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https://en.wikipedia.org/wiki/Mikko%20Kukkonen | Mikko Kukkonen (born 19 January 1988) is a Finnish former professional ice hockey defenceman.
Kukkonen played from 2006 to 2013 with KalPa.
Career statistics
References
External links
1988 births
Espoo Blues players
Finnish ice hockey defencemen
High1 players
Ilves players
Living people
KalPa players
People from Siilinjärvi
Ice hockey people from North Savo |
https://en.wikipedia.org/wiki/Henri%20Laurila | Henri Laurila is a Finnish professional ice hockey defenceman who currently plays for Rote Teufel Bad Nauheim of the German DEL2.
Career statistics
External links
Living people
Finnish ice hockey defencemen
1980 births
Asiago Hockey 1935 players
Espoo Blues players
Ilves players
KalPa players
Lahti Pelicans players
Modo Hockey players
Peliitat Heinola players
Rote Teufel Bad Nauheim players
SHC Fassa players
Ice hockey people from Lahti |
https://en.wikipedia.org/wiki/Affine%20plane | In geometry, an affine plane is a two-dimensional affine space.
Examples
Typical examples of affine planes are
Euclidean planes, which are affine planes over the reals equipped with a metric, the Euclidean distance. In other words, an affine plane over the reals is a Euclidean plane in which one has "forgotten" the metric (that is, one does not talk of lengths nor of angle measures).
Vector spaces of dimension two, in which the zero vector is not considered as different from the other elements
For every field or division ring F, the set F2 of the pairs of elements of F
The result of removing any single line (and all the points on this line) from any projective plane
Coordinates and isomorphism
All the affine planes defined over a field are isomorphic. More precisely, the choice of an affine coordinate system (or, in the real case, a Cartesian coordinate system) for an affine plane P over a field F induces an isomorphism of affine planes between P and F2.
In the more general situation, where the affine planes are not defined over a field, they will in general not be isomorphic. Two affine planes arising from the same non-Desarguesian projective plane by the removal of different lines may not be isomorphic.
Definitions
There are two ways to formally define affine planes, which are equivalent for affine planes over a field. The first one consists in defining an affine plane as a set on which a vector space of dimension two acts simply transitively. Intuitively, this means that an affine plane is a vector space of dimension two in which one has "forgotten" where the origin is. In incidence geometry, an affine plane is defined as an abstract system of points and lines satisfying a system of axioms.
Applications
In the applications of mathematics, there are often situations where an affine plane without the Euclidean metric is used instead of the Euclidean plane. For example, in a graph, which can be drawn on paper, and in which the position of a particle is plotted against time, the Euclidean metric is not adequate for its interpretation, since the distances between its points or the measures of the angles between its lines have, in general, no physical importance (in the affine plane the axes can use different units, which are not comparable, and the measures also vary with different units and scales).
Sources
References
Planes (geometry)
Mathematical physics |
https://en.wikipedia.org/wiki/Fl%C3%A1vio%20Campos | Flávio Henrique de Paiva Campos (born August 29, 1965) is a former Brazilian football player and manager.
Club statistics
References
External links
1965 births
Living people
Footballers from Rio de Janeiro (city)
Brazilian men's footballers
Brazilian expatriate men's footballers
Expatriate men's footballers in Japan
Brazilian football managers
Campeonato Brasileiro Série A players
Campeonato Brasileiro Série B players
J1 League players
CR Flamengo footballers
São Paulo FC players
Guarani FC players
CR Vasco da Gama players
Gamba Osaka players
Clube Atlético Bragantino players
Kyoto Sanga FC players
Esporte Clube Juventude players
América Futebol Clube (SP) players
Clube 15 de Novembro managers
Esporte Clube Juventude managers
Canoas Sport Club managers
Clube do Remo managers
Grêmio Esportivo Brasil managers
Sampaio Corrêa Futebol Clube managers
Clube Esportivo Lajeadense managers
Clube Esportivo Bento Gonçalves managers
Men's association football midfielders |
https://en.wikipedia.org/wiki/Marko%20Luomala | Marko Luomala (born June 2, 1980) is a Finnish former professional ice hockey player. He played in Liiga for Ässät, Ilves, Lukko, Oulun Kärpät, Kloten Flyers, HPK and Vaasan Sport.
Career statistics
References
External links
1980 births
Living people
Porin Ässät (men's ice hockey) players
Ferencvárosi TC (ice hockey) players
Finnish ice hockey forwards
HC Gardena players
HPK players
EHC Kloten players
Ilves players
Lukko players
Milton Keynes Lightning players
Olofströms IK players
Oulun Kärpät players
Vaasan Sport players
Sportspeople from Vaasa
Ice hockey people from Ostrobothnia (region) |
https://en.wikipedia.org/wiki/Prize%20of%20the%20Austrian%20Mathematical%20Society | The Prize of the Austrian Mathematical Society () is the highest mathematics award in Austria. It is awarded every year by the Austrian Mathematical Society to a promising young mathematician for outstanding achievements. A substantial part of the work must have been performed in Austria. The recipient receives, in addition to a monetary reward, a medal showing Rudolf Inzinger. The prize was established in 1955 and is awarded since 1956.
See also
Awards and Prizes of the Austrian Mathematical Society (in german)
List of mathematics awards
Mathematics awards
Awards established in 1955
1955 establishments in Austria |
https://en.wikipedia.org/wiki/Janne%20Ker%C3%A4nen | Janne Keränen (born 30 June 1987) is a Finnish ice hockey player who currently playing for Vaasan Sport of the Liiga.
Career statistics
Regular season and playoffs
References
External links
1987 births
Living people
People from Nurmijärvi
Finnish ice hockey forwards
HIFK sportspeople
Lukko players
KalPa players
Vaasan Sport players
HK Dukla Michalovce players
Ice hockey people from Uusimaa
Finnish expatriate ice hockey players in Slovakia |
https://en.wikipedia.org/wiki/Jussi%20Pernaa | Jussi Pernaa is a Finnish former ice hockey defenceman who played professionally in Finland for Lukko of the SM-liiga and Sport Vaasa.
Career statistics
References
External links
Living people
Finnish ice hockey defencemen
1983 births
FoPS players
Ilves players
Lempäälän Kisa players
Lukko players
Vaasan Sport players |
https://en.wikipedia.org/wiki/Auslander%E2%80%93Buchsbaum%20theorem | In commutative algebra, the Auslander–Buchsbaum theorem states that regular local rings are unique factorization domains.
The theorem was first proved by . They showed that regular local rings of dimension 3 are unique factorization domains, and had previously shown that this implies that all regular local rings are unique factorization domains.
References
Commutative algebra
Theorems in ring theory |
https://en.wikipedia.org/wiki/Auslander%E2%80%93Buchsbaum%20formula | In commutative algebra, the Auslander–Buchsbaum formula, introduced by , states that if R is a commutative Noetherian local ring and M is a non-zero finitely generated R-module of finite projective dimension, then:
Here pd stands for the projective dimension of a module, and depth for the depth of a module.
Applications
The Auslander–Buchsbaum theorem implies that a Noetherian local ring is regular if, and only if, it has finite global dimension. In turn this implies that the localization of a regular local ring is regular.
If A is a local finitely generated R-algebra (over a regular local ring R), then the Auslander–Buchsbaum formula implies that A is Cohen–Macaulay if, and only if, pdRA = codimRA.
References
Chapter 19 of
Commutative algebra
Theorems in ring theory |
https://en.wikipedia.org/wiki/Carlo%20Gr%C3%BCnn | Carlo Grünn (born April 30, 1981) is a Finnish former ice hockey player who last played professionally in France for Étoile Noire de Strasbourg of the French Ligue Magnus.
Career statistics
References
External links
1981 births
Living people
Dornbirn Bulldogs players
Espoo Blues players
ETC Crimmitschau players
Étoile Noire de Strasbourg players
Finnish ice hockey forwards
HC Sierre players
HIFK (ice hockey) players
HPK players
JYP Jyväskylä players
Kiekko-Vantaa players
Mikkelin Jukurit players
Lahti Pelicans players
SaiPa players
Ice hockey people from Espoo |
https://en.wikipedia.org/wiki/Moser%27s%20worm%20problem | Moser's worm problem (also known as mother worm's blanket problem) is an unsolved problem in geometry formulated by the Austrian-Canadian mathematician Leo Moser in 1966. The problem asks for the region of smallest area that can accommodate every plane curve of length 1. Here "accommodate" means that the curve may be rotated and translated to fit inside the region. In some variations of the problem, the region is restricted to be convex.
Examples
For example, a circular disk of radius 1/2 can accommodate any plane curve of length 1 by placing the midpoint of the curve at the center of the disk. Another possible solution has the shape of a rhombus with vertex angles of 60° and 120° and with a long diagonal of unit length. However, these are not optimal solutions; other shapes are known that solve the problem with smaller areas.
Solution properties
It is not completely trivial that a minimum-area cover exists. An alternative possibility would be that there is some minimal area that can be approached but not actually attained. However, there does exist a smallest convex cover. Its existence follows from the Blaschke selection theorem.
It is also not trivial to determine whether a given shape forms a cover. conjectured that a shape accommodates every unit-length curve if and only if it accommodates every unit-length polygonal chain with three segments, a more easily tested condition, but showed that no finite bound on the number of segments in a polychain would suffice for this test.
Known bounds
The problem remains open, but over a sequence of papers researchers have tightened the gap between the known lower and upper bounds. In particular, constructed a (nonconvex) universal cover and showed that the minimum shape has area at most 0.260437; and gave weaker upper bounds. In the convex case, improved an upper bound to 0.270911861. used a min-max strategy for area of a convex set containing a segment, a triangle and a rectangle to show a lower bound of 0.232239 for a convex cover.
In the 1970s, John Wetzel conjectured that a 30° circular sector of unit radius is a cover with area . Two proofs of the conjecture were independently claimed by and by . If confirmed, this will reduce the upper bound for the convex cover by about 3%.
See also
Moving sofa problem, the problem of finding a maximum-area shape that can be rotated and translated through an L-shaped corridor
Kakeya set, a set of minimal area that can accommodate every unit-length line segment (with translations allowed, but not rotations)
Lebesgue's universal covering problem, find the smallest convex area that can cover any planar set of unit diameter
Bellman's lost in a forest problem, find the shortest path to escape from a forest of known size and shape.
Notes
References
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Discrete geometry
Unsolved problems in geometry
Recreational mathematics |
https://en.wikipedia.org/wiki/Louis%20Leithold | Louis Leithold (San Francisco, United States, 16 November 1924 – Los Angeles, 29 April 2005) was an American mathematician and teacher. He is best known for authoring The Calculus, a classic textbook about calculus that changed the teaching methods for calculus in world high schools and universities. Known as "a legend in AP calculus circles," Leithold was the mentor of Jaime Escalante, the Los Angeles high-school teacher whose story is the subject of the 1988 movie Stand and Deliver.
Biography
Leithold attended the University of California, Berkeley, where is attained his B.A., M.A. and PhD. He went on to teach at Phoenix College (Arizona) (which has a math scholarship in his name), California State University, Los Angeles, the University of Southern California, Pepperdine University, and The Open University (UK). In 1968, Leithold published The Calculus, a "blockbuster best-seller" which simplified the teaching of calculus.
At age 72, after his retirement from Pepperdine, he began teaching calculus at Malibu High School, in Malibu, California, drilling his students for the Advanced Placement Calculus, and achieving considerable success. He regularly assigned two hours of homework per night, and had two training sessions at his own house that ran Saturdays or Sundays from 9AM to 4PM before the AP test. His teaching methods were praised for their liveliness, and his love for the topic was well known. He also taught workshops for calculus teachers. One of the people he influenced was Jaime Escalante, who taught math to minority students at Garfield High School in East Los Angeles. Escalante's subsequent success as a teacher is portrayed in the 1988 film Stand and Deliver.
Leithold died of natural causes the week before his class (which he had been "relentlessly drilling" for eight months) was to take the AP exam; his students went on to receive top scores. A memorial service was held in Glendale, and a scholarship established in his name.
Leithold experienced a notable legal event in his personal life in 1959 when he and his then-wife, musician Dr. Thyra N. Pliske, adopted a minor child, Gordon Marc Leithold. The couple eventually divorced in 1962, with an Arizona court granting Thyra custody of the child and Louis receiving certain visitation rights. Thyra later married Gilbert Norman Plass, and the family moved to Dallas, Texas in 1963.
In 1965, Louis filed a suit against his former wife and her new husband in the Juvenile Court of Dallas County, Texas. The suit, titled "Application for Modification of Visitation and Custody," sought significant changes to the Arizona decree based on allegations of changed conditions and circumstances. Following a hearing, the Dallas court modified the Arizona decree with respect to Louis' visitation rights. His son would die in 1994, at the age of 35 in Houston, Texas.
He was an art collector, and had art by Vasa Mihich. He also used art in his Calculus book by Patrick Caulfield.
References
University |
https://en.wikipedia.org/wiki/Groupoid%20algebra | In mathematics, the concept of groupoid algebra generalizes the notion of group algebra.
Definition
Given a groupoid (in the sense of a category with all arrows invertible) and a field , it is possible to define the groupoid algebra as the algebra over formed by the vector space having the elements of (the arrows of) as generators and having the multiplication of these elements defined by , whenever this product is defined, and otherwise. The product is then extended by linearity.
Examples
Some examples of groupoid algebras are the following:
Group rings
Matrix algebras
Algebras of functions
Properties
When a groupoid has a finite number of objects and a finite number of morphisms, the groupoid algebra is a direct sum of tensor products of group algebras and matrix algebras.
See also
Hopf algebra
Partial group algebra
Notes
References
Algebra |
https://en.wikipedia.org/wiki/Jussi%20Halme | Jussi Halme (born August 24, 1980) is a Finnish former professional ice hockey defenceman.
Halme played in the Liiga for Tappara, Blues, SaiPa and JYP.
