehran F.C. players
Persepolis F.C. players
Gostaresh Foulad F.C. players
Sportspeople from Babol
Men's association football forwards
F.C. Pars Jonoubi Jam players
Footballers from Mazandaran province |
https://en.wikipedia.org/wiki/Gilles-Gaston%20Granger | Gilles-Gaston Granger (; ; 28 January 1920 – 24 August 2016) was a French philosopher.
Work
His works discuss the philosophy of logic, mathematics, human and social sciences, Aristotle, Jean Cavaillès, and Ludwig Wittgenstein.
He produced the most authoritative French translation of Wittgenstein's Tractatus Logico-Philosophicus and published more than 150 scientific articles.
In 1968 he co-founded with Jules Vuillemin the journal L'Âge de la Science. He was president of the scientific committee of Jules Vuillemin's Archives.
Biography
Studied at École Normale Supérieure, Paris, France. Associate in philosophy, bachelor in mathematics, doctorate in philosophy.
1947–1953: Professor at the University of São Paulo, Brazil.
1953–1955: Associate professor at the Centre National de la Recherche Scientifique (CNRS).
1955–1962: Professor at the University of Rennes.
1962–1964: Director of the École Normale Supérieure d'Afrique Centrale, in Brazzaville, Republic of the Congo.
1964–1986: Professor at the Université de Provence, Aix-en-Provence, France.
1986: Professor at the Collège de France. Chair of Comparative Epistemology.
1990: Professor emeritus of the Collège de France.
2000: Invited professor at the Conservatoire National des Arts et Métiers.
Works
Méthodologie économique (PUF, 1955)
La raison (1955)
La mathématique sociale du marquis de Condorcet (PUF, 1956)
Pensée formelle et sciences de l'homme (Aubier, 1960)
Formal Thought and the Sciences of Man, translation by Alexander Rosenberg (Boston Studies in the Philosophy of Science, 1983)
Essai d'une philosophie du style (Armand Colin, 1968)
Wittgenstein (Seghers, 1969)
La théorie aristotélicienne de la science (Aubier, 1976)
Langage et épistémologie (Klincksieck, 1979)
Pour la connaissance philosophique (Odile Jacob, 1988)
Invitation à la lecture de Wittgenstein (Alinéa, 1990)
La vérification (Odile Jacob, 1992)
Le probable, le possible et le virtuel (Odile Jacob, 1995)
L'irrationnel (Odile Jacob, 1998)
La pensée de l'espace (Odile Jacob, 1999)
Notes and references
External links
Gilles Gaston Granger. "La contradiction", Travaux du Centre de Recherches Sémiologiques, 57, p. 39–53, 1988
Biography, list of works, on the site of the Collège de France
Bibliographie
Lacour, Philippe. Gilles-Gaston Granger et la critique de la raison symbolique
Lacour, Philippe. Le concept d'''histoire dans la philosophie de Gilles-Gaston Granger''
1920 births
2016 deaths
Writers from Paris
École Normale Supérieure alumni
Academic staff of the University of Provence
Academic staff of the University of São Paulo
Academic staff of the University of Rennes
Academic staff of the Collège de France
Rationalists
Epistemologists
Wittgensteinian philosophers
Philosophers of science
20th-century French philosophers
French male writers |
https://en.wikipedia.org/wiki/Euler%E2%80%93Poisson%E2%80%93Darboux%20equation | In mathematics, the Euler–Poisson–Darboux equation is the partial differential equation
This equation is named for Siméon Poisson, Leonhard Euler, and Gaston Darboux. It plays an important role in solving the classical wave equation.
This equation is related to
by , , where and some sources quote this equation when referring to the Euler–Poisson–Darboux equation.
References
External links
Differential calculus
Eponymous equations of physics
Partial differential equations
Leonhard Euler |
https://en.wikipedia.org/wiki/Transform%20theory | In mathematics, transform theory is the study of transforms, which relate a function in one domain to another function in a second domain. The essence of transform theory is that by a suitable choice of basis for a vector space a problem may be simplified—or diagonalized as in spectral theory.
Spectral theory
In spectral theory, the spectral theorem says that if A is an n×n self-adjoint matrix, there is an orthonormal basis of eigenvectors of A. This implies that A is diagonalizable.
Furthermore, each eigenvalue is real.
Transforms
Laplace transform
Fourier transform
Hankel transform
Joukowsky transform
Mellin transform
Z-transform
References
Keener, James P. 2000. Principles of Applied Mathematics: Transformation and Approximation. Cambridge: Westview Press. |
https://en.wikipedia.org/wiki/Courant%20minimax%20principle | In mathematics, the Courant minimax principle gives the eigenvalues of a real symmetric matrix. It is named after Richard Courant.
Introduction
The Courant minimax principle gives a condition for finding the eigenvalues for a real symmetric matrix. The Courant minimax principle is as follows:
For any real symmetric matrix A,
where is any matrix.
Notice that the vector x is an eigenvector to the corresponding eigenvalue λ.
The Courant minimax principle is a result of the maximum theorem, which says that for , A being a real symmetric matrix, the largest eigenvalue is given by , where is the corresponding eigenvector. Also (in the maximum theorem) subsequent eigenvalues and eigenvectors are found by induction and orthogonal to each other; therefore, with .
The Courant minimax principle, as well as the maximum principle, can be visualized by imagining that if ||x|| = 1 is a hypersphere then the matrix A deforms that hypersphere into an ellipsoid. When the major axis on the intersecting hyperplane are maximized — i.e., the length of the quadratic form q(x) is maximized — this is the eigenvector, and its length is the eigenvalue. All other eigenvectors will be perpendicular to this.
The minimax principle also generalizes to eigenvalues of positive self-adjoint operators on Hilbert spaces, where it is commonly used to study the Sturm–Liouville problem.
See also
Min-max theorem
Max–min inequality
Rayleigh quotient
References
(Pages 31–34; in most textbooks the "maximum-minimum method" is usually credited to Rayleigh and Ritz, who applied the calculus of variations in the theory of sound.)
Keener, James P. Principles of Applied Mathematics: Transformation and Approximation. Cambridge: Westview Press, 2000.
Mathematical principles |
https://en.wikipedia.org/wiki/Morwen%20Thistlethwaite | Morwen Bernard Thistlethwaite is a knot theorist and professor of mathematics for the University of Tennessee in Knoxville. He has made important contributions to both knot theory and Rubik's Cube group theory.
Biography
Morwen Thistlethwaite received his BA from the University of Cambridge in 1967, his MSc from the University of London in 1968, and his PhD from the University of Manchester in 1972 where his advisor was Michael Barratt. He studied piano with Tanya Polunin, James Gibb and Balint Vazsonyi, giving concerts in London before deciding to pursue a career in mathematics in 1975. He taught at the North London Polytechnic from 1975 to 1978 and the Polytechnic of the South Bank, London from 1978 to 1987. He served as a visiting professor at the University of California, Santa Barbara for a year before going to the University of Tennessee, where he currently is a professor. His wife, Stella Thistlethwaite, also teaches at the University of Tennessee-Knoxville. Thistlethwaite's son Oliver is also a mathematician.
Work
Tait conjectures
Morwen Thistlethwaite helped prove the Tait conjectures, which are:
Reduced alternating diagrams have minimal link crossing number.
Any two reduced alternating diagrams of a given knot have equal writhe.
Given any two reduced alternating diagrams D1,D2 of an oriented, prime alternating link, D1 may be transformed to D2 by means of a sequence of certain simple moves called flypes. Also known as the Tait flyping conjecture.(adapted from MathWorld—A Wolfram Web Resource. http://mathworld.wolfram.com/TaitsKnotConjectures.html)
Morwen Thistlethwaite, along with Louis Kauffman and Kunio Murasugi proved the first two Tait conjectures in 1987 and Thistlethwaite and William Menasco proved the Tait flyping conjecture in 1991.
Thistlethwaite's algorithm
Thistlethwaite also came up with a famous solution to the Rubik's Cube. The way the algorithm works is by restricting the positions of the cubes into a subgroup series of cube positions that can be solved using a certain set of moves. The groups are:
This group contains all possible positions of the Rubik's Cube.
This group contains all positions that can be reached (from the solved state) with quarter turns of the left, right, front and back sides of the Rubik's Cube, but only double turns of the up and down sides.
In this group, the positions are restricted to ones that can be reached with only double turns of the front, back, up and down faces and quarter turns of the left and right faces.
Positions in this group can be solved using only double turns on all sides.
The final group contains only one position, the solved state of the cube.
The cube is solved by moving from group to group, using only moves in the current group, for example, a scrambled cube always lies in group G0. A look up table of possible permutations is used that uses quarter turns of all faces to get the cube into group G1. Once in group G1, quarter turns of the up and down faces are disallowe |
https://en.wikipedia.org/wiki/Indians%20in%20Mozambique | Indian Mozambicans form the sixth-largest Indian diaspora community in Africa, according to the statistics of India's Ministry of External Affairs. Roughly 70,000 people of Indian descent reside in Mozambique, as well as 870 Indian expatriates.
Origins
India's links with Mozambique reach back over half a millennium. Indian Muslim traders from South India's Malabar region plied the trade routes of the Indian Ocean, bringing them up and down the eastern coast of Africa. Zhizo beads excavated from southern Africa and dated 8th-10th century AD are made using tube drawing methods which was specific to the Indian artisans, although scholars opine that beads were made by Indians residing in the Persian gulf or Omani coast where the ships would sail to southern Africa, scholars have also suggested Indian artisans resident at eastern African coast who received raw material and manufactured those beads at the local place. Blanche D'Souza states that Hindus had, by 1st millennium AD, begun using monsoon-led trade winds to establish trading activities between western parts of India and Mozambique, linking these to other eastern coastal regions of Africa and Arabian peninsula.
Arabic geographer Al-Idrisi (12th century) noted Indian settlements at Sofala and describes that settlements incorporated several towns, including Sayuna, which was;
Vasco da Gama also found Hindu traders in Mozambique when he paid the first Portuguese visit to ports there in 1499. By the 1800s, Vanika merchants from Diu had settled on the Island of Mozambique; in cooperation with Portuguese shippers, they were active in the trans-Atlantic slave trade. Muslim traders from the state of Kutch, closely allied with the Sultan of Oman, began to expand their activities in Southeast Africa in 1840, when the Sultanate relocated its seat of government to Zanzibar; they also bought and sold slaves in Mozambique, but shifted towards ivory under pressure from the British. Cashew nuts were another popular trade item.
More Gujaratis began to flow into Mozambique from South Africa in the latter half of the 19th century, also as petty traders or employees of the large Indian trading firms. Hindus from Diu and Sunni Muslims from Daman also came as masons and construction workers. Migration of all Asians was officially halted in 1899 due to an outbreak of plague, blamed on Indians; even after the relaxation of the restriction in 1907, Asians who sought to migrate to the colony had to pay a disembarkation fee of 3,000 reals at their port of arrival. Yet, with growing white hostility to the Indian presence in South Africa after 1911, more and more Gujaratis who had originally intended to settle in South Africa instead diverted north to Mozambique, especially in the area around Delagoa Bay.
Great Depression and World War II
Indian cashew nut traders continued to prosper even during the 1929–1934 Great Depression, as the price of cashew nuts remained stable. However, migration again came to a stop due t |
https://en.wikipedia.org/wiki/Indians%20in%20Madagascar | Indians in Madagascar form a community of roughly 25,000 individuals according to the statistics of India's Ministry of External Affairs; other estimates of their population range from 15,000 to 30,000. Among them are 867 non-resident Indians, with the rest being locally born descendants of early immigrants. They form a minority ethnic group in Madagascar.
History
By the 1780s, a community of roughly 200 Indian traders had formed at Mahajanga, a port on the north-west coast of Madagascar, near Bombetoka Bay at the mouth of the Betsiboka River. Confusion arose over their legal status; they often declared themselves to be Malagasy subjects in order to evade the laws against slave-holding or the building of stone houses, both forbidden to British subjects, while their dhows, which they used to transport goods to and from the African mainland, flew French flags. Initial arrivals were mainly Muslim Khojas, Ismailis and Daoudi Bohras, with some Hindus settling later. The 1911 census found 4,480 Indians in the country, making them 21% of the total foreign population and the second-largest foreign population after the French. Following the nationalisation of private businesses in the 1970s, many were compelled to leave; those who remained were largely uneducated, but stayed on and gradually built their businesses. By 2000, they were generally believed to control 50-60% of the country's economy, making them the target of demonstrators during periods of unrest.
See also
Chinese people in Madagascar
Hinduism in Madagascar
Islam in Madagascar
Demographics of Madagascar
India–Madagascar relations
References
Sources
Further reading
Ethnic groups in Madagascar
Malagasy people of Indian descent
Madagascar
Indian diaspora in Africa |
https://en.wikipedia.org/wiki/1987%20%28number%29 | 1987 is the natural number following 1986 and preceding 1988.
In mathematics
1987 is an odd number and the 300th prime number. It is the first number of a sexy prime triplet (1987, 1993, 1999). Being of the form 4n + 3, it is a Gaussian prime. It is a lucky number and therefore also a lucky prime. 1987 is a prime factor of the 9th number in Sylvester's sequence, and is the 15th prime to divide any number in the sequence.
There are 1987 polyiamonds with 12 cells that tile the plane isohedrally.
In other fields
There are 1987 ways to place four non-attacking chess kings on a 5 × 5 board.
References
Integers |
https://en.wikipedia.org/wiki/Zakharov%20system | In mathematics, the Zakharov system is a system of non-linear partial differential equations, introduced by Vladimir Zakharov in 1972 to describe the propagation of Langmuir waves in an ionized plasma. The system consists of a complex field u and a real field n satisfying the equations
where is the d'Alembert operator.
See also
Resonant interaction; the Zakharov equation describes non-linear resonant interactions.
References
Zakharov, V. E. (1968). Stability of periodic waves of finite amplitude on the surface of a deep fluid. Journal of Applied Mechanics and Technical Physics, 9(2), 190-194.
.
Partial differential equations
Waves in plasmas
Plasma physics |
https://en.wikipedia.org/wiki/Zakharov%E2%80%93Schulman%20system | In mathematics, the Zakharov–Schulman system is a system of nonlinear partial differential equations introduced in to describe the interactions of small amplitude, high frequency waves with acoustic waves.
The equations are
where L1, L2, and L3, are constant coefficient differential operators.
References
Partial differential equations
Acoustics |
https://en.wikipedia.org/wiki/Regression%20discontinuity%20design | In statistics, econometrics, political science, epidemiology, and related disciplines, a regression discontinuity design (RDD) is a quasi-experimental pretest-posttest design that aims to determine the causal effects of interventions by assigning a cutoff or threshold above or below which an intervention is assigned. By comparing observations lying closely on either side of the threshold, it is possible to estimate the average treatment effect in environments in which randomisation is unfeasible. However, it remains impossible to make true causal inference with this method alone, as it does not automatically reject causal effects by any potential confounding variable. First applied by Donald Thistlethwaite and Donald Campbell (1960) to the evaluation of scholarship programs, the RDD has become increasingly popular in recent years. Recent study comparisons of randomised controlled trials (RCTs) and RDDs have empirically demonstrated the internal validity of the design.
Example
The intuition behind the RDD is well illustrated using the evaluation of merit-based scholarships. The main problem with estimating the causal effect of such an intervention is the homogeneity of performance to the assignment of treatment (e.g. scholarship award). Since high-performing students are more likely to be awarded the merit scholarship and continue performing well at the same time, comparing the outcomes of awardees and non-recipients would lead to an upward bias of the estimates. Even if the scholarship did not improve grades at all, awardees would have performed better than non-recipients, simply because scholarships were given to students who were performing well before.
Despite the absence of an experimental design, an RDD can exploit exogenous characteristics of the intervention to elicit causal effects. If all students above a given grade — for example 80% — are given the scholarship, it is possible to elicit the local treatment effect by comparing students around the 80% cut-off. The intuition here is that a student scoring 79% is likely to be very similar to a student scoring 81% — given the pre-defined threshold of 80%. However, one student will receive the scholarship while the other will not. Comparing the outcome of the awardee (treatment group) to the counterfactual outcome of the non-recipient (control group) will hence deliver the local treatment effect.
Methodology
The two most common approaches to estimation using an RDD are non-parametric and parametric (normally polynomial regression).
Non-parametric estimation
The most common non-parametric method used in the RDD context is a local linear regression. This is of the form:
where is the treatment cutoff and is a binary variable equal to one if . Letting be the bandwidth of data used, we have . Different slopes and intercepts fit data on either side of the cutoff. Typically either a rectangular kernel (no weighting) or a triangular kernel are used. The rectangular kernel has a more st |
https://en.wikipedia.org/wiki/Cheung%20Kin%20Fung | Cheung Kin Fung (; born 1 January 1984 in Hong Kong) is a former Hong Kong professional footballer who played as a left back.
Career statistics
Club
As of 11 September 2009
International
As of 1 September 2016
Honours
Club
Kitchee
Hong Kong Premier League: 2014–15
Hong Kong First Division: 2013–14
Hong Kong Senior Shield: 2005–06
Hong Kong FA Cup: 2012–13, 2014–15
HKFA League Cup: 2005–06, 2006–07, 2014–15
Pegasus
Hong Kong Senior Shield: 2008–09
Hong Kong FA Cup: 2009–10
External links
1984 births
Living people
Hong Kong men's footballers
Men's association football defenders
Hong Kong Premier League players
Hong Kong Rangers FC players
Kitchee SC players
Hong Kong Pegasus FC players
Sun Hei SC players
South China AA players
Eastern Sports Club footballers
Yuen Long FC players
Footballers at the 2002 Asian Games
Footballers at the 2006 Asian Games
Asian Games competitors for Hong Kong
Hong Kong football managers |
https://en.wikipedia.org/wiki/Basketball%20statistician | In basketball, a basketball statistician is an official responsible for recording statistics during games, and providing reports to coaches, league officials, and (depending on the competition) media and spectators.
