source stringlengths 31 168 | text stringlengths 51 3k |
|---|---|
https://en.wikipedia.org/wiki/XYZ%20file%20format | The XYZ file format is a chemical file format. There is no formal standard and several variations exist, but a typical XYZ format specifies the molecule geometry by giving the number of atoms with Cartesian coordinates that will be read on the first line, a comment on the second, and the lines of atomic coordinates in the following lines. The file format is used in computational chemistry programs for importing and exporting geometries. The units are generally in ångströms. Some variations include using atomic numbers instead of atomic symbols, or skipping the comment line. Files using the XYZ format conventionally have the extension.
Format
The formatting of the .xyz file format is as follows:
<number of atoms>
comment line
<element> <X> <Y> <Z>
...
Connectivity information in the XYZ file format is implied rather than explicit. According to the main page for XYZ (part of XMol), Note that the XYZ format doesn't contain connectivity information. This intentional omission allows for greater flexibility: to create an XYZ file, you don't need to know where a molecule's bonds are; you just need to know where its atoms are. Connectivity information is generated automatically for XYZ files as they are read into XMol-related applications. Briefly, if the distance between two atoms is less than the sum of their covalent radii, they are considered bonded.
Example
The pyridine molecule can be described in the XYZ format by the following:
11
C -0.180226841 0.360945118 -1.120304970
C -0.180226841 1.559292118 -0.407860970
C -0.180226841 1.503191118 0.986935030
N -0.180226841 0.360945118 1.29018350
C -0.180226841 -0.781300882 0.986935030
C -0.180226841 -0.837401882 -0.407860970
H -0.180226841 0.360945118 -2.206546970
H -0.180226841 2.517950118 -0.917077970
H -0.180226841 2.421289118 1.572099030
H -0.180226841 -1.699398882 1.572099030
H -0.180226841 -1.796059882 -0.917077970
Animation
Most molecule viewers such as Jmol and VMD can show animations using .xyz files. The following is an example xyz format for m successive snapshot which can be rendered as an animation:
<number of atoms>
comment line
atom_symbol11 x-coord11 y-coord11 z-coord11
atom_symbol12 x-coord12 y-coord12 z-coord12
...
atom_symbol1n x-coord1n y-coord1n z-coord1n
<number of atoms>
comment line
atom_symbol21 x-coord21 y-coord21 z-coord21
atom_symbol22 x-coord22 y-coord22 z-coord22
...
atom_symbol2n x-coord2n y-coord2n z-coord2n
.
.
.
<number of atoms>
comment line
atom_symbolm1 x-coordm1 y-coordm1 z-coordm1
atom_symbolm2 x-coordm2 y-coordm2 z-coordm2
...
atom_symbolmn x-coordmn y-coordmn z-coordmn
Note that the xyz standard does not require that the number or chemical nature of atoms should be the same at subsequent snapshots, which allows for atoms disappearing from or coming into the field |
https://en.wikipedia.org/wiki/Semidiameter | In geometry, the semidiameter or semi-diameter of a set of points may be one half of its diameter; or, sometimes, one half of its extent along a particular direction.
Special cases
The semi-diameter of a sphere, circle, or interval is the same thing as its radius — namely, any line segment from the center to its boundary.
The semi-diameters of a non-circular ellipse are the halves of its extents along the two axes of symmetry. They are the parameters a, b of the implicit equation
Likewise, the semi-diameters of an ellipsoid are the parameters a, b, and c of its implicit equation
The semi-diameters of a superellipse, superellipsoid, or superquadric can be identified in the same way.
See also
Flattening
Semi-major and semi-minor axes
Semiperimeter
Geometric measurement |
https://en.wikipedia.org/wiki/Noriko%20Yui | Noriko Yui is a professor of mathematics at Queen's University in Kingston, Ontario.
Career
A native of Japan, Yui obtained her B.S. from Tsuda College, and her Ph.D. in Mathematics from Rutgers University in 1974 under the supervision of Richard Bumby.
Known internationally, Yui has been a visiting researcher at the Max-Planck-Institute in Bonn a number of times and a Bye-Fellow at Newnham College, University of Cambridge. Her research is based in arithmetic geometry with applications to mathematical physics and notably mirror symmetry. Currently, much of her work is focused upon the modularity of Calabi-Yau threefolds. Notably, she and Fernando Q. Gouvêa have shown that for , a projective rigid Calabi-Yau threefold defined over , the -function of is the -function of a certain modular form.
Yui has been the managing editor for the journal Communications in Number Theory and Physics since its inception in 2007. She has edited a number of monographs, and she has co-authored two books.
References
External links
Notable books co-authored by Yui
Living people
Year of birth missing (living people)
Japanese emigrants to Canada
Rutgers University alumni
Academic staff of Queen's University at Kingston
Tsuda University alumni
21st-century Japanese mathematicians
Canadian women mathematicians
21st-century Canadian mathematicians
21st-century women mathematicians |
https://en.wikipedia.org/wiki/Proebsting%27s%20paradox | In probability theory, Proebsting's paradox is an argument that appears to show that the Kelly criterion can lead to ruin. Although it can be resolved mathematically, it raises some interesting issues about the practical application of Kelly, especially in investing. It was named and first discussed by Edward O. Thorp in 2008. The paradox was named for Todd Proebsting, its creator.
Statement of the paradox
If a bet is equally likely to win or lose, and pays b times the stake for a win, the Kelly bet is:
times wealth. For example, if a 50/50 bet pays 2 to 1, Kelly says to bet 25% of wealth. If a 50/50 bet pays 5 to 1, Kelly says to bet 40% of wealth.
Now suppose a gambler is offered 2 to 1 payout and bets 25%. What should he do if the payout on new bets changes to 5 to 1? He should choose f* to maximize:
because if he wins he will have 1.5 (the 0.5 from winning the 25% bet at 2 to 1 odds) plus 5f*; and if he loses he must pay 0.25 from the first bet, and f* from the second. Taking the derivative with respect to f* and setting it to zero gives:
which can be rewritten:
So f* = 0.225.
The paradox is that the total bet, 0.25 + 0.225 = 0.475, is larger than the 0.4 Kelly bet if the 5 to 1 odds are offered from the beginning. It is counterintuitive that you bet more when some of the bet is at unfavorable odds. Todd Proebsting emailed Ed Thorp asking about this.
Ed Thorp realized the idea could be extended to give the Kelly bettor a nonzero probability of being ruined. He showed that if a gambler is offered 2 to 1 odds, then 4 to 1, then 8 to 1 and so on (2n to 1 for n = 1 to infinity) Kelly says to bet:
each time. The sum of all these bets is 1. So a Kelly gambler has a 50% chance of losing his entire wealth.
In general, if a bettor makes the Kelly bet on a 50/50 proposition with a payout of b1, and then is offered b2, he will bet a total of:
The first term is what the bettor would bet if offered b2 initially. The second term is positive if f2 > f1, meaning that if the payout improves, the Kelly bettor will bet more than he would if just offered the second payout, while if the payout gets worse he will bet less than he would if offered only the second payout.
Practical application
Many bets have the feature that payoffs and probabilities can change before the outcome is determined. In sports betting for example, the line may change several times before the event is held, and news may come out (such as an injury or weather forecast) that changes the probability of an outcome. In investing, a stock originally bought at $20 per share might be available now at $10 or $30 or any other price. Some sports bettors try to make income from anticipating line changes rather than predicting event outcomes. Some traders concentrate on possible short-term price movements of a security rather than its long-term fundamental prospects.
A classic investing example is a trader who has exposure limits, say he is not allowed to have more tha |
https://en.wikipedia.org/wiki/Central%20Bureau%20of%20Statistics%20%28Syria%29 | The Central Bureau of Statistics (CBS) () is the statistical agency responsible for the gathering of "information relating to economic, social and general activities and conditions" in the Syrian Arab Republic. The office is answerable to the office of the Prime Minister and has its main offices in Damascus. The CBS was established in 2005 and is administered by an administrative council headed by the deputy prime minister for economic affairs.
After the Syrian government began reconstructing infrastructure in 2011, the bureau began releasing data from 2011 to 2018.
References
External links
Government of Syria
Syria
Government agencies established in 2005
2005 establishments in Syria |
https://en.wikipedia.org/wiki/Resolution%20%28algebra%29 | In mathematics, and more specifically in homological algebra, a resolution (or left resolution; dually a coresolution or right resolution) is an exact sequence of modules (or, more generally, of objects of an abelian category), which is used to define invariants characterizing the structure of a specific module or object of this category. When, as usually, arrows are oriented to the right, the sequence is supposed to be infinite to the left for (left) resolutions, and to the right for right resolutions. However, a finite resolution is one where only finitely many of the objects in the sequence are non-zero; it is usually represented by a finite exact sequence in which the leftmost object (for resolutions) or the rightmost object (for coresolutions) is the zero-object.
Generally, the objects in the sequence are restricted to have some property P (for example to be free). Thus one speaks of a P resolution. In particular, every module has free resolutions, projective resolutions and flat resolutions, which are left resolutions consisting, respectively of free modules, projective modules or flat modules. Similarly every module has injective resolutions, which are right resolutions consisting of injective modules.
Resolutions of modules
Definitions
Given a module M over a ring R, a left resolution (or simply resolution) of M is an exact sequence (possibly infinite) of R-modules
The homomorphisms di are called boundary maps. The map ε is called an augmentation map. For succinctness, the resolution above can be written as
The dual notion is that of a right resolution (or coresolution, or simply resolution). Specifically, given a module M over a ring R, a right resolution is a possibly infinite exact sequence of R-modules
where each Ci is an R-module (it is common to use superscripts on the objects in the resolution and the maps between them to indicate the dual nature of such a resolution). For succinctness, the resolution above can be written as
A (co)resolution is said to be finite if only finitely many of the modules involved are non-zero. The length of a finite resolution is the maximum index n labeling a nonzero module in the finite resolution.
Free, projective, injective, and flat resolutions
In many circumstances conditions are imposed on the modules Ei resolving the given module M. For example, a free resolution of a module M is a left resolution in which all the modules Ei are free R-modules. Likewise, projective and flat resolutions are left resolutions such that all the Ei are projective and flat R-modules, respectively. Injective resolutions are right resolutions whose Ci are all injective modules.
Every R-module possesses a free left resolution. A fortiori, every module also admits projective and flat resolutions. The proof idea is to define E0 to be the free R-module generated by the elements of M, and then E1 to be the free R-module generated by the elements of the kernel of the natural map E0 → M etc. Dually, every R-modul |
https://en.wikipedia.org/wiki/Stably%20free%20module | In mathematics, a stably free module is a module which is close to being free.
Definition
A finitely generated module M over a ring R is stably free if there exist free finitely generated modules F and G over R such that
Properties
A projective module is stably free if and only if it possesses a finite free resolution.
An infinitely generated module is stably free if and only if it is free.
See also
Free object
Eilenberg–Mazur swindle
Hermite ring
References
Module theory
Free algebraic structures |
https://en.wikipedia.org/wiki/Jeep%20problem | The jeep problem, desert crossing problem or exploration problem is a mathematics problem in which a jeep must maximize the distance it can travel into a desert with a given quantity of fuel. The jeep can only carry a fixed and limited amount of fuel, but it can leave fuel and collect fuel at fuel dumps anywhere in the desert.
The problem first appeared in the 9th-century collection Propositiones ad Acuendos Juvenes (Problems to Sharpen the Young), attributed to Alcuin, with the puzzle being about a travelling camel eating grain. The De viribus quantitatis (c. 1500) of Luca Pacioli also discusses the problem. A modern treatment was given by N. J. Fine in 1947.
Variations of the problem are the camel and bananas problem where a merchant must maximize the number of bananas transported to a market using a camel that feeds on the bananas, the travelers across the desert problem where a number of travellers must all reach a destination and can only exchange supplies rather than leaving them, and the cars across the desert problem which again can only exchange their fuel, but where empty cars can be abandoned. This final problem has similarities to the operation of multistage rocket.
Problem
There are n units of fuel stored at a fixed base. The jeep can carry at most 1 unit of fuel at any time, and can travel 1 unit of distance on 1 unit of fuel (the jeep's fuel consumption is assumed to be constant). At any point in a trip the jeep may leave any amount of fuel that it is carrying at a fuel dump, or may collect any amount of fuel that was left at a fuel dump on a previous trip, as long as its fuel load never exceeds 1 unit. There are two variants of the problem:
Exploring the desert the jeep must return to the base at the end of every trip.
Crossing the desert the jeep must return to the base at the end of every trip except for the final trip, when the jeep travels as far as it can before running out of fuel.
In either case the objective is to maximize the distance traveled by the jeep on its final trip. Alternatively, the objective may be to find the least amount of fuel required to produce a final trip of a given distance.
Variations
In the classic problem the fuel in the jeep and at fuel dumps is treated as a continuous quantity. More complex variations on the problem have been proposed in which the fuel can only be left or collected in discrete amounts.
In the camel and bananas problem, the merchant has n units of bananas. The camel can carry at most 1 unit of bananas at any time, and can travel 1 unit of distance on 1 unit of bananas. The market is at m units of distance away. At any point in a trip the camel may leave any amount of bananas that it is carrying at a camp post, or may collect any amount of bananas that was left at a camp post on a previous trip, as long as its banana load never exceeds 1 unit. The problem asks for the maximum units of bananas that can be transported to the market.
In the travelers across the desert proble |
https://en.wikipedia.org/wiki/Vexillary | Vexillary may refer to:
an adjective meaning "flag-like"
the carrier of a Roman vexillum
Vexillary permutation in mathematics |
https://en.wikipedia.org/wiki/Diane%20Souvaine | Diane L. Souvaine is a professor of computer science and an adjunct professor of mathematics at Tufts University.
Contributions
Souvaine's research is in computational geometry and its applications, including robust non-parametric statistics and molecular modeling. She has also encouraged women and minorities to study and pursue careers in mathematics and the sciences and advocated gender neutrality in science teaching.
Education and career
After undergraduate and masters studies at Radcliffe College of Harvard University and at Dartmouth College, Souvaine earned her Ph.D. in 1986 from Princeton University under the supervision of David P. Dobkin. She held a faculty position at Rutgers University from 1986 to 1998, and from 1992 to 1994 served first as acting associate director and then as acting director of DIMACS. From 1994 to 1995 she took a visiting position in mathematics at the Institute for Advanced Study in Princeton, New Jersey, and in 1998 she took a permanent position at Tufts University.
Leadership and administration
At Tufts, Souvaine was department chair from 2002 to 2005 and (after a sabbatical at Harvard and the Massachusetts Institute of Technology) was reappointed as chair in 2006. She was Vice Provost for Research from 2012 to 2016.
She joined the National Science Board, a 24-member body that governs the National Science Foundation and advises the United States government about science policy, in 2008, and was the chair of the board for 2018–2020.
She also served for several years on the board of advisors for the Computer Science Department at the University of Vermont as well as for the Computer Science Department at Lehigh University.
Recognition
In 2008 Souvaine won Tufts' Lillian and Joseph Leibner Award for Excellence in Teaching and Advising of Students. In 2011, she was listed as a fellow of the Association for Computing Machinery for her research in computational geometry and her service to the computing community.
She became a fellow of the American Association for the Advancement of Science in 2016.
The Association for Women in Mathematics has included her in the 2020 class of AWM Fellows for "sustained advocacy, support and mentorship of women and students underrepresented in STEM fields in mathematics and theoretical computer science at multiple scales, from impacting individual mentees and advisees, to creating deep and broad institutional cultural change".
References
Year of birth missing (living people)
Living people
Radcliffe College alumni
Dartmouth College alumni
Princeton University alumni
Rutgers University faculty
Tufts University faculty
Researchers in geometric algorithms
American women mathematicians
American women computer scientists
Fellows of the American Association for the Advancement of Science
Fellows of the Association for Computing Machinery
Fellows of the Association for Women in Mathematics
American computer scientists
20th-century American mathematicians
21st-century American mathemati |
https://en.wikipedia.org/wiki/Thomas%20K%C3%A4rrbrandt | Thomas Kärrbrandt (born March 18, 1959) is a retired Swedish professional ice hockey player. He played for Västra Frölunda IF in Elitserien.
Career statistics
External links
1959 births
Frölunda HC players
Living people
Swedish ice hockey defencemen
Place of birth missing (living people) |
https://en.wikipedia.org/wiki/G%C3%B6ran%20Nilsson%20%28ice%20hockey%29 | Lars Göran Leonard Nilsson (born September 9, 1956) is a retired Swedish professional ice hockey player. He played for Västra Frölunda IF/HC and Malmö IF.
Career statistics
External links
1956 births
Frölunda HC players
Living people
Malmö Redhawks players
Swedish ice hockey defencemen |
https://en.wikipedia.org/wiki/Trans-spanning%20ligand | Trans-spanning ligands are bidentate ligands that can span opposite sites of a complex with square-planar geometry. A wide variety of ligands that chelate in the cis fashion already exist, but very few can link opposite vertices on a coordination polyhedron. Early attempts to generate trans-spanning bidentate ligands relied on long hydrocarbon chains to link the donor functionalities, but such ligands often lead to coordination polymers.
History
A diphosphane linked with pentamethylene was claimed to span across a square planar complex. This early attempt was followed by ligands with more rigid backbones. "TRANSPHOS" was the first trans-spanning diphosphane ligand that usually coordinates to palladium(II) and platinum(II) in a trans manner. TRANSPHOS features benzo[c]phenanthrene substituted by diphenylphosphinomethyl (Ph2PCH2) groups at the 1 and 11 positions. The polycyclic framework suffers sterically clashing hydrogen centers.
Xantphos, SPANphos, TRANSDIP and related ligands
TRANSDIP, based on a α-cyclodextrin, is the first ligand to give exclusively trans-spanned complexes, even with d8 metal ion halides. Xantphos is a trans-spanning ligand, with less steric bulk compared to TRANSPHOS. SPANphos is comparable to XANTPHOS but more reliably trans-spanning.