Career statistics
References
External links
1980 births
Living people
Denver Pioneers men's ice hockey players
Espoo Blues players
Finnish ice hockey defencemen
JYP Jyväskylä players
KooKoo players
Lempäälän Kisa players
NCAA men's ice hockey national champions
People from Nokia, Finland
SaiPa players
Södertälje SK players
Tappara players
Vaasan Sport players
Ice hockey people from Pirkanmaa |
https://en.wikipedia.org/wiki/David%20Buchsbaum | David Alvin Buchsbaum (November 6, 1929 – January 8, 2021) was a mathematician at Brandeis University who worked on commutative algebra, homological algebra, and representation theory. He proved the Auslander–Buchsbaum formula and the Auslander–Buchsbaum theorem.
Career
Buchsbaum earned his Ph.D. under Samuel Eilenberg in 1954 from Columbia University with thesis Exact Categories and Duality. Among his doctoral students are Peter J. Freyd and Hema Srinivasan. In 1995, he was elected to the American Academy of Arts and Sciences. In 2012, he became a fellow of the American Mathematical Society.
See also
Buchsbaum ring
References
External links
Home page of David Buchsbaum
1929 births
2021 deaths
20th-century American mathematicians
21st-century American mathematicians
Columbia University alumni
Brandeis University faculty
Fellows of the American Mathematical Society
Algebraists |
https://en.wikipedia.org/wiki/Antti%20Erkinjuntti | Antti Erkinjuntti (born 30 May 1986) is a Finnish ice hockey player. He is currently a free agent.
Career statistics
Regular season and playoffs
References
External links
1986 births
Living people
Finnish ice hockey forwards
Rovaniemen Kiekko players
Hokki players
Tappara players
HC TPS players
Lahti Pelicans players
SCL Tigers players
Vaasan Sport players
HK Dukla Michalovce players
Sportspeople from Rovaniemi
Finnish expatriate ice hockey players in Slovakia
Finnish expatriate ice hockey players in Switzerland |
https://en.wikipedia.org/wiki/Holtsmark%20distribution | The (one-dimensional) Holtsmark distribution is a continuous probability distribution. The Holtsmark distribution is a special case of a stable distribution with the index of stability or shape parameter equal to 3/2 and the skewness parameter of zero. Since equals zero, the distribution is symmetric, and thus an example of a symmetric alpha-stable distribution. The Holtsmark distribution is one of the few examples of a stable distribution for which a closed form expression of the probability density function is known. However, its probability density function is not expressible in terms of elementary functions; rather, the probability density function is expressed in terms of hypergeometric functions.
The Holtsmark distribution has applications in plasma physics and astrophysics. In 1919, Norwegian physicist Johan Peter Holtsmark proposed the distribution as a model for the fluctuating fields in plasma due to the motion of charged particles. It is also applicable to other types of Coulomb forces, in particular to modeling of gravitating bodies, and thus is important in astrophysics.
Characteristic function
The characteristic function of a symmetric stable distribution is:
where is the shape parameter, or index of stability, is the location parameter, and c is the scale parameter.
Since the Holtsmark distribution has its characteristic function is:
Since the Holtsmark distribution is a stable distribution with , represents the mean of the distribution. Since , also represents the median and mode of the distribution. And since , the variance of the Holtsmark distribution is infinite. All higher moments of the distribution are also infinite. Like other stable distributions (other than the normal distribution), since the variance is infinite the dispersion in the distribution is reflected by the scale parameter, c. An alternate approach to describing the dispersion of the distribution is through fractional moments.
Probability density function
In general, the probability density function, f(x), of a continuous probability distribution can be derived from its characteristic function by:
Most stable distributions do not have a known closed form expression for their probability density functions. Only the normal, Cauchy and Lévy distributions have known closed form expressions in terms of elementary functions. The Holtsmark distribution is one of two symmetric stable distributions to have a known closed form expression in terms of hypergeometric functions. When is equal to 0 and the scale parameter is equal to 1, the Holtsmark distribution has the probability density function:
where is the gamma function and is a hypergeometric function. One has also
where is the Airy function of the second kind and its derivative. The arguments of the functions are pure imaginary complex numbers, but the sum of the two functions is real. For positive, the function is related to the Bessel functions of fractional order and and its der |
https://en.wikipedia.org/wiki/General%20hypergeometric%20function | In mathematics, a general hypergeometric function or Aomoto–Gelfand hypergeometric function is a generalization of the hypergeometric function that was introduced by . The general hypergeometric function is a function that is (more or less) defined on a Grassmannian, and depends on a choice of some complex numbers and signs.
References
(English translation in collected papers, volume III.)
Aomoto, K. (1975), "Les équations aux différences linéaires et les intégrales des fonctions multiformes", J. Fac. Sci. Univ. Tokyo, Sect. IA Math. 22, 271-229.
Hypergeometric functions |
https://en.wikipedia.org/wiki/Roberto%20Marcolongo | Roberto Marcolongo (August 28, 1862 in Rome – May 16, 1943 in Rome) was an Italian mathematician, known for his research in vector calculus and theoretical physics.
He graduated in 1886, and later he was an assistant of Valentino Cerruti in Rome. In 1895 he became professor of rational mechanics at the University of Messina. In 1908 he moved to the University of Naples, where he remained until retirement in 1935.
He worked on vector calculus together with Cesare Burali-Forti, which was then known as "Italian notation". In 1906 he wrote an early work which used the four-dimensional formalism to account for relativistic invariance under Lorentz transformations.
In 1921 he published to Messina one of the first treaties on the special relativity and general, where he used the absolute differential calculus without coordinates, developed with Burali-Forti, as opposed to the absolute differential calculus with coordinates of Tullio Levi-Civita and Gregorio Ricci-Curbastro.
He was a member of the Accademia dei Lincei and other Italian academies.
Works
Teoria matematica dello equilibrio dei corpi elastici (Milano: U. Hoepli, 1904)
Meccanica razionale (Milano: U. Hoepli, 1905)
Elementi di Calcolo vettoriale con numerose Applicazioni (with Burali-Forti) (Bologna, Nicola Zanichelli, 1909)
Omografie vettoriali con Applicazioni (with Burali-Forti) (Torino, G. B. Petrini, 1909)
Analyse vectorielle générale: Transformations linéaires (with Cesare Burali-Forti, translated into French by Paul Baridon) (Pavia: Mattei & C., 1913)
Analyse vectorielle générale: Applications à la mécanique et à la physique (in French, with Cesare Burali-Forti and Tommaso Boggio) (Pavia:Mattei & C., 1913)
Il Problema dei Tre Corpi da Newton ai Nostri Giorni (Milano, Ulrico Hoepli, 1919)
Relatività (Messina, G. Principato, 1921)
Literature
Biography by Francesco Tricomi.
References
1862 births
1943 deaths
19th-century Italian mathematicians
20th-century Italian mathematicians |
https://en.wikipedia.org/wiki/Cayley%E2%80%93Klein%20metric | In mathematics, a Cayley–Klein metric is a metric on the complement of a fixed quadric in a projective space which is defined using a cross-ratio. The construction originated with Arthur Cayley's essay "On the theory of distance" where he calls the quadric the absolute. The construction was developed in further detail by Felix Klein in papers in 1871 and 1873, and subsequent books and papers. The Cayley–Klein metrics are a unifying idea in geometry since the method is used to provide metrics in hyperbolic geometry, elliptic geometry, and Euclidean geometry. The field of non-Euclidean geometry rests largely on the footing provided by Cayley–Klein metrics.
Foundations
The algebra of throws by Karl von Staudt (1847) is an approach to geometry that is independent of metric. The idea was to use the relation of projective harmonic conjugates and cross-ratios as fundamental to the measure on a line. Another important insight was the Laguerre formula by Edmond Laguerre (1853), who showed that the Euclidean angle between two lines can be expressed as the logarithm of a cross-ratio. Eventually, Cayley (1859) formulated relations to express distance in terms of a projective metric, and related them to general quadrics or conics serving as the absolute of the geometry. Klein (1871, 1873) removed the last remnants of metric concepts from von Staudt's work and combined it with Cayley's theory, in order to base Cayley's new metric on logarithm and the cross-ratio as a number generated by the geometric arrangement of four points. This procedure is necessary to avoid a circular definition of distance if cross-ratio is merely a double ratio of previously defined distances. In particular, he showed that non-Euclidean geometries can be based on the Cayley–Klein metric.
Cayley–Klein geometry is the study of the group of motions that leave the Cayley–Klein metric invariant. It depends upon the selection of a quadric or conic that becomes the absolute of the space. This group is obtained as the collineations for which the absolute is stable. Indeed, cross-ratio is invariant under any collineation, and the stable absolute enables the metric comparison, which will be equality. For example, the unit circle is the absolute of the Poincaré disk model and the Beltrami–Klein model in hyperbolic geometry. Similarly, the real line is the absolute of the Poincaré half-plane model.
The extent of Cayley–Klein geometry was summarized by Horst and Rolf Struve in 2004:
There are three absolutes in the real projective line, seven in the real projective plane, and 18 in real projective space. All classical non-euclidean projective spaces as hyperbolic, elliptic, Galilean and Minkowskian and their duals can be defined this way.
Cayley-Klein Voronoi diagrams are affine diagrams with linear hyperplane bisectors.
Cross ratio and distance
Cayley-Klein metric is first illustrated on the real projective line P(R) and projective coordinates. Ordinarily projective geometry is not associ |
https://en.wikipedia.org/wiki/Fenster | Fenster is a surname, from the German language word for "window". Notable persons with this surname include:
Della Dumbaugh, formerly Della Fenster, American historian of mathematics
Aaron Fenster, Canadian engineer
Ariel Fenster (born 1943), Canadian science promoter and lecturer at McGill University
Boris Fenster (1916–1960), Russian dancer, choreographer and ballet master
Darren Fenster (born 1978), American baseball player and coach
Fred Fenster (born 1934), American metalsmith
Gigi Fenster, South African-born New Zealand author, creative writing teacher and law lecturer
Julie M. Fenster (born 1957), American author of historical articles and books
Mark Fenster, American lawyer and author in Florida
Saul Fenster, president of New Jersey Institute of Technology during 1978–2002
Karol Martesko-Fenster, American media executive
Fictional characters
Arch Fenster, a character in the American 1962–63 sitcom I'm Dickens, He's Fenster
Fred Fenster, a character in the 1995 film The Usual Suspects
Other uses
Fenster, another name for a tectonic window (a geologic structure)
Fenster School, American school in Catalina Foothills, Arizona
Schnell Fenster, Australian band, active 1986–1992
"Tausend Fenster", Austrian entry in the Eurovision Song Contest 1968 |
https://en.wikipedia.org/wiki/Leslie%2C%20Saskatchewan | Leslie is a special service area in the Rural Municipality of Elfros No. 307, Saskatchewan, Canada. Listed as a designated place by Statistics Canada, the community had a population of 15 in the Canada 2016 Census. The community is located just off of Highway 16 between Foam Lake and Elfros.
The first post office was established in 1909 as Leslie Station (with C. A. Clarke as postmaster), with the name of the community changed to Leslie in 1962. The last postmaster was Victoria Ann St. Amand in 1987.
Demographics
In the 2021 Census of Population conducted by Statistics Canada, Leslie had a population of 20 living in 10 of its 15 total private dwellings, a change of from its 2016 population of 15. With a land area of , it had a population density of in 2021.
See also
List of communities in Saskatchewan
Special service area
Designated place
References
Designated places in Saskatchewan
Elfros No. 307, Saskatchewan
Former villages in Saskatchewan
Special service areas in Saskatchewan
Icelandic settlements in Saskatchewan
Populated places disestablished in 2006
Division No. 10, Saskatchewan |
https://en.wikipedia.org/wiki/Conway%20polynomial%20%28finite%20fields%29 | In mathematics, the Conway polynomial Cp,n for the finite field Fpn is a particular irreducible polynomial of degree n over Fp that can be used to define a standard representation of Fpn as a splitting field of Cp,n. Conway polynomials were named after John H. Conway by Richard A. Parker, who was the first to define them and compute examples. Conway polynomials satisfy a certain compatibility condition that had been proposed by Conway between the representation of a field and the representations of its subfields. They are important in computer algebra where they provide portability among different mathematical databases and computer algebra systems. Since Conway polynomials are expensive to compute, they must be stored to be used in practice. Databases of Conway polynomials are available in the computer algebra systems GAP, Macaulay2, Magma, SageMath, and at the web site of Frank Lübeck.
Background
Elements of Fpn may be represented as sums of the form an−1βn−1 + ... + a1β + a0 where β is a root of an irreducible polynomial of degree n over Fp and the aj are elements of Fp. Addition of field elements in this representation is simply vector addition. While there is a unique finite field of order pn up to isomorphism, the representation of the field elements depends on the choice of the irreducible polynomial. The Conway polynomial is a way of standardizing this choice.
The non-zero elements of a finite field form a cyclic group under multiplication. A primitive element, α, of Fpn is an element that generates this group. Representing the non-zero field elements as powers of α allows multiplication in the field to be performed efficiently. The primitive polynomial for α is the monic polynomial of smallest possible degree with coefficients in Fp that has α as a root in Fpn (the minimal polynomial for α). It is necessarily irreducible. The Conway polynomial is chosen to be primitive, so that each of its roots generates the multiplicative group of the associated finite field.
The subfields of Fpn are fields Fpm with m dividing n. The cyclic group formed from the non-zero elements of Fpm is a subgroup of the cyclic group of Fpn. If α generates the latter, then the smallest power of α that generates the former is αr where r = (pn − 1)/(pm − 1). If fn is a primitive polynomial for Fpn with root α, and if fm is a primitive polynomial for Fpm, then by Conway's definition, fm and fn are compatible if αr is a root of fm. This necessitates that fm(x) divide fn(xr). This notion of compatibility is called norm-compatibility by some authors. The Conway polynomial for a finite field is chosen so as to be compatible with the Conway polynomials of each of its subfields. That it is possible to make the choice in this way was proved by Werner Nickel.