In organized competition and at professional level, games may have a panel of one or more statisticians in attendance. The statistician's role is to record the game and provide a report (commonly known as a boxscore) during breaks between periods, and at the completion of each game. While the game scorer keeps track of points scored and fouls committed, statisticians also record other details of the game, such as assists, turnovers, and field goal percentage.
Game statistics can be recorded using tally sheets, or computer software designed for the purpose. Computerised methods are increasingly being used for professional competition and bigger tournaments.
Notable basketball statisticians
John Hollinger
Bill Mokray
Ken Pomeroy
External links
CREZ Basketball Systems Inc., Software to score your own basketball games.
FIBA Livestats Official FIBA Livestats program for covering games.
Notes
Basketball statistics
Basketball people |
https://en.wikipedia.org/wiki/Literacy%20in%20the%20United%20States | Literacy in the United States was categorized by the National Center for Education Statistics into different literacy levels, with 92% of American adults having at least "Level 1" literacy in 2014. Nationally, over 20% of adult Americans have a literacy proficiency at or below Level 1. Adults in this range have difficulty using or understanding print materials. Those on the higher end of this category can perform simple tasks based on the information they read, but adults below Level 1 may only understand very basic vocabulary or be functionally illiterate. According to a 2020 report by the U.S. Department of Education, 54% of adults in the United States have English prose literacy below the 6th-grade level.
In many nations, the ability to read a simple sentence suffices as literacy, and was the previous standard for the U.S. The definition of literacy has changed greatly; the term is presently defined as the ability to use printed and written information to function in society, to achieve one's goals, and to develop one's knowledge and potential.
The United States Department of Education assesses literacy in the general population through its National Assessment of Adult Literacy (NAAL). The NAAL survey defines three types of literacy:
Prose: the knowledge and skills needed to search, comprehend, and use continuous texts. Examples include editorials, news stories, brochures, and instructional materials.
Document: the knowledge and skills needed to search, comprehend, and use non-continuous texts in various formats. Examples include job applications, payroll forms, transportation schedules, maps, tables, and drug and food labels.
Quantitative: the knowledge and skills required to identify and perform computations, either alone or sequentially, using numbers embedded in printed materials. Examples include balancing a checkbook, figuring out tips, completing an order form, or determining an amount.
Modern jobs often demand a high literacy level, and its lack in adults and adolescents has been studied extensively.
According to a 1992 survey, about 40 million adults had Level 1 literary competency, the lowest level, comprising understanding only basic written instructions. A number of reports and studies are published annually to monitor the nation's status, and initiatives to improve literacy rates are funded by government and external sources.
History
In early U.S. colonial history, teaching children to read was the responsibility of the parents for the purpose of reading the Bible. The Massachusetts law of 1642 and the Connecticut law of 1650 required that not only children but also servants and apprentices were required to learn to read. During the industrial revolution, many nursery schools, preschools and kindergartens were established to formalize education. The majority of youth in southern states were not able to receive secondary schooling until the 1920s. Throughout the 20th century, there was an increase in federal acts and model |
https://en.wikipedia.org/wiki/Basis%20%28universal%20algebra%29 | In universal algebra, a basis is a structure inside of some (universal) algebras, which are called free algebras. It generates all algebra elements from its own elements by the algebra operations in an independent manner. It also represents the endomorphisms of an algebra by certain indexings of algebra elements, which can correspond to the usual matrices when the free algebra is a vector space.
Definitions
A basis (or reference frame) of a (universal) algebra is a function that takes some algebra elements as values and satisfies either one of the following two equivalent conditions. Here, the set of all is called the basis set, whereas several authors call it the "basis". The set of its arguments is called the dimension set. Any function, with all its arguments in the whole , that takes algebra elements as values (even outside the basis set) will be denoted by . Then, will be an .
Outer condition
This condition will define bases by the set of the -ary elementary functions of the algebra, which are certain functions that take every as argument to get some algebra element as value In fact, they consist of all the projections with in which are the functions such that for each , and of all functions that rise from them by repeated "multiple compositions" with operations of the algebra.
(When an algebra operation has a single algebra element as argument, the value of such a composed function is the one that the operation takes from the value of a single previously computed -ary function as in composition. When it does not, such compositions require that many (or none for a nullary operation) -ary functions are evaluated before the algebra operation: one for each possible algebra element in that argument. In case and the numbers of elements in the arguments, or “arity”, of the operations are finite, this is the finitary multiple composition .)
Then, according to the outer condition a basis has to generate the algebra (namely when ranges over the whole , gets every algebra element) and must be independent (namely whenever any two -ary elementary functions coincide at , they will do everywhere: implies ). This is the same as to require that there exists a single function that takes every algebra element as argument to get an -ary elementary function as value and satisfies for all in .
Inner condition
This other condition will define bases by the set E of the endomorphisms of the algebra, which are the homomorphisms from the algebra into itself, through its analytic representation by a basis. The latter is a function that takes every endomorphism e as argument to get a function m as value: , where this m is the "sample" of the values of e at b, namely for all i in the dimension set.
Then, according to the inner condition b is a basis, when is a bijection from E onto the set of all m, namely for each m there is one and only one endomorphism e such that . This is the same as to require that there exists an extension |
https://en.wikipedia.org/wiki/Pine%20Shadows%2C%20Alberta | Pine Shadows is an unincorporated community in central Alberta, Canada within Yellowhead County that is recognized as a designated place by Statistics Canada. It is located east of Edson.
Demographics
In the 2021 Census of Population conducted by Statistics Canada, Pine Shadows had a population of 127 living in 55 of its 60 total private dwellings, a change of from its 2016 population of 155. With a land area of , it had a population density of in 2021.
As a designated place in the 2016 Census of Population conducted by Statistics Canada, Pine Shadows had a population of 155 living in 61 of its 65 total private dwellings, a change of from its 2011 population of 152. With a land area of , it had a population density of in 2016.
See also
List of communities in Alberta
List of designated places in Alberta
References
Designated places in Alberta
Yellowhead County |
https://en.wikipedia.org/wiki/MacKay%2C%20Alberta | MacKay is a locality in west-central Alberta, Canada within Yellowhead County. It is located on the Yellowhead Highway (Highway 16) approximately east of Edson.
Statistics Canada recognizes MacKay as a designated place. It was designated as a hamlet between 1979 and 2019.
History
MacKay was designated a hamlet by the Government of Alberta on May 14, 1979 for the purpose of accessing street restoration funding. Yellowhead County repealed the hamlet designation on February 26, 2019.
Demographics
In the 2021 Census of Population conducted by Statistics Canada, MacKay had a population of 10 living in 4 of its 9 total private dwellings, a change of from its 2016 population of 10. With a land area of , it had a population density of in 2021.
As a designated place in the 2016 Census of Population conducted by Statistics Canada, MacKay had a population of 10 living in 7 of its 12 total private dwellings, a change of from its 2011 population of 5. With a land area of , it had a population density of in 2016.
See also
List of communities in Alberta
List of designated places in Alberta
References
Designated places in Alberta
Former hamlets in Alberta
Localities in Yellowhead County
Yellowhead County |
https://en.wikipedia.org/wiki/Koebe%20quarter%20theorem | In complex analysis, a branch of mathematics, the Koebe 1/4 theorem states the following:
Koebe Quarter Theorem. The image of an injective analytic function from the unit disk
onto a subset of the complex plane contains the disk whose center is and whose radius is .
The theorem is named after Paul Koebe, who conjectured the result in 1907. The theorem was proven by Ludwig Bieberbach in 1916. The example of the Koebe function shows that the constant in the theorem cannot be improved (increased).
A related result is the Schwarz lemma, and a notion related to both is conformal radius.
Grönwall's area theorem
Suppose that
is univalent in . Then
In fact, if , the complement of the image of the disk is a bounded domain . Its area is given by
Since the area is positive, the result follows by letting decrease to . The above proof shows equality holds if and only if the complement of the image of has zero area, i.e. Lebesgue measure zero.
This result was proved in 1914 by the Swedish mathematician Thomas Hakon Grönwall.
Koebe function
The Koebe function is defined by
Application of the theorem to this function shows that the constant in the theorem cannot be improved, as the image domain
does not contain the point and so cannot contain any disk centred at with radius larger than .
The rotated Koebe function is
with a complex number of absolute value . The Koebe function and its rotations are schlicht: that is, univalent (analytic and one-to-one) and satisfying and .
Bieberbach's coefficient inequality for univalent functions
Let
be univalent in . Then
This follows by applying Gronwall's area theorem to the odd univalent function
Equality holds if and only if is a rotated Koebe function.
This result was proved by Ludwig Bieberbach in 1916 and provided the basis for his celebrated conjecture that
, proved in 1985 by Louis de Branges.
Proof of quarter theorem
Applying an affine map, it can be assumed that
so that
If is not in , then
is univalent in .
Applying the coefficient inequality to and gives
so that
Koebe distortion theorem
The Koebe distortion theorem gives a series of bounds for a univalent function and its derivative. It is a direct consequence of Bieberbach's inequality for the second coefficient and the Koebe quarter theorem.
Let be a univalent function on normalized so that and and let . Then
with equality if and only if is a Koebe function
Notes
References
External links
Koebe 1/4 theorem at PlanetMath
Theorems in complex analysis |
https://en.wikipedia.org/wiki/Generalized%20Korteweg%E2%80%93De%20Vries%20equation | In mathematics, a generalized Korteweg–De Vries equation is the nonlinear partial differential equation
The function f
is sometimes taken to be f(u) = uk+1/(k+1) + u for some positive integer k (where the extra u is a "drift term" that makes the analysis a little easier). The case f(u) = 3u2 is the original Korteweg–De Vries equation.
References
Partial differential equations |
https://en.wikipedia.org/wiki/Algebra%20%26%20Number%20Theory | Algebra & Number Theory is a peer-reviewed mathematics journal published by the nonprofit organization Mathematical Sciences Publishers. It was launched on January 17, 2007, with the goal of "providing an alternative to the current range of commercial specialty journals in algebra and number theory, an alternative of higher quality and much lower cost."
The journal publishes original research articles in algebra and number theory, interpreted broadly, including algebraic geometry and arithmetic geometry, for example. ANT publishes high-quality articles of interest to a broad readership, at a level surpassing all but the top four or five generalist mathematics journals. Currently, it is regarded as the best journal specializing in number theory.
Issues are published both online and in print.
Editorial board
The Managing Editor is Bjorn Poonen of MIT, and the Editorial Board Chair is David Eisenbud of U. C. Berkeley.
See also
Jonathan Pila
References
External links
Mathematical Sciences Publishers
Mathematics journals
Academic journals established in 2007
Mathematical Sciences Publishers academic journals |
https://en.wikipedia.org/wiki/Mathematical%20Sciences%20Publishers | Mathematical Sciences Publishers is a nonprofit publishing company run by and for mathematicians.
It publishes several journals and the book series Geometry & Topology Monographs. It is run from a central office in the Department of Mathematics at the University of California, Berkeley.
Journals owned and published
Algebra & Number Theory
Algebraic & Geometric Topology
Analysis & PDE
Annals of K-Theory
Communications in Applied Mathematics and Computational Science
Geometry & Topology
Innovations in Incidence Geometry—Algebraic, Topological and Combinatorial
Involve: A Journal of Mathematics
Journal of Algebraic Statistics
Journal of Mechanics of Materials and Structures
Journal of Software for Algebra and Geometry
Mathematics and Mechanics of Complex Systems
Moscow Journal of Combinatorics and Number Theory
Pacific Journal of Mathematics
Probability and Mathematical Physics
Pure and Applied Analysis
Tunisian Journal of Mathematics
Journals distributed
Annals of Mathematics
Book series
Open Book Series
Geometry & Topology Monographs
References
Non-profit academic publishers |
https://en.wikipedia.org/wiki/Hill%20differential%20equation | In mathematics, the Hill equation or Hill differential equation is the second-order linear ordinary differential equation
where is a periodic function by minimal period . By these we mean that for all
and
and if is a number with , the equation must fail for some . It is named after George William Hill, who introduced it in 1886.
Because has period , the Hill equation can be rewritten using the Fourier series of :
Important special cases of Hill's equation include the Mathieu equation (in which only the terms corresponding to n = 0, 1 are included) and the Meissner equation.
Hill's equation is an important example in the understanding of periodic differential equations. Depending on the exact shape of , solutions may stay bounded for all time, or the amplitude of the oscillations in solutions may grow exponentially. The precise form of the solutions to Hill's equation is described by Floquet theory. Solutions can also be written in terms of Hill determinants.
Aside from its original application to lunar stability, the Hill equation appears in many settings including in modeling of a quadrupole mass spectrometer, as the one-dimensional Schrödinger equation of an electron in a crystal, quantum optics of two-level systems, accelerator physics and electromagnetic structures that are periodic in space and/or in time.
References
External links
Ordinary differential equations |
https://en.wikipedia.org/wiki/Denver%20Nuggets%20all-time%20roster | The following is a list of players, both past and current, who appeared at least in one game for the Denver Nuggets NBA franchise.
Players
Note: Statistics are correct through the end of the season.
A
|-
|align="left"| || align="center"|G || align="left"|LSU || align="center"|6 || align="center"|– || 439 || 12,481 || 903 || 1,756 || 7,029 || 28.4 || 2.1 || 4.0 || 16.0 || align=center|
|-
|align="left"| || align="center"|F || align="left"|San Jose State || align="center"|3 || align="center"|– || 64 || 1,210 || 189 || 70 || 380 || 18.9 || 3.0 || 1.1 || 5.9 || align=center|
|-
|align="left"| || align="center"|G || align="left"|Boston College || align="center"|4 || align="center"|– || 304 || 10,601 || 987 || 2,181 || 5,534 || 34.9 || 3.2 || 7.2 || 18.2 || align=center|
|-
|align="left"| || align="center"|G/F || align="left"|UCLA || align="center"|4 || align="center"|– || 266 || 8,381 || 880 || 556 || 3,305 || 31.5 || 3.3 || 2.1 || 12.4 || align=center|
|-
|align="left"| || align="center"|G || align="left"|Illinois State || align="center"|1 || align="center"| || 7 || 22 || 4 || 6 || 7 || 3.1 || 0.6 || 0.9 || 1.0 || align=center|
|-
|align="left"| || align="center"|F || align="left"|Duke || align="center"|1 || align="center"| || 64 || 1,110 || 214 || 74 || 503 || 17.3 || 3.3 || 1.2 || 7.9 || align=center|
|-
|align="left"| || align="center"|G || align="left"|Virginia || align="center"|3 || align="center"|– || 88 || 1,904 || 215 || 315 || 666 || 21.6 || 2.4 || 3.6 || 7.6 || align=center|
|-
|align="left"| || align="center"|G || align="left"|Penn || align="center"|1 || align="center"| || 25 || 251 || 33 || 43 || 64 || 10.0 || 1.3 || 1.7 || 2.6 || align=center|
|-
|align="left"| || align="center"|F/C || align="left"|Villanova || align="center"|1 || align="center"| || 51 || 456 || 82 || 16 || 105 || 8.9 || 1.6 || 0.3 || 2.1 || align=center|
|-
|align="left"| || align="center"|F/C || align="left"|Blinn || align="center"|7 || align="center"|–– || 378 || 6,571 || 1,940 || 164 || 1,938 || 17.4 || 5.1 || 0.4 || 5.1 || align=center|
|-
|align="left"| || align="center"|F/C || align="left"|Houston || align="center"|2 || align="center"|– || 123 || 3,452 || 1,178 || 90 || 1,159 || 28.1 || 9.6 || 0.7 || 9.4 || align=center|
|-
|align="left"| || align="center"|G/F || align="left"|Saint Joseph's || align="center"|1 || align="center"| || 3 || 22 || 4 || 4 || 6 || 7.3 || 1.3 || 1.3 || 2.0 || align=center|
|-
|align="left"| || align="center"|G || align="left"|USC || align="center"|1 || align="center"| || 5 || 33 || 2 || 3 || 21 || 6.6 || 0.4 || 0.6 || 4.2 || align=center|
|-
|align="left"| || align="center"|F/C || align="left"|UC Santa Barbara || align="center"|1 || align="center"| || 78 || 1,380 || 406 || 193 || 663 || 17.7 || 5.2 || 2.5 || 8.5 || align=center|
|-
|align="left" bgcolor="#FFCC00"|+ || align="center"|F || align="left"|Syracuse || align="center"|8 || align="center"|– || 564 || 20,521 || 3,566 || 1,729 || 13,970 || 36.4 || 6.3 || 3.1 || 24.8 || align=c |
https://en.wikipedia.org/wiki/Fathullah%20Shirazi | Sayyed Mīr Fathullāh Shīrāzī (; died 1588-89) was a Persian Sufi polymath and inventor who specialized in many subjects: theology, literature, grammar, philosophy, medicine, mathematics, astronomy, astrology, and mechanics. A close confidant of the Mughal Emperor Akbar, Shirazi held several important administrative positions in his imperial court.
Biography
Early life
Sayyed Mīr Fathullāh Shīrāzī was born and raised in Shiraz, Safavid Iran. He received his education at the school of Azar Kayvan. Here, he studied philosophy and logic under the guidance of Khwajah Jamaluddin Mahmud, a disciple of the logician Jalal al-Din Davani. Shirazi furthered his knowledge in medicine, mathematics, and science under the instruction of Mir Ghayasuddin Mansur. After completing his education, Shirazi embarked on a career in education in Shiraz. Among his notable students was Abdul Rahim Khan-i-Khanan, who served as the close confidant of the Mughal Emperor Akbar.
Arrival in India
Before Shirazi arrived in India, he served the Safavid nobility as a religious dignitary. He migrated to India after being invited by Sultan Ali Adil Shah I, who in turn covered his expenses for the journey. He lived in Bijapur until 1580.
Role in Akbar's Administration
In 1583, Shirazi received an invitation from Mughal Emperor Akbar and subsequently joined the imperial court in Agra. He soon earned the title of Amir and a rank (mansab) of 3000. Two years later, in 1584, Akbar appointed him as the Amin-ul-Mulk, also known as the Trustee of the State. Shirazi's first task was to reexamine and rectify the Mughal Empire's vast transaction records, which he accomplished with diligence and success. Along with his administrative work, Shirazi also undertook the task of regulating the intrinsic and bullion values of coins. He identified and corrected discrepancies in the currency, ensuring its reliability and trustworthiness.