References
Coordination chemistry |
https://en.wikipedia.org/wiki/Banach%E2%80%93Tarski%20paradox | The Banach–Tarski paradox is a theorem in set-theoretic geometry, which states the following: Given a solid ball in three-dimensional space, there exists a decomposition of the ball into a finite number of disjoint subsets, which can then be put back together in a different way to yield two identical copies of the original ball. Indeed, the reassembly process involves only moving the pieces around and rotating them without changing their shape. However, the pieces themselves are not "solids" in the usual sense, but infinite scatterings of points. The reconstruction can work with as few as five pieces.
An alternative form of the theorem states that given any two "reasonable" solid objects (such as a small ball and a huge ball), the cut pieces of either one can be reassembled into the other. This is often stated informally as "a pea can be chopped up and reassembled into the Sun" and called the "pea and the Sun paradox".
The theorem is called a paradox because it contradicts basic geometric intuition. "Doubling the ball" by dividing it into parts and moving them around by rotations and translations, without any stretching, bending, or adding new points, seems to be impossible, since all these operations ought, intuitively speaking, to preserve the volume. The intuition that such operations preserve volumes is not mathematically absurd and it is even included in the formal definition of volumes. However, this is not applicable here because in this case it is impossible to define the volumes of the considered subsets. Reassembling them reproduces a set that has a volume, which happens to be different from the volume at the start.
Unlike most theorems in geometry, the mathematical proof of this result depends on the choice of axioms for set theory in a critical way. It can be proven using the axiom of choice, which allows for the construction of non-measurable sets, i.e., collections of points that do not have a volume in the ordinary sense, and whose construction requires an uncountable number of choices.
It was shown in 2005 that the pieces in the decomposition can be chosen in such a way that they can be moved continuously into place without running into one another.
As proved independently by Leroy and Simpson, the Banach–Tarski paradox does not violate volumes if one works with locales rather than topological spaces. In this abstract setting, it is possible to have subspaces without point but still nonempty. The parts of the paradoxical decomposition do intersect a lot in the sense of locales, so much that some of these intersections should be given a positive mass. Allowing for this hidden mass to be taken into account, the theory of locales permits all subsets (and even all sublocales) of the Euclidean space to be satisfactorily measured.
Banach and Tarski publication
In a paper published in 1924, Stefan Banach and Alfred Tarski gave a construction of such a paradoxical decomposition, based on earlier work by Giuseppe Vitali concerning |
https://en.wikipedia.org/wiki/Steinitz%27s%20theorem | In polyhedral combinatorics, a branch of mathematics, Steinitz's theorem is a characterization of the undirected graphs formed by the edges and vertices of three-dimensional convex polyhedra: they are exactly the 3-vertex-connected planar graphs. That is, every convex polyhedron forms a 3-connected planar graph, and every 3-connected planar graph can be represented as the graph of a convex polyhedron. For this reason, the 3-connected planar graphs are also known as polyhedral graphs.
This result provides a classification theorem for the three-dimensional convex polyhedra, something that is not known in higher dimensions. It provides a complete and purely combinatorial description of the graphs of these polyhedra, allowing other results on them, such as Eberhard's theorem on the realization of polyhedra with given types of faces, to be proven more easily, without reference to the geometry of these shapes. Additionally, it has been applied in graph drawing, as a way to construct three-dimensional visualizations of abstract graphs. Branko Grünbaum has called this theorem "the most important and deepest known result on 3-polytopes."
The theorem appears in a 1922 publication of Ernst Steinitz, after whom it is named. It can be proven by mathematical induction (as Steinitz did), by finding the minimum-energy state of a two-dimensional spring system and lifting the result into three dimensions, or by using the circle packing theorem.
Several extensions of the theorem are known, in which the polyhedron that realizes a given graph has additional constraints; for instance, every polyhedral graph is the graph of a convex polyhedron with integer coordinates, or the graph of a convex polyhedron all of whose edges are tangent to a common midsphere.
Definitions and statement of the theorem
An undirected graph is a system of vertices and edges, each edge connecting two of the vertices. As is common in graph theory, for the purposes of Steinitz's theorem these graphs are restricted to being finite (the vertices and edges are finite sets) and simple (no two edges connect the same two vertices, and no edge connects a vertex to itself). From any polyhedron one can form a graph, by letting the vertices of the graph correspond to the vertices of the polyhedron and by connecting any two graph vertices by an edge whenever the corresponding two polyhedron vertices are the endpoints of an edge of the polyhedron. This graph is known as the skeleton of the polyhedron.
A graph is planar if it can be drawn with its vertices as points in the Euclidean plane, and its edges as curves that connect these points, such that no two edge curves cross each other and such that the point representing a vertex lies on the curve representing an edge only when the vertex is an endpoint of the edge. By Fáry's theorem, every planar drawing can be straightened so that the curves representing the edges are line segments. A graph is 3-connected if it has more than three vertices and, after |
https://en.wikipedia.org/wiki/Jordan%20Ellenberg | Jordan Stuart Ellenberg (born October 30, 1971) is an American mathematician who is a professor of mathematics at the University of Wisconsin–Madison. His research involves arithmetic geometry. He is also an author of both fiction and non-fiction writing.
Early life
Ellenberg was born in Potomac, Maryland. He was a child prodigy who taught himself to read at the age of two by watching Sesame Street. His mother discovered his ability one day while she was driving on the Capital Beltway when her toddler informed her: "The sign says 'Bethesda is to the right.'" In second grade, he helped his teenage babysitter with her math homework. By fourth grade, he was participating in high school competitions (such as the American Regions Mathematics League) as a member of the Montgomery County math team. And by eighth grade, he had started college-level work.
He was part of the Johns Hopkins University Study of Mathematically Precocious Youth longitudinal cohort. He scored a perfect 800 on the math portion and a 680 on the verbal portion of the SAT-I exam at the age of 12. When he was in eighth grade, he took honors calculus classes at the University of Maryland; when he was a junior at Winston Churchill High School, he earned a perfect score of 1600 on the SAT; and as a high school senior, he placed second in the national Westinghouse Science Talent Search. He participated in the International Mathematical Olympiads three times, winning gold medals in 1987 and 1989 (with perfect scores) and a silver medal in 1988. He was also a two-time Putnam fellow (1990 and 1992) while at Harvard.
Career
In 2004, he began teaching at the University of Wisconsin-Madison and is currently the John D. MacArthur Professor of Mathematics, a position he has held since 2015. In 2012 he became a fellow of the American Mathematical Society and was a plenary speaker at the 2013 Joint Mathematics Meetings where he spoke on the subject of number theory and algebraic topology, the study of abstract high-dimensional shapes and the relations between them. He was named a Guggenheim Fellow in 2015. He was elected as one of the six A.D. White Professors-at-Large at Cornell in 2019 His research focuses on "the fields of number theory and algebraic geometry."
In addition to his research articles, he has authored a novel, The Grasshopper King, which was a finalist for the 2004 Young Lions Fiction Award; the "Do the Math" column in Slate; two non-fiction books, How Not to Be Wrong; and Shape: The Hidden Geometry of Information, Biology, Strategy, Democracy, and Everything Else (2022), as well as articles on mathematical topics in many newspapers and general magazines.
Ellenberg was a mathematics consultant for the 2017 film Gifted, which features a math prodigy as its protagonist; he also made a cameo appearance in the film as a professor lecturing on the partition function and Ramanujan's congruences. This gives him a Erdős-Bacon number of 5.
Personal life
Ellenberg lives in Madi |
https://en.wikipedia.org/wiki/Tom%20Thurlby | Thomas Newman Thurlby (born November 9, 1938) is a Canadian former professional ice hockey defenceman who briefly played in the National Hockey League for the Oakland Seals.
Career statistics
Regular season and playoffs
External links
1938 births
Living people
Canadian ice hockey defencemen
Houston Apollos players
Oakland Seals players
Ice hockey people from Kingston, Ontario |
https://en.wikipedia.org/wiki/Takashi%20Kitano | is a Japanese football player who plays for Gainare Tottori.
Club statistics
As of 22 February 2018.
References
External links
Profile at Cerezo Osaka
Profile at Gainare Tottori
1982 births
Living people
Sapporo University alumni
Association football people from Sapporo
Japanese men's footballers
J1 League players
J2 League players
J3 League players
Albirex Niigata players
Omiya Ardija players
Cerezo Osaka players
Cerezo Osaka U-23 players
Yokohama FC players
Gainare Tottori players
Men's association football goalkeepers |
https://en.wikipedia.org/wiki/Hiroshi%20Nakano%20%28footballer%29 | is a Japanese former footballer.
Club statistics
References
External links
1983 births
Living people
University of Tsukuba alumni
Association football people from Saga Prefecture
Japanese men's footballers
J1 League players
J2 League players
Albirex Niigata players
Yokohama FC players
Tochigi SC players
Men's association football defenders |
https://en.wikipedia.org/wiki/Mitsuru%20Chiyotanda | is a former Japanese football player.
Club statistics
References
External links
1980 births
Living people
University of Tsukuba alumni
Japanese men's footballers
J1 League players
J2 League players
Avispa Fukuoka players
Albirex Niigata players
Nagoya Grampus players
Júbilo Iwata players
Tokushima Vortis players
Men's association football defenders
Association football people from Fukuoka (city) |
https://en.wikipedia.org/wiki/Splitting%20lemma%20%28functions%29 | In mathematics, especially in singularity theory, the splitting lemma is a useful result due to René Thom which provides a way of simplifying the local expression of a function usually applied in a neighbourhood of a degenerate critical point.
Formal statement
Let be a smooth function germ, with a critical point at 0 (so for ). Let V be a subspace of such that the restriction f |V is non-degenerate, and write B for the Hessian matrix of this restriction. Let W be any complementary subspace to V. Then there is a change of coordinates of the form with , and a smooth function h on W such that
This result is often referred to as the parametrized Morse lemma, which can be seen by viewing y as the parameter. It is the gradient version of the implicit function theorem.
Extensions
There are extensions to infinite dimensions, to complex analytic functions, to functions invariant under the action of a compact group, ...
References
.
.
Singularity theory
Functions and mappings |
https://en.wikipedia.org/wiki/Souleymane%20Bachir%20Diagne | Souleymane Bachir Diagne (born 8 November 1955 in Saint-Louis, Senegal) is a Senegalese philosopher. His work is focused on the history of logic and mathematics, epistemology, the tradition of philosophy in the Islamic world, identity formation, and African literatures and philosophies.
Biography
After passing his baccalauréat in Senegal, Diagne was admitted to the demanding public secondary school Lycée Louis-le-Grand in Paris, following in the footsteps, almost a half-century later, of his compatriot and the first president of Senegal, Léopold Sédar Senghor. There he prepared for the entrance exams to the École Normale Supérieure, meanwhile receiving his license and maîtrise level degrees in philosophy at the Université Paris 1 Panthéon-Sorbonne. At the École Normale Supérieure he studied with Althusser and Derrida. After receiving his agrégation in Philosophy (1978), Diagne spent a year at Harvard University in an exchange program. In 1982 he defended a doctoral thesis in mathematics at Université Paris I, where, in 1988, he also completed his doctorat d’Etat, under the direction of Jean-Toussaint Desanti, on George Boole’s algebra of logic.
In 1982 Diagne returned to his native country to teach philosophy at Cheikh Anta Diop University in Dakar, where he became vice-dean of the College of Humanities. The former president of the Republic of Senegal, Abdou Diouf, named him Counselor for Education and Culture, a position which he held from 1993 to 1999.
Diagne is co-director of Éthiopiques, a Senegalese journal of literature and philosophy, and a member of the editorial committees of numerous scholarly journals, including the Revue d’histoire des mathématiques, Présence africaine, and Public Culture. He is a member of the scientific committees of Diogenes (published by UNESCO’s International Council for Philosophy and Humanistic Studies), CODESRIA (Conseil pour le développement de la recherche en sciences sociales en Afrique), and of the African and Malagasy Committee for Higher Education (CAMES), as well as UNESCO’s Council on the Future. He has been named by Le Nouvel observateur one of the 50 thinkers of our time. In October 2007, he was invited to participate in a white paper commission on the defense and national security in the French Senate in Paris.
Work
His main publications include two books on George Boole, a book on the Pakistani poet-philosopher Muhammad Iqbal, Islam et société ouverte. La fidélité et le mouvement dans la pensée de Muhammad Iqbal (2001) and an examination of Senghor’s philosophy, Léopold Sédar Senghor. L’Art africain comme philosophie (2007). He published a book on Islam and philosophy: Comment philosopher en Islam in 2010.
Having taught for several years in the departments of Philosophy and Religion at Northwestern University (2002 to 2007), Diagne is currently Professor of French, and Chair of the Department of French and Romance Philology with a secondary appointment in the Department of Philosophy, at C |
https://en.wikipedia.org/wiki/Institutiones%20calculi%20differentialis | Institutiones calculi differentialis (Foundations of differential calculus) is a mathematical work written in 1748 by Leonhard Euler and published in 1755. It lays the groundwork for the differential calculus. It consists of a single volume containing two internal books; there are 9 chapters in book I, and 18 in book II.
writes that "this is the first textbook on the differential calculus which has any claim to be both complete and accurate, and it may be said that all modern treatises on the subject are based on it."
See also
Institutiones calculi integralis
List of important publications in mathematics
References
External links
Full text in Latin available from e-rara.ch.
German translation Vollständige Anleitung zur Differenzial-Rechnung available from e-rara.ch.
1748 non-fiction books
1755 non-fiction books
Mathematics literature
Differential calculus
Leonhard Euler
18th-century Latin books |
https://en.wikipedia.org/wiki/Appell%20series | In mathematics, Appell series are a set of four hypergeometric series F1, F2, F3, F4 of two variables that were introduced by and that generalize Gauss's hypergeometric series 2F1 of one variable. Appell established the set of partial differential equations of which these functions are solutions, and found various reduction formulas and expressions of these series in terms of hypergeometric series of one variable.
Definitions
The Appell series F1 is defined for |x| < 1, |y| < 1 by the double series
where is the Pochhammer symbol. For other values of x and y the function F1 can be defined by analytic continuation. It can be shown that
Similarly, the function F2 is defined for |x| + |y| < 1 by the series
and it can be shown that
Also the function F3 for |x| < 1, |y| < 1 can be defined by the series
and the function F4 for |x|½ + |y|½ < 1 by the series
Recurrence relations
Like the Gauss hypergeometric series 2F1, the Appell double series entail recurrence relations among contiguous functions. For example, a basic set of such relations for Appell's F1 is given by:
Any other relation valid for F1 can be derived from these four.
Similarly, all recurrence relations for Appell's F3 follow from this set of five:
Derivatives and differential equations
For Appell's F1, the following derivatives result from the definition by a double series:
From its definition, Appell's F1 is further found to satisfy the following system of second-order differential equations:
A system partial differential equations for F2 is
The system have solution
Similarly, for F3 the following derivatives result from the definition:
And for F3 the following system of differential equations is obtained:
A system partial differential equations for F4 is
The system has solution
Integral representations
The four functions defined by Appell's double series can be represented in terms of double integrals involving elementary functions only . However, discovered that Appell's F1 can also be written as a one-dimensional Euler-type integral:
This representation can be verified by means of Taylor expansion of the integrand, followed by termwise integration.
Special cases
Picard's integral representation implies that the incomplete elliptic integrals F and E as well as the complete elliptic integral Π are special cases of Appell's F1:
Related series
There are seven related series of two variables, Φ1, Φ2, Φ3, Ψ1, Ψ2, Ξ1, and Ξ2, which generalize Kummer's confluent hypergeometric function 1F1 of one variable and the confluent hypergeometric limit function 0F1 of one variable in a similar manner. The first of these was introduced by Pierre Humbert in 1920.
defined four functions similar to the Appell series, but depending on many variables rather than just the two variables x and y. These series were also studied by Appell. They satisfy certain partial differential equations, and can also be given in terms of Euler-type integrals and contour integrals.
References
|
https://en.wikipedia.org/wiki/Robert%20Hues | Robert Hues (1553 – 24 May 1632) was an English mathematician and geographer. He attended St. Mary Hall at Oxford, and graduated in 1578. Hues became interested in geography and mathematics, and studied navigation at a school set up by Walter Raleigh. During a trip to Newfoundland, he made observations which caused him to doubt the accepted published values for variations of the compass. Between 1586 and 1588, Hues travelled with Thomas Cavendish on a circumnavigation of the globe, performing astronomical observations and taking the latitudes of places they visited. Beginning in August 1591, Hues and Cavendish again set out on another circumnavigation of the globe. During the voyage, Hues made astronomical observations in the South Atlantic, and continued his observations of the variation of the compass at various latitudes and at the Equator. Cavendish died on the journey in 1592, and Hues returned to England the following year.
In 1594, Hues published his discoveries in the Latin work Tractatus de globis et eorum usu (Treatise on Globes and Their Use) which was written to explain the use of the terrestrial and celestial globes that had been made and published by Emery Molyneux in late 1592 or early 1593, and to encourage English sailors to use practical astronomical navigation. Hues' work subsequently went into at least 12 other printings in Dutch, English, French and Latin.
Hues continued to have dealings with Raleigh in the 1590s, and later became a servant of Thomas Grey, 15th Baron Grey de Wilton. While Grey was imprisoned in the Tower of London for participating in the Bye Plot, Hues stayed with him. Following Grey's death in 1614, Hues attended upon Henry Percy, the 9th Earl of Northumberland, when he was confined in the Tower; one source states that Hues, Thomas Harriot and Walter Warner were Northumberland's constant companions and known as his "Three Magi", although this is disputed. Hues tutored Northumberland's son Algernon Percy (who was to become the 10th Earl of Northumberland) at Oxford, and subsequently (in 1622–1623) Algernon's younger brother Henry. In later years, Hues lived in Oxford where he was a fellow of the University, and discussed mathematics and related subjects with like-minded friends. He died on 24 May 1632 in the city and was buried in Christ Church Cathedral.