Definition
The Conway polynomial Cp,n is defined as the lexicographically minimal monic primitive polynomial of degree n over Fp that is compatible with Cp,m for all m dividing n. This is an ind |
https://en.wikipedia.org/wiki/Anthony%20Hicks | Anthony Hicks (26 June 1943 – 26 May 2010) was a Welsh musicologist, music critic, editor, and writer.
Born in Swansea, a city in Wales, Hicks read mathematics at King's College London during the mid-1960s and worked for roughly a quarter of century as a computer systems analyst at the University of London, until he retired in 1993. Although he was educated in the fields of mathematics and computer science, his personal obsession with baroque music led him to pursue scholarly music research in his spare time. What began as more or less a hobby developed into a highly distinguished para-career as a historian and writer. He became one of the leading 20th-century scholars on George Frideric Handel.
As a music critic, Hicks wrote for Early Music Review and The Musical Times. For the 2001 edition of The New Grove Dictionary of Music and Musicians, he penned Handel's biography and several other Handel related entries. He also authored most of the Handel related articles in the New Grove Dictionary of Opera. He became an important advocate for historically informed performances just as the renewed enthusiasm for baroque music began to take off in the 1960s and 1970s. His research has been used widely in preparing baroque works for recordings and performance; most notably with the Academy of Ancient Music in Cambridge, with whom he worked closely for several decades. Hicks collaborated on recordings with musicians including Christopher Hogwood, Paul McCreesh, Robert King, Trevor Pinnock, Emma Kirkby, John Eliot Gardiner, and Alan Curtis, among many other distinguished baroque performers.
Hicks died at the age of 66 in London in 2010 of pulmonary fibrosis.
References
1943 births
2010 deaths
Alumni of King's College London
British musicologists
Deaths from pulmonary fibrosis
People associated with the University of London
Handel scholars |
https://en.wikipedia.org/wiki/1998%20Tajik%20League | Tajik League is the top division of the Tajikistan Football Federation, it was created in 1992. These are the statistics of the Tajik League in the 1998 season.
Table
External links
Tajikistan Higher League seasons
1
Tajik
Tajik |
https://en.wikipedia.org/wiki/1999%20Tajik%20League | Tajik League is the top division of the Tajikistan Football Federation, it was created in 1992. These are the statistics of the Tajik League in the 1999 season.
Table
Top scorers
External links
Tajikistan Higher League seasons
1
Tajik
Tajik |
https://en.wikipedia.org/wiki/2000%20Tajik%20League | Tajik League is the top division of the Tajikistan Football Federation, it was created in 1992. These are the statistics of the Tajik League in the 2000 season.
Table
Top scorers
External links
Tajikistan Higher League seasons
1
Tajik
Tajik |
https://en.wikipedia.org/wiki/2001%20Tajik%20League | Tajik League is the top division of the Tajikistan Football Federation, it was created in 1992. These are the statistics of the Tajik League in the 2001 season.
Table
Top scorers
External links
Tajikistan Higher League seasons
1
Tajik
Tajik |
https://en.wikipedia.org/wiki/2002%20Tajik%20League | Tajik League is the top division of the Tajikistan Football Federation, it was created in 1992. These are the statistics of the Tajik League in the 2002 season.
Table
Top scorers
External links
Tajikistan Higher League seasons
1
Tajik
Tajik |
https://en.wikipedia.org/wiki/2003%20Tajik%20League | Tajik League is the top division of the Tajikistan Football Federation, it was created in 1992. These are the statistics of the Tajik League in the 2003 season.
Table
Top scorers
External links
Tajikistan Higher League seasons
1
Tajik
Tajik |
https://en.wikipedia.org/wiki/2004%20Tajik%20League | Tajik League is the top division of the Tajikistan Football Federation, it was created in 1992. These are the statistics of the Tajik League in the 2004 season.
Table
Top scorers
External links
Tajikistan Higher League seasons
1
Tajik
Tajik |
https://en.wikipedia.org/wiki/2005%20Tajik%20League | Tajik League is the top division of the Tajikistan Football Federation, it was created in 1992. These are the statistics of the Tajik League in the 2005 season.
Table
Top scorers
External links
Tajikistan Higher League seasons
1
Tajik
Tajik |
https://en.wikipedia.org/wiki/2006%20Tajik%20League | Tajik League is the top division of the Tajikistan Football Federation, it was created in 1992. These are the statistics of the Tajik League in the 2006 season.
Table
Top scorers
External links
Tajikistan Higher League seasons
1
Tajik
Tajik |
https://en.wikipedia.org/wiki/1993%E2%80%9394%20Yemeni%20League | Statistics of the Yemeni League in the 1993-94 season.
Results
Relegated
Al-Shaab Ibb
Al-Ahly Taizz
Al Sha'ab Sana'a
Al-Yarmuk Sana'a
Other participants
Al-Wahda Sanaa
Al-Zohra Sanaa
Shamsan Aden
Al-Tilal Aden
Al-Shula Aden
Al-Shurta Aden
Al-Sha'ab Hadramaut
External links
Yem
Yemeni League seasons
football
football |
https://en.wikipedia.org/wiki/1994%E2%80%9395%20Yemeni%20League | Statistics of the Yemeni League in the 1994–95 season.
Results
Other participants
Al-Wahda Aden
Al-Zohra Sanaa
Shamsan Aden
Al-Tilal Aden
Al-Shula Aden
Al-Sha'ab Hadramaut
Al-Ahly Hudaida
External links
Yem
Yemeni League seasons
football
football |
https://en.wikipedia.org/wiki/1997%E2%80%9398%20Yemeni%20League | Statistics of the Yemeni League in the 1997–98 season.
Results
External links
Yem
Yemeni League seasons
football
football |
https://en.wikipedia.org/wiki/1998%E2%80%9399%20Yemeni%20League | Statistics of the Yemeni League in the 1998–99 season.
Results
External links
Yem
Yemeni League seasons
football
football |
https://en.wikipedia.org/wiki/1999%E2%80%932000%20Yemeni%20League | Statistics of the Yemeni League in the 1999-00 season.
Results
Group 1
Group 2
Playoffs
Semifinals
First Legs
[Apr 21]
Al-Ahli Sana 1-1 Al-Wahda Sana
[Apr 22]
Al-Tali'aa Taizz 0-0 Sha'ab M
Second Legs [Apr 28]
Al-Wahda Sana 1-2 Al-Ahli Sana
Sha'ab M 1-2 Al-Tali'aa Taizz
Third-place match
First Leg [May 5]
Sha'ab M 1-0 Al-Wahda Sana
Second Leg [May 11]
Al-Wahda Sana 3-0 Sha'ab M
Championship final
First Leg [May 5]
Al-Tali'aa Taizz 2-1 Al-Ahli Sana
Second Leg [May 11]
Al-Ahli Sana 5-1 Al-Tali'aa Taizz
External links
Yem
Yemeni League seasons
football
football |
https://en.wikipedia.org/wiki/2000%E2%80%9301%20Yemeni%20League | Statistics of the Yemeni League in the 2000–01 season.
Final table
External links
Yem
Yemeni League seasons
football
football |
https://en.wikipedia.org/wiki/2002%20Yemeni%20League | Statistics of the Yemeni League in the 2001-02 season.
Final table
External links
Yem
Yemeni League seasons
football
football |
https://en.wikipedia.org/wiki/2003%E2%80%9304%20Yemeni%20League | Statistics of the Yemeni League for the 2003–04 season.
Final table
References
External links
Yem
Yemeni League seasons
1 |
https://en.wikipedia.org/wiki/2006%20Yemeni%20League | Statistics of the Yemeni League in the 2005–06 season.
Final table
External links
Yemeni League seasons
Yem
1 |
https://en.wikipedia.org/wiki/2007%20Yemeni%20League | Statistics of the Yemeni League in the 2006–07 season.
Final table
External links
Yemeni League seasons
Yem
1 |
https://en.wikipedia.org/wiki/2007%E2%80%9308%20Yemeni%20League | Statistics of the Yemeni League in the 2007–08 season.
Final table
External links
Yemeni League seasons
Yem
1 |
https://en.wikipedia.org/wiki/Michal%20Mur%C4%8Dek | Michal Murček (born 29 January 1992) is a Slovak professional ice hockey player currently playing for HK Martin of the Slovak 1. Liga.
Career statistics
Regular season and playoffs
International
References
External links
Living people
MHC Martin players
HK Poprad players
Slovak ice hockey forwards
1992 births
MHk 32 Liptovský Mikuláš players
HC 07 Detva players
HC Košice players
HKM Zvolen players
Nacka HK players
MHK Dolný Kubín players
Ice hockey people from Martin, Slovakia
Slovak expatriate sportspeople in Norway
Expatriate ice hockey players in Norway
Slovak expatriate ice hockey players in Sweden |
https://en.wikipedia.org/wiki/Jaroslav%20Markovi%C4%8D | Jaroslav Markovič (born 22 May 1985) is a Slovak professional ice hockey player currently playing for Gamyo d'Épinal of the FFHG Division 1.
Career statistics
Regular season and playoffs
References
External links
Living people
1985 births
Slovak ice hockey forwards
HC Dynamo Pardubice players
Tri-City Storm players
VHK Vsetín players
HC Slavia Praha players
Heilbronner Falken players
HK Dukla Trenčín players
HKM Zvolen players
MsHK Žilina players
MHC Martin players
HC 07 Detva players
MHK Dolný Kubín players
HC Prešov players
Dauphins d'Épinal players
Ice hockey people from Martin, Slovakia
Slovak expatriate ice hockey players in Germany
Slovak expatriate ice hockey players in the United States
Slovak expatriate ice hockey players in the Czech Republic
Expatriate ice hockey players in France
Slovak expatriate sportspeople in France |
https://en.wikipedia.org/wiki/Keisuke%20Naito | is a Japanese footballer who plays for Tokyo Verdy.
Club statistics
Updated to 23 February 2018.
References
External links
1987 births
Living people
Kokushikan University alumni
Japanese men's footballers
J2 League players
J3 League players
Kataller Toyama players
Thespakusatsu Gunma players
FC Machida Zelvia players
Tokyo Verdy players
Men's association football goalkeepers
Association football people from Hiroshima |
https://en.wikipedia.org/wiki/Daisuke%20Asahi | is a former Japanese football player.
Club statistics
Updated to 23 February 2016.
References
External links
Profile at Kataller Toyama
1980 births
Living people
Kokushikan University alumni
Japanese men's footballers
J2 League players
J3 League players
Japan Football League players
Kataller Toyama players
Men's association football midfielders
Association football people from Hiroshima |
https://en.wikipedia.org/wiki/Edinho%20%28footballer%2C%20born%201974%29 | Edoson Silva Martins (born March 16, 1974) is a former Brazilian football player.
Club statistics
References
External links
1974 births
Living people
Brazilian men's footballers
Brazilian expatriate men's footballers
Expatriate men's footballers in Japan
J1 League players
Kashima Antlers players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Emil%20Jonassen | Emil Jonassen Sætervik (born 17 February 1993) is a Norwegian former footballer.
He started playing for local club Odd at the age of five, and made his way to the first team.
Career statistics
Club
References
External links
Odd Grenland profile
1993 births
Living people
Footballers from Skien
Norwegian men's footballers
Norway men's youth international footballers
Men's association football defenders
Eliteserien players
Norwegian First Division players
Odds BK players
FK Bodø/Glimt players
FC BATE Borisov players
Stabæk Fotball players
Norwegian expatriate men's footballers
Expatriate men's footballers in Belarus
Norwegian expatriate sportspeople in Belarus
21st-century Norwegian people |
https://en.wikipedia.org/wiki/Andr%C3%A9%20Paus | André Paus (born 9 October 1965 in Weerselo) is a Dutch former professional footballer and manager
Career statistics
Club
Managerial
As of 7 May 2022
Honours
Player
Júbilo Iwata
J.League Cup: Runner Up: 1994
Manager
WKE
Hoofdklasse: 2006–07, 2008–09
SV Spakenburg
Topklasse Zaterdag: 2011–12
Valletta
Maltese Premier League: 2013–14
Maltese FA Trophy: 2013–14
Enosis Neon Paralimni
Cypriot Second Division: 2017–18
References
External links
odn.ne.jp
1965 births
Living people
Dutch men's footballers
Dutch expatriate men's footballers
Eredivisie players
J1 League players
Japan Football League (1992–1998) players
FC Twente players
Júbilo Iwata players
Kawasaki Frontale players
Expatriate men's footballers in Japan
Dutch expatriate sportspeople in Cyprus
Dutch expatriate sportspeople in Japan
Dutch expatriate sportspeople in Malta
Expatriate football managers in Cyprus
Expatriate football managers in Malta
People from Weerselo
Dutch expatriate football managers
Valletta F.C. managers
Anorthosis Famagusta FC managers
WKE '16 managers
FC Lienden managers
Men's association football defenders
SV Spakenburg managers
Footballers from Overijssel |
https://en.wikipedia.org/wiki/Acta%20Mathematicae%20Applicatae%20Sinica | Acta Mathematicae Applicatae Sinica (English series) is a peer-reviewed mathematics journal published quarterly by Springer.
Established in 1984 by the Chinese Mathematical Society, the journal publishes articles on applied mathematics.
According to the Journal Citation Reports, the journal had a 2020 impact factor of 1.102.
References
External links
Mathematics journals
Academic journals established in 1984
English-language journals
Springer Science+Business Media academic journals
Quarterly journals |
https://en.wikipedia.org/wiki/Algebraic%20%26%20Geometric%20Topology | Algebraic & Geometric Topology is a peer-reviewed mathematics journal published quarterly by Mathematical Sciences Publishers.
Established in 2001, the journal publishes articles on topology.