Shirazi’s skills and talents also earned him various honors and titles. In 1585 and 1587, the emperor selected him to lead diplomatic missions to the Deccan, where he was recognized for his efforts with the title of Azud-ud-Dawlah, or the Arm of the Emperor. He also received a horse, 5000 rupees, a robe of honor, and the office of the Chief Sadr of Hindustan.
Death
Shirazi fell ill and died during Akbar’s stay in Kashmir in 1588-89. He was buried in the monastery of Mir Sayyid Ali Hamadani on the Koh-i-Sulaiman. His closeness to Akbar can be ascertained by the fact that sources say that Akbar was deeply disturbed by his death and stated the following:
Inventions
Anti-infantry volley gun with multiple gun barrels similar to a hand cannon.
A machine known as "Yarghu" which could clean sixteen gun barrels simultaneously and was operated by a cow.
A seventeen-barrel cannon fired with a matchlock.
A carriage praised by Abu'l-Fazl ibn Mubarak for its comfort. It was also used to grind corn when not transporting passengers.
A new curriculum for the madrasas which stres |
https://en.wikipedia.org/wiki/1976%E2%80%9377%20Atlanta%20Flames%20season | The 1976–77 Atlanta Flames season was the fifth season for the franchise.
Regular season
Record vs. opponents
Schedule and results
Player statistics
Skaters
Note: GP = Games played; G = Goals; A = Assists; Pts = Points; PIM = Penalty minutes
†Denotes player spent time with another team before joining Atlanta. Stats reflect time with the Flames only.
‡Traded mid-season
Goaltending
Note: GP = Games played; TOI = Time on ice (minutes); W = Wins; L = Losses; OT = Overtime/shootout losses; GA = Goals against; SO = Shutouts; GAA = Goals against average
Transactions
The Flames were involved in the following transactions during the 1976–77 season.
Trades
Draft picks
References
Flames on Hockey Database
Atlanta
Atlanta
Atlanta Flames seasons |
https://en.wikipedia.org/wiki/1977%E2%80%9378%20Atlanta%20Flames%20season | The 1977–78 Atlanta Flames season was the sixth season for the franchise.
Regular season
Final standings
Record vs. opponents
Schedule and results
Player statistics
Skaters
Note: GP = Games played; G = Goals; A = Assists; Pts = Points; PIM = Penalty minutes
†Denotes player spent time with another team before joining Atlanta. Stats reflect time with the Flames only.
‡Traded mid-season
Goaltending
Note: GP = Games played; TOI = Time on ice (minutes); W = Wins; L = Losses; OT = Overtime/shootout losses; GA = Goals against; SO = Shutouts; GAA = Goals against average
Transactions
The Flames were involved in the following transactions during the 1977–78 season.
Trades
Free agents
Draft picks
References
Flames on Hockey Database
Atlanta
Atlanta
Atlanta Flames seasons |
https://en.wikipedia.org/wiki/Shelton%2C%20Nottinghamshire | Shelton is an English village and civil parish in the Rushcliffe borough of Nottinghamshire. According to the 2001 census, Shelton had a population of 107,. At the 2011 census, the statistics for Shelton included Sibthorpe, and the population was 307. The village lies south of Newark-on-Trent, on the north side of the River Smite, near where it joins the River Devon. It has no parish council, only a parish meeting.
Heritage
The parish church of St Mary is Norman. The west tower was removed in 1837 and replaced with a bellcote. It has a Saxon cross shaft with interlace work. Shelton Hall to the west of the church dates from the late 18th century.
Transport
The village is served by twice-weekly Nottsbus Connect buses (Tuesday and Thursday) between Bottesford, Bingham and Lowdham. The nearest railway station is at Bottesford (5.5 miles/9 km), with services between Nottingham and Grantham or Skegness.
References
External links
Villages in Nottinghamshire
Civil parishes in Nottinghamshire
Rushcliffe |
https://en.wikipedia.org/wiki/Extraterrestrial%20Civilizations | Extraterrestrial Civilizations is a 1979 book by Isaac Asimov, in which the author estimates the probability of there being intelligent extraterrestrial civilizations within the Milky Way galaxy. This estimation is approached by progressively analyzing the requirements for life to exist.
Overview
The term "Earth-like world" is prominent, in that the assumption is made that any world where life could evolve would have certain similarities to Earth, such as temperature ranges and gravity sufficient for an atmosphere to exist. Asimov begins with the estimated number of stars in the galaxy, 300 billion.
This number is then reduced to 280 billion as stars without planetary systems are discarded, and then furthermore reduced as more factors are taken into consideration. This process culminates in the statement that "the number of planets in our galaxy on which a technological civilization is now in being is roughly 530,000."
See also
Drake equation
References
Extraterrestrial Civilizations
1979 non-fiction books |
https://en.wikipedia.org/wiki/1978%E2%80%9379%20Atlanta%20Flames%20season | The 1978–79 Atlanta Flames season was the seventh season for the franchise.
Regular season
Final standings
Record vs. opponents
Schedule and results
Player statistics
Skaters
Note: GP = Games played; G = Goals; A = Assists; Pts = Points; PIM = Penalty minutes
†Denotes player spent time with another team before joining Atlanta. Stats reflect time with the Flames only.
‡Traded mid-season.
Goaltending
Note: GP = Games played; TOI = Time on ice (minutes); W = Wins; L = Losses; OT = Overtime/shootout losses; GA = Goals against; SO = Shutouts; GAA = Goals against average
Transactions
The Flames were involved in the following transactions during the 1978–79 season.
Trades
Free agents
Draft picks
Bernhardt Engelbrecht was the first German player selected in the NHL Draft. The Flames selected him in the 12th round.
References
Flames on Hockey Database
Atlanta
Atlanta
Atlanta Flames seasons |
https://en.wikipedia.org/wiki/Benhalima%20Rouane | Benhalima Rouane (born February 28, 1979 in Frenda, Tiaret Province) is an Algerian football player.
National team statistics
External links
1979 births
Living people
People from Frenda
Algerian men's footballers
Algeria men's international footballers
USM Blida players
CA Bordj Bou Arréridj players
USM El Harrach players
AS Khroub players
MO Constantine players
JSM Tiaret players
Men's association football forwards
21st-century Algerian people |
https://en.wikipedia.org/wiki/Membership%20statistics%20of%20the%20Church%20of%20Jesus%20Christ%20of%20Latter-day%20Saints%20%28United%20States%29 | This page shows the membership statistics of the Church of Jesus Christ of Latter-day Saints (LDS Church) within the United States.
Official LDS Membership - Membership count on record provided by the LDS Church. These records include adults and children, and also include both active and less active members.
From religious surveys - General religious surveys conducted within the United States. These surveyed U.S. adults about their religious beliefs.
Membership defined
Membership reported by the Church of Jesus Christ of Latter-day Saints on December 31, 2022, was used to determine the number of members in each state. The church defines membership as:
"Those who have been baptized and confirmed."
"Those under age nine who have been blessed but not baptized."
"Those who are not accountable because of intellectual disabilities, regardless of age."
"Unblessed children under 8 when both of the following apply:
"At least one parent or one grandparent is a member of the Church."
"Both parents give permission for a record to be created. (If only one parent has legal custody of the child, the permission of that parent is sufficient.)"
The United States Census Bureau 2022 population estimates was used as the basis for the general population. Each state link gives a brief history and additional membership information for that state.
Table
Congregational
Members and growth
Territories
From religious surveys
2001 American Religious Identification Survey
The 2001 American Religious Identification Survey (ARIS) was based on a random digit-dialed telephone survey of 50,281 American adults in the continental U.S.
2007 Pew Forum on Religion & Public Life
The Pew Forum on Religion & Public Life published a survey of 35,556 adults living in the United States that was conducted in 2007. The 2007 survey, conducted by Princeton Survey Research Associates International (PSRAI), found 1.7% of the U.S. adult population self identified themselves as Mormon. The table below lists a few significant findings, from the survey, about Mormons. Note: some less populated states were combined in this survey. These include:Montana-Wyoming,D.C.-Maryland, North & South Dakota, New Hampshire-Vermont, and Connecticut-Rhode Island. The racial and ethnic composition of the U.S. membership is predominantly white with a lower percentage of blacks when compared to the U.S. average.
See also
Membership history of the Church of Jesus Christ of Latter-day Saints
Membership statistics of the Church of Jesus Christ of Latter-day Saints (Canada)
References
The Church of Jesus Christ of Latter-day Saints
Membership statistics
Religious demographics |
https://en.wikipedia.org/wiki/Membership%20statistics%20of%20the%20Church%20of%20Jesus%20Christ%20of%20Latter-day%20Saints%20%28Canada%29 | In the 2021 Canadian census the number of persons who self-identified with The Church of Jesus Christ of Latter-day Saints was 85,315 down from 105,365 in 2011. The following tables and graphs use general population data taken from Statistics Canada using the first quarter 2020 population estimates. The official membership statistics as of Jan 1, 2020 provided by the Church of Jesus Christ of Latter-day Saints (LDS Church) was used for all other data.
Table
See also
The Church of Jesus Christ of Latter-day Saints in Canada
LDS membership statistics (World)
LDS membership statistics (United States)
References
Membership statistics
Religious demographics |
https://en.wikipedia.org/wiki/Tomi%20Shimomura | is a former Japanese football player.
Club statistics
References
External links
1980 births
Living people
Osaka University of Health and Sport Sciences alumni
Association football people from Sapporo
Japanese men's footballers
J1 League players
J2 League players
Cerezo Osaka players
JEF United Chiba players
Montedio Yamagata players
Shonan Bellmare players
Giravanz Kitakyushu players
Japanese people of Austrian descent
Men's association football midfielders |
https://en.wikipedia.org/wiki/Stanley%20Townsend | Stanley Townsend (born August 1961) is an Irish actor.
Personal life
Townsend was born and brought up in Dublin. After attending Wesley College, Dublin, he studied mathematics and civil engineering at Trinity College. While there he joined the Dublin University Players, the college's Amateur Dramatic Society. He later co-founded co-operative theatre company Rough Magic with writer/director Declan Hughes and theatre director Lynne Parker, performing in numerous productions including The Country Wife, Nightshade, and Sexual Perversity in Chicago. He subsequently went on to perform in several productions at The Gate and The Abbey Theatres in Dublin. In London, he has worked with such directors as Sam Mendes in The Plough and the Stars, Richard Eyre in Guys and Dolls and Rufus Norris in Under the Blue Sky. Theatre appearances at the Royal Court include The Alice Trilogy directed by Ian Rickson and Shining City directed by Conor McPherson, for which he won an Irish Theatre Award and was nominated for the Evening Standard Theatre Award for Best Actor in 2004.
Career
Townsend's television work began on a number of shows for RTÉ in Dublin. Since moving to London, television appearances have included Spooks, The Commander, Hustle, Waking the Dead, and Omagh Bombing.
Film credits include Mike Newell's Into the West, Jim Sheridan's In the Name of the Father with Daniel Day-Lewis, The Van by Stephen Frears, Peter Greenaway's The Tulse Luper Suitcases, The Libertine with Johnny Depp, Paul Morrison's Wondrous Oblivion with Delroy Lindo, John Boorman's The Tiger's Tale and Michael Radford's Flawless. He currently lives in London.
Theatre
Townsend's work in theatre includes: Remember This, Guys and Dolls, Phedre and Happy Now? at the National Theatre, London; The Alice Trilogy, Shining City (for which he won the Irish Times Best Actor Award), Under the Blue Sky, The Weir and Tribes at the Royal Court, London; The Wake, Trinity for Two and Sacred Mysteries at the Abbey Theatre, Dublin; The Gingerbread Mix-up at St Andrews Lane, Dublin; Prayers of Sherkin at the Old Vic, London; Someone Who'll Watch Over Me at West Yorkshire Playhouse, Leeds; The Plough and the Stars at the Young Vic, London; Democracy at the Bush Theatre, London; Speed-the-Plow for Project Arts Centre, Dublin; Saint Oscar for Field Day Theatre Company, Derry; Sexual Perversity in Chicago, The Caucasian Chalk Circle, The Country Wife, Nightshade and The White Devil for Rough Magic, Dublin; Who Shall Be Happy...? for Mad Cow Productions, Belfast, London and tour; and 'Art' in the West End. He played Eddie Carbone in A View from the Bridge at the Royal Lyceum Theatre in Edinburgh in early 2011. His portrayal of Sims in The Nether for director Jeremy Herrin at the Royal Court Theatre in July 2014 won critical acclaim.
Television
Townsend's television credits include: Zen, Whistleblower, He Kills Coppers, Prosperity, Saddam's Tribe, Rough Diamond, Waking The Dead, Spooks, The Virgin Queen, Hustl |
https://en.wikipedia.org/wiki/Generalized%20estimating%20equation | In statistics, a generalized estimating equation (GEE) is used to estimate the parameters of a generalized linear model with a possible unmeasured correlation between observations from different timepoints. Although some believe that Generalized estimating equations are robust in everything even with the wrong choice of working-correlation matrix, Generalized estimating equations are only robust to loss of consistency with the wrong choice.
Regression beta coefficient estimates from the Liang Zeger GEE are consistent, unbiased, asymptotically normal even when the working correlation is misspecified, under mild regularity conditions. GEE is higher in efficiency than generalized linear iterative model GLIM (software) in the presence of high autocorrelation. When the true working-correlation is known, consistency does not require MCAR. Huber-White standard errors improve the efficiency of Liang Zeger GEE in the absence of serial Autocorrelation but may remove the marginal interpretation. GEE estimates the average response over the population ("population-averaged" effects) with Liang Zeger Standard Errors, and in individuals using Huber White Standard Errors also known as "robust standard error" or "sandwich variance" estimates. Huber-White GEE was used since 1997, and Liang Zeger GEE dates to the 1980s based on a limited literature review. Several independent formulations of these standard error estimators contribute to GEE theory. Placing the independent standard error estimators under the umbrella term "GEE" may exemplify Abuse of language.
GEEs belong to a class of regression techniques that are referred to as semiparametric because they rely on specification of only the first two moments. They are a popular alternative to the likelihood–based generalized linear mixed model which is more at risk for consistency loss at variance structure specification. The trade-off of variance-structure misspecification and consistent regression coefficient estimates is loss of efficiency, so inflated Wald test p-values as a result of higher variance of standard errors than that of the most optimal. They are commonly used in large epidemiological studies, especially multi-site cohort studies, because they can handle many types of unmeasured dependence between outcomes.
Formulation
Given a mean model for subject and time that depends upon regression parameters , and variance structure, , the estimating equation is formed via:
The parameters are estimated by solving and are typically obtained via the Newton–Raphson algorithm. The variance structure is chosen to improve the efficiency of the parameter estimates. The Hessian of the solution to the GEEs in the parameter space can be used to calculate robust standard error estimates. The term "variance structure" refers to the algebraic form of the covariance matrix between outcomes, Y, in the sample. Examples of variance structure specifications include independence, exchangeable, autoregressive, stati |
https://en.wikipedia.org/wiki/List%20of%20urban%20areas%20in%20Sweden | There are 1,956 urban areas in Sweden as defined by Statistics Sweden on 31 December 2010. The official term used by Statistics Sweden is "locality" () instead of "urban area" and they are defined as having a minimum of 200 inhabitants. The total population of the localities was 8,016,000 in 2010, which made up 85% of the population of the whole country.
The urban areas made up 1.3% of the land area of the whole country. The average population density of the urban areas was 1,491 inhabitants per square kilometre (km2).
References
General
Notes
Demographics of Sweden
Lists of populated places in Sweden |
https://en.wikipedia.org/wiki/Milwaukee%20Bucks%20all-time%20roster | The following is a list of players, both past and current, who appeared at least in one game for the Milwaukee Bucks NBA franchise.
Players
Note: Statistics were updated through the end of the season.
A
|-
|align="left"| || align="center"|F/C || align="left"|Duke || align="center"|1 || align="center"| || 12 || 159 || 37 || 10 || 64 || 13.3 || 3.1 || 0.8 || 5.3 || align=center|
|-
|align="left"| || align="center"|F/C || align="left"|Iowa State || align="center"|2 || align="center"|– || 109 || 2,474 || 981 || 95 || 913 || 22.7 || 9.0 || 0.9 || 8.4 || align=center|
|-
|align="left" bgcolor="#FFFF99"| (formerly Lew Alcindor)^ (#33) || align="center"|C || align="left"|UCLA || align="center"|6 || align="center"|– || 467 || 19,954 || bgcolor="#CFECEC"|7,161 || 2,008 || 14,211 || bgcolor="#CFECEC"|42.7 || bgcolor="#CFECEC"|15.3 || 4.3 || bgcolor="#CFECEC"|30.4 || align=center|
|-
|align="left"| || align="center"|G || align="left"|St. Bonaventure || align="center"|1 || align="center"| || 7 || 18 || 3 || 2 || 2 || 2.6 || 0.4 || 0.3 || 0.3 || align=center|
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|align="left"| || align="center"|F || align="left"|UConn || align="center"|1 || align="center"| || 28 || 705 || 218 || 31 || 305 || 25.2 || 7.8 || 1.1 || 10.9 || align=center|
|-
|align="left"| || align="center"|F || align="left"|West Virginia || align="center"|1 || align="center"| || 59 || 716 || 115 || 42 || 278 || 12.1 || 1.9 || 0.7 || 4.7 || align=center|
|-
|align="left"| || align="center"|G || align="left"|Duke || align="center"|2 || align="center"|– || 138 || 3,777 || 459 || 263 || 1,483 || 27.4 || 3.3 || 1.9 || 10.7 || align=center|
|-
|align="left"| || align="center"|G || align="left"|UCLA || align="center"|5 || align="center"|– || 303 || 8,901 || 1,007 || 1,347 || 4,185 || 29.4 || 3.3 || 4.4 || 13.8 || align=center|
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|align="left"| || align="center"|F/C || align="left"|Villanova || align="center"|1 || align="center"| || 49 || 579 || 103 || 35 || 156 || 11.8 || 2.1 || 0.7 || 3.2 || align=center|
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|align="left" bgcolor="#FFFF99"|^ || align="center"|G || align="left"|UConn || align="center"|7 || align="center"|– || 494 || 17,945 || 2,260 || 1,861 || 9,681 || 36.3 || 4.6 || 3.8 || 19.6 || align=center|
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|align="left"| || align="center"|G || align="left"|Fresno State || align="center"|3 || align="center"|– || 114 || 1,249 || 126 || 281 || 314 || 11.0 || 1.1 || 2.5 || 2.8 || align=center|
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|align="left"| || align="center"|F/C || align="left"|Houston || align="center"|2 || align="center"|– || 86 || 1,538 || 448 || 27 || 599 || 17.9 || 5.2 || 0.3 || 7.0 || align=center|
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|align="left" bgcolor="#FBCEB1"|* || align="center"|G/F || align="left"|Greece || align="center"|10 || align="center"|– || bgcolor="#CFECEC"|719 || bgcolor="#CFECEC"|23,378 || 6,891 || bgcolor="#CFECEC"|3,379 || bgcolor="#CFECEC"|16,280 || 32.5 || 9.6 || 4.7 || 22.6 || align=center|
|-
|align="left" bgcolor="#CCFFCC"|x || align="center"|F || align="left"|Greece || align="center"|4 || align="center"|– || 162 || 1,359 | |
https://en.wikipedia.org/wiki/2007%E2%80%9308%20Oldham%20Athletic%20A.F.C.%20season | This article details Oldham Athletic A.F.C.'s season in League One during the 2007–08 season.