Early years and education
Robert Hues was born in 1553 at Little Hereford in Herefordshire, England. In 1571, at the age of 18 years, he entered Brasenose College, University of Oxford. English antiquarian Anthony à Wood (1632–1695) wrote that when Hues arrived at Oxford he was "only a poor scholar or servitor ... he continued for some time a very sober and serious servant ... but being sensible of the loss of time which he sustained there by constant attendance, he transferred himself to St Mary's Hall". Hues graduated with a Bachelor of Arts (B.A.) degree on 12 July 1578, having shown marked skill in Greek. He later gave advice to the dramatist and po |
https://en.wikipedia.org/wiki/%27Anin | Anin () a Palestinian village in the West Bank governorate of Jenin. According to the Palestinian Central Bureau of Statistics, the village had a population of 4,216 inhabitants in 2017.
History
It has been suggested than 'Anin is the site of ancient Beth Anath, or Greek: Batanaia, mentioned in Eusebius' Onomasticon and in the Tosefta.
Potsherds from Iron Age I, IA II, Persian, early and late Roman, Byzantine, early Muslim and the Middle Ages have been found here.
"Immediately north of the village is a rock-cut passage large enough to walk along, extending about 50 feet and lined with cement; it then becomes about a foot high. This leads out on to a flat surface of rock.(...) Two rock-cut tombs, now blocked, exist west of this."
Ottoman era
In 1517 'Anin was incorporated into the Ottoman Empire with the rest of Palestine. During the 16th and 17th centuries, it belonged to the Turabay Emirate (1517-1683), which encompassed also the Jezreel Valley, Haifa, Jenin, Beit She'an Valley, northern Jabal Nablus, Bilad al-Ruha/Ramot Menashe, and the northern part of the Sharon plain. In the census of 1596 it was a part of the nahiya ("subdistrict") of Sahil Atlit which was under the administration of the liwa ("district") of Lajjun. The village had a population of 16 households, all Muslim. The villagers paid a fixed tax rate of 25% on wheat, barley, summer crops, olive trees, in addition to occasional revenues and a press for olive oil or grape syrup; a total of 3,600 akçe. Potsherds from the Ottoman era have also been found here.
In 1870/1871 (1288 AH), an Ottoman census listed the village in the nahiya of Shafa al-Gharby.
In 1882, the PEF's Survey of Western Palestine described Anin as: "a small village on a ridge, partly built of stone, with a small olive grove beneath it on the west, and two wells on that side. It has the appearance of an ancient site, having rock-cut tombs, and a curious channel for water."
British mandate era
In the 1922 census of Palestine, conducted by the British Mandate authorities, the village had a population of 360 Muslims, increasing in the 1931 census to 447 Muslims, in 68 houses.
In the 1944/5 statistics the population of Anin was 590 Muslims, with a total of 15,049 dunams of land, according to an official land and population survey. Of this, 1,769 dunams were used for plantations and irrigable land, 1,806 dunams for cereals, while 13 dunams were built-up (urban) land.
Jordanian era
After the 1948 Arab-Israeli War, 'Anin came under Jordanian rule.
The Jordanian census of 1961 found 752 inhabitants.
Post-1967
'Anin has been under Israeli control along with the rest of the West Bank since the 1967 Six-Day War.
References
Bibliography
External links
Welcome To 'Anin
Survey of Western Palestine, Map 8: IAA, Wikimedia commons
Olive wars, 2014, BBC, 'Anin 16.00-21:00
Villages in the West Bank
Jenin Governorate
Municipalities of the State of Palestine |
https://en.wikipedia.org/wiki/Per%20Morten%20Kristiansen | Per Morten Kristiansen (born 14 July 1981) is a Norwegian football goalkeeper who last played for FK Haugesund.
His former clubs are Greåker IF, Fredrikstad and Moss.
Career statistics
References
1981 births
Living people
Norwegian men's footballers
Fredrikstad FK players
Moss FK players
FK Haugesund players
Eliteserien players
Footballers from Sarpsborg
Men's association football goalkeepers |
https://en.wikipedia.org/wiki/Toral%20subalgebra | In mathematics, a toral subalgebra is a Lie subalgebra of a general linear Lie algebra all of whose elements are semisimple (or diagonalizable over an algebraically closed field). Equivalently, a Lie algebra is toral if it contains no nonzero nilpotent elements. Over an algebraically closed field, every toral Lie algebra is abelian; thus, its elements are simultaneously diagonalizable.
In semisimple and reductive Lie algebras
A subalgebra of a semisimple Lie algebra is called toral if the adjoint representation of on , is a toral subalgebra. A maximal toral Lie subalgebra of a finite-dimensional semisimple Lie algebra, or more generally of a finite-dimensional reductive Lie algebra, over an algebraically closed field of characteristic 0 is a Cartan subalgebra and vice versa. In particular, a maximal toral Lie subalgebra in this setting is self-normalizing, coincides with its centralizer, and the Killing form of restricted to is nondegenerate.
For more general Lie algebras, a Cartan subalgebra may differ from a maximal toral subalgebra.
In a finite-dimensional semisimple Lie algebra over an algebraically closed field of a characteristic zero, a toral subalgebra exists. In fact, if has only nilpotent elements, then it is nilpotent (Engel's theorem), but then its Killing form is identically zero, contradicting semisimplicity. Hence, must have a nonzero semisimple element, say x; the linear span of x is then a toral subalgebra.
See also
Maximal torus, in the theory of Lie groups
References
Properties of Lie algebras |
https://en.wikipedia.org/wiki/Integral%20expression | Integral expression may refer to:
Integral equation
More generally, a mathematical expression involving one or more integrals
Integer polynomial
An algebraic expression which is not in fractional form, see algebraic fraction |
https://en.wikipedia.org/wiki/Boris%20Levit | Boris Ya. Levit is a professor of statistics at Queen's University in Kingston, Ontario, Canada.
Career
Levit obtained his M.Sc. in mathematics from Moscow State University and his Ph.D. in statistics from Russian Academy of Science in 1975 (his advisor was Rafail Khasminskii). While at Moscow State University, he was influenced by many famous mathematicians of the era, including Andrei Kolmogorov.
Before undertaking a professorship at Queen's University, Levit spent several years lecturing in the United States. He has also spent nearly ten years in the Netherlands, as a professor of statistics at the University of Utrecht.
Well known internationally, Levit has made outstanding contributions to the field of statistics. His research has included statistical problems involving infinitely many parameters, as well as nonparametric statistics. In the 1980s, he discovered how to characterize high order approximation problems using the properties of corresponding elliptic differential operators. Levit was awarded a D.Sc. by Vilnius University for his use of differential geometry and partial differential equations in statistical research.
References
External links
Official site
Living people
Year of birth missing (living people)
Russian statisticians
21st-century Moldovan mathematicians
Canadian mathematicians
20th-century Moldovan mathematicians
Vilnius University alumni
Canadian statisticians
Academic staff of Queen's University at Kingston |
https://en.wikipedia.org/wiki/Afghanistan%20national%20football%20team%20results | This page details the match results and statistics of the Afghanistan national football team.
Key
Key to matches
Att.=Match attendance
(H)=Home ground
(A)=Away ground
(N)=Neutral ground
Key to record by opponent
Pld=Games played
W=Games won
D=Games drawn
L=Games lost
GF=Goals for
GA=Goals against
Results
Afghanistan's score is shown first in each case.
Notes
Record by opponent
References
Men's
Results |
https://en.wikipedia.org/wiki/Brunei%20national%20football%20team%20results | This page details the match results and statistics of the Brunei national football team.
Key
Key to matches
Att.=Match attendance
(H)=Home ground
(A)=Away ground
(N)=Neutral ground
Key to record by opponent
Pld=Games played
W=Games won
D=Games drawn
L=Games lost
GF=Goals for
GA=Goals against
Results
Brunei's score is shown first in each case.
Notes
Record by opponent
References
Brunei national football team results |
https://en.wikipedia.org/wiki/Harry%20Kesten | Harry Kesten (November 19, 1931 – March 29, 2019) was a Jewish American mathematician best known for his work in probability, most notably on random walks on groups and graphs, random matrices, branching processes, and percolation theory.
Biography
Harry Kesten was born in Duisburg, Germany in 1931, and grew up in the Netherlands, where he moved with his parents in 1933 to escape the Nazis. Surviving the Holocaust, Kesten initially studied chemistry, and later theoretical physics and mathematics, at the University of Amsterdam. He moved to the United States in 1956 and received his PhD in Mathematics in 1958 at Cornell University under the supervision of Mark Kac. He was an instructor at Princeton University and the Hebrew University before returning to Cornell in 1961.
Kesten died on March 29, 2019, in Ithaca at the age of 87.
Mathematical work
Kesten's work includes many fundamental contributions across almost the whole of probability, including the following highlights.
Random walks on groups. In his 1958 PhD thesis, Kesten studied symmetric random walks on countable groups G generated by a jump distribution with support G. He showed that the spectral radius equals the exponential decay rate of the return probabilities. He showed later that this is strictly less than 1 if and only if the group is non-amenable. The last result is known as Kesten's criterion for amenability. He calculated the spectral radius of the d-regular tree, namely .
Products of random matrices. Let be the product of the first n elements of an ergodic stationary sequence of random matrices. With Furstenberg in 1960, Kesten showed the convergence of , under the condition .
Self-avoiding walks. Kesten's ratio limit theorem states that the number of n-step self-avoiding walks from the origin on the integer lattice satisfies where is the connective constant. This result remains unimproved despite much effort. In his proof, Kesten proved his pattern theorem, which states that, for a proper internal pattern P, there exists such that the proportion of walks containing fewer than copies of P is exponentially smaller than .
Branching processes. Kesten and Stigum showed that the correct condition for the convergence of the population size, normalized by its mean, is that where L is a typical family size. With Ney and Spitzer, Kesten found the minimal conditions for the asymptotic distributional properties of a critical branching process, as discovered earlier, but subject to stronger assumptions, by Kolmogorov and Yaglom.
Random walk in a random environment. With Kozlov and Spitzer, Kesten proved a deep theorem about random walk in a one-dimensional random environment. They established the limit laws for the walk across the variety of situations that can arise within the environment.
Diophantine approximation. In 1966, Kesten resolved a conjecture of Erdős and Szűsz on the discrepancy of irrational rotations. He studied the discrepancy between the number o |
https://en.wikipedia.org/wiki/Polar%20action | In mathematics, a polar action is a proper and isometric action of a Lie group G on a complete Riemannian manifold M for which there exists a complete submanifold Σ that meets all the orbits and meets them always orthogonally; such a submanifold is called a section. A section is necessarily totally geodesic. If the sections of a polar action are flat with respect to the induced metric, then the action is called hyperpolar.
In the case of linear orthogonal actions on Euclidean spaces, polar actions are called polar representations. The isotropy representations of Riemannian symmetric spaces are basic examples of polar representations. Conversely, Dadok has classified polar representations of compact Lie groups on Euclidean spaces, and it follows from his classification that such a representation has the same orbits as the isotropy representation of a symmetric space.
References
Berndt, J; Olmos, C; Console, S. (2003). "Submanifolds and holonomy", Chapman & Hall/CRC, Research Notes in Mathematics, 434,
Differential geometry |
https://en.wikipedia.org/wiki/Choi%20Hyo-jin | Choi Hyo-Jin (, born 18 August 1983) is South Korean retired football player who used to play as a right wingback.
Club career statistics
International career
Results list South Korea's goal tally first.
NB: Friendly match against Poland (on 7 October 2011) was not full A-match.
Honors
Club
Incheon United
K League 1 Runner-up : 2005
Pohang Steelers
K League 1 Winner : 2007
Korean FA Cup
Winner : 2008
Runner-up : 2007
League Cup Winner : 2009
AFC Champions League Winner : 2009
FC Seoul
K League 1
Winners (2): 2010, 2012
League Cup
Winners (1): 2010
AFC Champions League
Runner-up : 2013
Korean FA Cup
Runner-up : 2014
Individual
Korean FA Cup MVP : 2008
K-League Best XI : 2008, 2009, 2010
References
External links
Choi Hyo-jin ? National Team Stats at KFA
1983 births
Living people
Men's association football fullbacks
South Korean men's footballers
South Korea men's international footballers
2011 AFC Asian Cup players
Incheon United FC players
Pohang Steelers players
FC Seoul players
Gimcheon Sangmu FC players
Jeonnam Dragons players
K League 1 players
K League 2 players
Ajou University alumni |
https://en.wikipedia.org/wiki/Hwang%20Jae-won | Hwang Jae-Won (; born 13 April 1981) is a South Korean football defender, who plays for Daejeon Citizen in the K League 2.
Club career statistics
International goals
Honours
Pohang Steelers
K-League: 2007
Korean FA Cup: 2008
K-League Cup: 2009
AFC Champions League: 2009
Individual
K-League Best XI: 2007, 2009
AFC footballer of the year nomination: 2009
References
External links
National Team Player Record
1981 births
Living people
Men's association football defenders
South Korean men's footballers
South Korea men's international footballers
2011 AFC Asian Cup players
Pohang Steelers players
Suwon Samsung Bluewings players
Seongnam FC players
Chungju Hummel FC players
Daegu FC players
Daejeon Hana Citizen players
K League 1 players
K League 2 players
Ajou University alumni
Footballers from Seoul |
https://en.wikipedia.org/wiki/FIVB%20Volleyball%20World%20Grand%20Prix%20statistics | The most successful teams, as of 2016, have been: Brazil, 11 times (1994, 1996, 1998, 2004, 2005, 2006, 2008, 2009, 2013, 2014, 2016); and United States, 6 times (1995, 2001, 2010, 2011, 2012, 2015). The competition has been won 3 times by Russia (1997, 1999, 2002), twice by Cuba (1993, 2000) and once by China (2003) and the Netherlands (2007).
References
External links
Honours (1993–2016)
Statistics
Volleyball records and statistics |
https://en.wikipedia.org/wiki/Aki%20Lahtinen | Aki Lahtinen (born 31 October 1958) is a Finnish former footballer.
External links
Finland - International Player Records
Veikkausliiga player statistics
1958 births
Living people
Finnish men's footballers
Finnish expatriate men's footballers
Finland men's international footballers
Footballers at the 1980 Summer Olympics
Olympic footballers for Finland
Notts County F.C. players
Mestaruussarja players
Men's association football defenders
Oulun Työväen Palloilijat players
Sportspeople from Jyväskylä
20th-century Finnish people |
https://en.wikipedia.org/wiki/Pakistani%20New%20Zealanders | Pakistani New Zealanders, also known as Pakistani Kiwis, are New Zealanders of Pakistani descent or Pakistan-born people who have immigrated to New Zealand.
Demographics
According to 2001 statistics, Pakistani Kiwis size around a population of 3,000. However, since that time, the population of Pakistani Kiwis has been growing at a fair pace across many parts of the country with significant figures in Auckland. In 2007, the population had grown to 5,000.
Pakistanis are located in almost all the major cities and towns of New Zealand, including Auckland, Hamilton, Wellington, Christchurch, Tauranga, Otago and Dunedin.
Religion
Most of the Pakistani New Zealanders are Muslims.
Notable people
Azhar Abbas - Auckland Aces cricketer
Haroon - English-born Pakistani pop singer of New Zealand origin
Billy Ibadulla - New Zealand-based former Pakistani cricketer and commentator
See also
Punjabi New Zealanders
New Zealand–Pakistan relations
References
External links
Cultural organisations
Pakistan Association of New Zealand
Pakistani Association of Canterbury New Zealand, in Christchurch and Canterbury region
Pakistan Association of New Zealand, based in Auckland
Pakistani Students Association at Massey University, New Zealand - organisation for students at all campuses of Massey University
Asian diaspora in New Zealand |
https://en.wikipedia.org/wiki/Los%20%C3%81lamos | Los Álamos is a Chilean commune and city in Arauco Province, Biobío Region.
Demographics
According to the 2002 census of the National Statistics Institute, Los Álamos spans an area of and has 18,632 inhabitants (9,456 men and 9,176 women). Of these, 16,394 (88%) lived in urban areas and 2,238 (12%) in rural areas. Between the 1992 and 2002 censuses, the population grew by 10.4% (1,762 persons).
The commune includes the locality of Antihuala.
Administration
As a commune, Los Álamos is a third-level administrative division of Chile administered by a municipal council, headed by an alcalde who is directly elected every four years. The 2008-2012 alcalde is Lautaro Melita Vinett (PS). Since 2013 and until the present the alcalde of Los Álamos is Jorge Fuentes Fetis
Within the electoral divisions of Chile, Los Álamos is represented in the Chamber of Deputies by Manuel Monsalve (PS) and Iván Norambuena (UDI) as part of the 46th electoral district, together with Lota, Lebu, Arauco, Curanilahue, Cañete, Contulmo and Tirúa. The commune is represented in the Senate by Victor Pérez Varela (UDI) and Mariano Ruiz-Esquide Jara (PDC) as part of the 13th senatorial constituency (Biobío-Coast).
Culture
In the literary field, Los Álamos stands out for its poets. Among these, one can name René Briones Sandoval, Maribel Castro Vergara, Olga Ester Garrido, Marta Díaz Pereira, María Rocha, Manuel Castro, Mac Karo, who were anthologized in the magazine Chonchón n°39, published in September 2020. In addition, During the years 2018 and 2019, the poets of Los Álamos participated in the I and II Latin American Meeting of Poets and Narrators in Lebu, events that included the presence of authors from the Province of Arauco, such as Lidia Mansilla Valenzuela and Alejandro Concha M., and from abroad, such as Jorge Canales and Amapola, from El Salvador, Chary Gumeta and José Baroja, from Mexico, and Felicidad Batista, from Spain, among other participants.