Its 2018 MCQ was 0.82, and its 2018 impact factor was 0.709.
External links
Mathematics journals
Academic journals established in 2001
English-language journals
Mathematical Sciences Publishers academic journals
Quarterly journals |
https://en.wikipedia.org/wiki/Algebraic%20interior | In functional analysis, a branch of mathematics, the algebraic interior or radial kernel of a subset of a vector space is a refinement of the concept of the interior.
Definition
Assume that is a subset of a vector space
The algebraic interior (or radial kernel) of with respect to is the set of all points at which is a radial set.
A point is called an of and is said to be if for every there exists a real number such that for every
This last condition can also be written as where the set
is the line segment (or closed interval) starting at and ending at
this line segment is a subset of which is the emanating from in the direction of (that is, parallel to/a translation of ).
Thus geometrically, an interior point of a subset is a point with the property that in every possible direction (vector) contains some (non-degenerate) line segment starting at and heading in that direction (i.e. a subset of the ray ).
The algebraic interior of (with respect to ) is the set of all such points. That is to say, it is the subset of points contained in a given set with respect to which it is radial points of the set.
If is a linear subspace of and then this definition can be generalized to the algebraic interior of with respect to is:
where always holds and if then where is the affine hull of (which is equal to ).
Algebraic closure
A point is said to be from a subset if there exists some such that the line segment is contained in
The , denoted by consists of and all points in that are linearly accessible from
Algebraic Interior (Core)
In the special case where the set is called the or of and it is denoted by or
Formally, if is a vector space then the algebraic interior of is
If is non-empty, then these additional subsets are also useful for the statements of many theorems in convex functional analysis (such as the Ursescu theorem):
If is a Fréchet space, is convex, and is closed in then but in general it is possible to have while is empty.
Examples
If then but and
Properties of core
Suppose
In general, But if is a convex set then:
and
for all then
is an absorbing subset of a real vector space if and only if
if
Both the core and the algebraic closure of a convex set are again convex.
If is convex, and then the line segment is contained in
Relation to topological interior
Let be a topological vector space, denote the interior operator, and then:
If is nonempty convex and is finite-dimensional, then
If is convex with non-empty interior, then
If is a closed convex set and is a complete metric space, then
Relative algebraic interior
If then the set is denoted by and it is called the relative algebraic interior of This name stems from the fact that if and only if and (where if and only if ).
Relative interior
If is a subset of a topological vector space then the relative interior of is the set
That is, it is the topologica |
https://en.wikipedia.org/wiki/System%20of%20parameters | In mathematics, a system of parameters for a local Noetherian ring of Krull dimension d with maximal ideal m is a set of elements x1, ..., xd that satisfies any of the following equivalent conditions:
m is a minimal prime over (x1, ..., xd).
The radical of (x1, ..., xd) is m.
Some power of m is contained in (x1, ..., xd).
(x1, ..., xd) is m-primary.
Every local Noetherian ring admits a system of parameters.
It is not possible for fewer than d elements to generate an ideal whose radical is m because then the dimension of R would be less than d.
If M is a k-dimensional module over a local ring, then x1, ..., xk is a system of parameters for M if the length of is finite.
General references
References
Commutative algebra
Ideals (ring theory) |
https://en.wikipedia.org/wiki/Marquinhos%20%28footballer%2C%20born%201966%29 | Marco Antonio da Silva (born May 9, 1966), also knows as Marquinhos is a former Brazilian football player.
Club statistics
National team statistics
References
External links
1966 births
Living people
Brazilian men's footballers
Brazil men's international footballers
Brazilian expatriate men's footballers
J1 League players
Japan Football League (1992–1998) players
Expatriate men's footballers in Japan
Clube Atlético Mineiro players
Sport Club Internacional players
América Futebol Clube (MG) players
Cerezo Osaka players
Men's association football midfielders
Footballers from Belo Horizonte |
https://en.wikipedia.org/wiki/Arif%20Salimov | Arif Salimov (A.A. Salimov, born 1956, ) is an Azerbaijani/Soviet mathematician, Honored Scientist of Azerbaijan, known for his research in differential geometry. He earned his B.Sc. degree from Baku State University, Azerbaijan, in 1978, a PhD and Doctor of Sciences (Habilitation) degrees in geometry from Kazan State University, Russia, in 1984 and 1998, respectively. His advisor was Vladimir Vishnevskii. Salimov is Full Professor and Head of the Department Algebra and Geometry, Faculty of Mechanics and Mathematics, Baku State University. He is an author and co-author of more than 100 articles. He is also an author of 2 monographs. His primary areas of research are:
theory of lifts in tensor bundles
geometrical applications of tensor operators
special Riemannian manifolds, indefinite metrics
general geometric structures on manifolds (almost complex, almost product, hypercomplex, Norden structures etc.)
References
External links
http://mechmath.bsu.edu.az/en/content/algebra_and_geometry_514 Dep. of Algebra and Geometry
https://president.az/articles/34950
Living people
1956 births
20th-century Azerbaijani mathematicians
Soviet mathematicians
Differential geometers
21st-century Azerbaijani mathematicians
Baku State University alumni
Academic staff of Baku State University |
https://en.wikipedia.org/wiki/Ivan%20%C4%8Eatelinka | Ivan Ďatelinka (born March 6, 1983) is a Slovak professional ice hockey defenceman who is currently playing for HC '05 Banská Bystrica of the Slovak Extraliga.
Career statistics
Regular season and playoffs
References
External links
1983 births
Living people
Sportspeople from Topoľčany
Ice hockey people from the Nitra Region
MHC Martin players
HC Slovan Bratislava players
Slovak ice hockey defencemen
MHK Dolný Kubín players
HK 36 Skalica players
HC '05 Banská Bystrica players |
https://en.wikipedia.org/wiki/Luk%C3%A1%C5%A1%20Koz%C3%A1k | Lukáš Kozák (born 29 October 1991) is a Slovak professional ice hockey defenceman who is currently playing for HC Nové Zámky of the Slovak Extraliga.
Career statistics
Regular season and playoffs
International
References
External links
1991 births
Living people
HK Dukla Trenčín players
HC Kometa Brno players
MHC Martin players
KHL Medveščak Zagreb players
HK 36 Skalica players
HC Slovan Bratislava players
MsHK Žilina players
HK Poprad players
HC Karlovy Vary players
Slovak ice hockey defencemen
Ice hockey people from Martin, Slovakia
HC RT Torax Poruba players
HC Nové Zámky players
Slovak expatriate ice hockey players in the Czech Republic
Expatriate ice hockey players in Croatia
Slovak expatriate sportspeople in Croatia |
https://en.wikipedia.org/wiki/Cavalieri%27s%20quadrature%20formula | In calculus, Cavalieri's quadrature formula, named for 17th-century Italian mathematician Bonaventura Cavalieri, is the integral
and generalizations thereof. This is the definite integral form; the indefinite integral form is:
There are additional forms, listed below. Together with the linearity of the integral, this formula allows one to compute the integrals of all polynomials.
The term "quadrature" is a traditional term for area; the integral is geometrically interpreted as the area under the curve y = xn. Traditionally important cases are y = x2, the quadrature of the parabola, known in antiquity, and y = 1/x, the quadrature of the hyperbola, whose value is a logarithm.
Forms
Negative n
For negative values of n (negative powers of x), there is a singularity at x = 0, and thus the definite integral is based at 1, rather than 0, yielding:
Further, for negative fractional (non-integer) values of n, the power xn is not well-defined, hence the indefinite integral is only defined for positive x. However, for n a negative integer the power xn is defined for all non-zero x, and the indefinite integrals and definite integrals are defined, and can be computed via a symmetry argument, replacing x by −x, and basing the negative definite integral at −1.
Over the complex numbers the definite integral (for negative values of n and x) can be defined via contour integration, but then depends on choice of path, specifically winding number – the geometric issue is that the function defines a covering space with a singularity at 0.
n = −1
There is also the exceptional case n = −1, yielding a logarithm instead of a power of x:
(where "ln" means the natural logarithm, i.e. the logarithm to the base e = 2.71828...).
The improper integral is often extended to negative values of x via the conventional choice:
Note the use of the absolute value in the indefinite integral; this is to provide a unified form for the integral, and means that the integral of this odd function is an even function, though the logarithm is only defined for positive inputs, and in fact, different constant values of C can be chosen on either side of 0, since these do not change the derivative. The more general form is thus:
Over the complex numbers there is not a global antiderivative for 1/x, due this function defining a non-trivial covering space; this form is special to the real numbers.
Note that the definite integral starting from 1 is not defined for negative values of a, since it passes through a singularity, though since 1/x is an odd function, one can base the definite integral for negative powers at −1. If one is willing to use improper integrals and compute the Cauchy principal value, one obtains which can also be argued by symmetry (since the logarithm is odd), so so it makes no difference if the definite integral is based at 1 or −1. As with the indefinite integral, this is special to the real numbers, and does not extend over the complex numbers.
Alternative form |
https://en.wikipedia.org/wiki/An%20Young-myung | An Young-myung (Hangul: 안영명, Hanja: 安永命; born November 19, 1984) is a South Korean right-handed starting pitcher who plays for the Hanwha Eagles of the KBO League.
External links
Career statistics and player information from Korea Baseball Organization
Hanwha Eagles players
Kia Tigers players
KBO League pitchers
South Korean baseball players
People from Cheonan
1984 births
Living people
Sportspeople from South Chungcheong Province |
https://en.wikipedia.org/wiki/Theory%20of%20Probability%20and%20Its%20Applications | Theory of Probability and Its Applications is a quarterly peer-reviewed scientific journal published by the Society for Industrial and Applied Mathematics. It was established in 1956 by Andrey Nikolaevich Kolmogorov and is a translation of the Russian journal Teoriya Veroyatnostei i ee Primeneniya. It is abstracted and indexed by Mathematical Reviews and Zentralblatt MATH. Its 2014 MCQ was 0.12. According to the Journal Citation Reports, the journal has a 2014 impact factor of 0.520.
References
External links
Academic journals established in 1956
English-language journals
SIAM academic journals
Quarterly journals
Probability journals |
https://en.wikipedia.org/wiki/Zoran%20%C5%A0kerjanc | Zoran Škerjanc (born 25 November 1964) is a retired Croatian football player who played for Rijeka, Dinamo, Recreativo Huelva, Orléans US, Pazinka and Göttingen 05.
Career statistics
As a player
References
External links
http://www.bdfutbol.com/j/j11995.html
1964 births
Living people
Footballers from Rijeka
Men's association football midfielders
Yugoslav men's footballers
Croatian men's footballers
HNK Rijeka players
GNK Dinamo Zagreb players
Recreativo de Huelva players
US Orléans players
NK Pazinka players
Yugoslav First League players
Segunda División players
Croatian Football League players
Yugoslav expatriate men's footballers
Expatriate men's footballers in Spain
Yugoslav expatriate sportspeople in Spain
Expatriate men's footballers in France
Yugoslav expatriate sportspeople in France
Croatian expatriate men's footballers
Expatriate men's footballers in Germany
Croatian expatriate sportspeople in Germany
HNK Rijeka non-playing staff |
https://en.wikipedia.org/wiki/James%20Stirling%20%28judge%29 | Sir James Stirling, FRS (3 May 1836 – 27 June 1916) was a British barrister, judge, and amateur scientist. In his youth he demonstrated exceptional ability in mathematics, becoming Senior Wrangler at Cambridge in 1860, regarded at the time as "the highest intellectual achievement attainable in Britain". He was a High Court judge in the Chancery Division from 1886 to 1900, and a Lord Justice of Appeal from 1900, when he was made a Privy Counsellor, until his retirement in 1906. He continued to pursue his scientific and mathematical interests during his legal career, and after retiring from the bench became vice-president of the Royal Society in 1909–1910.
Early life and education
James Stirling was born in Aberdeen, the eldest son of James Stirling (1797/8 – 1871), a United Presbyterian church minister, and Sarah Hendry Stirling (née Irvine, 1813–1875). He attended Aberdeen Grammar School from 1846 to 1851 and King's College at the University of Aberdeen from 1851, where he graduated MA in 1855, showing an exceptional ability in mathematics. He entered Trinity College at Cambridge University in 1856, was awarded the Sheepshanks exhibition in 1859, and became Senior Wrangler and first Smith's prizeman in 1860.
Career
As he was not a member of the Church of England, he was ineligible for a fellowship at Cambridge. Turning to the legal profession, he joined Lincoln's Inn in January 1860, and was called to the bar in November 1862.
He reported cases in the rolls court, first for the New Reports, then for Law Reports until 1876. He was chosen in 1881 by the attorney-general, Sir Henry James as his "devil", or Treasury Devil, a prestigious appointment which leads almost automatically to appointment to the High Court bench. In 1886, he became a judge in the Chancery Division of the High Court, and was knighted in the same year; the following year he received an honorary LLD from his alma mater, the University of Aberdeen. He was promoted to the Court of Appeal on 27 October 1900, when Sir Archibald Smith became Master of the Rolls. Stirling retired from the bench on 11 June 1906.
In his early career he gained a high reputation as a draughtsman and conveyancer, but was diffident in recognising his own abilities. It was said that his opinion was "the best in Lincoln's Inn, if only one could get it". Later, as a judge, he demonstrated a degree of equanimity and clarity which made him popular with the bar. He was criticised for his slowness, but he was careful and painstaking, and his judgments were rarely reversed.
Other interests
In 1878 he was recorded as being a member of the London Mathematical Society In 1898, a newspaper article noted that he still diligently studied mathematics and science. He became a Fellow of the Royal Society in 1902, and was its vice-president in 1909–1910.
He was also an amateur bryologist and member of the Moss Exchange Club, and owned a bryophyte herbarium, which included about 6000 varieties of mosses and liverwort |
https://en.wikipedia.org/wiki/C%20Series%20Index | The C Series Index (or C Series) was a consumer price index constructed by the Australian Bureau of Statistics in 1921 (back calculated to 1914) and discontinued in 1961. It was notable for its role in centralised wage bargaining in Australia, and for the indexation of working class wages over an extended period of time.