Club
Players
As of 15 March 2008:
Statistics leaders
Club Statistics | Oldham Athletic
Transfers
In
Out
Loan in
Loan out
League position
Results
Legend
League One
FA Cup
League Cup
Football League Trophy
References
External links
Oldham Athletic official website
Trust Oldham website (Supporters Trust)
Sky Sports
BBC Sport
Oldham Athletic A.F.C. seasons
Oldham Athletic |
https://en.wikipedia.org/wiki/Cognate%20linkage | In kinematics, cognate linkages are linkages that ensure the same coupler curve geometry or input-output relationship, while being dimensionally dissimilar. In case of four-bar linkage coupler cognates, the Roberts–Chebyshev Theorem, after Samuel Roberts and Pafnuty Chebyshev, states that each coupler curve can be generated by three different four-bar linkages. These four-bar linkages can be constructed using similar triangles and parallelograms, and the Cayley diagram (named after Arthur Cayley).
Overconstrained mechanisms can be obtained by connecting two or more cognate linkages together.
Roberts–Chebyshev theorem
The theorem states, for a given coupler curve produced by a four-bar linkage with four revolute (hinge) joints, there exist three four-bar linkages, three geared five-bar linkages, and more six-bar linkages which will generate the same path.
For a coupler curve produced by a four-bar linkage with four revolute joints and a prismatic (slider) joint, there exist only two four-bar linkages, as the third would be composed of two sliders, making it a four-bar linkage with two degrees of freedom.
Construction of four-bar coupler cognates
Cayley diagram
From original triangle, :
Sketch Cayley diagram.
Using parallelograms, find and and .
Using similar triangles, find and and .
Using a parallelogram, find .
Check similar triangles .
Separate left and right cognate.
Put dimensions on Cayley diagram.
Dimensional relationships
The lengths of the four members can be found by using the law of sines. Both and are found as follows.
Conclusions
If and only if the original is a Class I chain Both 4-bar cognates will be class I chains.
If the original is a drag-link (double crank), both cognates will be drag links.
If the original is a crank-rocker, one cognate will be a crank-rocker, and the second will be a double-rocker.
If the original is a double-rocker, the cognates will be crank-rockers.
Construction of geared five-bar cognates
A five-bar linkage has two degrees of freedom, and thus there does not exist a five-bar linkage which is capable of acting as a cognate. However, it is possible to generate a 5-bar cognate using gears.
Select four-bar linkage of choice.
Construct two parallelograms off of the center coupler link and the links connected to the ground.
On each parallelogram, find the sides opposite of the connecting link. Apply a 1:1 gear train between them.
Separate cognates.
The utilization of the 1:1 gear train is used because of the behavior of parallelogram linkages. Opposite 'sides' of the parallelogram linkages share the same rotational motion function. Because both parallelograms were constructed off of the center coupler link, the new links connected to the ground share identical rotational motion functions, allowing for a 1:1 gear train to be used to connect them together.
Construction of six-bar coupler cognates
Alternative to geared five-bar cognates
The geared five-bar cognate linka |
https://en.wikipedia.org/wiki/Bernoulli%20Society%20for%20Mathematical%20Statistics%20and%20Probability | The Bernoulli Society is a professional association that aims to further the progress of probability and mathematical statistics, founded as part of the International Statistical Institute in 1975. It is named after the Bernoulli family of mathematicians and scientists, whose researchers covered "most areas of scientific knowledge".
The society publishes two journals, Bernoulli and Stochastic Processes and their Applications, and a newsletter, Bernoulli News. Additionally, it co-sponsors several other journals including Electronic Communications in Probability, Electronic Journal of Probability, Electronic Journal of Statistics, Probability Surveys, and Statistics Surveys.
Presidents of the Bernoulli Society
A list of the presidents of the society from its foundation to the current day.
1975 David George Kendall
1975 David Blackwell
1977 Klaus Krickeberg
1979 David Cox
1981 Pál Révész
1983 Elizabeth Scott
1985 Chris Heyde
1987 Willem van Zwet
1989 Albert Shiryaev
1991 Peter J. Bickel
1993 Ole Barndorff-Nielsen
1995 Jozef Teugels
1997 Louis Chen
1999 David Siegmund
2001 Peter G. Hall
2003 Donald A. Dawson
2005 Peter Jagers
2007 Jean Jacod
2009 Victor Perez-Abreu
2011 Edward C. Waymire
2013 Wilfrid Kendall
2015 Sara van de Geer
2017 Susan Murphy
2019 Claudia Klüppelberg
2021 Adam Jakubowski
2023 Victor Panaretos
2025 Nancy Reid
References
External links
Bernoulli Society for Mathematical Statistics and Probability
Statistical societies |
https://en.wikipedia.org/wiki/Michigan%20Mathematical%20Journal | The Michigan Mathematical Journal (established 1952) is published by the mathematics department at the University of Michigan. An important early editor for the Journal was George Piranian.
Historically, the Journal has been published a small number of times in a given year (currently four), in all areas of mathematics. The current Managing Editor is Mircea Mustaţă.
References
External links
Mathematics journals
University of Michigan
1952 establishments in Michigan
Academic journals established in 1952 |
https://en.wikipedia.org/wiki/U-statistic | In statistical theory, a U-statistic is a class of statistics that is especially important in estimation theory; the letter "U" stands for unbiased. In elementary statistics, U-statistics arise naturally in producing minimum-variance unbiased estimators.
The theory of U-statistics allows a minimum-variance unbiased estimator to be derived from each unbiased estimator of an estimable parameter (alternatively, statistical functional) for large classes of probability distributions. An estimable parameter is a measurable function of the population's cumulative probability distribution: For example, for every probability distribution, the population median is an estimable parameter. The theory of U-statistics applies to general classes of probability distributions.
History
Many statistics originally derived for particular parametric families have been recognized as U-statistics for general distributions. In non-parametric statistics, the theory of U-statistics is used to establish for statistical procedures (such as estimators and tests) and estimators relating to the asymptotic normality and to the variance (in finite samples) of such quantities. The theory has been used to study more general statistics as well as stochastic processes, such as random graphs.
Suppose that a problem involves independent and identically-distributed random variables and that estimation of a certain parameter is required. Suppose that a simple unbiased estimate can be constructed based on only a few observations: this defines the basic estimator based on a given number of observations. For example, a single observation is itself an unbiased estimate of the mean and a pair of observations can be used to derive an unbiased estimate of the variance. The U-statistic based on this estimator is defined as the average (across all combinatorial selections of the given size from the full set of observations) of the basic estimator applied to the sub-samples.
Sen (1992) provides a review of the paper by Wassily Hoeffding (1948), which introduced U-statistics and set out the theory relating to them, and in doing so Sen outlines the importance U-statistics have in statistical theory. Sen says, “The impact of Hoeffding (1948) is overwhelming at the present time and is very likely to continue in the years to come.” Note that the theory of U-statistics is not limited to the case of independent and identically-distributed random variables or to scalar random-variables.
Definition
The term U-statistic, due to Hoeffding (1948), is defined as follows.
Let be either the real or complex numbers, and let be a -valued function of -dimensional variables.
For each the associated U-statistic is defined to be the average of the values over the set of -tuples of indices from with distinct entries.
Formally,
.
In particular, if is symmetric the above is simplified to
,
where now denotes the subset of of increasing tuples.
Each U-statistic is necessarily a symmetric function.
U-s |
https://en.wikipedia.org/wiki/Calogero%E2%80%93Degasperis%E2%80%93Fokas%20equation | In mathematics, the Calogero–Degasperis–Fokas equation is the nonlinear partial differential equation
This equation was named after F. Calogero, A. Degasperis, and A. Fokas.
See also
Boomeron equation
Zoomeron equation
External links
Partial differential equations
Integrable systems |
https://en.wikipedia.org/wiki/Constrained%20generalized%20inverse | In linear algebra, a constrained generalized inverse is obtained by solving a system of linear equations with an additional constraint that the solution is in a given subspace. One also says that the problem is described by a system of constrained linear equations.
In many practical problems, the solution of a linear system of equations
is acceptable only when it is in a certain linear subspace of .
In the following, the orthogonal projection on will be denoted by .
Constrained system of linear equations
has a solution if and only if the unconstrained system of equations
is solvable. If the subspace is a proper subspace of , then the matrix of the unconstrained problem may be singular even if the system matrix of the constrained problem is invertible (in that case, ). This means that one needs to use a generalized inverse for the solution of the constrained problem. So, a generalized inverse of is also called a -constrained pseudoinverse of .
An example of a pseudoinverse that can be used for the solution of a constrained problem is the Bott–Duffin inverse of constrained to , which is defined by the equation
if the inverse on the right-hand-side exists.
Matrices |
https://en.wikipedia.org/wiki/Bouabdellah%20Daoud | Bouabdellah Daoud (born February 3, 1978 in Oran, Algeria) is an Algerian footballer.
Daoud has 19 caps for the Algerian National Team.
National team statistics
References
External links
1978 births
Algerian men's footballers
Algeria men's international footballers
Living people
JS Kabylie players
Footballers from Oran
CR Témouchent players
MC Oran players
Expatriate men's footballers in Tunisia
Espérance Sportive de Tunis players
WA Tlemcen players
ASO Chlef players
Algerian expatriate sportspeople in Tunisia
People from Aïn Témouchent Province
IRB Maghnia players
Algerian Ligue Professionnelle 1 players
Algerian Ligue 2 players
Men's association football forwards
21st-century Algerian people |
https://en.wikipedia.org/wiki/Director%20string | In mathematics, in the area of lambda calculus and computation, directors or director strings are a mechanism for keeping track of the free variables in a term. Loosely speaking, they can be understood as a kind of memoization for free variables; that is, as an optimization technique for rapidly locating the free variables in a term algebra or in a lambda expression. Director strings were introduced by Kennaway and Sleep in 1982 and further developed by Sinot, Fernández and Mackie as a mechanism for understanding and controlling the computational complexity cost of beta reduction.
Motivation
In beta reduction, one defines the value of the expression on the left to be that on the right:
or (Replace all x in E(body) by y)
While this is a conceptually simple operation, the computational complexity of the step can be non-trivial: a naive algorithm would scan the expression E for all occurrences of the free variable x. Such an algorithm is clearly O(n) in the length of the expression E. Thus, one is motivated to somehow track the occurrences of the free variables in the expression. One may attempt to track the position of every free variable, wherever it may occur in the expression, but this can clearly become very costly in terms of storage; furthermore, it provides a level of detail that is not really needed. Director strings suggest that the correct model is to track free variables in a hierarchical fashion, by tracking their use in component terms.
Definition
Consider, for simplicity, a term algebra, that is, a collection of free variables, constants, and operators which may be freely combined. Assume that a term t takes the form
where f is a function, of arity n, with no free variables, and the are terms that may or may not contain free variables. Let V denote the set of all free variables that may occur in the set of all terms. The director is then the map
from the free variables to the power set of the set . The values taken by are simply a list of the indices of the in which a given free variable occurs. Thus, for example, if a free variable occurs in and but in no other terms, then one has .
Thus, for every term in the set of all terms T, one maintains a function , and instead of working only with terms t, one works with pairs . Thus, the time complexity of finding the free variables in t is traded for the space complexity of maintaining a list of the terms in which a variable occurs.
General case
Although the above definition is formulated in terms of a term algebra, the general concept applies more generally, and can be defined both for combinatory algebras and for lambda calculus proper, specifically, within the framework of explicit substitution.
See also
Term rewrite system
Explicit substitution
Memoization
References
F.-R. Sinot. "Director Strings Revisited: A Generic Approach to the Efficient Representation of Free Variables in Higher-order Rewriting." Journal of Logic and Computation 15(2), pages 201- |
https://en.wikipedia.org/wiki/List%20of%20idioms%20of%20improbability | There are many idioms of improbability, or adynata, used to denote that a given event is impossible or extremely unlikely to occur.
In English
Events that can never happen
As a response to an unlikely proposition, "when pigs fly", "when pigs have wings", or simply "pigs might fly".
"When Hell freezes over" and "on a cold day in Hell" are based on the understanding that Hell is eternally an extremely hot place.
The "Twelfth of Never" will never come to pass. A song of the same name was written by Johnny Mathis.
"On Tibb's Eve" refers to the saint's day of a saint who never existed.
"If the sky falls, we shall catch larks" means that it is pointless to worry about things that will never happen.
Events that rarely or might never happen
"Once in a blue moon" refers to a rare event. In fact, a "blue moon" occurs every two to three years in a year that has 13 full moons instead of the more usual 12. The "blue moon" is the third full moon in a season having four full moons.
"Don't hold your breath" implies that if you hold your breath while waiting for a particular thing to happen, you will die first.
Tasks that are difficult or impossible to perform
To have "a snowball's chance in Hell".
"Like getting blood from a stone", and "like squeezing water from a stone".
"Like finding a needle in a haystack"
"Like herding cats"
Things that are impossible to find
"As rare as hen's teeth".
"As rare as rocking-horse poo".
People or things that are of no use
"As much use as a one-legged man at an arse-kicking contest".
"As much use as a chocolate teapot".
In other languages
Afrikaans – as die perde horings kry ("when horses grow horns")
Albanian – ne 36 gusht ("on the thirty-sixth of August")
Arabic has a wide range of idioms differing from a region to another. In some Arab countries of the Persian Gulf, one would say إذا حجت البقرة على قرونها idha ḥajjit il-bagara `ala gurunha ("when the cow goes on pilgrimage on its horns"). In Egypt, one says في المشمش fil-mishmish ("when the apricots bloom"). Other Arab people, mainly Palestinian, use the expression لما ينور الملح lemma ynawwar il-malḥ, which roughly translates into "when salt blossoms" or "when salt flowers"
Breton - Pa nijo ar moc'h ("when pigs fly")
Chinese – 太陽從西邊升起 ("when the sun rises in the West")
Czech – až naprší a uschne meaning "When it rains and dries". Another expression is až opadá listí z dubu ("When the leaves fall from the oak")
Danish – når der er to torsdage i én uge ("when there are two Thursdays in one week")
Dutch – met , or als Pinksteren en Pasen op één dag vallen ("when Pentecost and Easter are on the same day")
Esperanto – je la tago de Sankta Neniam ("on Saint Never's Day") — a loan-translation from German (see below).
Finnish – sitten kun lehmät lentävät - when the cows fly. Also jos lehmällä olisi siivet, se lentäisi (if cow had wings, it would fly), implying futile speculations. Also kun lipputanko kukkii ("when flagpole blossoms") and Tuohikuussa Pukin-päivän aika |
https://en.wikipedia.org/wiki/First%20variation%20of%20area%20formula | In the mathematical field of Riemannian geometry, every submanifold of a Riemannian manifold has a surface area. The first variation of area formula is a fundamental computation for how this quantity is affected by the deformation of the submanifold. The fundamental quantity is to do with the mean curvature.
Let denote a Riemannian manifold, and consider an oriented smooth manifold (possibly with boundary) together with a one-parameter family of smooth immersions of into . For each individual value of the parameter , the immersion induces a Riemannian metric on , which itself induces a differential form on known as the Riemannian volume form . The first variation of area refers to the computation
in which is the mean curvature vector of the immersion and denotes the variation vector field Both of these quantities are vector fields along the map . The second term in the formula represents the exterior derivative of the interior product of the volume form with the vector field on , defined as the tangential projection of . Via Cartan's magic formula, this term can also be written as the Lie derivative of the volume form relative to the tangential projection. As such, this term vanishes if each is reparametrized by the corresponding one-parameter family of diffeomorphisms of .
Both sides of the first variation formula can be integrated over , provided that the variation vector field has compact support. In that case it is immediate from Stokes' theorem that
In many contexts, is a closed manifold or the variation vector field is every orthogonal to the submanifold. In either case, the second term automatically vanishes. In such a situation, the mean curvature vector is seen as entirely governing how the surface area of a submanifold is modified by a deformation of the surface. In particular, the vanishing of the mean curvature vector is seen as being equivalent to submanifold being a critical point of the volume functional. This shows how a minimal submanifold can be characterized either by the critical point theory of the volume functional or by an explicit partial differential equation for the immersion.
The special case of the first variation formula arising when is an interval on the real number line is particularly well-known. In this context, the volume functional is known as the length functional and its variational analysis is fundamental to the study of geodesics in Riemannian geometry.