References
External links
Municipality of Los Álamos
Communes of Chile
Populated places in Arauco Province |
https://en.wikipedia.org/wiki/Stephen%20Wiggins | Stephen Ray Wiggins (born 1959) is a Cherokee-American applied mathematics researcher and educator, also of British heritage, best known for his contributions in nonlinear dynamics, chaos theory and nonlinear phenomena. His wide contributions include Lagrangian aspects of fluid dynamics and reaction dynamics in theoretical chemistry.
Early life and education
Wiggins was born in Oklahoma City, Oklahoma in 1959, and has two younger siblings. He is enrolled as a member of the Cherokee Nation. He received a BSc in physics and mathematics from Pittsburg State University in 1980, an MA in mathematics and an MSc in physics from the University of Wisconsin-Madison in 1983, and a PhD in theoretical and applied mechanics from Cornell University in 1985. He also attended the Open University in Great Britain, where he earned a Bachelor of Laws, with honors, in 2005.
Academic career and field of study
Wiggins was influenced heavily by his PhD advisor Philip Holmes. His dissertation was on "Slowly Varying Oscillators." From 1987 to 2001, he was a professor at Caltech. He is actively working on the advancement of computational applied mathematics at the University of Bristol, where he was the head of the mathematics department from 2004 until 2008, and was the school research director. As of August 2020 Wiggins had 12 PhD students and 60 academic descendants.
Wiggins has contributed in many different areas of applied mathematics, science, and engineering using applied and computational dynamics as the framework for his approach and analysis.
His current focus is on developing the phase space approach to chemical reaction dynamics in the setting of the CHAMPS (Chemistry and Mathematics in Phase Space) project. Previously he has established quite successful US-UK-Spain research network in building novel foundational connection between applied mathematics and theoretical chemistry.
Honors
Wiggins received the Presidential Young Investigators Award from the National Science Foundation (NSF) in August 1989.
He was a Stanislaw M. Ulam Visiting Scholar at the Center for Nonlinear Studies, Los Alamos National Laboratory, from 1989 to 1990.
He received the US Office of Naval Research (ONR) Young Investigator Award in Applied Analysis in 1989.
Selected publications
V.J.García-Garrido; M.Katsanikas; M.Agaoglou; S.Wiggins: Tuning the branching ratio in a symmetric potential energy surface with a post-transition state bifurcation using external time dependence, Chemical Physics Letters, 2020-09: DOI: 10.1016/j.cplett.2020.137714
Fang Yang; Yayun Zheng; Jinqiao Duan; Ling Fu; Stephen Wiggins: The tipping times in an Arctic sea ice system under influence of extreme events, Chaos: An Interdisciplinary Journal of Nonlinear Science, 2020-06: DOI: 10.1063/5.0006626
Books
Global Bifurcations and Chaos -- Analytical Methods. Springer-Verlag Applied Mathematical Science Series. 1988, second printing 1990.
Introduction to Applied Nonlinear Dynamical Systems and Chaos. |
https://en.wikipedia.org/wiki/Toponogov%27s%20theorem | In the mathematical field of Riemannian geometry, Toponogov's theorem (named after Victor Andreevich Toponogov) is a triangle comparison theorem.
It is one of a family of comparison theorems that quantify the assertion that a pair of geodesics emanating from a point p spread apart more slowly in a region of high curvature than they would in a region of low curvature.
Let M be an m-dimensional Riemannian manifold with sectional curvature K satisfying
Let pqr be a geodesic triangle, i.e. a triangle whose sides are geodesics, in M, such that the geodesic pq is minimal and if δ > 0, the length of the side pr is less than .
Let p′q′r′ be a geodesic triangle in the model space Mδ, i.e. the simply connected space of constant curvature δ, such that the lengths of sides p′q′ and p′r′ are equal to that of pq and pr respectively and the angle at p′ is equal to that at p.
Then
When the sectional curvature is bounded from above, a corollary to the Rauch comparison theorem yields an analogous statement, but with the reverse inequality .
References
External links
Pambuccian V., Zamfirescu T. "Paolo Pizzetti: The forgotten originator of triangle comparison geometry". Hist Math 38:8 (2011)
Theorems in Riemannian geometry
Geometric inequalities |
https://en.wikipedia.org/wiki/Redlich%E2%80%93Kwong%20equation%20of%20state | In physics and thermodynamics, the Redlich–Kwong equation of state is an empirical, algebraic equation that relates temperature, pressure, and volume of gases. It is generally more accurate than the van der Waals equation and the ideal gas equation at temperatures above the critical temperature. It was formulated by Otto Redlich and Joseph Neng Shun Kwong in 1949. It showed that a two-parameter, cubic equation of state could well reflect reality in many situations, standing alongside the much more complicated Beattie–Bridgeman model and Benedict–Webb–Rubin equation that were used at the time. The Redlich–Kwong equation has undergone many revisions and modifications, in order to improve its accuracy in terms of predicting gas-phase properties of more compounds, as well as in better simulating conditions at lower temperatures, including vapor–liquid equilibria.
Equation
The Redlich–Kwong equation is formulated as:
where:
p is the gas pressure
R is the gas constant,
T is temperature,
Vm is the molar volume (V/n),
a is a constant that corrects for attractive potential of molecules, and
b is a constant that corrects for volume.
The constants are different depending on which gas is being analyzed. The constants can be calculated from the critical point data of the gas:
where:
Tc is the temperature at the critical point, and
Pc is the pressure at the critical point.
The Redlich–Kwong equation can also be represented as an equation for the compressibility factor of gas, as a function of temperature and pressure:
where:
Or more simply:
This equation only implicitly gives Z as a function of pressure and temperature, but is easily solved numerically, originally by graphical interpolation, and now more easily by computer. Moreover, analytic solutions to cubic functions have been known for centuries and are even faster for computers.
For all Redlich–Kwong gases:
where:
Zc is the compressibility factor at the critical point
Using the equation of state can be written in the reduced form:
And since it follows: with
From the Redlich–Kwong equation, the fugacity coefficient of a gas can be estimated:
Critical constants
It is possible to express the critical constants Tc and Pc as functions of a and b by reversing the following system of 2 equations a(Tc, Pc) and b(Tc, Pc) with 2 variables Tc, Pc:
Because of the definition of compressibility factor at critical condition, it is possible to reverse it to find the critical molar volume Vm,c, by knowing previous found Pc, Tc and Zc=1/3.
Multiple components
The Redlich–Kwong equation was developed with an intent to also be applicable to mixtures of gases. In a mixture, the b term, representing the volume of the molecules, is an average of the b values of the components, weighted by the mole fractions:
or
where:
xi is the mole fraction of the ith component of the mixture,
bi is the b value of the ith component of the mixture, and
Bi is the B value of the ith component of the mixture
The |
https://en.wikipedia.org/wiki/South%20East%20Asian%20Mathematics%20Competition | The South East Asian Mathematics Competition (SEAMC) is an annual three-day non-profit mathematics competition for Southeast Asian students at different grade levels. It is a qualifying competition organized by Eunoia Ventures for invitation to the World Mathematics Championships.
Teams have participated from China, Thailand, Hong Kong, Malaysia, Singapore, Brunei, Vietnam, Cambodia, and Nepal.
Host venue locations of the SEAMC changes annually. An online version was held due to the COVID-19 Pandemic.
Eligibility
The Senior Competition is open to all students in Grade 12 (Year 13) or younger.
The Junior Competition is open to all students in Grade 9 (Year 10) or younger.
The Secondary Competition is open to all students in Grade 7 (Year 8) or younger during the month of the event and
Primary level for Grade 5 (Year 6) or younger.
The competition
History
SEAMC is a mathematics collaboration experience for school students located in South or North East Asia to come together for 2-3 days.
SEAMC was conceived of by Steve Warry, who taught at Alice Smith School in Kuala Lumpur. He organised SEAMC in March 2001. He died one week prior to the first competition. Teams competed for the Warry Cup, which is named in Steve's honour.
From 2014, the NEAMC sister event has been organised for students in Northeast Asia. The organizers enlisted the Nanjing International School to host it initially in February 2014 with the help of Malcolm Coad.
In 2017, the SNEAMC family of events became the World Mathematics Championships.
Format
Each school enters teams of 3 students each. The competition has nine rounds.
All WMC qualifying competitions have:
3 days of engagement
9 equally weighted rounds
6 skills categories for prizes
The best sum ranking across all 9 rounds win
School teams engage within the Communication skills rounds.
The Collaboration skills rounds (Open, Lightning and Innovation) are in buddy teams of three.
The Challenge are skills rounds undertaken as individuals.
Three skills rounds are (subject specific skills and procedures) knowledge based,
three are (plan and execute) strategy focused and three depend upon (new and imaginative ideas) creativity.
So each strategy, creative and knowledge skill category is engaged in alone, in school teams and in buddy teams.
Past questions can be found around the web.
In many SEAMC competitions, there are initial icebreaker events.
Prizes
All participants receive a transcript of relative attainment in each of the 9 rounds.
The highest ranked individuals in each category receive medals.
The highest ranked individuals across all 9 rounds receive medals.
The best ranked school team across all 9 rounds receive a respectively named Cup (for the SEAMC Junior competition, this is the original Warry Cup).
The better ranked teams across all of the competition venues that year are invited to the ultimate World Mathematics Championships showdown, hosted by Trinity College, University of Melbou |
https://en.wikipedia.org/wiki/Craig%20Tracy | Craig Arnold Tracy (born September 9, 1945) is an American mathematician, known for his contributions to mathematical physics and probability theory.
Born in United Kingdom, he moved as infant to Missouri where he grew up and
obtained a B.Sc. in physics from University of Missouri (1967).
He studied as a Woodrow Wilson Fellow
at the Stony Brook University where he obtained a Ph.D. on the thesis entitled Spin-Spin Scale-Functions in the Ising and XY-Models (1973)
advised by Barry M. McCoy,
in which (also jointly with Tai Tsun Wu and Eytan Barouch) he studied Painlevé functions in exactly
solvable statistical mechanical models.
He then was on the faculty of Dartmouth College (1978–84) before
joining University of California, Davis (1984) where he is now
a professor. With Harold Widom he worked on the asymptotic analysis of Toeplitz determinants and their various operator theoretic generalizations. This work gave them both the George Pólya and the Norbert Wiener prizes, and the Tracy–Widom distribution is named after them.
Awards
Woodrow Wilson Fellowship, 1967–68.
Japan Society for the Promotion of Science Fellowship 1991
2002 Pólya Prize (SIAM) shared with Harold Widom
Fellow American Academy of Arts and Sciences 2006
Norbert Wiener Prize 2007, shared with Harold Widom.
Fellow of the American Mathematical Society, 2012
References
20th-century American mathematicians
21st-century American mathematicians
1945 births
University of Missouri alumni
Mathematicians from Missouri
Stony Brook University alumni
Dartmouth College faculty
University of California, Davis faculty
Fellows of the American Academy of Arts and Sciences
Fellows of the American Mathematical Society
Living people
Fellows of the Society for Industrial and Applied Mathematics |
https://en.wikipedia.org/wiki/Cosmic%20space | In mathematics, particularly topology, a cosmic space is any topological space that is a continuous image of some separable metric space. Equivalently (for regular T1 spaces but not in general), a space is cosmic if and only if it has a countable network; namely a countable collection of subsets of the space such that any open set is the union of a subcollection of these sets.
Cosmic spaces have several interesting properties. There are a number of unsolved problems about them.
Examples and properties
Any open subset of a cosmic space is cosmic since open subsets of separable spaces are separable.
Separable metric spaces are trivially cosmic.
Unsolved problems
It is unknown as to whether X is cosmic if:
a) X2 contains no uncountable discrete space;
b) the countable product of X with itself is hereditarily separable and hereditarily Lindelöf.
References
External links
A book of unsolved problems in topology; see page 91 for cosmic spaces
Topology
Topological spaces |
https://en.wikipedia.org/wiki/Fluctuation | Fluctuation may refer to:
Physics and mathematics
Statistical fluctuations, in statistics, statistical mechanics, and thermodynamics
Thermal fluctuations, statistical fluctuations in a thermodynamic variable
Quantum fluctuation, arising from the uncertainty principle
Primordial fluctuations, density variations in the early universe
Universal conductance fluctuations, a quantum physics phenomenon encountered in electrical transport experiments in mesoscopic species
Finance and economics
Economic conjuncture, a critical combination of events in economics
Volatility (finance), price fluctuation |
https://en.wikipedia.org/wiki/Dixon%27s%20identity | In mathematics, Dixon's identity (or Dixon's theorem or Dixon's formula) is any of several different but closely related identities proved by A. C. Dixon, some involving finite sums of products of three binomial coefficients, and some evaluating a hypergeometric sum. These identities famously follow from the MacMahon Master theorem, and can now be routinely proved by computer algorithms .
Statements
The original identity, from , is
A generalization, also sometimes called Dixon's identity, is
where a, b, and c are non-negative integers .
The sum on the left can be written as the terminating well-poised hypergeometric series
and the identity follows as a limiting case (as a tends to an integer) of
Dixon's theorem evaluating a well-poised 3F2 generalized hypergeometric series at 1, from :
This holds for Re(1 + a − b − c) > 0. As c tends to −∞ it reduces to Kummer's formula for the hypergeometric function 2F1 at −1. Dixon's theorem can be deduced from the evaluation of the Selberg integral.
q-analogues
A q-analogue of Dixon's formula for the basic hypergeometric series in terms of the q-Pochhammer symbol is given by
where |qa1/2/bc| < 1.
References
Enumerative combinatorics
Factorial and binomial topics
Hypergeometric functions
Mathematical identities |
https://en.wikipedia.org/wiki/Bulnes%2C%20Chile | Bulnes is a Chilean city and commune in Diguillín Province, Ñuble Region.
Demographics
According to the 2002 census of the National Statistics Institute, Bulnes spans an area of and has 20,595 inhabitants (10,275 men and 10,320 women). Of these, 12,514 (60.8%) lived in urban areas and 8,081 (39.2%) in rural areas. Between the 1992 and 2002 censuses, the population grew by 4.5% (882 persons).
Administration
As a commune, Bulnes is a third-level administrative division of Chile administered by a municipal council, headed by an alcalde who is directly elected every four years. The 2008-2012 alcalde is Rodrigo De La Puente Acuña (ILE). The municipal council has the following members:
Ricardo Rodriguez Penrros (RN)
Alejandro Valle Elgueta (ILC)
Juan Arévalo Rojas (RN)
Max Pacheco Palma (UDI)
Oscar Troncoso Stuardo (PS)
Mario Urra Riquelme (PDC)
Within the electoral divisions of Chile, Bulnes is represented in the Chamber of Deputies by Jorge Sabag (PDC) and Frank Sauerbaum (RN) as part of the 42nd electoral district, together with San Fabián, Ñiquén, San Carlos, San Nicolás, Ninhue, Quirihue, Cobquecura, Treguaco, Portezuelo, Coelemu, Ránquil, Quillón, Cabrero and Yumbel. The commune is represented in the Senate by Alejandro Navarro Brain (MAS) and Hosain Sabag Castillo (PDC) as part of the 12th senatorial constituency (Biobío-Cordillera).
References
External links
Municipality of Bulnes
Communes of Chile
Populated places in Diguillín Province |
https://en.wikipedia.org/wiki/Ninhue | Ninhue () is a Chilean commune and town in the Itata Province, Ñuble Region.
Demographics
According to the 2002 census of the National Statistics Institute, Ninhue spans an area of and has 5,738 inhabitants (2,920 men and 2,818 women). Of these, 1,433 (25%) lived in urban areas and 4,305 (75%) in rural areas. The population fell by 10.6% (679 persons) between the 1992 and 2002 censuses.
Administration
As a commune, Ninhue is a third-level administrative division of Chile administered by a municipal council, headed by an alcalde who is directly elected every four years. The 2008-2012 alcalde is Luis Molina Melo (PDC).
Within the electoral divisions of Chile, Ninhue is represented in the Chamber of Deputies by Jorge Sabag (PDC) and Frank Sauerbaum (RN) as part of the 42nd electoral district, together with San Fabián, Ñiquén, San Carlos, San Nicolás, Quirihue, Cobquecura, Treguaco, Portezuelo, Coelemu, Ránquil, Quillón, Bulnes, Cabrero and Yumbel. The commune is represented in the Senate by Alejandro Navarro Brain (MAS) and Hosain Sabag Castillo (PDC) as part of the 12th senatorial constituency (Biobío-Cordillera).
References
External links
Comuna de Ninhue
Communes of Chile
Populated places in Itata Province |
https://en.wikipedia.org/wiki/Dual%20polygon | In geometry, polygons are associated into pairs called duals, where the vertices of one correspond to the edges of the other.
Properties
Regular polygons are self-dual.
The dual of an isogonal (vertex-transitive) polygon is an isotoxal (edge-transitive) polygon. For example, the (isogonal) rectangle and (isotoxal) rhombus are duals.
In a cyclic polygon, longer sides correspond to larger exterior angles in the dual (a tangential polygon), and shorter sides to smaller angles. Further, congruent sides in the original polygon yields congruent angles in the dual, and conversely. For example, the dual of a highly acute isosceles triangle is an obtuse isosceles triangle.
In the Dorman Luke construction, each face of a dual polyhedron is the dual polygon of the corresponding vertex figure.
Duality in quadrilaterals
As an example of the side-angle duality of polygons we compare properties of the cyclic and tangential quadrilaterals.
This duality is perhaps even more clear when comparing an isosceles trapezoid to a kite.
Kinds of duality
Rectification
The simplest qualitative construction of a dual polygon is a rectification operation, where the edges of a polygon are truncated down to vertices at the center of each original edge. New edges are formed between these new vertices.
This construction is not reversible. That is, the polygon generated by applying it twice is in general not similar to the original polygon.
Polar reciprocation
As with dual polyhedra, one can take a circle (be it the inscribed circle, circumscribed circle, or if both exist, their midcircle) and perform polar reciprocation in it.