Adoption
Australia's Bureau of Statistics maintained an A Series Index of prices from 1912, back calculated to 1901, the date of Australian Federation. As a result of the 1920 Royal Inquiry into the Basic Wage the ABS developed the C Series Index of different price bundles. The importance of statistical price series was caused by the Australian basic wage, a conception of minimal requirements for a family of four or five, based on a single male unskilled wage earner, as given in the Harvester Judgement. The basic wage was a common component of almost all Australian workers' wages (supplemented in most cases by a margin paid for advanced skills by award), and due to inflation the judgement required periodic updating to account for inflation.
Adoption as a wage setting device
Despite being crafted as a result of a Royal Commission into basic wages, the C Series was only adopted by the courts as a basic wage adjusting measure in 1934 by the Commonwealth Court of Conciliation and Arbitration. Wages were then adjusted by the C Series by the Court until 1953 when indexation was discontinued. After indexation of wages based on the C Series was discontinued, trade unions and employee associations maintained demands for C Series wage indexation or wage indexation in general into the late 1960s.
Coverage
The C Series Index covered, "food and groceries, house rents (4 and 5-roomed houses), clothing, household drapery, household utensils, fuel, lighting, urban transport fares, smoking and some miscellaneous items."
Emendation and discontinuance
The C Series was emended in 1936 to reflect changed living requirements. Notably, in the post war environment, the C Series was not adjusted until its discontinuance.
Notes
Bibliography
Australian Bureau of Statistics, "History of retail/consumer price indexes in Australia" In Year Book Australia, 2005 (ABS 1301.0), Canberra, ACT: Australian Bureau of Statistics, 2005.
Economic history of Australia
Price indices |
https://en.wikipedia.org/wiki/Walter%20%28footballer%2C%20born%201968%29 | Walter Henrique de Oliveira (born October 21, 1968) is a former Brazilian football player.
Club statistics
References
External links
1968 births
Living people
Brazilian men's footballers
Brazilian expatriate men's footballers
J1 League players
J2 League players
Japan Football League (1992–1998) players
Júbilo Iwata players
Honda FC players
Hokkaido Consadole Sapporo players
Montedio Yamagata players
Expatriate men's footballers in Japan
Men's association football midfielders |
https://en.wikipedia.org/wiki/List%20of%20lakes%20of%20Manitoba | This is an incomplete list of lakes of Manitoba, a province of Canada.
Larger lake statistics
The total area of a lake includes the area of islands. Lakes lying across provincial boundaries are listed in the province with the greater lake area.
List of lakes
A
Lake Agassiz
Alberts Lake
Antons Lake
Armit Lake
Assean Lake
Aswapiswanan Lake
B
Bennett Lake
Beresford Lake
Bernic Lake
Betula Lake
Big Island Lake
Big Whiteshell Lake
Birch Lake
Birds Hill Lake
Bolton Lake
Boon Lake
Booster Lake
Bowden Lake
Boundary Lake
Brereton Lake
Bryan Lake
Buckland Lake
Burge Lake
Burton Lake
C
Cabin Lake
Caddy Lake
Camp Lake
Cedar Lake
Clear Lake (Riding Mountain National Park, Manitoba)
Clear Lake (Rural Municipality of Grahamdale, Manitoba)
Clearwater Lake
Cormorant Lake
Crescent Lake
Cross Lake
Crowduck Lake
Culdesac Lake
D
Dauphin Lake
De Gueldres Lake
Delta Marsh
Dennis Lake
Ditch Lake
Dog Lake
E
Echo Lake
Eden Lake (Manitoba)
Egenolf Lake
Egg Lake
Elton Lake
F
Falcon Lake
Falcons Bow Lake
Fisher Lake
Fox Lake
Foxwarren Lake
G
Gauer Lake
Gods Lake
Good Lake
H
Holt Lake
Horseshoe Lake
I
Island Lake
J
Jessica Lake
Joey Lake
K
Kakat Lake
Kakwusis Lake
Kasmere Lake
Kawakwunwit Lake
Kingfisher Lake
Kinsmen Lake
Kipahigan Lake
Kiskitto Lake
Kiskittogisu Lake
Kisseynew Lake
Kississing Lake
Knee Lake
L
Lac Brochet
Lac du Bonnet
Lake Athapapuskow
Lake Cargill
Lake Devonian
Lake Manitoba
Lake of the Prairies
Lake of the Woods
Lake St. Martin
Lake Wahtopanah
Lake Winnipeg
Lake Winnipegosis
Leo Lake
Limestone Lake
Lindals Lake
Little Bolton Lake
Little Limestone Lake
Liz Lake
Lizard Lake
Lone Island Lake
Lonely Lake
Loon Lake
Lost Fry Lake
Lynx Lake
M
Mackie Lake
Manitoba memorial lakes
Marchand Lake
Mid Lake
McKay Lake
Minnedosa Lake
Mitatut Lake
Molson Lake
Montago Lake
Moose Lake
Mud Turtle Lake
Muir Lake
Munroe Lake
Murray Lake
Musketasonan Lake
N
Nao Lake
Naosap Lake
Naosap Mud Lake
Natalie Lake
Nejanalini Lake
Nelson Rapids
Neso Lake
Nesosap Lake
Netley Lake
Nikotwasik Lake
Nisto Lake
Nistosap Lake
Niyanun Lake
Norman Mitchell Lake
Norris Lake
Nueltin Lake
O
Oak Hammock Marsh
Oak Lake (Manitoba)
Olafson Lake
One Stone Lake
Ospawagon Lake
Oxford Lake
P
Paint Lake
Payuk Lake
Payukosap Lake
Pekwachnamaykoskwaskwaypinwanik Lake
Pelican Lake
Persian Lake
Playgreen Lake
Prime Lake
Putahow Lake
R
Red Deer Lake
Red Sucker Lake
Reindeer Lake
Rice Lake
Rock Lake
Roderick Lake
Rushforth Lake
S
Schist Lake
Shethanei Lake
Setting Lake
Shellmouth Reservoir
Shoal Lakes
Sipiwesk Lake
Snowshoe Lake
Southern Indian Lake
South Lake
Split Lake
Springer Lake
St. Malo Reservoir
Stephenfield Lake
Stephens Lake
Stony Lake
Stonys Lake
Stupid Lake
Swamp Lake
Swan Lake
T
Tamarack Lake
Tapukok Lake
Thompson Lake
Toews Lake
Touchwood Lake
Twin Lake
U
Unruh Lake
Uyenanao Lake
V
Vermilyea Lake
W
Wallace Lake
War Eagle Lake
Wargatie Lake
Wasp Lake
Waterhen Lake
Weir Lake
West Hawk Lake
West Lynn Lake
White Lake
Whitefish Lake
Whitemouth Lake
Woollard Lake
See also
List o |
https://en.wikipedia.org/wiki/List%20of%20lakes%20of%20Quebec | This is an incomplete list of lakes of Quebec, a province of Canada.
Larger lake statistics
This is a list of lakes of Quebec with an area larger than .
List of Lakes
0–9
Lake 3.1416
A
Lake Abitibi in Ontario and Quebec
Lake Albanel
Allioux Lake
Archange Lake (Mékinac)
Lake Arpin
Lake Aylmer
B
Baskatong Reservoir
Batiscan Lake, Quebec
Lac Beauchamp
Lake Bermen
Lake Bienville
Lac aux Biscuits
Reservoir Blanc
Lac La Blanche
Lake Blouin
Blue Sea Lake
Boyd Lake (Quebec)
Brome Lake
Lake Brompton
Burnt Lake (Canada)
Lake Burton (Quebec)
C
Cabonga Reservoir
Caniapiscau Reservoir
Causapscal Lake
Clearwater Lakes or Lac a l'Eau-Claire
Lake Champlain in Quebec and New York, Vermont
Lake Charest (Mékinac)
Châteauvert Lake (La Tuque)
Lac des Chats
Cinconsine Lake
Lac des Chicots (Sainte-Thècle)
Croche Lake (Sainte-Thècle)
Lake of the Cross (Lac-Édouard)
D
Du Pretre
Du Cardinal
Lake Dana
Lac Deschênes
Dozois Reservoir
Lac Dumoine
Duncan Lake (Quebec)
E
Eastmain Reservoir
Lake Édouard (Quebec)
Lake Evans (Quebec)
F
Lake Fontaine (Mékinac)
Lac du Fou (Mékinac)
G
Gouin Reservoir
Lac Grand, Quebec
Grand Lake Bostonnais
Grand Lac Nominingue
Lake Guindon
Lac Guillaume-Delisle
H
Lake Hackett (Mékinac)
Harrington Lake
J
Jacqueline Lake
Lake Jesuit
Lake Juillet
Julian Lake
K
Lake Kapibouska
Kempt Lake (Matawinie)
Kenogami Lake
Lake Kipawa
Lake Kiskissink
L
La Pêche Lake
Lac à la Perdrix
Lac des Écorces (Antoine-Labelle)
Lac La Blanche
Little Cedar Lake
Leamy Lake
Lake Lescarbot
Lake Louisa
Lacs des Loups Marins
Lake Lovering
Low Lake
M
Lake Magog
Manicouagan Reservoir
Petit lac Manicouagan
Lake Manouane
Lake Masketsi (Mékinac)
Lake Massawippi
Lake Matagami
Lake Matapedia
Lac McArthur
McTavish reservoir
Meech Lake
Mékinac Lake
Lake Mégantic
Lake Memphremagog
Lake Minto
Missionary Lake
Lake Mistassini
Mondonac Lake
Montauban Lake (Portneuf)
Musquaro Lake
N
Lake Naococane
Lac des Nations
Lake Nedlouc
Lake Nemiscau
Petit Lac Nominingue
O
Lake Olga
Opiscoteo Lake
Osisko Lake
Lake Ouareau
P
Lac Paradis
Lake Péribonca
Lake Pierre-Paul (Mékinac)
Pink Lake
Lac des Pins, Aumond, Quebec
Pingualuit crater lake
Pipmuacan Reservoir
Lac Phillipe
Lake Plétipi
Lake Pohenegamook
Lake Poncheville
R
Lake Roberge (Grandes-Piles)
Lake Roberge (Lac-Masketsi)
Robert-Bourassa Reservoir
Roggan Lake
S
Lake Saint François (Estrie)
Lake Saint Francis (Canada)
Lake Saint-Charles
Lake Saint-Jean
Lake Saint-Louis
Petit Lac Saint-François
Lake Saint Pierre
Lac au Saumon
Lac Sauvage (Mont-Blanc)
Lac-des-Seize-Îles, or "Sixteen Islands Lake"
Lac Simard (Temiscamingue)
Selby Lake
Simard Lake (Gouin Reservoir)
Simard Lake (Petit-Mécatina)
Soscumica Lake
Lake Stukely
T
Taureau Reservoir
Taylor Lake (Quebec)
Lake Témiscouata
Lake Terrien (Mékinac)
Lake Timiskaming in Ontario and Quebec
Lake Tourouvre
Lake Traverse (Mékinac)
Lake Tremblant
Lake Trenche (Lac-Ashuapmushuan)
Lake Troilus
Lake of Two Mountains
V
Lake Ventadour (La Tuque)
Lake Verneuil
Lake Vlimeux (Mékinac)
W
Lake Wab |
https://en.wikipedia.org/wiki/List%20of%20lakes%20of%20Newfoundland%20and%20Labrador | This is an incomplete list of lakes of Newfoundland and Labrador, a province of Canada.
Larger lake statistics
List of lakes
See also
List of lakes of Canada
References
Newfoundland
Lakes |
https://en.wikipedia.org/wiki/List%20of%20lakes%20of%20the%20Northwest%20Territories | This is an incomplete list of lakes of the Northwest Territories in Canada.
Larger lake statistics
"The total area of a lake includes the area of islands. Lakes lying across provincial boundaries are listed in the province with the greater lake area."
List of lakes
See also
List of lakes of Canada
References
Lakes |
https://en.wikipedia.org/wiki/List%20of%20lakes%20of%20Nunavut | This is an incomplete list of lakes of Nunavut, a territory of Canada.
Larger lake statistics
"The total area of a lake includes the area of islands. Lakes lying across provincial boundaries are listed in the province with the greater lake area."
List of lakes
See also
List of lakes of Canada
References
Nunavut
Lakes |
https://en.wikipedia.org/wiki/Taiwanese%20Journal%20of%20Mathematics | Taiwanese Journal of Mathematics is a peer-reviewed mathematics journal published by Mathematical Society of the Republic of China (Taiwan).
Established in 1973 as the Chinese Journal of Mathematics, the journal was renamed to its current name in 1997. It is indexed by Mathematical Reviews and Zentralblatt MATH.
Its 2017 impact factor was 0.718.
External links
Mathematics journals
Academic journals established in 1973
English-language journals
Bimonthly journals |
https://en.wikipedia.org/wiki/Probability%20Theory%20and%20Related%20Fields | Probability Theory and Related Fields is a peer-reviewed mathematics journal published by Springer.
Established in 1962, it was originally named Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete, with the English replacing the German starting from volume 71 (1986). The journal publishes articles on probability.
The journal is indexed by Mathematical Reviews and Zentralblatt MATH.
Its 2019 MCQ was 2.29, and its 2019 impact factor was 2.125.
The current editors-in-chief are Fabio Toninelli (Technical University of Vienna) and Bálint Tóth (University of Bristol and Alfréd Rényi Institute of Mathematics).
The journal CiteScore is 3.8 and its SCImago Journal Rank is 3.198, both from 2020. It is currently ranked 11th in the field of Probability & Statistics with Applications according to Google Scholar.