References
Riemannian geometry |
https://en.wikipedia.org/wiki/Beauville%E2%80%93Laszlo%20theorem | In mathematics, the Beauville–Laszlo theorem is a result in commutative algebra and algebraic geometry that allows one to "glue" two sheaves over an infinitesimal neighborhood of a point on an algebraic curve. It was proved by .
The theorem
Although it has implications in algebraic geometry, the theorem is a local result and is stated in its most primitive form for commutative rings. If A is a ring and f is a nonzero element of A, then we can form two derived rings: the localization at f, Af, and the completion at Af, Â; both are A-algebras. In the following we assume that f is a non-zero divisor. Geometrically, A is viewed as a scheme X = Spec A and f as a divisor (f) on Spec A; then Af is its complement Df = Spec Af, the principal open set determined by f, while  is an "infinitesimal neighborhood" D = Spec  of (f). The intersection of Df and Spec  is a "punctured infinitesimal neighborhood" D0 about (f), equal to Spec  ⊗A Af = Spec Âf.
Suppose now that we have an A-module M; geometrically, M is a sheaf on Spec A, and we can restrict it to both the principal open set Df and the infinitesimal neighborhood Spec Â, yielding an Af-module F and an Â-module G. Algebraically,
(Despite the notational temptation to write , meaning the completion of the A-module M at the ideal Af, unless A is noetherian and M is finitely-generated, the two are not in fact equal. This phenomenon is the main reason that the theorem bears the names of Beauville and Laszlo; in the noetherian, finitely-generated case, it is, as noted by the authors, a special case of Grothendieck's faithfully flat descent.) F and G can both be further restricted to the punctured neighborhood D0, and since both restrictions are ultimately derived from M, they are isomorphic: we have an isomorphism
Now consider the converse situation: we have a ring A and an element f, and two modules: an Af-module F and an Â-module G, together with an isomorphism φ as above. Geometrically, we are given a scheme X and both an open set Df and a "small" neighborhood D of its closed complement (f); on Df and D we are given two sheaves which agree on the intersection D0 = Df ∩ D. If D were an open set in the Zariski topology we could glue the sheaves; the content of the Beauville–Laszlo theorem is that, under one technical assumption on f, the same is true for the infinitesimal neighborhood D as well.
Theorem: Given A, f, F, G, and φ as above, if G has no f-torsion, then there exist an A-module M and isomorphisms
consistent with the isomorphism φ: φ is equal to the composition
The technical condition that G has no f-torsion is referred to by the authors as "f-regularity". In fact, one can state a stronger version of this theorem. Let M(A) be the category of A-modules (whose morphisms are A-module homomorphisms) and let Mf(A) be the full subcategory of f-regular modules. In this notation, we obtain a commutative diagram of categories (note Mf(Af) = M(Af)):
in which the arrows are the base-chan |
https://en.wikipedia.org/wiki/King%27s%20Oak%20Academy | King's Oak Academy, formerly Kingsfield School and Kingswood Grammar School, is a Mathematics and Computing College located in Kingswood in Bristol, England. The education authority Ofsted rated it as "good" in 2018.
Location and admissions
The school is located just within the unitary authority of South Gloucestershire, which borders Bristol. It is situated at the roundabout of the A420 and the A4174 (Bristol ring road), between Warmley Hill and Warmley.
It is a mixed comprehensive school providing education for 950 students , predominantly from a catchment area of around .
History
Grammar school
The school was founded in 1921 as Kingswood Grammar School (KGS), a co-educational grammar school administered by the Gloucestershire Education Committee.
On 15 October 1946, 13-year-old Robert Hayes of Kingswood died at Cossham Memorial Hospital after being injured at the school when playing with blank cartridges he had found at an ammunition dump. His right hand was blown off and he had other injuries to his body.
In the 1960s the school had around 850 boys and girls, with 250 in the sixth form.
Comprehensive school
By 1970 it had been converted into a comprehensive school and was renamed Kingsfield School. The school was rebuilt after burning to the ground in 1976.
Academy
Kingsfield School was officially rebranded as King's Oak Academy in September 2011. Its motto is "Work hard, be kind".
Blue jumpers and red ties (formerly brown and blue) are worn, with coloured stripes according to house colour: Olympus (yellow stripes); Orpheus (blue stripes); Pegasus (red stripes); and Hercules (green stripes).
Notable alumni
Kingswood Rugby Club
Kingswood RFC Old Boys was founded in 1954/55 by a group of former students of Kingswood Grammar School. The club continues to play in the grammar school's blue and brown colours.
References
External links
Kingswood, South Gloucestershire
Primary schools in South Gloucestershire District
Secondary schools in South Gloucestershire District
Academies in South Gloucestershire District
Educational institutions established in 1921
1921 establishments in England
People educated at King's Oak Academy |
https://en.wikipedia.org/wiki/NUTS%20statistical%20regions%20of%20Bulgaria | The Nomenclature of Territorial Units for Statistics (NUTS) is a geocode standard for referencing the subdivisions of Bulgaria for statistical purposes. The standard is developed and regulated by the European Union. The NUTS standard is instrumental in delivering the European Union's Structural Funds. The NUTS code for Bulgaria is BG and a hierarchy of three levels is established by Eurostat. Below these is a further levels of geographic organisation - the local administrative unit (LAU). In Bulgaria, the LAU 1 is municipalities and the LAU 2 is settlements.
Overall
NUTS Levels
Local Administrative Units
Below the NUTS levels, the two LAU (Local Administrative Units) levels are:
The LAU codes of Bulgaria can be downloaded here:
NUTS codes
In the 2003 version, the codes were as follows:
BG1 North Bulgaria
BG11 North West
BG111 Vidin
BG112 Montana
BG113 Vratsa
BG12 North Central
BG121 Pleven
BG122 Lovech
BG123 Veliko Tarnovo
BG124 Gabrovo
BG125 Ruse
BG13 North East
BG131 Varna
BG132 Dobrich
BG133 Shumen
BG134 Targovishte
BG135 Razgrad
BG136 Silistra
BG2 South Bulgaria
BG21 South West
BG211 Grad Sofiya
BG212 Sofiya
BG213 Blagoevgrad
BG214 Pernik
BG215 Kyustendil
BG22 South Central
BG221 Plovdiv
BG222 Stara Zagora
BG223 Haskovo
BG224 Pazardzhik
BG225 Smolyan
BG226 Kardzhali
BG23 South East
BG231 Burgas
BG232 Sliven
BG233 Yambol
NUTS 2 regions redrawing
Some of the present NUTS II regions of Bulgaria no longer meet the relevant technical requirements, mostly due to general population decline and increasing regional disproportion. A 2013 study by FLGR Consult commissioned by the Ministry of Regional Development and Public Works analyzed the state and trends of change in the characteristics of these regions to identify several options for the pending redrawing of the NUTS II map of the country. The process was restarted in 2017 with certain modified versions considered, and final decision due by the end of 2018. The relevant Regional Development (Amendment) Bill, released for public consultation by the Council of Ministers in October 2018, is based on a four-regions version chosen from the shortlist of three options developed by an inter-ministerial working group led by the Ministry of Regional Development and Public Works.
See also
Subdivisions of Bulgaria
ISO 3166-2 codes of Bulgaria
FIPS region codes of Bulgaria
List of Bulgarian regions by Human Development Index
Notes
Sources
Hierarchical list of the Nomenclature of territorial units for statistics - NUTS and the Statistical regions of Europe
Overview map of EU Countries - NUTS level 1
BULGARIA - NUTS level 2
BULGARIA - NUTS level 3
Correspondence between the NUTS levels and the national administrative units
List of current NUTS codes
Download current NUTS codes (ODS format)
Regions of Bulgaria, Statoids.com
Bulgaria
Nuts |
https://en.wikipedia.org/wiki/Arithmetic%20derivative | In number theory, the Lagarias arithmetic derivative or number derivative is a function defined for integers, based on prime factorization, by analogy with the product rule for the derivative of a function that is used in mathematical analysis.
There are many versions of "arithmetic derivatives", including the one discussed in this article (the Lagarias arithmetic derivative), such as Ihara's arithmetic derivative and Buium's arithmetic derivatives.
Early history
The arithmetic derivative was introduced by Spanish mathematician Josè Mingot Shelly in 1911. The arithmetic derivative also appeared in the 1950 Putnam Competition.
Definition
For natural numbers , the arithmetic derivative is defined as follows:
for any prime .
for any (Leibniz rule).
Extensions beyond natural numbers
Edward J. Barbeau extended the domain to all integers by showing that the choice , which uniquely extends the domain to the integers and is consistent with the product formula. Barbeau also further extended it to the rational numbers, showing that the familiar quotient rule gives a well-defined derivative on :
Victor Ufnarovski and Bo Åhlander expanded it to the irrationals that can be written as the product of primes raised to arbitrary rational powers, allowing expressions like to be computed.
The arithmetic derivative can also be extended to any unique factorization domain (UFD), such as the Gaussian integers and the Eisenstein integers, and its associated field of fractions. If the UFD is a polynomial ring, then the arithmetic derivative is the same as the derivation over said polynomial ring. For example, the regular derivative is the arithmetic derivative for the rings of univariate real and complex polynomial and rational functions, which can be proven using the fundamental theorem of algebra.
The arithmetic derivative has also been extended to the ring of integers modulo n.
Elementary properties
The Leibniz rule implies that (take ) and (take ).
The power rule is also valid for the arithmetic derivative. For any integers and :
This allows one to compute the derivative from the prime factorization of an integer, :
where , a prime omega function, is the number of distinct prime factors in , and is the p-adic valuation of .
For example:
or
The sequence of number derivatives for begins :
Related functions
The logarithmic derivative
is a totally additive function:
The arithmetic partial derivative of with respect to is defined as
So, the arithmetic derivative of is given as
An arithmetic function is Leibniz-additive if there is a totally multiplicative function such that
for all positive integers and . A motivation for this concept is the fact that Leibniz-additive functions are generalizations of the arithmetic derivative ; namely, is Leibniz-additive with .
The function given in Section 3.5 of the book by Sandor and Atanassov is, in fact, exactly the same as the usual arithmetic derivative .
Inequalities and bounds
E |
https://en.wikipedia.org/wiki/Collapsing%20manifold | In Riemannian geometry, a collapsing or collapsed manifold is an n-dimensional manifold M that admits a sequence of Riemannian metrics gi, such that as i goes to infinity the manifold is close to a k-dimensional space, where k < n, in the Gromov–Hausdorff distance sense. Generally there are some restrictions on the sectional curvatures of (M, gi). The simplest example is a flat manifold, whose metric can be rescaled by 1/i, so that the manifold is close to a point, but its curvature remains 0 for all i.
Examples
Generally speaking there are two types of collapsing:
(1) The first type is a collapse while keeping the curvature uniformly bounded, say .
Let be a sequence of dimensional Riemannian manifolds, where denotes the sectional curvature of the ith manifold. There is a theorem proved by Jeff Cheeger, Kenji Fukaya and Mikhail Gromov, which states that: There exists a constant such that if and , then admits an N-structure, with denoting the injectivity radius of the manifold M. Roughly speaking the N-structure is a locally action of a nilmanifold, which is a generalization of an F-structure, introduced by Cheeger and Gromov. This theorem generalized previous theorems of Cheeger-Gromov and Fukaya where they only deal with the torus action and bounded diameter cases respectively.
(2) The second type is the collapsing while keeping only the lower bound of curvature, say .
This is closely related to the so-called almost nonnegatively curved manifold case which generalizes non-negatively curved manifolds as well as almost flat manifolds. A manifold is said to be almost nonnegatively curved if it admits a sequence of metrics , such that and . The role that an almost nonnegatively curved manifold plays in this collapsing case when curvature is bounded below is the same as an almost flat manifold plays in the curvature bounded case.
When curvature is bounded only from below, the limit space called is an Alexandrov space. Yamaguchi proved that on the regular part of the limit space, there is a locally trivial fibration form to when is sufficiently large, the fiber is an almost nonnegatively curved manifold. Here the regular means the -strainer radius is uniformly bounded from below by a positive number, or roughly speaking, the space locally closed to the Euclidean space.
What happens at a singular point of ? There is no answer to this question in general. But on dimension 3, Shioya and Yamaguchi give a full classification of this type collapsed manifold. They proved that there exists a and such that if a 3-dimensional manifold satisfies then one of the following is true: (i) M is a graph manifold or (ii) has diameter less than and has finite fundamental group.
Riemannian geometry
Manifolds |
https://en.wikipedia.org/wiki/Australian%20cricket%20team%20in%202008 | This article contains information, results and statistics regarding the Australian national cricket team in the 2008 season. Statisticians class the 2008 season as matches played on tours that started between May 2008 and August 2008.
Player contracts
The 2008–09 list was announced on 9 April 2008. Note that uncontracted players still are available for selection for the national cricket team.
Match summary
M = Matches Played, W = Won, L = Lost, D = Drawn, T = Tied, NR = No Result
Series Summary
Australia retained the Frank Worrell Trophy against the West Indies 2–0
Australia won the ODI series against the West Indies 5–0
Australia won the ODI series against Bangladesh 3–0
Tour of West Indies
Australia's tour of the West Indies commenced on 16 May with a tour match against a Jamaica Select XI in Trelawny and will conclude on 6 July with a One Day International in Basseterre.
Tour matches
Tour Match: 16–18 May, Trelawny
Tour Match: 21 June, Bridgetown
Test series
First Test: 22–26 May, Kingston
Australian XI: Phil Jaques, Simon Katich, Ricky Ponting (c), Michael Hussey, Brad Hodge, Andrew Symonds, Brad Haddin (wk), Brett Lee, Mitchell Johnson, Stuart Clark, Stuart MacGill
Test debut: Brad Haddin
Second Test: 30 May-3 June, North Sound
Australian XI: Phil Jaques, Simon Katich, Ricky Ponting (c), Michael Hussey, Michael Clarke, Andrew Symonds, Brad Haddin (wk), Brett Lee, Mitchell Johnson, Stuart Clark, Stuart MacGill
Third Test: 12–16 June, Bridgetown
Australian XI: Phil Jaques, Simon Katich, Ricky Ponting (c), Michael Hussey, Michael Clarke, Andrew Symonds, Brad Haddin (wk), Beau Casson, Brett Lee, Mitchell Johnson, Stuart Clark
Test debut: Beau Casson
Man of the Series: Shivnarine Chanderpaul
Twenty20 International
Only Twenty20 International: 20 June, Bridgetown
Twenty20 International debuts: Shaun Marsh, Luke Ronchi
One Day International series
First ODI: 24 June, Kingstown
One Day International debut: Shaun Marsh
Second ODI: 27 June, St George's
One Day International debut: Luke Ronchi
Third ODI: 29 June, St George's
Fourth ODI: 4 July, Basseterre
One Day International debut: David Hussey
Fifth ODI: 6 July, Basseterre
Man of the Series: Shane Watson
Bangladesh in Australia
Bangladesh will travel to Australia for a 3 match One Day International series at the end of August.
Practice matches
Practice match: 28 August, Darwin
One Day International series
First ODI: 30 August, Darwin
One Day International debut: Brett Geeves
Second ODI: 3 September, Darwin
Third ODI: 6 September, Darwin
Man of the Series: Michael Hussey
Statistics
Matches Played
The following is a table of statistics charting appearances by Australian cricketers in the 2008 season. The minimum requirement for inclusion is one match played. The players will be arranged in alphabetical order.
Source: cricinfo.com
Batting
Twenty20 Internationals
The following is a table of statistics charting Australian batsmen in Twenty20 Internat |
https://en.wikipedia.org/wiki/Matching%20distance | In mathematics, the matching distance is a metric on the space of size functions.
The core of the definition of matching distance is the observation that the
information contained in a size function can be combinatorially stored in a formal series of lines and points of the plane, called respectively cornerlines and cornerpoints.
Given two size functions and , let (resp. ) be the multiset of
all cornerpoints and cornerlines for (resp. ) counted with their
multiplicities, augmented by adding a countable infinity of points of the
diagonal .
The matching distance between and is given by
where varies among all the bijections between and and
Roughly speaking, the matching distance
between two size functions is the minimum, over all the matchings
between the cornerpoints of the two size functions, of the maximum
of the -distances between two matched cornerpoints. Since
two size functions can have a different number of cornerpoints,
these can be also matched to points of the diagonal . Moreover, the definition of implies that matching two points of the diagonal has no cost.
See also
Size theory
Size function
Size functor
Size homotopy group
Natural pseudodistance
References
Topology |
https://en.wikipedia.org/wiki/Partition%20function%20%28mathematics%29 | The partition function or configuration integral, as used in probability theory, information theory and dynamical systems, is a generalization of the definition of a partition function in statistical mechanics. It is a special case of a normalizing constant in probability theory, for the Boltzmann distribution. The partition function occurs in many problems of probability theory because, in situations where there is a natural symmetry, its associated probability measure, the Gibbs measure, has the Markov property. This means that the partition function occurs not only in physical systems with translation symmetry, but also in such varied settings as neural networks (the Hopfield network), and applications such as genomics, corpus linguistics and artificial intelligence, which employ Markov networks, and Markov logic networks. The Gibbs measure is also the unique measure that has the property of maximizing the entropy for a fixed expectation value of the energy; this underlies the appearance of the partition function in maximum entropy methods and the algorithms derived therefrom.
The partition function ties together many different concepts, and thus offers a general framework in which many different kinds of quantities may be calculated. In particular, it shows how to calculate expectation values and Green's functions, forming a bridge to Fredholm theory. It also provides a natural setting for the information geometry approach to information theory, where the Fisher information metric can be understood to be a correlation function derived from the partition function; it happens to define a Riemannian manifold.
When the setting for random variables is on complex projective space or projective Hilbert space, geometrized with the Fubini–Study metric, the theory of quantum mechanics and more generally quantum field theory results. In these theories, the partition function is heavily exploited in the path integral formulation, with great success, leading to many formulas nearly identical to those reviewed here. However, because the underlying measure space is complex-valued, as opposed to the real-valued simplex of probability theory, an extra factor of i appears in many formulas. Tracking this factor is troublesome, and is not done here. This article focuses primarily on classical probability theory, where the sum of probabilities total to one.