Projective duality
Under projective duality, the dual of a point is a line, and of a line is a point – thus the dual of a polygon is a polygon, with edges of the original corresponding to vertices of the dual and conversely.
From the point of view of the dual curve, where to each point on a curve one associates the point dual to its tangent line at that point, the projective dual can be interpreted thus:
every point on a side of a polygon has the same tangent line, which agrees with the side itself – they thus all map to the same vertex in the dual polygon
at a vertex, the "tangent lines" to that vertex are all lines through that point with angle between the two edges – the dual points to these lines are then the edge in the dual polygon.
Combinatorially
Combinatorially, one can define a polygon as a set of vertices, a set of edges, and an incidence relation (which vertices and edges touch): two adjacent vertices determine an edge, and dually, two adjacent edges determine a vertex. Then the dual polygon is obtained by simply switching the vertices and edges.
Thus for the triangle with vertices {A, B, C} and edges {AB, BC, CA}, the dual triangle has vertices {AB, BC, CA}, and edges {B, C, A}, where B connects AB & BC, and so forth.
This is not a particularly fruitful avenue, as combinatorially, there is a single family of polygons (giv |
https://en.wikipedia.org/wiki/Juul%20Bjerke | Juul Bjerke (14 April 192828 February 2014) was a Norwegian economist.
He was born in Hof, Vestfold. He took the cand.oecon degree and was hired in Statistics Norway in 1950. He served as State Secretary in the Ministry of Finance from 1971 to 1972, in Bratteli's First Cabinet. He was later a head of department in Statistics Norway from 1973 to 1983, then led the Economy Department at the Norwegian Confederation of Trade Unions from 1983 to 1993. He was also a member of the board of directors of the Bank of Norway from 1978 to 1993.
He is the father of Siri and Rune Bjerke, and father-in-law of Libe Rieber-Mohn. He died in February 2014 in Motril, Spain.
References
1928 births
2014 deaths
Norwegian civil servants
Norwegian state secretaries
Labour Party (Norway) politicians
Norwegian trade unionists
20th-century Norwegian economists
People from Hof, Vestfold |
https://en.wikipedia.org/wiki/Artouz | Artouz (, [ʕar'tˤuːz]; Syriac: ܥܰܪܛܽܘܙ; Hebrew: עַרטוּז) is a town situated to the southwest of Damascus, Syria. According to the Syria Central Bureau of Statistics, the town had a population of 16,199 in the 2004 census.
Etymology
The name of the town is of uncertain etymology.
The prevalent presumption traces the meaning of ʻArṭūz back to Syriac (ܥܰܪܛܽܘܙ), loosely translating into being aside or the one out of the way, which is a reference to the town's original, secluded location on a nearby mountain away from the usual routes back then. Furthermore, the two, Arabic quadriliteral roots of ʻ-r-ṭ-z and ʻ-r-ṭ-s both mean to evade, which supports the presumption that the town was named after its remote position.
A less popular translation assumes that ʻArṭūz means the scent of apple, and that the nearby mountain it was once situated on was called the mountain of apples.
History
Evidence of the town's history is scarce. Throughout time, the region that cradles modern-day Artouz has been under the rule of a plethora of peoples, e.g., ancient Middle Eastern civilisations, the Neo-Assyrian Empire, the Byzantine Empire, the Umayyad Caliphate, the Abbasid Caliphate, the Mamluk Sultanate, the Ottoman Empire, and more.
There are historical references to a town in approximately the same location as Artouz during the Neo-Assyrian Empire.
A system of canals constructed at the time of the Roman reign is still in use to this day to irrigate the fields in the northwestern part of Artouz.
Artouz is believed to be the location of the New Testament event known as the Conversion of Saint Paul the Apostle. On his road to Damascus in pursuit of persecuting early Christians, Saul (later christened Paul) was interrupted by the ascended Jesus in the whereabouts of today's Artouz, a place called Tal Kokab (Levantine Arabic: تَل كوكَب, /'tal koː'kab/). The location where Jesus Christ appeared is now commemorated by an abbey named the Vision of Saint Paul the Apostle Patriarchal Monastery, which was visited by Pope John Paul II during his pilgrimage to Syria in May, 2001.
Originally, and during the Ottoman Empire's rule, Artouz was located on a nearby mountain 2000 metres to the northwest of its present place. However, the destructive Near East earthquakes of 1759 reduced the little town to ruins. The inhabitants who survived and chose not to migrate elsewhere became displaced, and later descended from the mountains and occupied the region that is known today as Artouz. The region was an ideal choice because the people depended on water for their agriculture, and the Awaj river ran there after the earthquakes had altered its course.
In 1838, Eli Smith noted Artouz as a predominantly Sunni Muslim village.
Artouz al-Kharaab (Levantine Arabic: عَرْطُوْز الخَرَاب, romanized: ʻArṭūz al-ḵarāb, /ʕar'tˤuːz elxa'raːb/) is a term used by the present inhabitants to refer to the remaining shambles of the old Artouz that used to exist on the nearby mountain. It means Artouz |
https://en.wikipedia.org/wiki/Small%20cancellation%20theory | In the mathematical subject of group theory, small cancellation theory studies groups given by group presentations satisfying small cancellation conditions, that is where defining relations have "small overlaps" with each other. Small cancellation conditions imply algebraic, geometric and algorithmic properties of the group. Finitely presented groups satisfying sufficiently strong small cancellation conditions are word hyperbolic and have word problem solvable by Dehn's algorithm. Small cancellation methods are also used for constructing Tarski monsters, and for solutions of Burnside's problem.
History
Some ideas underlying the small cancellation theory go back to the work of Max Dehn in the 1910s. Dehn proved that fundamental groups of closed orientable surfaces of genus at least two have word problem solvable by what is now called Dehn's algorithm. His proof involved drawing the Cayley graph of such a group in the hyperbolic plane and performing curvature estimates via the Gauss–Bonnet theorem for a closed loop in the Cayley graph to conclude that such a loop must contain a large portion (more than a half) of a defining relation.
A 1949 paper of Tartakovskii was an immediate precursor for small cancellation theory: this paper provided a solution of the word problem for a class of groups satisfying a complicated set of combinatorial conditions, where small cancellation type assumptions played a key role. The standard version of small cancellation theory, as it is used today, was developed by Martin Greendlinger in a series of papers in the early 1960s, who primarily dealt with the "metric" small cancellation conditions. In particular, Greendlinger proved that finitely presented groups satisfying the C′(1/6) small cancellation condition have word problem solvable by Dehn's algorithm. The theory was further refined and formalized in the subsequent work of Lyndon, Schupp and Lyndon-Schupp, who also treated the case of non-metric small cancellation conditions and developed a version of small cancellation theory for amalgamated free products and HNN-extensions.
Small cancellation theory was further generalized by Alexander Ol'shanskii who developed a "graded" version of the theory where the set of defining relations comes equipped with a filtration and where a defining relator of a particular grade is allowed to have a large overlap with a defining relator of a higher grade. Olshaskii used graded small cancellation theory to construct various "monster" groups, including the Tarski monster and also to give a new proof that free Burnside groups of large odd exponent are infinite (this result was originally proved by Adian and Novikov in 1968 using more combinatorial methods).
Small cancellation theory supplied a basic set of examples and ideas for the theory of word-hyperbolic groups that was put forward by Gromov in a seminal 1987 monograph "Hyperbolic groups".
Main definitions
The exposition below largely follows Ch. V of the book of Lyndon an |
https://en.wikipedia.org/wiki/Dyson%20conjecture | In mathematics, the Dyson conjecture is a conjecture about the constant term of certain Laurent polynomials, proved independently in 1962 by Wilson and Gunson. Andrews generalized it to the q-Dyson conjecture, proved by Zeilberger and Bressoud and sometimes called the Zeilberger–Bressoud theorem. Macdonald generalized it further to more general root systems with the Macdonald constant term conjecture, proved by Cherednik.
Dyson conjecture
The Dyson conjecture states that the Laurent polynomial
has constant term
The conjecture was first proved independently by and . later found a short proof, by observing that the Laurent polynomials, and therefore their constant terms, satisfy the recursion relations
The case n = 3 of Dyson's conjecture follows from the Dixon identity.
and used a computer to find expressions for non-constant coefficients of
Dyson's Laurent polynomial.
Dyson integral
When all the values ai are equal to β/2, the constant term in Dyson's conjecture is the value of Dyson's integral
Dyson's integral is a special case of Selberg's integral after a change of variable and has value
which gives another proof of Dyson's conjecture in this special case.
q-Dyson conjecture
found a q-analog of Dyson's conjecture, stating that the constant term of
is
Here (a;q)n is the q-Pochhammer symbol.
This conjecture reduces to Dyson's conjecture for q=1, and was proved by , using a combinatorial approach inspired by
previous work of Ira Gessel and Dominique Foata. A shorter proof, using formal Laurent series, was given in 2004 by Ira Gessel and Guoce Xin, and
an even shorter proof, using a quantitative form, due to Karasev and Petrov, and independently to Lason, of Noga Alon's Combinatorial Nullstellensatz,
was given in 2012 by Gyula Karolyi and Zoltan Lorant Nagy.
The latter method was extended, in 2013, by Shalosh B. Ekhad and Doron Zeilberger to derive explicit expressions of any specific coefficient, not just the
constant term, see http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/qdyson.html, for detailed references.
Macdonald conjectures
extended the conjecture to arbitrary finite or affine root systems, with Dyson's original conjecture corresponding to
the case of the An−1 root system and Andrews's conjecture corresponding to the affine An−1 root system. Macdonald reformulated these conjectures as conjectures about the norms of Macdonald polynomials. Macdonald's conjectures were proved by using doubly affine Hecke algebras.
Macdonald's form of Dyson's conjecture for root systems of type BC is closely related to Selberg's integral.
References
Enumerative combinatorics
Algebraic combinatorics
Factorial and binomial topics
Mathematical identities
Freeman Dyson
Conjectures that have been proved |
https://en.wikipedia.org/wiki/Parseval%E2%80%93Gutzmer%20formula | In mathematics, the Parseval–Gutzmer formula states that, if is an analytic function on a closed disk of radius r with Taylor series
then for z = reiθ on the boundary of the disk,
which may also be written as
Proof
The Cauchy Integral Formula for coefficients states that for the above conditions:
where γ is defined to be the circular path around origin of radius r. Also for we have: Applying both of these facts to the problem starting with the second fact:
Further Applications
Using this formula, it is possible to show that
where
This is done by using the integral
References
Theorems in complex analysis |
https://en.wikipedia.org/wiki/Journal%20of%20Official%20Statistics | The Journal of Official Statistics is a peer-reviewed scientific journal that publishes papers related to official statistics. It is published by Statistics Sweden, the national statistical office of Sweden. The journal was established in 1985, when it replaced the Swedish language journal Statistisk Tidskrift (Statistical Review). It publishes four issues each year.
Abstracting and indexing
Journal of Official Statistics is indexed in the Current Index to Statistics.
References
External links
, 2013–present.
Archive, 1985–2012.
Academic journals established in 1985
Statistics journals
Quarterly journals
English-language journals
Official statistics
Open access journals |
https://en.wikipedia.org/wiki/J%C3%A1nos%20Pach | János Pach (born May 3, 1954) is a mathematician and computer scientist working in the fields of combinatorics and discrete and computational geometry.
Biography
Pach was born and grew up in Hungary. He comes from a noted academic family: his father, (1919–2001) was a well-known historian, and his mother Klára (née Sós, 1925–2020) was a university mathematics teacher; his maternal aunt Vera T. Sós and her husband Pál Turán are two of the best-known Hungarian mathematicians.
Pach received his Candidate degree from the Hungarian Academy of Sciences, in 1983, where his advisor was Miklós Simonovits.
Since 1977, he has been affiliated with the Alfréd Rényi Institute of Mathematics of the Hungarian Academy of Sciences.
He was Research Professor at the Courant Institute of Mathematical Sciences at NYU (since 1986), Distinguished Professor of Computer Science at City College, CUNY (1992-2011), and Neilson Professor at Smith College (2008-2009).
Between 2008 and 2019, he was Professor of the Chair of Combinatorial Geometry at École Polytechnique Fédérale de Lausanne.
He was the program chair for the International Symposium on Graph Drawing in 2004 and
Symposium on Computational Geometry in 2015. He is co-editor-in-chief of the journal Discrete and Computational Geometry, and he serves on the editorial boards of several other journals including Combinatorica, SIAM Journal on Discrete Mathematics, Computational Geometry, Graphs and Combinatorics, Central European Journal of Mathematics, and Moscow Journal of Combinatorics and Number Theory.
He was an invited speaker at the Combinatorics session of the International Congress of Mathematicians, in Seoul, 2014.
He was a plenary speaker at the European Congress of Mathematics (Portorož), 2021.
Research
Pach has authored several books and over 300 research papers. He was one of the most frequent collaborators of Paul Erdős, authoring over 20 papers with him and thus has an Erdős number of one.
Pach's research is focused in the areas of combinatorics and discrete geometry.
In 1981, he solved Ulam's problem, showing that there exists
no universal planar graph.
In the early 90s
together with Micha Perles, he initiated the systematic study of extremal problems on topological and
geometric graphs.
Some of Pach's most-cited research work concerns the combinatorial complexity of families of curves in the plane and their applications to motion planning problems the maximum number of k-sets and halving lines that a planar point set may have, crossing numbers of graphs, embedding of planar graphs onto fixed sets of points, and lower bounds for epsilon-nets.
Awards and honors
Pach received the Grünwald Medal of the János Bolyai Mathematical Society (1982), the Ford Award from the Mathematical Association of America (1990), and the Alfréd Rényi Prize from the Hungarian Academy of Sciences (1992). He was an Erdős Lecturer at Hebrew University of Jerusalem in 2005.
In 2011 he was listed as a fellow of the Asso |
https://en.wikipedia.org/wiki/Aryeh%20Dvoretzky | Aryeh (Arie) Dvoretzky (, ; May 3, 1916 – May 8, 2008) was a Ukrainian-born Israeli mathematician, the winner of the 1973 Israel Prize in Mathematics. He is best known for his work in functional analysis, statistics and probability. He was the eighth president of the Weizmann Institute of Science.
Biography
Aryeh Dvoretzky was born in Khorol, Imperial Russia (now Ukraine). His family immigrated to Palestine in 1922. He graduated from the Hebrew Reali School in Haifa in 1933, and received his Ph.D. at the Hebrew University of Jerusalem in 1941. His advisor was Michael Fekete. He continued working in Jerusalem, becoming a full professor in 1951, the first graduate of the Hebrew University to achieve this distinction.
Dvoretzky's son Gideon was killed in the 1973 Yom Kippur War.
Academic career
Dvoretzky had visiting appointments at a number of universities, including Collège de France, Columbia University, Purdue University, Stanford University, and the University of California, Berkeley. He also visited twice the Institute for Advanced Study in Princeton (in 1948–1950 and in 1957–1958).
In 1975, he founded the Institute for Advanced Studies of Jerusalem based on the Princeton IAS model. Dvoretzky was the Dean of the Faculty of Sciences (1955–1956) and Vice President of the Hebrew University (1959–1961). He was elected president of the Israel Academy of Sciences and Humanities (1974–1980) and became the eighth president of the Weizmann Institute of Science (1986–1989). He was awarded an honorary doctorate from Tel Aviv University in 1996. Dvoretzky's students included Branko Grünbaum and Joram Lindenstrauss.
Business and civic career
In 1960, he became the head of Rafael, the weapons development authority. He later became the chief scientist for the Israel Ministry of Defense.
Awards and recognition
In 1998, received the Solomon Bublick Award of the Hebrew University of Jerusalem. In 1973, he was awarded Israel Prize in Mathematics.
References
External links
Webpage at the Weitzmann Institute
1966 interview in Moscow, Russia; Eugene Dynkin Collection of Mathematics Interviews, Cornell University Library.
20th-century Israeli mathematicians
Probability theorists
Israel Prize in exact science recipients who were mathematicians
Presidents of Weizmann Institute of Science
Academic staff of Weizmann Institute of Science
Academic staff of the Hebrew University of Jerusalem
Hebrew University of Jerusalem alumni
Members of the Israel Academy of Sciences and Humanities
Soviet emigrants to Mandatory Palestine
Ukrainian Jews
1916 births
2008 deaths
Presidents of the Israel Academy of Sciences and Humanities
Functional analysts
Solomon Bublick Award recipients
Presidents of universities in Israel
Burials at Har HaMenuchot |
https://en.wikipedia.org/wiki/Closed%20geodesic | In differential geometry and dynamical systems, a closed geodesic on a Riemannian manifold is a geodesic that returns to its starting point with the same tangent direction. It may be formalized as the projection of a closed orbit of the geodesic flow on the tangent space of the manifold.
Definition
In a Riemannian manifold (M,g), a closed geodesic is a curve that is a geodesic for the metric g and is periodic.
Closed geodesics can be characterized by means of a variational principle. Denoting by the space of smooth 1-periodic curves on M, closed geodesics of period 1 are precisely the critical points of the energy function , defined by
If is a closed geodesic of period p, the reparametrized curve is a closed geodesic of period 1, and therefore it is a critical point of E. If is a critical point of E, so are the reparametrized curves , for each , defined by . Thus every closed geodesic on M gives rise to an infinite sequence of critical points of the energy E.
Examples
On the unit sphere with the standard round Riemannian metric, every great circle is an example of a closed geodesic. Thus, on the sphere, all geodesics are closed. On a smooth surface topologically equivalent to the sphere, this may not be true, but there are always at least three simple closed geodesics; this is the theorem of the three geodesics. Manifolds all of whose geodesics are closed have been thoroughly investigated in the mathematical literature. On a compact hyperbolic surface, whose fundamental group has no torsion, closed geodesics are in one-to-one correspondence with non-trivial conjugacy classes of elements in the Fuchsian group of the surface.