Past Editors-in-chief
1961-1971:
Leopold Schmetterer (Vienna)
1971-1985:
Klaus Krickeberg (Bielefeld)
1985-1991:
Hermann Rost (Heidelberg)
1991-1994:
Olav Kallenberg (Auburn AL)
1994-2000:
Erwin Bolthausen (Zurich)
2000-2005:
Geoffrey Grimmett (Cambridge)
2005-2010:
Jean-Francois Le Gall (Paris) and
Jean Bertoin (Paris)
2010-2015:
Gérard Ben Arous (New York) and
Amir Dembo (Stanford)
2015-2020:
Michel Ledoux (Toulouse) and
Fabio Martinelli (Rome)
2021-2024:
Fabio Toninelli (Vienna) and
Bálint Tóth (Budapest and Bristol)
References
External links
PTRF on Scimago
PTRF on Mathscinet
Probability journals
Academic journals established in 1962
English-language journals
Springer Science+Business Media academic journals
Monthly journals |
https://en.wikipedia.org/wiki/Marco%20Aur%C3%A9lio%20%28footballer%2C%20born%201972%29 | Marco Aurélio Silva Businhani (born February 8, 1972), known as Marco Aurélio or just Marco, is a former Brazilian football player.
Club statistics
References
External links
Profile at Zerozero.pt
1972 births
Living people
Brazilian men's footballers
Brazilian expatriate men's footballers
J1 League players
Shimizu S-Pulse players
Expatriate men's footballers in Japan
Men's association football forwards
Footballers from Bauru |
https://en.wikipedia.org/wiki/Monatshefte%20f%C3%BCr%20Mathematik | Monatshefte für Mathematik is a peer-reviewed mathematics journal established in 1890. Among its well-known papers is "Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I" by Kurt Gödel, published in 1931.
The journal was founded by Gustav von Escherich and Emil Weyr in 1890 as Monatshefte für Mathematik und Physik and published until 1941. In 1947 it was reestablished by Johann Radon under its current title. It is currently published by Springer in cooperation with the Austrian Mathematical Society. The journal is indexed by Mathematical Reviews and Zentralblatt MATH.
Its 2009 MCQ was 0.58, and its 2009 impact factor was 0.764.
External links
Monatshefte für Mathematik und Physik vol. 1–29 (1890–1918) at ALO
Monatshefte für Mathematik vol. 52–126 (1948–1998) at GDZ
Mathematics journals
Academic journals established in 1890
English-language journals
Springer Science+Business Media academic journals
Monthly journals |
https://en.wikipedia.org/wiki/Rendiconti%20del%20Seminario%20Matematico%20della%20Universit%C3%A0%20di%20Padova | Rendiconti del Seminario Matematico della Università di Padova (The Mathematical Journal of the University of Padua) is a peer-reviewed mathematics journal published by Seminario Matematico of the University of Padua, established in 1930.
The journal is indexed by Mathematical Reviews and Zentralblatt MATH. Its 2009 MCQ was 0.22, and its 2009 impact factor was 0.311.
See also
Rendiconti del Seminario Matematico Università e Politecnico di Torino
Rendiconti di Matematica e delle sue Applicazioni
Rivista di Matematica della Università di Parma
External links
Mathematics journals
Academic journals established in 1930
English-language journals
Biannual journals
European Mathematical Society academic journals
Academic journals associated with universities and colleges |
https://en.wikipedia.org/wiki/Arkiv%20f%C3%B6r%20Matematik | The Arkiv för Matematik is a biannual peer-reviewed open-access scientific journal covering mathematics. The journal was established in 1949 when Arkiv för matematik, astronomi och fysik was split into separate journals, and is currently published by the International Press of Boston on behalf of the Institut Mittag-Leffler of the Royal Swedish Academy of Sciences. The current Editor-in-Chief is Hans Ringström.
The journal is indexed by Mathematical Reviews and Zentralblatt MATH. Its 2009 MCQ was 0.47.
According to the Journal Citation Reports, the journal has a 2020 impact factor of 0.896, ranking it 177th out of 330 journals in the category "MATHEMATICS".
References
External links
Open archive on Project Euclid
Mathematics journals
Academic journals established in 1949
English-language journals
Biannual journals |
https://en.wikipedia.org/wiki/J%C3%BAnior%20%28footballer%2C%20born%201969%29 | Jose Alves dos Santos Júnior (born July 29, 1969), known as just Júnior, is a former Brazilian football player.
Club statistics
References
External links
1969 births
Living people
Brazilian men's footballers
Brazilian expatriate men's footballers
J1 League players
Expatriate men's footballers in Japan
Expatriate men's footballers in Portugal
América Futebol Clube (MG) players
Fluminense FC players
Clube Náutico Capibaribe players
Shonan Bellmare players
S.C. Beira-Mar players
Men's association football defenders |
https://en.wikipedia.org/wiki/Archiv%20der%20Mathematik | Archiv der Mathematik is a peer-reviewed mathematics journal published by Springer, established in 1948.
Abstracting and indexing
The journal is abstracted and indexed in:
Mathematical Reviews
Zentralblatt MATH
Scopus
SCImago
According to the Journal Citation Reports, the journal has a 2020 impact factor of 0.608.
References
External links
Mathematics journals
Academic journals established in 1948
English-language journals
Springer Science+Business Media academic journals
Monthly journals |
https://en.wikipedia.org/wiki/Mary%20Frances%20Winston%20Newson | Mary Frances Winston Newson (August 7, 1869 December 5, 1959) was an American mathematician. She became the first female American to receive a PhD in mathematics from a European university, namely the University of Göttingen in Germany. She was also the first person to translate Hilbert's problems into English.
Early life
Mary Newson was born Mary Frances Winston in Forreston, Illinois, the name Newson being the name of the husband she married. She was always known as May by her friends and family. Her parents were Thomas Winston, a country doctor, and Caroline Eliza Mumford. Thomas Winston had been born in Wales but had come to the United States at the age of two years when his parents emigrated. Caroline had been a teacher before her marriage, teaching French, art and mathematics. Mary was one of her parents' seven surviving children. She was taught at home by her mother, who taught herself Latin and Greek so that she could prepare her children for a university education. Her mother had also studied geology, taking a correspondence course with the Field Museum in Chicago.
Education
She and her older brother enrolled at the University of Wisconsin in 1884, when she was 15. She graduated with honors in mathematics in 1889. After teaching at Downer College in Fox Lake, Wisconsin, she applied for a fellowship at Bryn Mawr College in Pennsylvania in 1890. Charlotte Scott was the professor of mathematics at Bryn Mawr and she encouraged Winston to apply again for the fellowship in the following year having narrowly failed to gain the fellowship at her first attempt. Winston taught for a second year at Downer College and she was awarded the fellowship the next year but chose to continue her studies at the University of Chicago which was opening on 1 October 1892, spending the year 1891–92 at Bryn Mawr College. Winston was awarded a fellowship to study at Chicago and she spent the year 1892-93 there.
At the International Mathematical Congress held at the 1893 World's Columbian Exposition, she met Felix Klein, who urged her to study at the University of Göttingen. With financial assistance from Christine Ladd-Franklin, she arrived in Germany at the same time as two other American students, Margaret Maltby and Grace Chisholm. Her first paper, on the topic of hypergeometric functions, was published in 1894. The Association of Collegiate Alumnae gave Winston a fellowship to fund her during the academic year 1895–96. She graduated magna cum laude and was awarded her PhD upon the publication of her dissertation, "Über den Hermite'schen Fall der Lamé'schen Differentialgleichungen" (On the Hermitian case of the Lamé differential equations), in the summer of 1896 and was examined in July 1896. She had to have the thesis published before she could be awarded a doctorate and she returned to the United States with the manuscript of the work intending to publish it there. However, no publisher in the United States was able to print the mathematical symbols i |
https://en.wikipedia.org/wiki/Tangle%20%28mathematics%29 | In mathematics, a tangle is generally one of two related concepts:
In John Conway's definition, an n-tangle is a proper embedding of the disjoint union of n arcs into a 3-ball; the embedding must send the endpoints of the arcs to 2n marked points on the ball's boundary.
In link theory, a tangle is an embedding of n arcs and m circles into – the difference from the previous definition is that it includes circles as well as arcs, and partitions the boundary into two (isomorphic) pieces, which is algebraically more convenient – it allows one to add tangles by stacking them, for instance.
(A quite different use of 'tangle' appears in Graph minors X. Obstructions to tree-decomposition by N. Robertson and P. D. Seymour, Journal of Combinatorial Theory B 52 (1991) 153–190, who used it to describe separation in graphs. This usage has been extended to matroids.)
The balance of this article discusses Conway's sense of tangles; for the link theory sense, see that article.
Two n-tangles are considered equivalent if there is an ambient isotopy of one tangle to the other keeping the boundary of the 3-ball fixed. Tangle theory can be considered analogous to knot theory except instead of closed loops, strings whose ends are nailed down are used. See also braid theory.
Tangle diagrams
Without loss of generality, consider the marked points on the 3-ball boundary to lie on a great circle. The tangle can be arranged to be in general position with respect to the projection onto the flat disc bounded by the great circle. The projection then gives us a tangle diagram, where we make note of over and undercrossings as with knot diagrams.
Tangles often show up as tangle diagrams in knot or link diagrams and can be used as building blocks for link diagrams, e.g. pretzel links.
Rational and algebraic tangles
A rational tangle is a 2-tangle that is homeomorphic to the trivial 2-tangle by a map of pairs consisting of the 3-ball and two arcs. The four endpoints of the arcs on the boundary circle of a tangle diagram are usually referred as NE, NW, SW, SE, with the symbols referring to the compass directions.
An arbitrary tangle diagram of a rational tangle may look very complicated, but there is always a diagram of a particular simple form: start with a tangle diagram consisting of two horizontal (vertical) arcs; add a "twist", i.e. a single crossing by switching the NE and SE endpoints (SW and SE endpoints); continue by adding more twists using either the NE and SE endpoints or the SW and SE endpoints. One can suppose each twist does not change the diagram inside a disc containing previously created crossings.
We can describe such a diagram by considering the numbers given by consecutive twists around the same set of endpoints, e.g. (2, 1, -3) means start with two horizontal arcs, then 2 twists using NE/SE endpoints, then 1 twist using SW/SE endpoints, and then 3 twists using NE/SE endpoints but twisting in the opposite direction from before. The list begins with 0 |
https://en.wikipedia.org/wiki/Robin%20Kov%C3%A1%C5%99 | Robin Kovář (born April 2, 1984) is a Czech professional ice hockey player who is currently playing for the Milton Keynes Lightning in the National Ice Hockey League.
Career statistics
References
External links
1984 births
Living people
Blackburn Hawks players
Czech expatriate ice hockey players in Canada
Czech ice hockey forwards
Edmonton Oilers draft picks
Czech expatriate ice hockey people
HC Havířov players
HC Kometa Brno players
HC Slovan Ústečtí Lvi players
HKM Zvolen players
Hokej Šumperk 2003 players
Kemphanen Eindhoven players
Manchester Phoenix players
MHk 32 Liptovský Mikuláš players
People from Valašské Meziříčí
PSG Berani Zlín players
Regina Pats players
SK Horácká Slavia Třebíč players
Swindon Wildcats players
Vancouver Giants players
VHK Vsetín players
Yertis Pavlodar players
Milton Keynes Lightning players
Ice hockey people from the Zlín Region
Expatriate ice hockey players in the Netherlands
Czech expatriate sportspeople in England
Czech expatriate sportspeople in Hungary
Czech expatriate sportspeople in Kazakhstan
Expatriate ice hockey players in England
Expatriate ice hockey players in Kazakhstan
Expatriate ice hockey players in Hungary
Czech expatriate ice hockey players in Slovakia |
https://en.wikipedia.org/wiki/James%20D.%20Murray | James Dickson Murray FRSE FRS, (born 2 January 1931) is professor emeritus of applied mathematics at University of Washington and University of Oxford. He is best known for his authoritative and extensive work entitled Mathematical Biology.
Early life
Murray was born in Moffat, Scotland, and was educated at St. Andrews University, where he received with honours a bachelor's degree in mathematics in 1953, he took his PhD there in 1956.
Research and career
His first post was at the University of Durham, UK; later he has held positions at Harvard University, London and Oxford, becoming professor of mechanical engineering at the University of Michigan in 1965, at the age of 34.
He later became professor of mathematical biology at the University of Oxford, a fellow and tutor in mathematics at Corpus Christi College, Oxford and founder and director of the Centre for Mathematical Biology. He left Oxford in the late 1980s for the University of Washington in Seattle, where he spent the rest of his career as professor of mathematics and adjunct professor of zoology.
His research is characterised by its great range and depth: an early example is his fundamental contributions to understanding the biomechanics of the human body when launched from an aircraft in an ejection seat. He has made contributions to many other areas, ranging from understanding and preventing severe scarring; fingerprint formation; sex determination, modelling of animal coat and territory formation in wolf-deer interacting populations.
Awards and honours
Murray was elected a Fellow of the Royal Society of Edinburgh in 1979 and a Fellow of the Royal Society (FRS) in 1985.
In 2008 Murray and Professor T. J. Pedley, FRS were jointly awarded the Gold Medal of the Institute of Mathematics and its Applications in recognition of their "outstanding contributions to mathematics and its applications over a period of years".
References
20th-century Scottish mathematicians
21st-century Scottish mathematicians
Theoretical biologists
Alumni of the University of St Andrews
Fellows of Corpus Christi College, Oxford
Academics of Durham University
Harvard University faculty
University of Michigan faculty
Members of the French Academy of Sciences
Fellows of the Royal Society
University of Washington faculty
Living people
1931 births |
https://en.wikipedia.org/wiki/De%20Moivre%27s%20theorem | de Moivre's theorem may be:
de Moivre's formula, a trigonometric identity
Theorem of de Moivre–Laplace, a central limit theorem
Mathematics disambiguation pages |
https://en.wikipedia.org/wiki/C%C3%A0dl%C3%A0g | In mathematics, a càdlàg (French: "continue à droite, limite à gauche"), RCLL ("right continuous with left limits"), or corlol ("continuous on (the) right, limit on (the) left") function is a function defined on the real numbers (or a subset of them) that is everywhere right-continuous and has left limits everywhere. Càdlàg functions are important in the study of stochastic processes that admit (or even require) jumps, unlike Brownian motion, which has continuous sample paths. The collection of càdlàg functions on a given domain is known as Skorokhod space.