Definition
Given a set of random variables taking on values , and some sort of potential function or Hamiltonian , the partition function is defined as
The function H is understood to be a real-valued function on the space of states , while is a real-valued free parameter (conventionally, the inverse temperature). The sum over the is understood to be a sum over all possible values that each of the random variables may take. Thus, the sum is to be replaced by an integral when the are continuous, rather than discrete. Thus, one writes
for the case of continuously-varying .
When H is an observ |
https://en.wikipedia.org/wiki/Saint-Pascal%2C%20Quebec | Saint-Pascal () is a city in Kamouraska Regional County Municipality in the Bas-Saint-Laurent region of Quebec.
Demographics
In the 2021 Census of Population conducted by Statistics Canada, Saint-Pascal had a population of living in of its total private dwellings, a change of from its 2016 population of . With a land area of , it had a population density of in 2021.
Government
Mayor: Cécile Joseph
Councillors: Renald Bernier, Daniel Drapeau, Claude Lavoie, Rémi Pelletier, Francine Soucy, Yvan Soucy
Notable people
Annie St-Pierre, film director and producer
See also
List of cities in Quebec
References
External links
Cities and towns in Quebec
Incorporated places in Bas-Saint-Laurent |
https://en.wikipedia.org/wiki/Masaki%20Watanabe%20%28footballer%29 | Masaki Watanabe (渡邉 将基, born December 2, 1986) is a Japanese football player who plays as a defender for Terengganu FC II.
Club statistics
Updated to 23 February 2018.
References
External links
Profile at Ventforet Kofu
Profile at Yokohama FC
1986 births
Living people
Kyoto Sangyo University alumni
Association football people from Kyoto Prefecture
Japanese men's footballers
J1 League players
J2 League players
Malaysia Super League players
Sagan Tosu players
Yokohama FC players
Giravanz Kitakyushu players
Ventforet Kofu players
FC Gifu players
Perlis F.A. players
FELDA United F.C. players
Men's association football defenders |
https://en.wikipedia.org/wiki/Separoid | In mathematics, a separoid is a binary relation between disjoint sets which is stable as an ideal in the canonical order induced by inclusion. Many mathematical objects which appear to be quite different, find a common generalisation in the framework of separoids; e.g., graphs, configurations of convex sets, oriented matroids, and polytopes. Any countable category is an induced subcategory of separoids when they are endowed with homomorphisms (viz., mappings that preserve the so-called minimal Radon partitions).
In this general framework, some results and invariants of different categories turn out to be special cases of the same aspect; e.g., the pseudoachromatic number from graph theory and the Tverberg theorem from combinatorial convexity are simply two faces of the same aspect, namely, complete colouring of separoids.
The axioms
A separoid is a set endowed with a binary relation on its power set, which satisfies the following simple properties for :
A related pair is called a separation and we often say that A is separated from B. It is enough to know the maximal separations to reconstruct the separoid.
A mapping is a morphism of separoids if the preimages of separations are separations; that is, for
Examples
Examples of separoids can be found in almost every branch of mathematics. Here we list just a few.
1. Given a graph G=(V,E), we can define a separoid on its vertices by saying that two (disjoint) subsets of V, say A and B, are separated if there are no edges going from one to the other; i.e.,
2. Given an oriented matroid M = (E,T), given in terms of its topes T, we can define a separoid on E by saying that two subsets are separated if they are contained in opposite signs of a tope. In other words, the topes of an oriented matroid are the maximal separations of a separoid. This example includes, of course, all directed graphs.
3. Given a family of objects in a Euclidean space, we can define a separoid in it by saying that two subsets are separated if there exists a hyperplane that separates them; i.e., leaving them in the two opposite sides of it.
4. Given a topological space, we can define a separoid saying that two subsets are separated if there exist two disjoint open sets which contains them (one for each of them).
The basic lemma
Every separoid can be represented with a family of convex sets in some Euclidean space and their separations by hyperplanes.
References
Further reading
Binary relations |
https://en.wikipedia.org/wiki/Saint-L%C3%A9andre%2C%20Quebec | Saint-Léandre is a parish municipality in the Canadian province of Quebec, located in La Matanie Regional County Municipality.
Demographics
In the 2021 Census of Population conducted by Statistics Canada, Saint-Léandre had a population of living in of its total private dwellings, a change of from its 2016 population of . With a land area of , it had a population density of in 2021.
Census data before 2001:
Population in 1996: 401 (+1.3% from 1991)
Population in 1991: 396
See also
List of parish municipalities in Quebec
References
Parish municipalities in Quebec
Incorporated places in Bas-Saint-Laurent |
https://en.wikipedia.org/wiki/Saint-No%C3%ABl%2C%20Quebec | Saint-Noël is a village municipality in the Canadian province of Quebec, located in La Matapédia Regional County Municipality.
Demographics
In the 2021 Census of Population conducted by Statistics Canada, Saint-Noël had a population of living in of its total private dwellings, a change of from its 2016 population of . With a land area of , it had a population density of in 2021.
Canada Census data before 2001:
Population in 1996: 509 (+0.2% from 1991)
Population in 1991: 508
Municipal council
Mayor: Gilbert Sénéchal
Councillors: Marcel D'Astous, Francine Gagné, Gilbert Marquis, Steeve Parent, Jean-Louis Roussel, Jean-Marc Turcotte
See also
List of village municipalities in Quebec
References
Villages in Quebec
Incorporated places in Bas-Saint-Laurent
La Matapédia Regional County Municipality |
https://en.wikipedia.org/wiki/1996%E2%80%9397%201.Lig | Statistics of Turkish First Football League in the 1996/1997 season.
Overview
It was contested by 18 teams, and Galatasaray S.K. won the championship. Sarıyer G.K., Denizlispor and Zeytinburnuspor relegated to Second League.
League table
Results
Top scorers
References
Turkey - List of final tables (RSSSF)
Süper Lig seasons
1996–97 in Turkish football
Turkey |
https://en.wikipedia.org/wiki/1997%E2%80%9398%201.Lig | Statistics of Turkish First Football League in the 1997–98 season.
Overview
It was contested by 18 teams, and Galatasaray S.K. won the championship. And demotion of Kayserispor, Şekerspor, Vanspor was decided.
League table
Results
Top scorers
References
Turkey - List of final tables (RSSSF)
Süper Lig seasons
1997–98 in Turkish football
Turkey |
https://en.wikipedia.org/wiki/1998%E2%80%9399%201.Lig | Statistics of Turkish First Football League in the 1998–99 season.
Overview
It was contested by 18 teams, and Galatasaray S.K. won the championship. And demotion of Sakaryaspor, Çanakkale Dardanelspor, Karabükspor was decided.
League table
Results
Top scorers
References
Turkey - List of final tables (RSSSF)
Süper Lig seasons
1998–99 in Turkish football
Turkey |
https://en.wikipedia.org/wiki/1999%E2%80%932000%201.Lig | Statistics of Turkish First Football League in the 1999–2000 season.
Overview
It was contested by 18 teams, and Galatasaray S.K. won the championship. And demotion of Altay S.K., Göztepe A.Ş., Vanspor was decided.
League table
Results
Top scorers
References
turkfutbolu.net by Alper Duruk
Turkey - List of final tables (RSSSF)
Turkey
Süper Lig seasons
1999–2000 in Turkish football |
https://en.wikipedia.org/wiki/Pappus%20chain | In geometry, the Pappus chain is a ring of circles between two tangent circles investigated by Pappus of Alexandria in the 3rd century AD.
Construction
The arbelos is defined by two circles, CU and CV, which are tangent at the point A and where CU is enclosed by CV. Let the radii of these two circles be denoted as rU and rV, respectively, and let their respective centers be the points U and V. The Pappus chain consists of the circles in the shaded grey region, which are externally tangent to CU (the inner circle) and internally tangent to CV (the outer circle). Let the radius, diameter and center point of the nth circle of the Pappus chain be denoted as rn, dn and Pn, respectively.
Properties
Centers of the circles
Ellipse
All the centers of the circles in the Pappus chain are located on a common ellipse, for the following reason. The sum of the distances from the nth circle of the Pappus chain to the two centers U and V of the arbelos circles equals a constant
Thus, the foci of this ellipse are U and V, the centers of the two circles that define the arbelos; these points correspond to the midpoints of the line segments AB and AC, respectively.
Coordinates
If r = AC/AB, then the center of the nth circle in the chain is:
Radii of the circles
If r = AC/AB, then the radius of the nth circle in the chain is:
Circle inversion
The height hn of the center of the nth circle above the base diameter ACB equals n times dn. This may be shown by inverting in a circle centered on the tangent point A. The circle of inversion is chosen to intersect the nth circle perpendicularly, so that the nth circle is transformed into itself. The two arbelos circles, CU and CV, are transformed into parallel lines tangent to and sandwiching the nth circle; hence, the other circles of the Pappus chain are transformed into similarly sandwiched circles of the same diameter. The initial circle C0 and the final circle Cn each contribute ½dn to the height hn, whereas the circles C1–Cn−1 each contribute dn. Adding these contributions together yields the equation hn = n dn.
The same inversion can be used to show that the points where the circles of the Pappus chain are tangent to one another lie on a common circle. As noted above, the inversion centered at point A transforms the arbelos circles CU and CV into two parallel lines, and the circles of the Pappus chain into a stack of equally sized circles sandwiched between the two parallel lines. Hence, the points of tangency between the transformed circles lie on a line midway between the two parallel lines. Undoing the inversion in the circle, this line of tangent points is transformed back into a circle.
Steiner chain
In these properties of having centers on an ellipse and tangencies on a circle, the Pappus chain is analogous to the Steiner chain, in which finitely many circles are tangent to two circles.
References
Bibliography
External links
Arbelos
Inversive geometry
Circle packing |
https://en.wikipedia.org/wiki/Bankoff%20circle | In geometry, the Bankoff circle or Bankoff triplet circle is a certain Archimedean circle that can be constructed from an arbelos; an Archimedean circle is any circle with area equal to each of Archimedes' twin circles. The Bankoff circle was first constructed by Leon Bankoff in 1974.
Construction
The Bankoff circle is formed from three semicircles that create an arbelos. A circle C1 is then formed tangent to each of the three semicircles, as an instance of the problem of Apollonius. Another circle C2 is then created, through three points: the two points of tangency of C1 with the smaller two semicircles, and the point where the two smaller semicircles are tangent to each other. C2 is the Bankoff circle.
Radius of the circle
If r = AB/AC, then the radius of the Bankoff circle is:
References
External links
Bankoff Circle by Jay Warendorff, the Wolfram Demonstrations Project.
Online catalogue of Archimedean circles, Floor van Lamoen.
Arbelos
Elementary geometry |
https://en.wikipedia.org/wiki/Annual%20Review%20of%20Public%20Health | The Annual Review of Public Health is a peer-reviewed academic journal that publishes review articles about public health, including epidemiology, biostatistics, occupational safety and health, environmental health, and health policy. It has had three editors: Lester Breslow, Gilbert S. Omenn, and Jonathan E. Fielding.
The journal is published open access under the Subscribe to Open (S2O) publishing model.
According to the 2023 Journal Citation Reports, the journal has a 2022 impact factor of 20.8, ranking it fourth out of 180 journals in the category "Public, Environmental & Occup. Health (Social Science)" and eighth out of 207 in the category "Public, Environmental & Occup. Health (Science)".
History
The journal published its first volume in 1980, in response to a second American "public health revolution". The preface of the first volume noted the shift towards chronic health conditions like cancer and heart disease. It also noted the rising cost of diagnosing and treating disease in the US, which had doubled from 1950 to 1975. The first editor was Lester Breslow.
Initially, the journal was organized into five subtopics, age and disease-specific public health, behavioral aspects of health, environmental health, epidemiology/biostatistics, and health services. In volume 13 (1992), a sixth subtopic was added: public health practice. The five subtopics in volume 15 (1994) were epidemiology and biostatistics, public health practice, behavioral aspects of health, health services, and environmental and occupational health.
In April 2017, Annual Reviews made the Annual Review of Public Health open access as part of a grant from the Robert Wood Johnson Foundation. By May 2019, usage of the journal had increased eight-fold relative to 2016 to about 200,000 downloads monthly. For comparison, the titles for clinical psychology and medicine that maintained gated access showed no change in usage. Additionally, the audience for the journal increased from 1,100 institutions in 57 countries (2016) to 7,220 institutions in 137 countries (2018). Based on this success, Annual Reviews created the Subscribe to Open (S2O) publishing model to convert some of its other journals from gated to open access on a year-to-year basis.
Editorial processes
The Annual Review of Public Health is helmed by the editor. The editor is assisted by the editorial committee, which includes associate editors, regular members, and occasionally guest editors. Guest members participate at the invitation of the editor, and serve terms of one year. All other members of the editorial committee are appointed by the Annual Reviews board of directors and serve five-year terms. The editorial committee determines which topics should be included in each volume and solicits reviews from qualified authors. Unsolicited manuscripts are not accepted. Peer review of accepted manuscripts is undertaken by the editorial committee.
Editors of volumes
Dates indicate publication years in which someone wa |
https://en.wikipedia.org/wiki/Twin%20circles | In geometry, the twin circles are two special circles associated with an arbelos.
An arbelos is determined by three collinear points , , and , and is the curvilinear triangular region between the three semicircles that have , , and as their diameters. If the arbelos is partitioned into two smaller regions by a line segment through the middle point of , , and , perpendicular to line , then each of the two twin circles lies within one of these two regions, tangent to its two semicircular sides and to the splitting segment.
These circles first appeared in the Book of Lemmas, which showed (Proposition V) that the two circles are congruent.
Thābit ibn Qurra, who translated this book into Arabic, attributed it to Greek mathematician Archimedes. Based on this claim the twin circles, and several other circles in the Arbelos congruent to them, have also been called Archimedes's circles. However, this attribution has been questioned by later scholarship.
Construction
Specifically, let , , and be the three corners of the arbelos, with between and . Let be the point where the larger semicircle intercepts the line perpendicular to the through the point . The segment divides the arbelos in two parts. The twin circles are the two circles inscribed in these parts, each tangent to one of the two smaller semicircles, to the segment , and to the largest semicircle.
Each of the two circles is uniquely determined by its three tangencies. Constructing it is a special case of the Problem of Apollonius.
Alternative approaches to constructing two circles congruent to the twin circles have also been found. These circles have also been called Archimedean circles. They include the Bankoff circle, Schoch circles, and Woo circles.
Properties
Let a and b be the diameters of two inner semicircles, so that the outer semicircle has diameter a + b. The diameter of each twin circle is then
Alternatively, if the outer semicircle has unit diameter, and the inner circles have diameters and , the diameter of each twin circle is
The smallest circle that encloses both twin circles has the same area as the arbelos.
See also
Schoch line
References
Arbelos |
https://en.wikipedia.org/wiki/Unfolding%20%28functions%29 | In mathematics, an unfolding of a smooth real-valued function ƒ on a smooth manifold, is a certain family of functions that includes ƒ.
Definition
Let be a smooth manifold and consider a smooth mapping Let us assume that for given and we have . Let be a smooth -dimensional manifold, and consider the family of mappings (parameterised by ) given by We say that is a -parameter unfolding of if for all In other words the functions and are the same: the function is contained in, or is unfolded by, the family
Example
Let be given by An example of an unfolding of would be given by
As is the case with unfoldings, and are called variables, and and are called parameters, since they parameterise the unfolding.
Well-behaved unfoldings
In practice we require that the unfoldings have certain properties. In , is a smooth mapping from to and so belongs to the function space As we vary the parameters of the unfolding, we get different elements of the function space. Thus, the unfolding induces a function The space , where denotes the group of diffeomorphisms of etc., acts on The action is given by If lies in the orbit of under this action then there is a diffeomorphic change of coordinates in and , which takes to (and vice versa). One property that we can impose is that
where "" denotes "transverse to". This property ensures that as we vary the unfolding parameters we can predict – by knowing how the orbit foliates – how the resulting functions will vary.
Versal unfoldings
There is an idea of a versal unfolding. Every versal unfolding has the property that
, but the converse is false. Let be local coordinates on , and let denote the ring of smooth functions. We define the Jacobian ideal of , denoted by , as follows:
Then a basis for a versal unfolding of is given by the quotient
.
This quotient is known as the local algebra of . The dimension of the local algebra is called the Milnor number of . The minimum number of unfolding parameters for a versal unfolding is equal to the Milnor number; that is not to say that every unfolding with that many parameters will be versal. Consider the function . A calculation shows that
This means that give a basis for a versal unfolding, and that
is a versal unfolding. A versal unfolding with the minimum possible number of unfolding parameters is called a miniversal unfolding.
Bifurcations sets of unfoldings
An important object associated to an unfolding is its bifurcation set. This set lives in the parameter space of the unfolding, and gives all parameter values for which the resulting function has degenerate singularities.
Other terminology
Sometimes unfoldings are called deformations, versal unfoldings are called versal deformations, etc.
References
V. I. Arnold, S. M. Gussein-Zade & A. N. Varchenko, Singularities of differentiable maps, Volume 1, Birkhäuser, (1985).
J. W. Bruce & P. J. Giblin, Curves & singularities, second edition, Cambridge University |
https://en.wikipedia.org/wiki/Anna%20Johnson%20Pell%20Wheeler | Anna Johnson Pell Wheeler (née Johnson; May 5, 1883 – March 26, 1966) was an American mathematician. She is best known for early work on linear algebra in infinite dimensions, which has later become a part of functional analysis.
Biography
Anna Johnson was born on May 5, 1883, to Swedish immigrant parents in Calliope, Iowa in the United States. Her father, Andrew Gustav Johnson, was a furniture dealer and undertaker. Her mother, Amelia (née Friberg), was a homemaker. Both of Johnson's parents came from the parish of Lyrestad, in Västergötland, Sweden. Johnson had two older siblings, Esther and Elmer. At the age of nine her family moved to Akron, Iowa and she was enrolled in a private school. In 1899 she joined her sister at the University of South Dakota where they took many of the same classes. She graduated in 1903 and began graduate work at the University of Iowa. Her thesis, titled The extension of Galois theory to linear differential equations, earned her a master's degree in 1904. She obtained a second graduate degree one year later from Radcliffe College, where she took courses from Maxime Bôcher and William Fogg Osgood.