See also
Lyusternik–Fet theorem
Theorem of the three geodesics
Curve-shortening flow
Selberg trace formula
Selberg zeta function
Zoll surface
References
Besse, A.: "Manifolds all of whose geodesics are closed", Ergebisse Grenzgeb. Math., no. 93, Springer, Berlin, 1978.
Differential geometry
Dynamical systems
Geodesic (mathematics) |
https://en.wikipedia.org/wiki/Method%20of%20dominant%20balance | In mathematics, the method of dominant balance is used to determine the asymptotic behavior of solutions to an ordinary differential equation without fully solving the equation. The process is iterative, in that the result obtained by performing the method once can be used as input when the method is repeated, to obtain as many terms in the asymptotic expansion as desired.
The process goes as follows:
Assume that the asymptotic behavior has the form
Make an informed guess as to which terms in the ODE might be negligible in the limit of interest.
Drop these terms and solve the resulting simpler ODE.
Check that the solution is consistent with step 2. If this is the case, then one has the controlling factor of the asymptotic behavior; otherwise, one needs try dropping different terms in step 2, instead.
Repeat the process to higher orders, relying on the above result as the leading term in the solution.
Example: solving polynomial equation
To solve the equation at the limit of small , we can consider performing a serial expansion of form . This however encounters the issue: when , the equation has just one root . However for nonzero the equation has 5 roots. The main issue is that 4 of these roots escape to infinity as .
This suggests the use of the dominant balance method. That is, for small , we should have , so we would approximately solve the equation as , giving . So plugging in , we obtain There are five roots , and expanding each root as a power series in , we obtain the five series:
Example
For arbitrary constants and , consider
This differential equation cannot be solved exactly. However, it is useful to consider how the solutions behave for large : it turns out that behaves like as x → ∞ .
More rigorously, we will have , not .
Since we are interested in the behavior of in the large limit, we change variables to = exp(S(x)), and re-express the ODE in terms of S(x),
or
where we have used the product rule and chain rule to evaluate the derivatives of .
Now suppose first that a solution to this ODE satisfies
as x → ∞, so that
as x → ∞. Obtain then the dominant asymptotic behaviour by setting
If satisfies the above asymptotic conditions, then the above assumption is consistent. The terms we dropped will have been negligible with respect to the ones we kept.
is not a solution to the ODE for , but it represents the dominant asymptotic behavior, which is what we are interested in. Check that this choice for is consistent,
Everything is indeed consistent.
Thus the dominant asymptotic behaviour of a solution to our ODE has been found,
By convention, the full asymptotic series is written as
so to get at least the first term of this series we have to take a further step to see if there is a power of out the front.
Proceed by introducing a new subleading dependent variable,
and then seek asymptotic solutions for C(x). Substituting into the above ODE for S(x) we find
Repeating the same process |
https://en.wikipedia.org/wiki/Canadian%20Journal%20of%20Mathematics | The Canadian Journal of Mathematics () is a bimonthly mathematics journal published by the Canadian Mathematical Society.
It was established in 1949 by H. S. M. Coxeter and G. de B. Robinson. The current editors-in-chief of the journal are Louigi Addario-Berry and Eyal Goren.
The journal publishes articles in all areas of mathematics.
See also
Canadian Mathematical Bulletin
References
External links
University of Toronto Press academic journals
Mathematics journals
Academic journals established in 1949
Bimonthly journals
Multilingual journals
Cambridge University Press academic journals
Academic journals associated with learned and professional societies of Canada |
https://en.wikipedia.org/wiki/Equilateral%20pentagon | In geometry, an equilateral pentagon is a polygon in the Euclidean plane with five sides of equal length. Its five vertex angles can take a range of sets of values, thus permitting it to form a family of pentagons. In contrast, the regular pentagon is unique, because it is equilateral and moreover it is equiangular (its five angles are equal; the measure is 108 degrees).
Four intersecting equal circles arranged in a closed chain are sufficient to determine a convex equilateral pentagon. Each circle's center is one of four vertices of the pentagon. The remaining vertex is determined by one of the intersection points of the first and the last circle of the chain.
Examples
Internal angles of a convex equilateral pentagon
When a convex equilateral pentagon is dissected into triangles, two of them appear as isosceles (triangles in orange and blue) while the other one is more general (triangle in green). We assume that we are given the adjacent angles and .
According to the law of sines the length of the line dividing the green and blue triangles is:
The square of the length of the line dividing the orange and green triangles is:
According to the law of cosines, the cosine of δ can be seen from the figure:
Simplifying, δ is obtained as function of α and β:
The remaining angles of the pentagon can be found geometrically: The remaining angles of the orange and blue triangles are readily found by noting that two angles of an isosceles triangle are equal while all three angles sum to 180°. Then and the two remaining angles of the green triangle can be found from four equations stating that the sum of the angles of the pentagon is 540°, the sum of the angles of the green triangle is 180°, the angle is the sum of its three components, and the angle is the sum of its two components.
A cyclic pentagon is equiangular if and only if it has equal sides and thus is regular. Likewise, a tangential pentagon is equilateral if and only if it has equal angles and thus is regular.
Tiling
There are two infinite families of equilateral convex pentagons that tile the plane, one having two adjacent supplementary angles and the other having two non-adjacent supplementary angles. Some of those pentagons can tile in more than one way, and there is one sporadic example of an equilateral pentagon that can tile the plane but does not belong to either of those two families; its angles are roughly 89°16', 144°32.5', 70°55', 135°22', and 99°54.5', no two supplementary.
A two-dimensional mapping
Equilateral pentagons can intersect themselves either not at all, once, twice, or five times. The ones that don't intersect themselves are called simple, and they can be classified as either convex or concave. We here use the term "stellated" to refer to the ones that intersect themselves either twice or five times. We rule out, in this section, the equilateral pentagons that intersect themselves precisely once.
Given that we rule out the pentagons that i |
https://en.wikipedia.org/wiki/Kharkov%20Mathematical%20Society | The Kharkov Mathematical Society (, ) is an association of professional mathematicians in Kharkiv aimed at advancement of mathematical research and education, popularizing achievements of mathematics. The structure of the Society includes mathematicians of Verkin Institute for Low Temperature Physics and Engineering, V. N. Karazin Kharkiv National University and other higher educational institutions of Kharkov.
History and members of the Kharkov Mathematical Society
Kharkov Mathematical Society was established in 1879 at Kharkov University by the initiative of
Vasilii Imshenetskii, who also later founded the St. Petersburg Mathematical Society.
According to the statute of the society, "the aim of the Kharkov Mathematical Society was to support the development of mathematical science and education".
From 1885 to 1902 in Kharkov lived and worked an outstanding Russian mathematician, Aleksandr Lyapunov: during this period, Lyapunov's activities played an important role in the development of the Society.
From 1902 to 1906, the Kharkov Mathematical Society was headed by Vladimir Steklov, the outstanding student of Aleksandr Lyapunov,
who later organized and became the first director of the Institute of Physics and Mathematics of the Russian Academy of Sciences in Moscow.
Since 1906 and for the next almost forty years the Society was headed by a well-known geometer Dmitrii Sintsov.
Due to his initiatives, the activities of the Society significantly contributed to the improvement of mathematical education in Kharkov.
In 1933 Naum Akhiezer had moved to Kharkov and headed the Institute of Mathematics.
From 1947 Akhiezer became the head of KMS.
Thanks to his efforts, the mathematical community of Kharkiv has significantly strengthened.
Later, the Society was headed by Aleksei Pogorelov, Vladimir Marchenko, Iossif Ostrovskii.
Currently, the president of the Society is Yeugen Kruslov.
At different times, members of society were
Konstantin Andreev,
Naum Akhiezer,
Yeugen von Beyer,
Sergei Bernstein,
Yakov Blank,
Alexander Borisenko,
Valentina Borok,
Dmitry Grave,
Israel Glazman,
Vladimir Drinfeld,
Gershon Drinfeld,
Alexandre Eremenko,
Emmanuil Zhmud,
Vladimir Kadets,
Mikhail Kadets,
Mark Krein,
Lev Landau,
Naum Landkof,
Boris Levin,
Boris Levitan,
Mikhail Livsic,
Yury Lyubich,
Aleksandr Lyapunov,
Vladimir Marchenko,
Anatoly Myshkis,
Iossif Ostrovskii,
Leonid Pastur,
Alexander Povzner,
Aleksei Pogorelov,
Dmitrii Sintsov,
Vladimir Steklov,
Anton Sushkevich,
Gennady Feldman,
Yeugen Kruslov,
Igor Chueshov,
Dmitry Shepelsky,
Maria Scherbina.
In 1990 Vladimir Drinfeld was awarded by Fields Medal.
Publishing activities of the Society
Almost immediately after the foundation, since 1880, the Society published the Communications of the Kharkov Mathematical Society
().
At first, there were two issues a year in size ranging from two to five printed sheets.
In 1960, the publications of the Communications of the Kharkov Mathematical Society were suspended.
L |
https://en.wikipedia.org/wiki/Pakistanis%20in%20the%20Netherlands | Dutch Pakistanis formed a population of 27,261 individuals (persons born in Pakistan or with at least one parent born there) according to the latest official statistics published by the Netherlands Centraal Bureau voor de Statistiek on 1 January 2022.
Notable people
Imran Khan - singer and musician
Kamal Raja - singer and musician
F1rstman - rapper and beatboxer
Rahil Ahmed - cricketer
Mudassar Bukhari - cricketer
Mohammad Kashif - cricketer
Asim Khan - cricketer
Adeel Raja - cricketer
Madiea Ghafoor - athlete and Olympian
See also
Netherlands–Pakistan relations
Pakistani Americans
Pakistani Canadians
Pakistanis in Ireland
Pakistanis in the United Kingdom
Pakistanis in France
Pakistanis in Belgium
Pakistanis in Germany
Pakistanis in Switzerland
Pakistanis in Italy
Pakistanis in Denmark
Pakistanis in Norway
Pakistanis in Sweden
Pakistani Australians
Pakistani New Zealanders
References
Further reading
Muslim communities in Europe
Netherlands |
https://en.wikipedia.org/wiki/The%20Whetstone%20of%20Witte | The Whetstone of Witte is the shortened title of Robert Recorde's mathematics book published in 1557, the full title being The whetstone of , is the : The Coßike practise, with the rule of Equation: and the of Surde Nombers. The book covers topics including whole numbers, the extraction of roots and irrational numbers. The work is notable for containing the first recorded use of the equals sign and also for being the first book in English to use the plus and minus signs.
Recordian notation for exponentiation, however, differed from the later Cartesian notation . Recorde expressed indices and surds larger than 3 in a systematic form based on the prime factorization of the exponent: a factor of two he termed a zenzic, and a factor of three, a cubic. Recorde termed the larger prime numbers appearing in this factorization sursolids, distinguishing between them by use of ordinal numbers: that is, he defined 5 as the first sursolid, written as ʃz and 7 as the second sursolid, written as Bʃz.
He also devised symbols for these factors: a zenzic was denoted by z, and a cubic by &. For instance, he referred to p8=p2×2×2 as zzz (the zenzizenzizenzic), and q12=q2×2×3 as zz& (the zenzizenzicubic).
Later in the book he includes a chart of exponents all the way up to p80=p2×2×2×2×5 written as zzzzʃz. There is an error in the chart, however, writing p69 as Sʃz, despite it not being a prime. It should be p3×23 or &Gʃz.
Page images have been made available by Victor Katz and Frank Swetz through Convergence, a publication of Mathematical Association of America.
References
External links
The Whetstone of Witte at The Internet Archive
Mathematics books
British non-fiction literature
1557 books
History of mathematics |
https://en.wikipedia.org/wiki/Mechanica | Mechanica (; 1736) is a two-volume work published by mathematician Leonhard Euler which describes analytically the mathematics governing movement.
Euler both developed the techniques of analysis and applied them to numerous problems in mechanics,
notably in later publications the calculus of variations. Euler's laws of motion expressed scientific laws of Galileo and Newton in terms of points in reference frames and coordinate systems making them useful for calculation when the statement of a problem or example is slightly changed from the original.
Newton–Euler equations express the dynamics of a rigid body. Euler has been credited with contributing to the rise of Newtonian mechanics especially in topics other than gravity.
References
External links
Mechanica Vol. 1 [E015] – Latin.
Mechanica Vol. 1 – English translation by Ian Bruce.
Mechanica Vol. 2 [E016] – Latin.
Mechanica Vol. 2 – English translation by Ian Bruce.
Mathematics books
18th-century Latin books |
https://en.wikipedia.org/wiki/Mahler%27s%20inequality | In mathematics, Mahler's inequality, named after Kurt Mahler, states that the geometric mean of the term-by-term sum of two finite sequences of positive numbers is greater than or equal to the sum of their two separate geometric means:
when xk, yk > 0 for all k.
Proof
By the inequality of arithmetic and geometric means, we have:
and
Hence,
Clearing denominators then gives the desired result.
See also
Minkowski inequality
References
Minkowski inequality in the Encyclopedia of Mathematics
Inequalities
Articles containing proofs |
https://en.wikipedia.org/wiki/List%20of%20fields%20of%20application%20of%20statistics | Statistics is the mathematical science involving the collection, analysis and interpretation of data. A number of specialties have evolved to apply statistical and methods to various disciplines. Certain topics have "statistical" in their name but relate to manipulations of probability distributions rather than to statistical analysis.
Actuarial science is the discipline that applies mathematical and statistical methods to assess risk in the insurance and finance industries.
Astrostatistics is the discipline that applies statistical analysis to the understanding of astronomical data.
Biostatistics is a branch of biology that studies biological phenomena and observations by means of statistical analysis, and includes medical statistics.
Business analytics is a rapidly developing business process that applies statistical methods to data sets (often very large) to develop new insights and understanding of business performance & opportunities
Chemometrics is the science of relating measurements made on a chemical system or process to the state of the system via application of mathematical or statistical methods.
Demography is the statistical study of all populations. It can be a very general science that can be applied to any kind of dynamic population, that is, one that changes over time or space.
Econometrics is a branch of economics that applies statistical methods to the empirical study of economic theories and relationships.
Environmental statistics is the application of statistical methods to environmental science. Weather, climate, air and water quality are included, as are studies of plant and animal populations.
Epidemiology is the study of factors affecting the health and illness of populations, and serves as the foundation and logic of interventions made in the interest of public health and preventive medicine.
Forensic statistics is the application of probability models and statistical techniques to scientific evidence, such as DNA evidence, and the law. In contrast to "everyday" statistics, to not engender bias or unduly draw conclusions, forensic statisticians report likelihoods as likelihood ratios (LR).
Spatial statistics is a branch of applied statistics that deals with the analysis of spatial data
Geostatistics is a branch of geography that deals with the analysis of data from disciplines such as petroleum geology, hydrogeology, hydrology, meteorology, oceanography, geochemistry, geography.
Jurimetrics is the application of probability and statistics to law.
Machine learning is the subfield of computer science that formulates algorithms in order to make predictions from data.
Operations research (or operational research) is an interdisciplinary branch of applied mathematics and formal science that uses methods such as mathematical modeling, statistics, and algorithms to arrive at optimal or near optimal solutions to complex problems; Management science focuses on problems in the business world.
Population ecology is a sub-field of |
https://en.wikipedia.org/wiki/Surface%20map | In mathematics, geology, and cartography, a surface map is a 2D perspective representation of a 3-dimensional surface.
Surface maps usually represent real-world entities such as landforms or the surfaces of objects. They can, however, serve as an abstraction where the third, or even all of the dimensions correspond to non-spatial data. In this capacity they act more as graphs than maps.
Maps |
https://en.wikipedia.org/wiki/Systolic%20freedom | In differential geometry, systolic freedom refers to the fact that closed Riemannian manifolds may have arbitrarily small volume regardless of their systolic invariants.
That is, systolic invariants or products of systolic invariants do not in general provide universal (i.e. curvature-free) lower bounds for the total volume of a closed Riemannian manifold.
Systolic freedom was first detected by Mikhail Gromov in an I.H.É.S. preprint in 1992 (which eventually appeared as ), and was further developed by Mikhail Katz, Michael Freedman and others. Gromov's observation was elaborated on by . One of the first publications to study systolic freedom in detail is by .
Systolic freedom has applications in quantum error correction. survey the main results on systolic freedom.
Example
The complex projective plane admits Riemannian metrics of arbitrarily small volume, such that every essential surface is of area at least 1. Here a surface is called "essential" if it cannot be contracted to a point in the ambient 4-manifold.
Systolic constraint
The opposite of systolic freedom is systolic constraint, characterized by the presence of systolic inequalities such as Gromov's systolic inequality for essential manifolds.
References
. Astérisque 216, Exp. No. 771, 5, 279–310.
.
.
.
.
.
.
Differential geometry
Riemannian geometry
Systolic geometry |
https://en.wikipedia.org/wiki/Marriage%20theorem | In mathematics, the marriage theorem may refer to:
Hall's marriage theorem giving necessary and sufficient conditions for the existence of a system of distinct representatives for a set system, or for a perfect matching in a bipartite graph
The stable marriage theorem, stating that every stable marriage problem has a solution |
https://en.wikipedia.org/wiki/Covering%20number | In mathematics, a covering number is the number of spherical balls of a given size needed to completely cover a given space, with possible overlaps. Two related concepts are the packing number, the number of disjoint balls that fit in a space, and the metric entropy, the number of points that fit in a space when constrained to lie at some fixed minimum distance apart.
Definition
Let (M, d) be a metric space, let K be a subset of M, and let r be a positive real number. Let Br(x) denote the ball of radius r centered at x. A subset C of M is an r-external covering of K if:
.
In other words, for every there exists such that .
If furthermore C is a subset of K, then it is an r-internal covering.
The external covering number of K, denoted , is the minimum cardinality of any external covering of K. The internal covering number, denoted , is the minimum cardinality of any internal covering.