Two related terms are càglàd, standing for "continue à gauche, limite à droite", the left-right reversal of càdlàg, and càllàl for "continue à l'un, limite à l’autre" (continuous on one side, limit on the other side), for a function which at each point of the domain is either càdlàg or càglàd.
Definition
Let be a metric space, and let . A function is called a càdlàg function if, for every ,
the left limit exists; and
the right limit exists and equals .
That is, is right-continuous with left limits.
Examples
All functions continuous on a subset of the real numbers are càdlàg functions on that subset.
As a consequence of their definition, all cumulative distribution functions are càdlàg functions. For instance the cumulative at point correspond to the probability of being lower or equal than , namely . In other words, the semi-open interval of concern for a two-tailed distribution is right-closed.
The right derivative of any convex function defined on an open interval, is an increasing cadlag function.
Skorokhod space
The set of all càdlàg functions from to is often denoted by (or simply ) and is called Skorokhod space after the Ukrainian mathematician Anatoliy Skorokhod. Skorokhod space can be assigned a topology that, intuitively allows us to "wiggle space and time a bit" (whereas the traditional topology of uniform convergence only allows us to "wiggle space a bit"). For simplicity, take and — see Billingsley for a more general construction.
We must first define an analogue of the modulus of continuity, . For any , set
and, for , define the càdlàg modulus to be
where the infimum runs over all partitions , with . This definition makes sense for non-càdlàg (just as the usual modulus of continuity makes sense for discontinuous functions) and it can be shown that is càdlàg if and only if .
Now let denote the set of all strictly increasing, continuous bijections from to itself (these are "wiggles in time"). Let
denote the uniform norm on functions on . Define the Skorokhod metric on by
where is the identity function. In terms of the "wiggle" intuition, measures the size of the "wiggle in time", and measures the size of the "wiggle in space".
It can be shown that the Skorokhod metric is indeed a metric. The topology generated by is called the Skorokhod topology on .
An equivalent metric,
was introduced independently and utilized in control theory |
https://en.wikipedia.org/wiki/Jacobi%20polynomials | In mathematics, Jacobi polynomials (occasionally called hypergeometric polynomials)
are a class of classical orthogonal polynomials. They are orthogonal with respect to the weight
on the interval . The Gegenbauer polynomials, and thus also the Legendre, Zernike and Chebyshev polynomials, are special cases of the Jacobi polynomials.
The Jacobi polynomials were introduced by Carl Gustav Jacob Jacobi.
Definitions
Via the hypergeometric function
The Jacobi polynomials are defined via the hypergeometric function as follows:
where is Pochhammer's symbol (for the rising factorial). In this case, the series for the hypergeometric function is finite, therefore one obtains the following equivalent expression:
Rodrigues' formula
An equivalent definition is given by Rodrigues' formula:
If , then it reduces to the Legendre polynomials:
Alternate expression for real argument
For real the Jacobi polynomial can alternatively be written as
and for integer
where is the gamma function.
In the special case that the four quantities , , ,
are nonnegative integers, the Jacobi polynomial can be written as
The sum extends over all integer values of for which the arguments of the factorials are nonnegative.
Special cases
Basic properties
Orthogonality
The Jacobi polynomials satisfy the orthogonality condition
As defined, they do not have unit norm with respect to the weight. This can be corrected by dividing by the square root of the right hand side of the equation above, when .
Although it does not yield an orthonormal basis, an alternative normalization is sometimes preferred due to its simplicity:
Symmetry relation
The polynomials have the symmetry relation
thus the other terminal value is
Derivatives
The th derivative of the explicit expression leads to
Differential equation
The Jacobi polynomial is a solution of the second order linear homogeneous differential equation
Recurrence relations
The recurrence relation for the Jacobi polynomials of fixed , is:
for .
Writing for brevity , and , this becomes in terms of
Since the Jacobi polynomials can be described in terms of the hypergeometric function, recurrences of the hypergeometric function give equivalent recurrences of the Jacobi polynomials. In particular, Gauss' contiguous relations correspond to the identities
Generating function
The generating function of the Jacobi polynomials is given by
where
and the branch of square root is chosen so that .
Asymptotics of Jacobi polynomials
For in the interior of , the asymptotics of for large is given by the Darboux formula
where
and the "" term is uniform on the interval for every .
The asymptotics of the Jacobi polynomials near the points is given by the Mehler–Heine formula
where the limits are uniform for in a bounded domain.
The asymptotics outside is less explicit.
Applications
Wigner d-matrix
The expression () allows the expression of the Wigner d-matrix
(for )
in terms of Jacobi polynomials:
See also
Askey– |
https://en.wikipedia.org/wiki/Perrin%20number | In mathematics, the Perrin numbers are defined by the recurrence relation
for ,
with initial values
.
The sequence of Perrin numbers starts with
3, 0, 2, 3, 2, 5, 5, 7, 10, 12, 17, 22, 29, 39, ...
The number of different maximal independent sets in an -vertex cycle graph is counted by the th Perrin number for .
History
This sequence was mentioned implicitly by Édouard Lucas (1876). In 1899, the same sequence was mentioned explicitly by François Olivier Raoul Perrin. The most extensive treatment of this sequence was given by Adams and Shanks (1982).
Properties
Generating function
The generating function of the Perrin sequence is
Matrix formula
Binet-like formula
The Perrin numbers can be written in terms of powers of the roots of the equation
This equation has 3 roots; one real root p (known as the plastic number) and two complex conjugate roots q and r. Given these three roots, the Perrin sequence analogue of the Lucas sequence Binet formula is
Since the absolute values of the complex roots q and r are both less than 1, the powers of these roots approach 0 for large n. For large n the formula reduces to
This formula can be used to quickly calculate values of the Perrin sequence for large n. The ratio of successive terms in the Perrin sequence approaches p, a.k.a. the plastic number, which has a value of approximately 1.324718. This constant bears the same relationship to the Perrin sequence as the golden ratio does to the Lucas sequence. Similar connections exist also between p and the Padovan sequence, between the golden ratio and Fibonacci numbers, and between the silver ratio and Pell numbers.
Multiplication formula
From the Binet formula, we can obtain a formula for G(kn) in terms of G(n − 1), G(n) and G(n + 1); we know
which gives us three linear equations with coefficients over the splitting field of ; by inverting a matrix we can solve for and then we can raise them to the kth power and compute the sum.
Example magma code:
P<x> := PolynomialRing(Rationals());
S<t> := SplittingField(x^3-x-1);
P2<y> := PolynomialRing(S);
p,q,r := Explode([r[1] : r in Roots(y^3-y-1)]);
Mi:=Matrix([[1/p,1/q,1/r],[1,1,1],[p,q,r]])^(-1);
T<u,v,w> := PolynomialRing(S,3);
v1 := ChangeRing(Mi,T) *Matrix([[u],[v],[w]]);
[p^i*v1[1,1]^3 + q^i*v1[2,1]^3 + r^i*v1[3,1]^3 : i in [-1..1]];
with the result that, if we have , then
The number 23 here arises from the discriminant of the defining polynomial of the sequence.
This allows computation of the nth Perrin number using integer arithmetic in multiplies.
Primes and divisibility
Perrin pseudoprimes
It has been proven that for all primes p, p divides P(p). However, the converse is not true: for some composite numbers n, n may still divide P(n). If n has this property, it is called a "Perrin pseudoprime".
The first few Perrin pseudoprimes are
271441, 904631, 16532714, 24658561, 27422714, 27664033, 46672291, 102690901, 130944133, 196075949, 214038533, 517697641, 545670533, 801123451, 85507 |
https://en.wikipedia.org/wiki/List%20of%20recreational%20number%20theory%20topics | This is a list of recreational number theory topics (see number theory, recreational mathematics). Listing here is not pejorative: many famous topics in number theory have origins in challenging problems posed purely for their own sake.
See list of number theory topics for pages dealing with aspects of number theory with more consolidated theories.
Number sequences
Integer sequence
Fibonacci sequence
Golden mean base
Fibonacci coding
Lucas sequence
Padovan sequence
Figurate numbers
Polygonal number
Triangular number
Square number
Pentagonal number
Hexagonal number
Heptagonal number
Octagonal number
Nonagonal number
Decagonal number
Centered polygonal number
Centered square number
Centered pentagonal number
Centered hexagonal number
Tetrahedral number
Pyramidal number
Triangular pyramidal number
Square pyramidal number
Pentagonal pyramidal number
Hexagonal pyramidal number
Heptagonal pyramidal number
Octahedral number
Star number
Perfect number
Quasiperfect number
Almost perfect number
Multiply perfect number
Hyperperfect number
Semiperfect number
Primitive semiperfect number
Unitary perfect number
Weird number
Untouchable number
Amicable number
Sociable number
Abundant number
Deficient number
Amenable number
Aliquot sequence
Super-Poulet number
Lucky number
Powerful number
Primeval number
Palindromic number
Telephone number
Triangular square number
Harmonic divisor number
Sphenic number
Smith number
Double Mersenne number
Zeisel number
Heteromecic number
Niven numbers
Superparticular number
Highly composite number
Highly totient number
Practical number
Juggler sequence
Look-and-say sequence
Digits
Polydivisible number
Automorphic number
Armstrong number
Self number
Harshad number
Keith number
Kaprekar number
Digit sum
Persistence of a number
Perfect digital invariant
Happy number
Perfect digit-to-digit invariant
Factorion
Emirp
Palindromic prime
Home prime
Normal number
Stoneham number
Champernowne constant
Absolutely normal number
Repunit
Repdigit
Prime and related sequences
Semiprime
Almost prime
Unique prime
Factorial prime
Permutable prime
Palindromic prime
Cuban prime
Lucky prime
Magic squares, etc.
Ulam spiral
Magic star
Magic square
Frénicle standard form
Prime reciprocal magic square
Trimagic square
Multimagic square
Panmagic square
Satanic square
Most-perfect magic square
Geometric magic square
Conway's Lux method for magic squares
Magic cube
Perfect magic cube
Semiperfect magic cube
Bimagic cube
Trimagic cube
Multimagic cube
Magic hypercube
Magic constant
Squaring the square
Recreational number theory |
https://en.wikipedia.org/wiki/Moulay%20Haddou | Moulay Haddou (born June 14, 1975 in Oran, Algeria) is a retired Algerian international footballer. He last played for MC Oran in the Algerian Championnat National.
National team statistics
Honours
Club:
Won the Algerian Cup once with MC Oran in 1996
Won the Algerian League Cup once with MC Oran in 1996
Won the Arab Cup Winners' Cup twice with MC Oran in 1997 and 1998
Won the Arab Super Cup once with MC Oran in 1999
Finalist of the Arab Champions League once with MC Oran in 2001
Won the Algerian League once with USM Alger in 2005
Runner-up of the Algerian League four times with MC Oran in 1995, 1996, 1997 and 2000
Finalist of the Algerian Cup three times:
Twice with MC Oran in 1998 and 2002
Once with USM Alger in 2006
Participated in 3 editions of the African Cup of Nations: 2000, 2002 and 2004
Has 56 caps and 1 goal for the Algerian National Team
References
1975 births
2004 African Cup of Nations players
2000 African Cup of Nations players
2002 African Cup of Nations players
Algerian men's footballers
Algeria men's international footballers
Algeria men's under-23 international footballers
Competitors at the 1997 Mediterranean Games
ASM Oran players
Living people
MC Oran players
Footballers from Oran
USM Alger players
Men's association football defenders
Mediterranean Games competitors for Algeria
21st-century Algerian people |
https://en.wikipedia.org/wiki/European%20science%20in%20the%20Middle%20Ages | European science in the Middle Ages comprised the study of nature, mathematics and natural philosophy in medieval Europe. Following the fall of the Western Roman Empire and the decline in knowledge of Greek, Christian Western Europe was cut off from an important source of ancient learning. Although a range of Christian clerics and scholars from Isidore and Bede to Jean Buridan and Nicole Oresme maintained the spirit of rational inquiry, Western Europe would see a period of scientific decline during the Early Middle Ages. However, by the time of the High Middle Ages, the region had rallied and was on its way to once more taking the lead in scientific discovery. Scholarship and scientific discoveries of the Late Middle Ages laid the groundwork for the Scientific Revolution of the Early Modern Period.
According to Pierre Duhem, who founded the academic study of medieval science as a critique of the Enlightenment-positivist theory of a 17th-century anti-Aristotelian and anticlerical scientific revolution, the various conceptual origins of that alleged revolution lay in the 12th to 14th centuries, in the works of churchmen such as Thomas Aquinas and Buridan.
In the context of this article, "Western Europe" refers to the European cultures bound together by the Catholic Church and the Latin language.
Western Europe
As Roman imperial power effectively ended in the West during the 5th century, Western Europe entered the Middle Ages with great difficulties that affected the continent's intellectual production dramatically. Most classical scientific treatises of classical antiquity written in Greek were unavailable, leaving only simplified summaries and compilations. Nonetheless, Roman and early medieval scientific texts were read and studied, contributing to the understanding of nature as a coherent system functioning under divinely established laws that could be comprehended in the light of reason. This study continued through the Early Middle Ages, and with the Renaissance of the 12th century, interest in this study was revitalized through the translation of Greek and Arabic scientific texts. Scientific study further developed within the emerging medieval universities, where these texts were studied and elaborated, leading to new insights into the phenomena of the universe. These advances are virtually unknown to the lay public of today, partly because most theories advanced in medieval science are today obsolete, and partly because of the caricature of the Middle Ages as a supposedly "Dark Age" which placed "the word of religious authorities over personal experience and rational activity."