In 1905 she won an Alice Freeman Palmer Fellowship from Wellesley College to spend a year at the University of Göttingen, where she studied under David Hilbert, Felix Klein, Hermann Minkowski, and Karl Schwarzschild. As she worked toward a doctorate, her relationship with Alexander Pell, a former professor from the University of South Dakota, intensified. He traveled to Göttingen and they were married in July 1907. This trip posed a significant threat to Pell's life, since he was a former Russian double agent whose real name was Sergey Degayev.
After the wedding, the Pells returned to Vermillion, South Dakota, where she taught classes in the theory of functions and differential equations. By 1908 she was back in Göttingen, working on her dissertation; an argument with Hilbert, however, made its completion impossible. She moved with her husband to Chicago, where she worked with E. H. Moore to finish her dissertation, Biorthogonal Systems of Functions with Applications to the Theory of Integral Equations, and received a Ph.D. in 1909.
She began looking for a teaching position, but found hostility in every mathematics department. She wrote to a friend: "I had hoped for a position in one of the good univ. like Wisc., Ill. etc., but there is such an objection to women that they prefer a man even if he is inferior both in training and research". In 1911 her husband had a stroke and she, after teaching his classes at the Armout Institute for the remainder of the semester. She then accepted a position at Mount Holyoke College and taught there for seven years.
In 1917, her last year at Mount Holyoke College, she published (together with R. L. Gordon) a paper regarding Sturm's theorem. In that they solved a problem that had eluded J. J. Sylvester (1853) and E. B. Van Vleck (1899). That paper (along with their theorem) was forgo |
https://en.wikipedia.org/wiki/List%20of%20types%20of%20functions | In mathematics, functions can be identified according to the properties they have. These properties describe the functions' behaviour under certain conditions. A parabola is a specific type of function.
Relative to set theory
These properties concern the domain, the codomain and the image of functions.
Injective function: has a distinct value for each distinct input. Also called an injection or, sometimes, one-to-one function. In other words, every element of the function's codomain is the image of at most one element of its domain.
Surjective function: has a preimage for every element of the codomain, that is, the codomain equals the image. Also called a surjection or onto function.
Bijective function: is both an injection and a surjection, and thus invertible.
Identity function: maps any given element to itself.
Constant function: has a fixed value regardless of its input.
Empty function: whose domain equals the empty set.
Set function: whose input is a set.
Choice function called also selector or uniformizing function: assigns to each set one of its elements.
Relative to an operator (c.q. a group or other structure)
These properties concern how the function is affected by arithmetic operations on its argument.
The following are special examples of a homomorphism on a binary operation:
Additive function: preserves the addition operation: f (x + y) = f (x) + f (y).
Multiplicative function: preserves the multiplication operation: f (xy) = f (x)f (y).
Relative to negation:
Even function: is symmetric with respect to the Y-axis. Formally, for each x: f (x) = f (−x).
Odd function: is symmetric with respect to the origin. Formally, for each x: f (−x) = −f (x).
Relative to a binary operation and an order:
Subadditive function: for which the value of f (x + y) is less than or equal to f (x) + f (y).
Superadditive function: for which the value of f (x + y) is greater than or equal to f (x) + f (y).
Relative to a topology
Continuous function: in which preimages of open sets are open.
Nowhere continuous function: is not continuous at any point of its domain; for example, the Dirichlet function.
Homeomorphism: is a bijective function that is also continuous, and whose inverse is continuous.
Open function: maps open sets to open sets.
Closed function: maps closed sets to closed sets.
Compactly supported function: vanishes outside a compact set.
Càdlàg function, called also RCLL function, corlol function, etc.: right-continuous, with left limits.
Quasi-continuous function: roughly, close to f (x) for some but not all y near x (rather technical).
Relative to topology and order:
Semicontinuous function: upper or lower semicontinuous.
Right-continuous function: no jump when the limit point is approached from the right. Left-continuous function: defined similarly.
Locally bounded function: bounded around every poi |
https://en.wikipedia.org/wiki/Data%20matrix | Data matrix may refer to:
Matrix (mathematics), rectangular array of elements
Data Matrix, a two-dimensional barcode
Data matrix (multivariate statistics), mathematical matrix of data whose rows represent different repetition of an experiment, and whose columns represent different kinds of datum taken for each repetition
Data set, collection of data in tabular form |
https://en.wikipedia.org/wiki/Abdulalim%20A.%20Shabazz | Abdulalim Abdullah Shabazz (May 22, 1927 – June 25, 2014) was an African American Professor of Mathematics. He received the National Association of Mathematicians Distinguished Service Award for his years of mentoring and teaching excellence. President of the United States Bill Clinton awarded Shabazz a National Mentor award in September 2000.
Biography
Shabazz was born Lonnie Cross in Bessemer, Alabama. In 1949, he earned a Bachelor of Arts in chemistry and mathematics from Lincoln University. Two years later he earned a Master of Science in Mathematics at the Massachusetts Institute of Technology in mathematics and a Doctor of Philosophy in 1955 in mathematical analysis from Cornell University. His subject of his doctoral dissertation was "The Distribution of Eigenvalues of the Equation: Integral of A(S-T) PHI (T) with Respect to T Between Lower Limit -A and Upper Limit A=Rho (Integral of B(S-T))".
Shabazz was appointed an assistant professor of mathematics by Tuskegee Institute in 1956. From 1957 until 1963, he served as chairman and associate professor of mathematics at Clark Atlanta University. One of his students was David Lee Hunter.
Shabazz announced in 1961 that he was a member of the Nation of Islam (later he converted to orthodox Islam).
From 1975 until 1986, Shabazz taught in Chicago, Detroit, and in Mecca, Saudi Arabia. In 1986, Shabazz came back to Clark Atlanta, where he served as chair from 1990 until 1995. From 1998 until 2000, Shabazz was Chairman of the Mathematics and Computer Science Department at Lincoln University (Pennsylvania).
The American Association for the Advancement of Science presented him with its 1992 "Mentor Award" for his leadership in efforts to increase the participation of women, minorities, and individuals with physical disabilities in science and engineering. He received the National Association of Mathematicians Distinguished Service Award for his years of mentoring and teaching excellence. President Clinton awarded Shabazz a Presidential Award for Excellence in Science, Mathematics and Engineering Mentoring award in September 2000.
In 2001, the Association of African American Educators awarded Shabazz its Lifetime Achievement Award for outstanding work with African Americans in mathematics. He was a professor and endowed chair in mathematics at Grambling State University.
Dr. Shabazz died on June 25, 2014.
References
Selected publications
External links
Official website
SUMMA Archival Record at MAA—includes a biography
1927 births
2014 deaths
Cornell University alumni
American Muslims
African-American Muslims
Grambling State University faculty
Lincoln University (Pennsylvania) alumni
People from Bessemer, Alabama
20th-century African-American academics
20th-century American academics
21st-century African-American academics
21st-century American academics |
https://en.wikipedia.org/wiki/Schoch%20line | In geometry, the Schoch line is a line defined from an arbelos and named by Peter Woo after Thomas Schoch, who had studied it in conjunction with the Schoch circles.
Construction
An arbelos is a shape bounded by three mutually-tangent semicircular arcs with collinear endpoints, with the two smaller arcs nested inside the larger one; let the endpoints of these three arcs be (in order along the line containing them) A, B, and C. Let K1 and K2 be two more arcs, centered at A and C, respectively, with radii AB and CB, so that these two arcs are tangent at B; let K3 be the largest of the three arcs of the arbelos. A circle, with the center A1, is then created tangent to the arcs K1, K2, and K3. This circle is congruent with Archimedes' twin circles, making it an Archimedean circle; it is one of the Schoch circles. The Schoch line is perpendicular to the line AC and passes through the point A1. It is also the location of the centers of infinitely many Archimedean circles, e.g. the Woo circles.
Radius and center of A1
If r = AB/AC, and AC = 1, then the radius of A1 is
and the center is
References
Further reading
.
External links
Arbelos
de:Archimedischer Kreis#Schoch-Kreise und Schoch-Gerade |
https://en.wikipedia.org/wiki/The%20American%20Statistician | The American Statistician is a quarterly peer-reviewed scientific journal covering statistics published by Taylor & Francis on behalf of the American Statistical Association. It was established in 1947. The editor-in-chief is Daniel R. Jeske, a professor at the University of California, Riverside.
External links
Taylor & Francis academic journals
Statistics journals
Academic journals established in 1947
English-language journals
Quarterly journals
1947 establishments in the United States
Academic journals associated with learned and professional societies of the United States |
https://en.wikipedia.org/wiki/Circle%20packing | In geometry, circle packing is the study of the arrangement of circles (of equal or varying sizes) on a given surface such that no overlapping occurs and so that no circle can be enlarged without creating an overlap. The associated packing density, , of an arrangement is the proportion of the surface covered by the circles. Generalisations can be made to higher dimensions – this is called sphere packing, which usually deals only with identical spheres.
The branch of mathematics generally known as "circle packing" is concerned with the geometry and combinatorics of packings of arbitrarily-sized circles: these give rise to discrete analogs of conformal mapping, Riemann surfaces and the like.
Densest packing
In the two-dimensional Euclidean plane, Joseph Louis Lagrange proved in 1773 that the highest-density lattice packing of circles is the hexagonal packing arrangement, in which the centres of the circles are arranged in a hexagonal lattice (staggered rows, like a honeycomb), and each circle is surrounded by six other circles. For circles of diameter and hexagons of side length , the hexagon area and the circle area are, respectively:
The area covered within each hexagon by circles is:
Finally, the packing density is:
In 1890, Axel Thue published a proof that this same density is optimal among all packings, not just lattice packings, but his proof was considered by some to be incomplete. The first rigorous proof is attributed to László Fejes Tóth in 1942.
While the circle has a relatively low maximum packing density, it does not have the lowest possible, even among centrally-symmetric convex shapes: the smoothed octagon has a packing density of about 0.902414, the smallest known for centrally-symmetric convex shapes and conjectured to be the smallest possible. (Packing densities of concave shapes such as star polygons can be arbitrarily small.)
Other packings
At the other extreme, Böröczky demonstrated that arbitrarily low density arrangements of rigidly packed circles exist.
There are eleven circle packings based on the eleven uniform tilings of the plane. In these packings, every circle can be mapped to every other circle by reflections and rotations. The hexagonal gaps can be filled by one circle and the dodecagonal gaps can be filled with seven circles, creating 3-uniform packings. The truncated trihexagonal tiling with both types of gaps can be filled as a 4-uniform packing. The snub hexagonal tiling has two mirror-image forms.
On the sphere
A related problem is to determine the lowest-energy arrangement of identically interacting points that are constrained to lie within a given surface. The Thomson problem deals with the lowest energy distribution of identical electric charges on the surface of a sphere. The Tammes problem is a generalisation of this, dealing with maximising the minimum distance between circles on sphere. This is analogous to distributing non-point charges on a sphere.
In bounded areas
Packing circles in simpl |
https://en.wikipedia.org/wiki/Voorburg%20group | The Voorburg Group on Services Statistics was created in 1986, in response to a request from the United Nations Statistical Office (UNSO), for assistance in developing services statistics. The first meeting, hosted by the Netherlands Statistical Office (CBS) was held in January 1987 in Voorburg, Netherlands, from which the Group derives its name.
Purpose
The purpose of the Voorburg Group (VG) is to address issues related to the production of service statistics, including service product outputs and inputs, the estimation of the real product of service activities, price indices of service products and industries, and their implications for product and industry classification (Central Product Classification (CPC) and International Standard Classification of All Economic Activities (ISIC)).
In 2005, the VG received a renewed mandate from the United Nations Statistical Commission concerning its objective, focus and scope. The objective of the VG is to establish an internationally comparable methodology for measuring the constant dollar outputs of the service industries. The focus of the VG is to develop concepts, methods, and best practices in the area of services. The scope of the VG is centered on producer price indices (PPIs) for services, turnover by products, and classifications.
The Voorburg Group has contributed over the years to building up and sharing a considerable and growing body of knowledge of Service Sector Statistics. It has prompted international cooperation in the development of standards and has assisted in resolving statistical and measurement challenges in the Service Sector.
External links
Voorburg Group website
UN's page on Voorburg Group
Statistical organizations |
https://en.wikipedia.org/wiki/Chebyshev%20center | In geometry, the Chebyshev center of a bounded set having non-empty interior is the center of the minimal-radius ball enclosing the entire set , or alternatively (and non-equivalently) the center of largest inscribed ball of .
In the field of parameter estimation, the Chebyshev center approach tries to find an estimator for given the feasibility set , such that minimizes the worst possible estimation error for x (e.g. best worst case).
Mathematical representation
There exist several alternative representations for the Chebyshev center.
Consider the set and denote its Chebyshev center by . can be computed by solving:
with respect to the Euclidean norm , or alternatively by solving:
Despite these properties, finding the Chebyshev center may be a hard numerical optimization problem. For example, in the second representation above, the inner maximization is non-convex if the set Q is not convex.
Properties
In inner product spaces and two-dimensional spaces, if is closed, bounded and convex, then the Chebyshev center is in . In other words, the search for the Chebyshev center can be conducted inside without loss of generality.
In other spaces, the Chebyshev center may not be in , even if is convex. For instance, if is the tetrahedron formed by the convex hull of the points (1,1,1), (-1,1,1), (1,-1,1) and (1,1,-1), then computing the Chebyshev center using the norm yields
Relaxed Chebyshev center
Consider the case in which the set can be represented as the intersection of ellipsoids.
with
By introducing an additional matrix variable , we can write the inner maximization problem of the Chebyshev center as:
where is the trace operator and
Relaxing our demand on by demanding , i.e. where is the set of positive semi-definite matrices, and changing the order of the min max to max min (see the references for more details), the optimization problem can be formulated as:
with
This last convex optimization problem is known as the relaxed Chebyshev center (RCC).
The RCC has the following important properties:
The RCC is an upper bound for the exact Chebyshev center.
The RCC is unique.
The RCC is feasible.
Constrained least squares
It can be shown that the well-known constrained least squares (CLS) problem is a relaxed version of the Chebyshev center.
The original CLS problem can be formulated as:
with
It can be shown that this problem is equivalent to the following optimization problem:
with
One can see that this problem is a relaxation of the Chebyshev center (though different than the RCC described above).
RCC vs. CLS
A solution set for the RCC is also a solution for the CLS, and thus .
This means that the CLS estimate is the solution of a looser relaxation than that of the RCC.
Hence the CLS is an upper bound for the RCC, which is an upper bound for the real Chebyshev center.
Modeling constraints
Since both the RCC and CLS are based upon relaxation of the real feasibility set , the f |
https://en.wikipedia.org/wiki/Affine%20Grassmannian | In mathematics, the affine Grassmannian of an algebraic group G over a field k is an ind-scheme—a colimit of finite-dimensional schemes—which can be thought of as a flag variety for the loop group G(k((t))) and which describes the representation theory of the Langlands dual group LG through what is known as the geometric Satake correspondence.
Definition of Gr via functor of points
Let k be a field, and denote by and the category of commutative k-algebras and the category of sets respectively. Through the Yoneda lemma, a scheme X over a field k is determined by its functor of points, which is the functor which takes A to the set X(A) of A-points of X. We then say that this functor is representable by the scheme X. The affine Grassmannian is a functor from k-algebras to sets which is not itself representable, but which has a filtration by representable functors. As such, although it is not a scheme, it may be thought of as a union of schemes, and this is enough to profitably apply geometric methods to study it.
Let G be an algebraic group over k. The affine Grassmannian GrG is the functor that associates to a k-algebra A the set of isomorphism classes of pairs (E, φ), where E is a principal homogeneous space for G over Spec A and φ is an isomorphism, defined over Spec A((t)), of E with the trivial G-bundle G × Spec A((t)). By the Beauville–Laszlo theorem, it is also possible to specify this data by fixing an algebraic curve X over k, a k-point x on X, and taking E to be a G-bundle on XA and φ a trivialization on (X − x)A. When G is a reductive group, GrG is in fact ind-projective, i.e., an inductive limit of projective schemes.
Definition as a coset space
Let us denote by the field of formal Laurent series over k, and by the ring of formal power series over k. By choosing a trivialization of E over all of , the set of k-points of GrG is identified with the coset space .
References
Algebraic geometry |
https://en.wikipedia.org/wiki/Dispersionless%20equation | Dispersionless (or quasi-classical) limits of integrable partial differential equations (PDE) arise in various problems of mathematics and physics and have been intensively studied in recent literature (see e.g. references below). They typically arise when considering slowly modulated long waves of an integrable dispersive PDE system.
Examples
Dispersionless KP equation
The dispersionless Kadomtsev–Petviashvili equation (dKPE), also known (up to an inessential linear change of variables) as the Khokhlov–Zabolotskaya equation, has the form
It arises from the commutation
of the following pair of 1-parameter families of vector fields
where is a spectral parameter. The dKPE is the -dispersionless limit of the celebrated Kadomtsev–Petviashvili equation, arising when considering long waves of that system. The dKPE, like many other (2+1)-dimensional integrable dispersionless systems, admits a (3+1)-dimensional generalization.
The Benney moment equations
The dispersionless KP system is closely related to the Benney moment hierarchy, each of which is a dispersionless integrable system:
These arise as the consistency condition between
and the simplest two evolutions in the hierarchy are:
The dKP is recovered on setting
and eliminating the other moments, as well as identifying and .
If one sets , so that the countably many moments are expressed in terms of just two functions, the classical shallow water equations result:
These may also be derived from considering slowly modulated wave train solutions of the nonlinear Schrodinger equation. Such 'reductions', expressing the moments in terms of finitely many dependent variables, are described by the Gibbons-Tsarev equation.
Dispersionless Korteweg–de Vries equation
The dispersionless Korteweg–de Vries equation (dKdVE) reads as
It is the dispersionless or quasiclassical limit of the Korteweg–de Vries equation.