A subset P of K is a packing if and the set is pairwise disjoint. The packing number of K, denoted , is the maximum cardinality of any packing of K.
A subset S of K is r-separated if each pair of points x and y in S satisfies d(x, y) ≥ r. The metric entropy of K, denoted , is the maximum cardinality of any r-separated subset of K.
Examples
Properties
The following properties relate to covering numbers in the standard Euclidean space, :
Application to machine learning
Let be a space of real-valued functions, with the l-infinity metric (see example 3 above).
Suppose all functions in are bounded by a real constant .
Then, the covering number can be used to bound the generalization error
of learning functions from ,
relative to the squared loss:
where and is the number of samples.
See also
Polygon covering
Kissing number
References
Topology
Metric geometry |
https://en.wikipedia.org/wiki/San%20Nicol%C3%A1s%2C%20Chile | San Nicolás is a Chilean town and commune in Punilla Province, Ñuble Region.
Demographics
According to the 2002 census of the National Statistics Institute, San Nicolás spans an area of and has 9,741 inhabitants (5,032 men and 4,709 women). Of these, 3,428 (35.2%) lived in urban areas and 6,313 (64.8%) in rural areas. Between the 1992 and 2002 censuses, the population grew by 2.6% (246 persons).
Administration
As a commune, San Nicolás is a third-level administrative division of Chile administered by a municipal council, headed by an alcalde who is directly elected every four years. The 2008-2012 alcalde is Víctor Ramón Toro Leiva (PDC).The municipal council has the following members:
Feliciano Arnoldo Parra Pérez (PDC)
Elena Rivas Toro (PRI)
Rogelio Hernandez Gonzalez (PS)
Luis Antonio Guzmán Álvarez (RN)
Ramón Toro Leiva (PDC)
Manuel Bello Núñez (PPD)
Within the electoral divisions of Chile, San Nicolás is represented in the Chamber of Deputies by Jorge Sabag (PDC) and Frank Sauerbaum (RN) as part of the 42nd electoral district, together with San Fabián, Ñiquén, San Carlos, Ninhue, Quirihue, Cobquecura, Treguaco, Portezuelo, Coelemu, Ránquil, Quillón, Bulnes, Cabrero and Yumbel. The commune is represented in the Senate by Alejandro Navarro Brain (MAS) and Hosain Sabag Castillo (PDC) as part of the 12th senatorial constituency (Biobío-Cordillera).
External links
Municipality of San Nicolás
References
Communes of Chile
Populated places in Punilla Province |
https://en.wikipedia.org/wiki/Elliptic%20hypergeometric%20series | In mathematics, an elliptic hypergeometric series is a series Σcn such that the ratio
cn/cn−1 is an elliptic function of n, analogous to generalized hypergeometric series where the ratio is a rational function of n, and basic hypergeometric series where the ratio is a periodic function of the complex number n. They were introduced by Date-Jimbo-Kuniba-Miwa-Okado (1987) and in their study of elliptic 6-j symbols.
For surveys of elliptic hypergeometric series see , or .
Definitions
The q-Pochhammer symbol is defined by
The modified Jacobi theta function with argument x and nome p is defined by
The elliptic shifted factorial is defined by
The theta hypergeometric series r+1Er is defined by
The very well poised theta hypergeometric series r+1Vr is defined by
The bilateral theta hypergeometric series rGr is defined by
Definitions of additive elliptic hypergeometric series
The elliptic numbers are defined by
where the Jacobi theta function is defined by
The additive elliptic shifted factorials are defined by
The additive theta hypergeometric series r+1er is defined by
The additive very well poised theta hypergeometric series r+1vr is defined by
Further reading
References
Hypergeometric functions |
https://en.wikipedia.org/wiki/Albert%20Baldwin%20Dod | Albert Baldwin Dod (March 24, 1805 – November 20, 1845) was an American Presbyterian theologian and professor of mathematics.
Early life
Dod was born on March 24, 1805, in Mendham, New Jersey. He was the son of Daniel Dod (1778–1823) and Nancy (née Squire) Dod (1780–1851). His mother was the sister of Dr. Ezra Squire, of Caldwell, New Jersey.
Career
After a religious awakening while at college in Princeton, where he graduated with the class of 1822, Dod became affiliated with the influential Princeton Theologians. He published frequently in the group's chief outlet, the Biblical Repertory and Princeton Review, edited by Charles Hodge. Among his publications there, an attack on Transcendentalism (perhaps written with James Waddel Alexander; published in the January 1839 issue) attracted wide notice and was later republished by Andrews Norton.
For much of his life he taught mathematics at the college, and participated in theological discussion and preaching at the Seminary, in Princeton. The Doctorate in Divinity, though, was conferred on him by the University of North Carolina and by New York University.
Personal life
Dod married Caroline Smith Bayard (1807–1891), the daughter of Samuel Bayard (1766-1840) and granddaughter of Continental Congressman John Bubenheim Bayard (1738-1808), all descendants of Peter Stuyvesant. Together, Albert and Caroline had eight children:
Martha Bayard Dod (1831–1899), who married Edwin Augustus Stevens (1795–1868), founder of Stevens Institute of Technology.
Caroline Bayard Dod (1832–1859), who married Richard Stockton (1824–1876), son of Robert F. Stockton and grandson of Richard Stockton, both U.S. senators.
Albert Baldwin Dod (1835–1880), a Captain during the U.S. Civil War who married Elizabeth A. Mcintosh on June 16, 1858.
Julia Washington Dod (1836–1837), who died young.
Samuel Bayard Dod (1837–1907), who married Isabella Williamson Green (1840–1883), the granddaughter of Ashbel Green, 8th President of Princeton University.
Susan Bratford Dod (1840–1912), who married her brother-in-law Richard Stockton after her sister's death in 1859.
Charles Hodge Dod (1841–1864), a Captain on the staff of Maj. General Winfield Scott Hancock during the civil war who died in service.
Mary Dod (b. 1843).
The 1840 US census records Dod as owning one female slave aged ten to twenty-four. This is the latest known instance of a Princeton professor owning slaves; Dod was also one of the last slaveholders in the community of Princeton as well as New Jersey overall. The state adopted a system of gradual emancipation in 1804, meaning that the woman in Dod's household was born to an enslaved mother between 1816 and 1830, and that she would be manumitted when she came of age.
Dod died of pleurisy after a brief illness on November 20, 1845.
Legacy
In 1869, his son Samuel Bayard Dod (Princeton Class of 1857) established an Endowed Professorship at Princeton University in mathematics in memory of him. In 1926, his grea |
https://en.wikipedia.org/wiki/Ross%20Ihaka | George Ross Ihaka (born 1954) is a New Zealand statistician who was an associate professor of statistics at the University of Auckland until his retirement in 2017. Alongside Robert Gentleman, he is one of the creators of the R programming language. In 2008, Ihaka received the Pickering Medal, awarded by the Royal Society of New Zealand, for his work on R.
Education
Ihaka completed his undergraduate education at the University of Auckland, and obtained his PhD in 1985 from the University of California, Berkeley supervised by David R. Brillinger. His thesis was on statistical modelling for seismic interferometry and was titled Rūaumoko, after the god of earthquakes, volcanoes and seasons in Māori mythology.
Career and research
As of 2010, he was working on a new statistical programming language based on Lisp. The Department of Statistics at the University of Auckland started a public lecture series in his honour in 2017.
Personal life
Ihaka is of Ngāti Kahungunu, Rangitāne and Ngati Pākehā (New Zealand European) descent.
References
Living people
New Zealand statisticians
Academic staff of the University of Auckland
University of California, Berkeley alumni
R (programming language) people
New Zealand Māori academics
Ngāti Kahungunu people
Māori and Pacific Island scientists
1954 births |
https://en.wikipedia.org/wiki/Value%20system%20%28disambiguation%29 | Value system may refer to:
Value system - social scientific concept - meaning the set of cultural and moral values a person or a group has.
'Value system' in mathematics, which means a set of interrelated values.
'Value system' an extension of the value chain concept. |
https://en.wikipedia.org/wiki/H.%20Blaine%20Lawson | Herbert Blaine Lawson, Jr. is a mathematician best known for his work in minimal surfaces, calibrated geometry, and algebraic cycles. He is currently a Distinguished Professor of Mathematics at Stony Brook University. He received his PhD from Stanford University in 1969 for work carried out under the supervision of Robert Osserman.
Research
Minimal surfaces
Lawson found in 1970 a method to solve free boundary value problems for unstable Euclidean constant-mean-curvature surfaces by solving a corresponding Plateau problem for minimal surfaces in S3. He constructed compact minimal surfaces in the 3-sphere of arbitrary genus by applying Charles B. Morrey, Jr.'s solution of the Plateau problem in general manifolds. This work of Lawson contains a rich set of ideas, among them the conjugate surface construction for minimal and constant mean curvature surfaces.
Calibrated geometry
The theory of calibrations, whose roots are in the work of Marcel Berger, finds its genesis in a 1982 Acta Mathematica paper of
Reese Harvey and Blaine Lawson. The theory of calibrations has grown to be important because of its many applications to gauge theory and mirror symmetry.
Algebraic cycles
In his 1989 Annals of Mathematics paper "Algebraic Cycles and Homotopy Theory", Lawson proved a theorem which is now called the Lawson suspension theorem. This theorem is the cornerstone of Lawson homology and morphic cohomology which are defined by taking the homotopy groups of algebraic cycle spaces of complex varieties.
These two theories are dual to each other for smooth varieties and have properties similar to those of Chow groups.
Awards and honors
He was a 1973 recipient of the American Mathematical Society's Leroy P. Steele Prize, and was elected to the National Academy of Sciences in 1995. He is a former recipient of both the Sloan Fellowship and the Guggenheim Fellowship, and has delivered two invited addresses at International Congresses of Mathematicians, one on geometry, and one on topology. He has served as Vice President of the American Mathematical Society, and is a foreign member of the Brazilian Academy of Sciences.
In 2012 he became a fellow of the American Mathematical Society. He was elected to the American Academy of Arts and Sciences in 2013.
Major publications
Books
See also
Spin geometry
References
External links
Homepage
20th-century American mathematicians
21st-century American mathematicians
Differential geometers
Stanford University alumni
Stony Brook University faculty
Living people
Members of the United States National Academy of Sciences
Fellows of the American Mathematical Society
Fellows of the American Academy of Arts and Sciences
1942 births
Mathematicians from Pennsylvania |
https://en.wikipedia.org/wiki/List%20of%20statistics%20journals | This is a list of scientific journals published in the field of statistics.
Introductory and outreach
The American Statistician
Significance
General theory and methodology
Annals of the Institute of Statistical Mathematics
Annals of Statistics
AStA Wirtschafts- und Sozialstatistisches Archiv
Biometrika
The Canadian Journal of Statistics
Communications in Statistics
International Statistical Review
Journal of the American Statistical Association
Journal of Multivariate Analysis
Journal of the Royal Statistical Society
Probability and Mathematical Statistics
Sankhyā: The Indian Journal of Statistics
Scandinavian Journal of Statistics
Statistica Sinica
Statistical Science
Stochastic Processes and their Applications
Applications
Annals of Applied Statistics
Journal of Applied Statistics
Journal of the Royal Statistical Society, Series C: Applied Statistics
Journal of Statistical Software
Statistical Modelling
Statistics and its Interface
The R Journal
The Stata Journal
The Journal of Risk Model Validation
Statistics education
Journal of Statistics Education
Specialized journals in various areas of statistics
Biostatistics
Biometrical Journal
Biometrics
Biometrika
Biostatistics
The International Journal of Biostatistics
Pharmaceutical Statistics
Statistical Applications in Genetics and Molecular Biology
Statistical Methods in Medical Research
Statistics in Medicine (journal)
Computational statistics
Communications in Statistics - Simulation and Computation
Computational Statistics
Computational Statistics & Data Analysis
Journal of Computational and Graphical Statistics
Journal of Statistical Computation and Simulation
Statistics and Computing
Econometrics
Applied Econometrics and International Development
Econometric Reviews
Econometric Theory
Econometrica
Journal of Applied Econometrics
Journal of Business & Economic Statistics
Journal of Econometrics
The Review of Economics and Statistics
Environmental and ecological sciences
Atmospheric Environment
Journal of Agricultural, Biological, and Environmental Statistics
Physical sciences, technology, and quality
Chemometrics and Intelligent Laboratory Systems
Journal of Chemometrics
Journal of Statistical Mechanics: Theory and Experiment
Journal of Statistical Physics
Physica A: Statistical mechanics and its applications
Technometrics
Social sciences
British Journal of Mathematical and Statistical Psychology
Journal of Educational and Behavioral Statistics
Journal of the Royal Statistical Society, Series A: Statistics in Society
Multivariate Behavioral Research
Psychological Methods
Psychometrika
Structural Equation Modeling
Time-series analysis
International Journal of Forecasting
Journal of Time Series Analysis
Open access statistics journals
The following journals are considered open access:
Bayesian Analysis
Brazilian Journal of Probability and Statistics
Chilean Journal of Statistics
Electronic Journal of Statistics
Journal of Official Statistics
Journal of Modern App |
https://en.wikipedia.org/wiki/El%20Carmen%2C%20Chile | El Carmen is a Chilean commune and town in Diguillín Province, Ñuble Region.
Demographics
According to the 2002 census of the National Statistics Institute, El Carmen spans an area of and has 12,845 inhabitants (6,567 men and 6,278 women). Of these, 4,426 (34.5%) lived in urban areas and 8,419 (65.5%) in rural areas. The population fell by 9.3% (1316 persons) between the 1992 and 2002 censuses.
Administration
As a commune, El Carmen is a third-level administrative division of Chile administered by a municipal council, headed by an alcalde who is directly elected every four years. The 2008-2012 alcalde is Juan Diaz González (Ind.).
Within the electoral divisions of Chile, El Carmen is represented in the Chamber of Deputies by Carlos Abel Jarpa (PRSD) and Rosauro Martínez (RN) as part of the 41st electoral district, together with Chillán, Coihueco, Pinto, San Ignacio, Pemuco, Yungay and Chillán Viejo. The commune is represented in the Senate by Victor Pérez Varela (UDI) and Mariano Ruiz-Esquide Jara (PDC) as part of the 13th senatorial constituency (Biobío-Coast).
References
External links
Municipality of El Carmen
Communes of Chile
Populated places in Diguillín Province |
https://en.wikipedia.org/wiki/Pemuco | Pemuco is a Chilean town and commune in Diguillín Province, Ñuble Region.
Demographics
According to the 2002 census of the National Statistics Institute, Pemuco spans an area of and has 8,821 inhabitants (4,578 men and 4,243 women). Of these, 3,844 (43.6%) lived in urban areas and 4,977 (56.4%) in rural areas. The population grew by 4.8% (408 persons) between the 1992 and 2002 censuses.
Administration
As a commune, Pemuco is a third-level administrative division of Chile administered by a municipal council, headed by an alcalde who is directly elected every four years. The 2008-2012 alcalde is Julio Muñoz Salazar (PDC).
Within the electoral divisions of Chile, Pemuco is represented in the Chamber of Deputies by Carlos Abel Jarpa (PRSD) and Rosauro Martínez (RN) as part of the 41st electoral district, together with Chillán, Coihueco, Pinto, San Ignacio, El Carmen, Yungay and Chillán Viejo. The commune is represented in the Senate by Victor Pérez Varela (UDI) and Mariano Ruiz-Esquide Jara (PDC) as part of the 13th senatorial constituency (Biobío-Coast).
References
External links
Municipality of Pemuco
Communes of Chile
Populated places in Diguillín Province |
https://en.wikipedia.org/wiki/R%C3%A1nquil | Ránquil is a Chilean commune in Itata Province, Ñuble Region. The communal capital is the town of Ránquil.
Demographics
According to the 2002 census of the National Statistics Institute Ránquil had 5,683 inhabitants (2,896 men and 2,787 women). Of these, 1,337 (23.5%) lived in urban areas and 4,346 (76.5%) in rural areas. The population fell by 11.3% (721 persons) between the 1992 and 2002 censuses.
Administration
As a commune, Ránquil is a third-level administrative division of Chile administered by a municipal council, headed by an alcalde who is directly elected every four years. The 2008-2012 alcalde is Carlos Garrido Carcamo (UDI).
Within the electoral divisions of Chile, Ránquil is represented in the Chamber of Deputies by Jorge Sabag (PDC) and Frank Sauerbaum (RN) as part of the 42nd electoral district, together with San Fabián, Ñiquén, San Carlos, San Nicolás, Ninhue, Quirihue, Cobquecura, Treguaco, Portezuelo, Coelemu, Quillón, Bulnes, Cabrero and Yumbel. The commune is represented in the Senate by Alejandro Navarro Brain (MAS) and Hosain Sabag Castillo (PDC) as part of the 12th senatorial constituency (Biobío-Cordillera).
References
Communes of Chile
Populated places in Itata Province |
https://en.wikipedia.org/wiki/Quill%C3%B3n | Quillón is a Chilean city and commune and Diguillín Province, Ñuble Region.
Demographics
According to the 2002 census of the National Statistics Institute, Quillón spans an area of and has 15,146 inhabitants (7,699 men and 7,447 women). Of these, 7,536 (49.8%) lived in urban areas and 7,610 (50.2%) in rural areas. The population grew by 4% (584 persons) between the 1992 and 2002 censuses.
Administration
As a commune, Quillón is a third-level administrative division of Chile administered by a municipal council, headed by an alcalde who is directly elected every four years. The 2008–2012 alcalde is Jaime Catalán Saldias (PDC).
Within the electoral divisions of Chile, Quillón is represented in the Chamber of Deputies by Jorge Sabag (PDC) and Frank Sauerbaum (RN) as part of the 42nd electoral district, (together with San Fabián, Ñiquén, San Carlos, San Nicolás, Ninhue, Quirihue, Cobquecura, Treguaco, Portezuelo, Coelemu, Ránquil, Bulnes, Cabrero and Yumbel). The commune is represented in the Senate by Alejandro Navarro Brain (MAS) and Hosain Sabag Castillo (PDC) as part of the 12th senatorial constituency (Biobío-Cordillera).