Early Middle Ages (AD 476–1000)
In the ancient world, Greek had been the primary language of science. Even under the Roman Empire, Latin texts drew extensively on Greek work, some pre-Roman, some contemporary; while advanced scientific research and teaching continued to be carried on in the Hellenistic side of the empire, in Greek. Late Roman attempts to tran |
https://en.wikipedia.org/wiki/German%20Mathematical%20Society | The German Mathematical Society (, DMV) is the main professional society of German mathematicians and represents German mathematics within the European Mathematical Society (EMS) and the International Mathematical Union (IMU). It was founded in 1890 in Bremen with the set theorist Georg Cantor as first president. Founding members included
Georg Cantor,
Felix Klein,
Walther von Dyck,
David Hilbert,
Hermann Minkowski,
Carl Runge,
Rudolf Sturm,
Hermann Schubert, and
Heinrich Weber.
The current president of the DMV is Ilka Agricola (2021–2022).
Activities
In honour of its founding president, Georg Cantor, the society awards the Cantor Medal. The DMV publishes two scientific journals, the Jahresbericht der DMV and Documenta Mathematica. It also publishes a quarterly magazine for its membership the Mitteilungen der DMV. The annual meeting of the DMV is called the Jahrestagung; the DMV traditionally meets every four years together with the Austrian Mathematical Society (ÖMG) and every four years together with the Gesellschaft für Didaktik der Mathematik (GDM). It sometimes organises its meetings jointly with other societies (e.g., 2014 with the Polish Mathematical Society, PTM, or 2016 with the Gesellschaft für Angewandte Mathematik und Mechanik, GAMM).
Twice annually, it organises the Gauß Lecture, a public audience lecture by well-known mathematicians.
Cantor Medal
Governance
See :Category:Presidents of the German Mathematical Society
Since 1995, the DMV is led by a president, before that by a chairperson.
1890–1893: Georg Cantor
1894: Paul Gordan
1895, 1904: Heinrich Weber
1896, 1907: Alexander von Brill
1897, 1903 und 1908: Felix Klein
1898: Aurel Voss
1899: Max Noether
1900: David Hilbert
1901, 1912: Walther von Dyck
1902: Wilhelm Franz Meyer
1905: Paul Stäckel
1906: Alfred Pringsheim
1909: Martin Krause, Dresden
1910: Friedrich Engel
1911: Friedrich Schur
1913: Karl Rohn
1914: Carl Runge
1915: Sebastian Finsterwalder
1916: Ludwig Kiepert
1917: Kurt Hensel
1918: Otto Hölder
1919: Hans von Mangoldt
1920: Robert Fricke
1921: Edmund Landau
1922: Arthur Moritz Schoenflies
1923: Erich Hecke
1924: Otto Blumenthal
1925: Heinrich Tietze
1926: Hans Hahn
1927: Friedrich Schilling, Danzig
1928, 1936: Erhard Schmidt
1929: Adolf Kneser
1930: Rudolf Rothe, Berlin
1931: Ernst Sigismund Fischer
1932: Hermann Weyl
1933: Richard Baldus
1934: Oskar Perron
1935: Georg Hamel
1937: Walther Lietzmann
1938–1945: Wilhelm Süss
1946: Kurt Reidemeister
1948–1952: Erich Kamke
1953, 1955: Georg Nöbeling
1954: Hellmuth Kneser
1956: Karl Heinrich Weise
1957: Emanuel Sperner
1958: Gottfried Köthe
1959: Willi Rinow
1960: Wilhelm Maak
1961: Ott-Heinrich Keller
1962: Friedrich Hirzebruch
1963: Wolfgang Haack
1964–1965: Heinrich Behnke
1966: Karl Stein
1967: Wolfgang Franz
1968–1977: Martin Barner
1977: Heinz Bauer
1978, 1979: Hermann Witting
1980–1981: Gerd Fischer
1982–1983: Helmut Werner, Bonn
1984–1985: Al |
https://en.wikipedia.org/wiki/Rasiowa%E2%80%93Sikorski%20lemma | In axiomatic set theory, the Rasiowa–Sikorski lemma (named after Helena Rasiowa and Roman Sikorski) is one of the most fundamental facts used in the technique of forcing. In the area of forcing, a subset E of a poset (P, ≤) is called dense in P if for any p ∈ P there is e ∈ E with e ≤ p. If D is a family of dense subsets of P, then a filter F in P is called D-generic if
F ∩ E ≠ ∅ for all E ∈ D.
Now we can state the Rasiowa–Sikorski lemma:
Let (P, ≤) be a poset and p ∈ P. If D is a countable family of dense subsets of P then there exists a D-generic filter F in P such that p ∈ F.
Proof of the Rasiowa–Sikorski lemma
The proof runs as follows: since D is countable, one can enumerate the dense subsets of P as D1, D2, …. By assumption, there exists p ∈ P. Then by density, there exists p1 ≤ p with p1 ∈ D1. Repeating, one gets … ≤ p2 ≤ p1 ≤ p with pi ∈ Di. Then G = { q ∈ P: ∃ i, q ≥ pi} is a D-generic filter.
The Rasiowa–Sikorski lemma can be viewed as an equivalent to a weaker form of Martin's axiom. More specifically, it is equivalent to MA().
Examples
For (P, ≤) = (Func(X, Y), ⊇), the poset of partial functions from X to Y, reverse-ordered by inclusion, define Dx = {s ∈ P: x ∈ dom(s)}. If X is countable, the Rasiowa–Sikorski lemma yields a {Dx: x ∈ X}-generic filter F and thus a function F: X → Y.
If we adhere to the notation used in dealing with D-generic filters, {H ∪ G0: PijPt} forms an H-generic filter.
If D is uncountable, but of cardinality strictly smaller than 2ℵ0 and the poset has the countable chain condition, we can instead use Martin's axiom.
See also
References
External links
Timothy Chow's paper A beginner’s guide to forcing is a good introduction to the concepts and ideas behind forcing.
Forcing (mathematics)
Lemmas in set theory |
https://en.wikipedia.org/wiki/J%C3%A1nos%20Bolyai%20Mathematical%20Institute | Bolyai Institute is the mathematics institute of the Faculty of Sciences of the University of Szeged, named after the Hungarian mathematicians, Farkas Bolyai, and his son János Bolyai, the co-discoverer of non-Euclidean geometry. Its director is László Zádori. Among the former members of the institute are Frigyes Riesz, Alfréd Haar, Rudolf Ortvay, Tibor Radó, Béla Szőkefalvi-Nagy, László Kalmár, Géza Fodor.
Departments
Algebra and Number Theory (head: Mária Szendrei)
Analysis (head: Lajos Molnár)
Applied and Numerical Mathematics (head: Tibor Krisztin)
Geometry (head: Árpád Kurusa)
Set Theory and Mathematical Logic (head: Péter Hajnal)
Stochastics (head: Gyula Pap)
External links
Official website
A short history of the Bolyai Institute
Mathematical institutes
University of Szeged
Research institutes in Hungary |
https://en.wikipedia.org/wiki/Wolnei%20Caio | Wolnei Caio (born August 10, 1968) is a former Brazilian football player.
Club statistics
References
External links
odn.ne.jp
1968 births
Living people
Brazilian men's footballers
J1 League players
Kashiwa Reysol players
Brazilian expatriate men's footballers
Expatriate men's footballers in Japan
Men's association football midfielders |
https://en.wikipedia.org/wiki/Jarque%E2%80%93Bera%20test | In statistics, the Jarque–Bera test is a goodness-of-fit test of whether sample data have the skewness and kurtosis matching a normal distribution. The test is named after Carlos Jarque and Anil K. Bera.
The test statistic is always nonnegative. If it is far from zero, it signals the data do not have a normal distribution.
The test statistic JB is defined as
where n is the number of observations (or degrees of freedom in general); S is the sample skewness, K is the sample kurtosis :
where and are the estimates of third and fourth central moments, respectively, is the sample mean, and
is the estimate of the second central moment, the variance.
If the data comes from a normal distribution, the JB statistic asymptotically has a chi-squared distribution with two degrees of freedom, so the statistic can be used to test the hypothesis that the data are from a normal distribution. The null hypothesis is a joint hypothesis of the skewness being zero and the excess kurtosis being zero. Samples from a normal distribution have an expected skewness of 0 and an expected excess kurtosis of 0 (which is the same as a kurtosis of 3). As the definition of JB shows, any deviation from this increases the JB statistic.
For small samples the chi-squared approximation is overly sensitive, often rejecting the null hypothesis when it is true. Furthermore, the distribution of p-values departs from a uniform distribution and becomes a right-skewed unimodal distribution, especially for small p-values. This leads to a large Type I error rate. The table below shows some p-values approximated by a chi-squared distribution that differ from their true alpha levels for small samples.
{| class="wikitable"
|+Calculated p-values equivalents to true alpha levels at given sample sizes
! True α level !! 20 !! 30 !! 50 !! 70 !! 100
|-
! 0.1
| 0.307 || 0.252 || 0.201 || 0.183 || 0.1560
|-
! 0.05
| 0.1461 || 0.109 || 0.079 || 0.067 || 0.062
|-
! 0.025
| 0.051 || 0.0303 || 0.020 || 0.016 || 0.0168
|-
! 0.01
| 0.0064 || 0.0033 || 0.0015 || 0.0012 || 0.002
|}
(These values have been approximated using Monte Carlo simulation in Matlab)
In MATLAB's implementation, the chi-squared approximation for the JB statistic's distribution is only used for large sample sizes (> 2000). For smaller samples, it uses a table derived from Monte Carlo simulations in order to interpolate p-values.
History
The statistic was derived by Carlos M. Jarque and Anil K. Bera while working on their Ph.D. Thesis at the Australian National University.
Jarque–Bera test in regression analysis
According to Robert Hall, David Lilien, et al. (1995) when using this test along with multiple regression analysis the right estimate is:
where n is the number of observations and k is the number of regressors when examining residuals to an equation.
Implementations
ALGLIB includes an implementation of the Jarque–Bera test in C++, C#, Delphi, Visual Basic, etc.
gretl includes an implementation of the Jarque–Bera tes |
https://en.wikipedia.org/wiki/Pedro%20Massacessi | Pedro Massacessi (born January 9, 1966) is a former Argentine football player.
Club statistics
References
External links
odn.ne.jp
Pedro Massacessi photos
1966 births
Living people
Argentine men's footballers
Argentine expatriate men's footballers
Argentine expatriate sportspeople in Japan
J1 League players
Veikkausliiga players
Liga MX players
Club Atlético Independiente footballers
Club Universidad de Chile footballers
Yokohama F. Marinos players
FC Jazz players
Atlante F.C. footballers
Club Universidad Nacional footballers
Expatriate men's footballers in Chile
Expatriate men's footballers in Finland
Expatriate men's footballers in Mexico
Men's association football midfielders |
https://en.wikipedia.org/wiki/International%20Mathematics%20Research%20Notices | The International Mathematics Research Notices is a peer-reviewed mathematics journal. Originally published by Duke University Press and Hindawi Publishing Corporation, it is now published by Oxford University Press. The Executive Editor is Zeev Rudnick (Tel Aviv University). According to the Journal Citation Reports, the journal has a 2018 impact factor of 1.452, ranking it 40th out of 317 journals in the category "Mathematics". According to SCImago Journal & Country Rank, International Mathematics Research Notices is ranked top 48th of more than 371 internationally circulated journals in the field of mathematics. Since its founding, International Mathematics Research Notices has established a reputation for fast turnaround and outstanding quality.
References
External links
Mathematics journals
Oxford University Press academic journals
Academic journals established in 1991
Monthly journals
English-language journals |
https://en.wikipedia.org/wiki/Semigroup%20Forum | Semigroup Forum (print , electronic ) is a mathematics research journal published by Springer. The journal serves as a platform for the speedy and efficient transmission of information on current research in semigroup theory. Coverage in the journal includes: algebraic semigroups, topological semigroups, partially ordered semigroups, semigroups of measures and harmonic analysis on semigroups, transformation semigroups, and applications of semigroup theory to other disciplines such as ring theory, category theory, automata, and logic. Semigroups of operators were initially considered off-topic, but began being included in the journal in 1985.
Contents
Semigroup Forum features survey and research articles. It also contains research announcements, which describe new results, mostly without proofs, of full length papers appearing elsewhere as well as short notes, which detail such information as new proofs, significant generalizations of known facts, comments on unsolved problems, and historical remarks. In addition, the journal contains research problems; announcements of conferences, seminars, and symposia on semigroup theory; abstracts and bibliographical items; as well as listings of books, papers, and lecture notes of interest.
History
The journal published its first issue in 1970. It is indexed in Science Citation Index Expanded, Journal Citation Reports/Science Edition, SCOPUS, and Zentralblatt Math.
"Semigroup Forum was a pioneering journal ... one of the early instances of a highly specialized journal, of which there are now many. Indeed, it was during the 1960s that many of the current specialised journals began to appear, probably in connection with research specialization ...among many other examples, the journals Topology, Journal of Algebra, Journal of Combinatorial Theory, and Journal of Number Theory were launched in 1962, 1964, 1966 and 1996 respectively. Semigroup Forum simply followed in this trend, with academic publishers realizing that there was a market for such narrowly focused journals.
This journal has been called "in many ways a point of crystallization for semigroup theory and its community", and "an indicator of a field which is mathematically active".
References
Mathematics journals
Semigroup theory |
https://en.wikipedia.org/wiki/Cypriot%20National%20Badminton%20Championships | Cypriot National Badminton Championships are held in Cyprus since 1990. The international championships already started 1987.
Winners
External links
Statistics
Cyprus Badminton
National badminton championships
Badminton tournaments in Cyprus
Badminton
Recurring sporting events established in 1990
1990 establishments in Cyprus |
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