It is satisfied by -independent solutions of the dKP system.
It is also obtainable from the -flow of the Benney hierarchy on setting
Dispersionless Novikov–Veselov equation
The dispersionless Novikov-Veselov equation is most commonly written as the following equation for a real-valued function :
where the following standard notation of complex analysis is used: , . The function here is an auxiliary function, defined uniquely from up to a holomorphic summand.
Multidimensional integrable dispersionless systems
See for systems with contact Lax pairs, and e.g., and references therein for other systems.
See also
Integrable systems
Nonlinear Schrödinger equation
Nonlinear systems
Davey–Stewartson equation
Dispersive partial differential equation
Kadomtsev–Petviashvili equation
Korteweg–de Vries equation
References
Citations
Bibliography
Kodama Y., Gibbons J. "Integrability of the dispersionless KP hierarchy", Nonlinear World 1, (1990).
Zakharov V.E. "Dispersionless limit of integrable systems in 2+1 dimensions", Singular Limits of Dispersive Waves, NATO ASI series, Vol |
https://en.wikipedia.org/wiki/Predator%20satiation | Predator satiation (less commonly called predator saturation) is an anti-predator adaptation in which prey briefly occur at high population densities, reducing the probability of an individual organism being eaten.
When predators are flooded with potential prey, they can consume only a certain amount, so by occurring at high densities prey benefit from a safety in numbers effect. This strategy has evolved in a diverse range of prey, including notably many species of plants, insects, and fish. Predator satiation can be considered a type of refuge from predators.
As available food increases, a predator has more chances of survival, growth, and reproduction. However, as food supply begins to overwhelm the predator's ability to consume and process it, consumption levels off. This pattern is evident in the functional response of type II. There are also limits to population growth (numerical response), dependent on the generation time of the predator species.
This phenomenon is particularly conspicuous when it takes the form of mast seeding, the production of large numbers of seeds by a population of plants. An important element of the masting strategy is synchronicity in production, which is most effective when it is staggered. This means that there should be years of mass production of seeds followed by years of very little seed production.
Some bamboos do a mass flowering, fruiting, and die-off at long intervals (many years).
Some periodical cicada (Magicicada) species erupt in large numbers from their larval stage at intervals in years that are prime numbers, 13 or 17. At high-density sites, research finds that the number eaten by birds does not increase with the number of cicada individuals and the risk of predation for each individual decreases.
In contrast to predator satiation, a different pattern is seen in response to mutualistic consumers, which benefit an organism by feeding from it (such as frugivores, which disperse seeds). For example, a vine's berries may ripen at different times, ensuring frugivores are not swamped with food and so resulting in a larger proportion of its seeds being dispersed.
See also
Reproductive synchrony
Selfish herd theory
Semelparity
Surplus killing
Human wave attack
References
Antipredator adaptations
Population ecology |
https://en.wikipedia.org/wiki/Archimedes%27%20quadruplets | In geometry, Archimedes' quadruplets are four congruent circles associated with an arbelos. Introduced by Frank Power in the summer of 1998, each have the same area as Archimedes' twin circles, making them Archimedean circles.
Construction
An arbelos is formed from three collinear points A, B, and C, by the three semicircles with diameters AB, AC, and BC. Let the two smaller circles have radii r1 and r2, from which it follows that the larger semicircle has radius r = r1+r2. Let the points D and E be the center and midpoint, respectively, of the semicircle with the radius r1. Let H be the midpoint of line AC. Then two of the four quadruplet circles are tangent to line HE at the point E, and are also tangent to the outer semicircle. The other two quadruplet circles are formed in a symmetric way from the semicircle with radius r2.
Proof of congruency
According to Proposition 5 of Archimedes' Book of Lemmas, the common radius of Archimedes' twin circles is:
By the Pythagorean theorem:
Then, create two circles with centers Ji perpendicular to HE, tangent to the large semicircle at point Li, tangent to point E, and with equal radii x. Using the Pythagorean theorem:
Also:
Combining these gives:
Expanding, collecting to one side, and factoring:
Solving for x:
Proving that each of the Archimedes' quadruplets' areas is equal to each of Archimedes' twin circles' areas.
References
More readings
Arbelos: Book of Lemmas, Pappus Chain, Archimedean Circle, Archimedes' Quadruplets, Archimedes' Twin Circles, Bankoff Circle, S.
Arbelos |
https://en.wikipedia.org/wiki/Superperfect%20number | In number theory, a superperfect number is a positive integer that satisfies
where is the divisor summatory function. Superperfect numbers are not a generalization of perfect numbers, but have a common generalization. The term was coined by D. Suryanarayana (1969).
The first few superperfect numbers are :
2, 4, 16, 64, 4096, 65536, 262144, 1073741824, ... .
To illustrate: it can be seen that 16 is a superperfect number as , and , thus .
If is an even superperfect number, then must be a power of 2, , such that is a Mersenne prime.
It is not known whether there are any odd superperfect numbers. An odd superperfect number would have to be a square number such that either or is divisible by at least three distinct primes. There are no odd superperfect numbers below 7.
Generalizations
Perfect and superperfect numbers are examples of the wider class of m-superperfect numbers, which satisfy
corresponding to m=1 and 2 respectively. For m ≥ 3 there are no even m-superperfect numbers.
The m-superperfect numbers are in turn examples of (m,k)-perfect numbers which satisfy
With this notation, perfect numbers are (1,2)-perfect, multiperfect numbers are (1,k)-perfect, superperfect numbers are (2,2)-perfect and m-superperfect numbers are (m,2)-perfect. Examples of classes of (m,k)-perfect numbers are:
{| class="wikitable"
|-
! m
! k
! (m,k)-perfect numbers
! OEIS sequence
|-
| 2
| 2
| 2, 4, 16, 64, 4096, 65536, 262144
|
|-
| 2
| 3
| 8, 21, 512
|
|-
| 2
| 4
| 15, 1023, 29127
|
|-
| 2
| 6
| 42, 84, 160, 336, 1344, 86016, 550095, 1376256, 5505024
|
|-
| 2
| 7
| 24, 1536, 47360, 343976
|
|-
| 2
| 8
| 60, 240, 960, 4092, 16368, 58254, 61440, 65472, 116508, 466032, 710400, 983040, 1864128, 3932160, 4190208, 67043328, 119304192, 268173312, 1908867072
|
|-
| 2
| 9
| 168, 10752, 331520, 691200, 1556480, 1612800, 106151936
|
|-
| 2
| 10
| 480, 504, 13824, 32256, 32736, 1980342, 1396617984, 3258775296
|
|-
| 2
| 11
| 4404480, 57669920, 238608384
|
|-
| 2
| 12
| 2200380, 8801520, 14913024, 35206080, 140896000, 459818240, 775898880, 2253189120
|
|-
| 3
| any
| 12, 14, 24, 52, 98, 156, 294, 684, 910, 1368, 1440, 4480, 4788, 5460, 5840, ...
|
|-
| 4
| any
| 2, 3, 4, 6, 8, 10, 12, 15, 18, 21, 24, 26, 32, 39, 42, 60, 65, 72, 84, 96, 160, 182, ...
|
|}
Notes
References
Divisor function
Integer sequences
Unsolved problems in number theory |
https://en.wikipedia.org/wiki/Kari%20Laitinen | Kari Juhani Laitinen (born April 9, 1964) is a Finnish ice hockey player. He won a silver medal at the 1988 Winter Olympics.
Career statistics
Regular season and playoffs
International
References
External links
Biography on DatabaseOlympics.com
1964 births
Living people
Finnish ice hockey right wingers
Ice hockey players at the 1988 Winter Olympics
Olympic ice hockey players for Finland
Olympic medalists in ice hockey
Olympic silver medalists for Finland
Ice hockey people from Vantaa
Medalists at the 1988 Winter Olympics |
https://en.wikipedia.org/wiki/Alexander%20Gerasimov%20%28ice%20hockey%29 | Aleksandr Gerasimov (19 March 1959 – 21 May 2020) was a Soviet ice hockey player. He won a gold medal at the 1984 Winter Olympics.
Career statistics
Regular season and playoffs
International
Death
Gerasimov died on 21 May 2020.
References
External links
1959 births
2020 deaths
Ice hockey players at the 1984 Winter Olympics
Olympic gold medalists for the Soviet Union
Russian ice hockey players
Soviet ice hockey players
Olympic medalists in ice hockey
Medalists at the 1984 Winter Olympics
Sportspeople from Penza |
https://en.wikipedia.org/wiki/Perigon | Perigon can refer to
In mathematics, an angle of 360° (see )
Périgon, a town in the fictional province of Averoigne in the writings of Clark Ashton Smith
See also
Perigone (disambiguation) |
https://en.wikipedia.org/wiki/JGT | JGT may refer to:
Journal of Graph Theory
Journal of Graphics Tools
Journal of Group Theory |
https://en.wikipedia.org/wiki/G2-structure | {{DISPLAYTITLE:G2-structure}}
In differential geometry, a -structure is an important type of G-structure that can be defined on a smooth manifold. If M is a smooth manifold of dimension seven, then a G2-structure is a reduction of structure group of the frame bundle of M to the compact, exceptional Lie group G2.
Equivalent conditions
The condition of M admitting a structure is equivalent to any of the following conditions:
The first and second Stiefel–Whitney classes of M vanish.
M is orientable and admits a spin structure.
The last condition above correctly suggests that many manifolds admit -structures.
History
A manifold with holonomy was first introduced by Edmond Bonan in 1966, who constructed the parallel 3-form, the parallel 4-form and showed that this manifold was Ricci-flat. The first complete, but noncompact 7-manifolds with holonomy were constructed by Robert Bryant and Salamon in 1989. The first compact 7-manifolds with holonomy were constructed by Dominic Joyce in 1994, and compact manifolds are sometimes known as "Joyce manifolds", especially in the physics literature. In 2013, it was shown by M. Firat Arikan, Hyunjoo Cho, and Sema Salur that any manifold with a spin structure, and, hence, a -structure, admits a compatible almost contact metric structure, and an explicit compatible almost contact structure was constructed for manifolds with -structure. In the same paper, it was shown that certain classes of -manifolds admit a contact structure.
Remarks
The property of being a -manifold is much stronger than that of admitting a -structure. Indeed, a -manifold is a manifold with a -structure which is torsion-free.
The letter "G" occurring in the phrases "G-structure" and "-structure" refers to different things. In the first case, G-structures take their name from the fact that arbitrary Lie groups are typically denoted with the letter "G". On the other hand, the letter "G" in "" comes from the fact that its Lie algebra is the seventh type ("G" being the seventh letter of the alphabet) in the classification of complex simple Lie algebras by Élie Cartan.
See also
G2, G2-manifold, Spin(7) manifold
Notes
References
.
Differential geometry
Riemannian geometry
Structures on manifolds |
https://en.wikipedia.org/wiki/Wilf%E2%80%93Zeilberger%20pair | In mathematics, specifically combinatorics, a Wilf–Zeilberger pair, or WZ pair, is a pair of functions that can be used to certify certain combinatorial identities. WZ pairs are named after Herbert S. Wilf and Doron Zeilberger, and are instrumental in the evaluation of many sums involving binomial coefficients, factorials, and in general any hypergeometric series. A function's WZ counterpart may be used to find an equivalent and much simpler sum. Although finding WZ pairs by hand is impractical in most cases, Gosper's algorithm provides a sure method to find a function's WZ counterpart, and can be implemented in a symbolic manipulation program.
Definition
Two functions F and G form a WZ pair if and only if the following two conditions hold:
Together, these conditions ensure that
because the function G telescopes:
Therefore,
that is
The constant does not depend on n.
Its value can be found by substituting n = n0for a particular n0.
If F and G form a WZ pair, then they satisfy the relation
where is a rational function of n and k and is called the WZ proof certificate.
Example
A Wilf–Zeilberger pair can be used to verify the identity
Divide the identity by its right-hand side:
Use the proof certificate
to verify that the left-hand side does not depend on n,
where
Now F and G form a Wilf–Zeilberger pair.
To prove that the constant in the right-hand side of the identity is 1, substitute n = 0, for instance.
References
.
See also
Almkvist–Zeilberger method, an analog of WZ method for evaluating definite integrals.
External links
Gosper's algorithm gives a method for generating WZ pairs when they exist.
Generatingfunctionology provides details on the WZ method of identity certification.
Combinatorics |
https://en.wikipedia.org/wiki/Multiphase%20topology%20optimisation | The Multi Phase Topology Optimisation is a simulation technique based on the principle of the finite element method which is able to determine the optimal distribution of two or more different materials in combination under thermal and mechanical loads.
The objective of optimization is to minimize the component's elastic energy. Conventional topology optimisation methods which simulate adaptive bone mineralization have the disadvantage that there is a continuous change of mass by the growth process. However, MPTO keeps all initial material concentrations and uses methods adapted for molecular dynamics to find energy minimum. Applying MPTO to Mechanically loaded components with a high number of different material densities, the optimization results show graded and sometimes anisotropic porosity distributions which are very similar to natural bone structures. This allows the macro- and microstructure of a mechanical component in one step. This method uses the Rapid Prototyping techniques, 3D printing and selective laser sintering to produce very stiff, light weight components with graded porosities calculated by MPTO.
References
Finite element method
Structural analysis |
https://en.wikipedia.org/wiki/1980%20North%20American%20Soccer%20League%20season | Statistics of North American Soccer League in season 1980. This was the 13th season of the NASL.
Overview
The league comprised 24 teams; for the only time in NASL history, the lineup of teams was identical to the year before, with no clubs joining or dropping out, franchise shifts or even name changes. The New York Cosmos defeated the Fort Lauderdale Strikers in the finals on September 21 to win the championship. For the third time in league history the team with the most wins (Seattle) did not win the regular season due to the NASL's system of awarding bonus points for goals scored.
Changes from the previous season
The 1980 season saw the regular season expand from 30 games to 32 games. Three North Americans were required to be among the eleven playing in the match for each team, up from two during the previous season.
New teams
None
Teams folding
None
Teams moving
None
Name changes
None
Regular season
W = Wins, L = Losses, GF = Goals For, GA = Goals Against, PT= point system
6 points for a win,
0 points for a loss,
1 point for each regulation goal scored up to three per game.
-Premiers (most points). -Best record. -Other playoff teams.
American Conference
National Conference
NASL All-Stars
Playoffs
The top two teams from each division qualified for the playoffs automatically. The last two spots would go to the next best teams in the conference, regardless of division. The top three conference seeds went to the division winners, seeds 4-6 went to the second place teams and the last two seeds were given wild-card berths. The winners of each successive round would be reseeded within the conference by regular season point total, regardless of first-round seeding. The Soccer Bowl remained a single game final.
In 1979 and 1980, if a playoff series was tied at one win apiece, a full 30 minute mini-game was played. If there was no winner after the 30 minutes ended, the teams would then move on to a shoot-out to determine a series winner.
Bracket
First round
Conference semifinals
Conference Championships
Soccer Bowl '80
1980 NASL Champions: New York Cosmos
Post season awards
Most Valuable Player: Roger Davies, Seattle
Coach of the year: Alan Hinton, Seattle
Rookie of the year: Jeff Durgan, New York
North American Player of the Year: Jack Brand, Seattle
References
External links
Video of 1980 goals of the year
Complete Results and Standings
North American Soccer League (1968–1984) seasons
1980 in American soccer leagues
1980 in Canadian soccer |
https://en.wikipedia.org/wiki/1981%20North%20American%20Soccer%20League%20season | Statistics of North American Soccer League in season 1981. This was the 14th season of the NASL.
Overview
There were a total of 21 teams participating. Three teams (Houston, Rochester and Washington) folded, while four others (Memphis, Detroit, New England and Philadelphia) moved to new cities. Playoff series were switched from the two matches plus a mini-game tiebreaker used since 1977, to a best-of-three full matches played on three separate dates. The Chicago Sting defeated the New York Cosmos in Soccer Bowl '81 on September 26 to win the championship.
When Major League Baseball players went on strike on June 12, there was speculation that other sports, especially soccer, would see larger crowds. However, the 157 NASL matches played during the baseball work stoppage (which ended August 9) drew an average attendance of only 13,419, less than the full-season average of 14,084.
Changes from the previous season
New teams
None
Teams folding
Houston Hurricane
Rochester Lancers
Washington Diplomats
Teams moving
Memphis Rogues to Calgary Boomers
Detroit Express to Washington Diplomats
New England Tea Men to Jacksonville Tea Men
Philadelphia Fury to Montreal Manic
Name changes
None
Regular season
W = Wins, L = Losses, GF = Goals For, GA = Goals Against, PT= point system
6 points for a win in regulation and overtime, 4 point for a shootout win,
0 points for a loss,
1 bonus point for each regulation goal scored, up to three per game.
-Premiers (most points). -Other playoff teams.
NASL All-Stars
Playoffs
15 teams qualified for the playoffs – each first and second-place team across the divisions plus the five next best teams. Division winners were seeded 1 through 5, the second-place teams were seeded 6 through 10, and the last five teams were seeded 11 through 15 regardless of division placing. The top seed received a bye, and the remaining 14 teams paired off to play the first round. Series winners would be reseeded by season point total after each round.
The 'best of two' format used from 1978 to 1980 was discarded for a more straightforward best of three games format in the first three rounds.
Bracket
First round
#Due to a scheduling conflict between the Calgary Boomers and the Billy Graham Crusade, the Fort Lauderdale Strikers hosted both Games 1 and 2 (instead of Game 1 only), there-by gaining home field advantage even though they were the lower seed.
*Seattle Sounders hosted Game 2 (instead of Game 1) due to a scheduling conflict with the Mariners baseball club.
Quarterfinals
Semifinals
Soccer Bowl '81
1981 NASL Champions: Chicago Sting
*From 1977 through 1984 the NASL had a variation of the penalty shoot-out procedure for tied matches. The shoot-out started 35 yards from the goal and allowed the player 5 seconds to attempt a shot. The player could make as many moves as he wanted in a breakaway situation within the time frame. Even though this particular match was a scoreless tie after overtime, NASL procedure also called for th |
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