Temperature record
On January 26, 2017, while the central zone was affected by large forest fires, in Quillón the highest temperature in the country's history was recorded at , although this is disputed as it is thought that the forest fires influenced the thermometer reading.
References
Communes of Chile
Populated places in Diguillín Province |
https://en.wikipedia.org/wiki/BCK | BCK is the abbreviation of:
Bahria College Karachi college in Karachi, Pakistan
BC Kosher, a kosher certification agency in Canada
BCK algebra, in mathematics, BCK or BCI algebras are algebraic structures
British Rail coach type code representing a Brake composite corridor coach
Buckley railway station, a railway station in the UK
Buckie, a town in Scotland
Compagnie du chemin de fer du bas-Congo au Katanga, former railway company in Congo
3-Methyl-2-oxobutanoate dehydrogenase (acetyl-transferring) kinase, an enzyme |
https://en.wikipedia.org/wiki/MPIR | MPIR may refer to:
Max Planck Institute for Radio Astronomy, in Bonn, Germany
MPIR (mathematics software)
See also
Mpiri
Minnesota Public Interest Research Group |
https://en.wikipedia.org/wiki/Red%20auxiliary%20number | In the study of ancient Egyptian mathematics, red auxiliary numbers are numbers written in red ink in the Rhind Mathematical Papyrus, apparently used as aids for arithmetic computations involving fractions.It is considered to be the first examples of method that uses Least common multiples.
References
Egyptian mathematics
Egyptian fractions
Mathematics manuscripts |
https://en.wikipedia.org/wiki/Vietnamese%20people%20in%20Finland | Vietnamese people in Finland (; ) form one of the country's largest groups of Southeast Asian people. According to Statistics Finland, in 2017 there are 10,817 people with a Vietnamese background, 9,872 people whose mother tongue is Vietnamese, 8,012 people who have been born in Vietnam, and 5,603 people with Vietnamese citizenship residing in Finland. The Vietnamese-Finnish community includes both ethnic Vietnamese and Sino-Vietnamese.
Demographics
Religion
The majority of the Vietnamese in Finland are Mahayana Buddhist, with a 12% Christian minority.
Notable Finnish people of Vietnamese descent
See also
Finland–Vietnam relations
References
Sources
Ethnic groups in Finland
Finland |
https://en.wikipedia.org/wiki/Hemicube | Hemicube can mean:
Hemicube (computer graphics), a concept in 3D computer graphics rendering
Hemicube (geometry), an abstract regular polytope
Demihypercube, an n-dimensional uniform polytope, also known as the n-hemicube |
https://en.wikipedia.org/wiki/Frederick%20Lincoln%20Emory | Frederick Lincoln Emory (April 10, 1867 – December 31, 1919) was an American football coach and professor of mechanics and applied mathematics. He served as the first head football coach at West Virginia University, coaching one game in 1891. The single game that he coached was played on November 28, 1891 against Washington and Jefferson. The West Virginia Mountaineers lost by a score of 72 to zero, the second-worst loss in the history of the program.
He died in 1919 from heart-related problems.
Head coaching record
References
External links
1867 births
1919 deaths
West Virginia Mountaineers football coaches
People from Lunenburg, Massachusetts
Sportspeople from Worcester County, Massachusetts
Coaches of American football from Massachusetts
American mathematicians |
https://en.wikipedia.org/wiki/Graneros | Graneros is a Chilean commune and city in Cachapoal Province, O'Higgins Region.
Demographics
According to the 2002 census of the National Statistics Institute, Graneros spans an area of and has 25,961 inhabitants (12,992 men and 12,969 women). Of these, 22,674 (87.3%) lived in urban areas and 3,287 (12.7%) in rural areas. The population grew by 15.6% (3,508 persons) between the 1992 and 2002 censuses.
Administration
As a commune, Graneros is a third-level administrative division of Chile administered by a municipal council, headed by an alcalde who is directly elected every four years. The 2008-2012 alcalde is Juan Pablo Díaz Burgos. The council has the following members:
Juan Carlos Reyes
Antonio Pereira
Miguel Gutierrez L.
Carlos Ortega
Raquel Campos
Ximena Jeldres
Within the electoral divisions of Chile, Graneros is represented in the Chamber of Deputies by Eugenio Bauer (UDI) and Ricardo Rincón (PDC) as part of the 33rd electoral district, together with Mostazal, Codegua, Machalí, Requínoa, Rengo, Olivar, Doñihue, Coinco, Coltauco, Quinta de Tilcoco and Malloa. The commune is represented in the Senate by Andrés Chadwick Piñera (UDI) and Juan Pablo Letelier Morel (PS) as part of the 9th senatorial constituency (O'Higgins Region).
References
External links
Municipality of Graneros
Communes of Chile
Populated places in Cachapoal Province |
https://en.wikipedia.org/wiki/Machal%C3%AD | Machalí is a Chilean commune and city in Cachapoal Province, O'Higgins Region.
Demographics
According to the 2002 census of the National Statistics Institute, Machalí spans an area of and has 28,628 inhabitants (14,297 men and 14,331 women). Of these, 26,852 (93.8%) lived in urban areas and 1,776 (6.2%) in rural areas. The population grew by 18.5% (4,476 persons) between the 1992 and 2002 censuses.
Administration
As a commune, Machalí is a third-level administrative division of Chile administered by a municipal council, headed by an alcalde who is directly elected every four years. The 2008-2012 alcalde is José Miguel Urrutia.
Within the electoral divisions of Chile, Machalí is represented in the Chamber of Deputies by Eugenio Bauer (UDI) and Ricardo Rincón (PDC) as part of the 33rd electoral district, together with Mostazal, Graneros, Codegua, Requínoa, Rengo, Olivar, Doñihue, Coinco, Coltauco, Quinta de Tilcoco and Malloa. The commune is represented in the Senate by Andrés Chadwick Piñera (UDI) and Juan Pablo Letelier Morel (PS) as part of the 9th senatorial constituency (O'Higgins Region).
References
External links
Municipality of Machalí
Communes of Chile
Populated places in Cachapoal Province |
https://en.wikipedia.org/wiki/Requ%C3%ADnoa | Requínoa () is a Chilean commune and city in Cachapoal Province, O'Higgins Region.
Demographics
According to the 2002 census of the National Statistics Institute, Requínoa spans an area of and had 22,161 inhabitants (11,378 men and 10,783 women). Of these, 11,167 (50.4%) lived in urban areas and 10,994 (49.6%) in rural areas. The population grew by 14% (2,729 persons) between the 1992 and 2002 censuses. The 2012 census reported 26,089 inhabitants, an increase of 17.7% from 2002 to 2012.
Administration
As a commune, Requínoa is a third-level administrative division of Chile administered by a municipal council, headed by an alcalde who is directly elected every four years. The 2008-2012 alcalde is Antonio Silva Vargas (Ind.). The council has the following members:
Daniel Elías Martínez Higueras (PS)
María Eliana Berríos Bustos (ILE)
Rolando Andrés Guajardo Arévalo (ILC)
Hugo Alejandro Núñez Guerrero (UDI)
Sergio Cabezas Díaz (RN)
Francisco Odeón Caro Godoy (Ind.)
Within the electoral divisions of Chile, Requínoa is represented in the Chamber of Deputies by Eugenio Bauer (UDI) and Ricardo Rincón (PDC) as part of the 33rd electoral district, together with Mostazal, Graneros, Codegua, Machalí, Rengo, Olivar, Doñihue, Coinco, Coltauco, Quinta de Tilcoco and Malloa. The commune is represented in the Senate by Andrés Chadwick Piñera (UDI) and Juan Pablo Letelier Morel (PS) as part of the 9th senatorial constituency (O'Higgins Region).
References
Communes of Chile
Populated places in Cachapoal Province |
https://en.wikipedia.org/wiki/Quinta%20de%20Tilcoco | Quinta de Tilcoco is a Chilean commune and city in Cachapoal Province, O'Higgins Region.
Demographics
According to the 2002 census of the National Statistics Institute, Quinta de Tilcoco spans an area of and has 11,380 inhabitants (5,811 men and 5,569 women). Of these, 5,850 (51.4%) lived in urban areas and 5,530 (48.6%) in rural areas. The population grew by 5.5% (598 persons) between the 1992 and 2002 censuses.
Administration
As a commune, Quinta de Tilcoco is a third-level administrative division of Chile administered by a municipal council, headed by an alcalde who is directly elected every four years. The 2008-2002 alcalde is Nelson Patricio Barrios.
Within the electoral divisions of Chile, Quinta de Tilcoco is represented in the Chamber of Deputies by Eugenio Bauer (UDI) and Ricardo Rincón (PDC) as part of the 33rd electoral district, together with Mostazal, Graneros, Codegua, Machalí, Requínoa, Rengo, Olivar, Doñihue, Coinco, Coltauco and Malloa. The commune is represented in the Senate by Andrés Chadwick Piñera (UDI) and Juan Pablo Letelier Morel (PS) as part of the 9th senatorial constituency (O'Higgins Region).
References
External links
Municipality of Quinta de Tilcoco
Communes of Chile
Populated places in Cachapoal Province |
https://en.wikipedia.org/wiki/San%20Vicente%20de%20Tagua%20Tagua | San Vicente de Tagua Tagua, or just San Vicente, is a Chilean commune and city in Cachapoal Province, O'Higgins Region.
Demographics
According to the 2002 census of the National Statistics Institute, San Vicente spans an area of and had 40,253 inhabitants (20,095 men and 20,158 women). Of these, 21,965 (54.6%) lived in urban areas and 18,288 (45.4%) in rural areas. The population grew by 14.5% (5,086 persons) between the 1992 and 2002 censuses. The 2012 census reported 44,046 inhabitants, an increase of 9.4% from 2002 to 2012.
Administration
As a commune, San Vicente is a third-level administrative division administered by a municipal council, headed by an alcalde who is directly elected every four years.
Within the electoral divisions of Chile, San Vicente is represented in the Chamber of Deputies by Alejandra Sepúlveda (PRI) and Javier Macaya (UDI) as part of the 34th electoral district, together with San Fernando, Chimbarongo, Peumo, Pichidegua and Las Cabras. The commune is represented in the Senate by Andrés Chadwick Piñera (UDI) and Juan Pablo Letelier Morel (PS) as part of the 9th senatorial constituency (O'Higgins Region).
Archaeology
Tagua-Tagua represents a very early Paleo-Indian archaeological site, and it is dated to 11,380 ±380 14C yr BP (before present).
This is an ancient pleistocene site where humans butchered large animals that they hunted. The site was discovered in the 1860s.
An upper, younger stratum is about 1 m below the surface. The older stratum is about 2.4 m below the surface, and contains chipped stone tools. Horse and mastodon remains are represented, as well as smaller animals.
Notes and references
External links
Municipality of San Vicente de Tagua Tagua
Communes of Chile
Populated places in Cachapoal Province
Pre-Clovis archaeological sites in the Americas |
https://en.wikipedia.org/wiki/Pichidegua | Pichidegua () is a Chilean commune and town in Cachapoal Province, O'Higgins Region.
Demographics
According to the 2002 census of the National Statistics Institute, Pichidegua spans an area of and has 17,756 inhabitants (9,208 men and 8,548 women). Of these, 4,965 (28%) lived in urban areas and 12,791 (72%) in rural areas. The population grew by 7% (1,162 persons) between the 1992 and 2002 censuses.
Administration
As a commune, Pichidegua is a third-level administrative division of Chile administered by a municipal council, headed by an alcalde who is directly elected every four years.
Within the electoral divisions of Chile, Pichidegua is represented in the Chamber of Deputies by Alejandra Sepúlveda (PRI) and Javier Macaya (UDI) as part of the 34th electoral district, together with San Fernando, Chimbarongo, San Vicente, Peumo and Las Cabras. The commune is represented in the Senate by Andrés Chadwick Piñera (UDI) and Juan Pablo Letelier Morel (PS) as part of the 9th senatorial constituency (O'Higgins Region).
References
External links
Municipality of Pichidegua
Communes of Chile
Populated places in Cachapoal Province |
https://en.wikipedia.org/wiki/Discrete%20%26%20Computational%20Geometry | Discrete & Computational Geometry is a peer-reviewed mathematics journal published quarterly by Springer. Founded in 1986 by Jacob E. Goodman and Richard M. Pollack, the journal publishes articles on discrete geometry and computational geometry.
Abstracting and indexing
The journal is indexed in:
Mathematical Reviews
Zentralblatt MATH
Science Citation Index
Current Contents/Engineering, Computing and Technology
Notable articles
Two articles published in Discrete & Computational Geometry, one by Gil Kalai in 1992 with a proof of a subexponential upper bound on the diameter of a polytope and another by Samuel Ferguson in 2006 on the Kepler conjecture on optimal three-dimensional sphere packing, earned their authors the Fulkerson Prize.
References
External links
Mathematics journals
Academic journals established in 1986
English-language journals
Springer Science+Business Media academic journals
Quarterly journals
Computational geometry
Discrete geometry |
https://en.wikipedia.org/wiki/2008%E2%80%9309%20Galatasaray%20S.K.%20season | The 2008–09 season was Galatasarays 105th in existence and the 51st consecutive season in the Süper Lig. This article shows statistics of the club's players in the season, and also lists all matches that the club have played in the season.
Current squad
As of March 10, 2009; according to the official website. .
Transfers
In
Out
Loaned out
Squad statistics
Statistics accurate as of match played June 1, 2009
Competitions
Turkish Super CupAll times at CESTSüper Lig
League table
Results summary
Results by round
MatchesKick-off listed in local time (EEST)Turkish CupKick-off listed in local time (EEST)Group stage
Quarter-finals
UEFA Champions LeagueAll times at CETThird qualifying round
UEFA CupAll times at CET''
First round
Group stage
Knockout phase
Round of 32
Round of 16
Attendance
References
External links
Galatasaray Sports Club Official Website
Turkish Football Federation - Galatasaray A.Ş.
uefa.com - Galatasaray AŞ
2008-09
Turkish football clubs 2008–09 season
2000s in Istanbul
Galatasaray Sports Club 2008–09 season |
https://en.wikipedia.org/wiki/Jerzy%20Browkin | Jerzy Browkin (5 November 1934 – 23 November 2015) was a Polish mathematician, studying mainly algebraic number theory. He was a professor at the Institute of Mathematics of the Polish Academy of Sciences. In 1994, together with Juliusz Brzeziński, he formulated the n-conjecture—a version of the abc conjecture involving n > 2 integers.
References
1934 births
2015 deaths
20th-century Polish mathematicians
21st-century Polish mathematicians
Number theorists |
https://en.wikipedia.org/wiki/Walter%20Dubislav | Walter Dubislav (20 September 1895 – 17 September 1937) was a German logician and philosopher of science (Wissenschaftstheoretiker).
Biography
After studying mathematics and philosophy, Dubislav attained a doctorate in 1922 with "Contributions to the theories of definition and proof within mathematical logic" (Beiträge zur Lehre von der Definition und vom Beweis vom Standpunkt der mathematischen Logik aus). In 1928 he became a private lecturer in philosophy of mathematics and the natural sciences at the Technical University of Berlin and from 1931 was Professor Extraordinarius (außerordentlicher Professor, ao. Prof.). In 1936 he emigrated to Prague.
He was joint founder (with Hans Reichenbach and Kurt Grelling) of the 'Berlin Society for Empirical (later: Scientific) Philosophy' (Berliner Gesellschaft für empirische Philosophie), which, along with the Vienna Circle, is one of the points of origin of logical empiricism. The founding members of the Berlin Circle were listed as sympathisers within the Vienna Circle.
Dubislav focused on a logical and mechanistic foundation of mathematics and physics, influenced by Bernard Bolzano's "Theory of Science" (Wissenschaftslehre). He presented a formalised account of Gottlob Frege's theory of definitions.
Publications
With Claubberg, K.W.: "A Systematic Dictionary of Philosophy" (Systematisches Wörterbuch der Philosophie). Felix Meiner, Leipzig 1923.
"On Definitions" (Über die Definition). Weiss, Berlin 1926; 2nd edition published 1927; "Definition" (Die Definition), revised and augmented 3rd edition, Felix Meiner, Leipzig 1931; 4th edition, with an introduction by Wilhelm K. Essler, published by Meiner, Hamburg 1981 .
"On the so-called analytic and synthetic judgements" (Über die sogennanten analytischen und synthetischen Urteile). Weiss, Berlin 1926.
"Fries' Theory of Meaning" (Die Friessche Lehre von der Begründung) in "Representation and Criticism" (Darstellung und Kritik), E. Mattig, Dömitz 1926.
"On the Theory of the so-called Creative Definitions" (Zur Lehre von den sog. schöpferischen Definitionen). Fulda 1928.
"On the so-called Object in Mathematics" (Über den sogenannten Gegenstand in der Mathematik) in "The Annual Report of the German Mathematics Convention, 37" (Jahresbericht der Deutschen Mathematiker-Vereinigung 37), pp27–48, Leipzig 1928.
"On the Methodology of Critical Philosophy" (Zur Methodenlehre des Kritizismus). H. Beyer & Sons, Langensalza 1929.
"Contemporary Philosophy of Mathematics" (Die Philosophie der Mathematik in der Gegenwart). (Philosophische Forschungsberichte 13) Junker & Dünnhaupt, Berlin 1932.
"Philosophy of Nature" (Naturphilosophie). (Philosophische Grundrisse Heft 2) Junker & Dünnhaupt, Berlin 1933; also in
References
1895 births
1937 deaths
German logicians
Philosophers of science
People from Berlin
German male writers
Vienna Circle
20th-century German philosophers
Technical University of Berlin alumni |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.