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https://en.wikipedia.org/wiki/1829%20in%20science | The year 1829 in science and technology involved some significant events, listed below.
Chemistry
Isaac Holden produces a form of friction match.
Mathematics
Peter Gustav Lejeune Dirichlet publishes a memoir giving the Dirichlet conditions, showing for which functions the convergence of the Fourier series holds; in... |
https://en.wikipedia.org/wiki/Fa%C3%A0%20di%20Bruno%27s%20formula | Faà di Bruno's formula is an identity in mathematics generalizing the chain rule to higher derivatives. It is named after , although he was not the first to state or prove the formula. In 1800, more than 50 years before Faà di Bruno, the French mathematician Louis François Antoine Arbogast had stated the formula in a c... |
https://en.wikipedia.org/wiki/North%20Carolina%20School%20of%20Science%20and%20Mathematics | The North Carolina School of Science and Mathematics (NCSSM) is a two-year, public residential high school with two physical campuses located in Durham, North Carolina and Morganton, North Carolina that focuses on the intensive study of science, mathematics and technology. It accepts rising juniors from across North Ca... |
https://en.wikipedia.org/wiki/Colliers%2C%20Newfoundland%20and%20Labrador | Colliers is a town on the Avalon Peninsula in Newfoundland and Labrador, Canada. It is in Division 1 on Conception Bay.
According to the 2016 Statistics Canada Census: the area had a population of 654, with 424 dwellings.
Colliers was considered by John Guy and his associates as a preferred place for the first settle... |
https://en.wikipedia.org/wiki/Division%20No.%201%2C%20Subdivision%20Y%2C%20Newfoundland%20and%20Labrador | Division No. 1, Subdivision Y is an unorganized subdivision on the Avalon Peninsula in Newfoundland and Labrador, Canada. It is in Division 1 on Trinity Bay.
According to the 2016 Statistics Canada Census:
Population: 1,118
% Change (2011 to 2016): -4.9
Dwellings: 857
Area: 190.87 km2
Density: 5.9 people/km2
Newfound... |
https://en.wikipedia.org/wiki/HC | HC, hc or H/C may refer to:
Science, technology, and mathematics
Medicine
Health Canada
Hemicrania continua
Hyperelastosis cutis or hereditary equine regional dermal asthenia
Chemistry
Hemocyanin, a metalloprotein abbreviated Hc
HC smoke, a US military designation for Hexachloroethane
Homocapsaicin, a capsai... |
https://en.wikipedia.org/wiki/Division%20No.%207%2C%20Subdivision%20M%2C%20Newfoundland%20and%20Labrador | Division No. 7, Subdivision M is an unorganised subdivision in eastern Newfoundland, Newfoundland and Labrador, Canada. It is in Division No. 7 on Trinity Bay.
According to the 2016 Statistics Canada Census:
Population: 1,966
% Change (2011-2016): -4.3
Dwellings: 1,183
Area (km2.): 454.42
Density (persons per km2.): 4... |
https://en.wikipedia.org/wiki/Division%20No.%207%2C%20Subdivision%20K%2C%20Newfoundland%20and%20Labrador | Division No. 7, Subd. K is an unorganized subdivision on the Bonavista Peninsula in Newfoundland and Labrador, Canada. It is in Division No. 7 on Trinity Bay.
According to the 2001 Statistics Canada Census:
Population: 1,152
% Change (1996-2001): -9.9
Dwellings: 695
Area (km2.): 486.16
Density (persons per km2.): 2.4
... |
https://en.wikipedia.org/wiki/Division%20No.%207%2C%20Subdivision%20E%2C%20Newfoundland%20and%20Labrador | Division No. 7, Subd. E is an unorganized subdivision in eastern Newfoundland, Newfoundland and Labrador, Canada. It is in Division No. 7 on Bonavista Bay.
According to the 2016 Statistics Canada Census:
Population: 2,644
% Change (2011-2016): -2.6
Dwellings: 1,682
Area (km2.): 1,664.58
Density (persons per km2.): 1.6... |
https://en.wikipedia.org/wiki/Division%20No.%207%2C%20Subdivision%20D%2C%20Newfoundland%20and%20Labrador | Division No. 7, Subd. D is an unorganized subdivision in eastern Newfoundland, Newfoundland and Labrador, Canada. It is in Division No. 7 on Bonavista Bay.
According to the 2016 Statistics Canada Census:
Population: 230
% Change (2011-2016): -0.9
Dwellings: 734
Area (km2.): 2,483.46
Density (persons per km2.): 0.1
Ne... |
https://en.wikipedia.org/wiki/Division%20No.%207%2C%20Subdivision%20N%2C%20Newfoundland%20and%20Labrador | Division No. 7, Subd. N is an unorganized subdivision in eastern Newfoundland, Newfoundland and Labrador, Canada. It is in Division No. 7 on Freshwater Bay.
According to the 2016 Statistics Canada Census:
Population: 49
% Change (2011-2016): -15.5
Dwellings: 166
Area (km2.): 1,407.16
Density (persons per km2.): 0
New... |
https://en.wikipedia.org/wiki/Division%20No.%206%2C%20Subdivision%20E%2C%20Newfoundland%20and%20Labrador | Division No. 6, Subd. E is an unorganized subdivision in northeastern Newfoundland, Newfoundland and Labrador, Canada. It is in Division No. 6.
According to the 2016 Statistics Canada Census:
Population: 194
% Change (2011-2016): -10.2
Dwellings: 631
Area (km2): 2,309.6
Density (persons per km2): 0.1
Newfoundland an... |
https://en.wikipedia.org/wiki/Mutual%20information | In probability theory and information theory, the mutual information (MI) of two random variables is a measure of the mutual dependence between the two variables. More specifically, it quantifies the "amount of information" (in units such as shannons (bits), nats or hartleys) obtained about one random variable by obser... |
https://en.wikipedia.org/wiki/ARS-based%20programming | ARS-based programming is built on three principles: abstraction, reference and synthesis. These principles can be seen as a generalized form of the basic operations of the Lambda calculus. All essential features of a programming language can be derived from ARS, even the three major programming paradigms: functional pr... |
https://en.wikipedia.org/wiki/List%20of%20transforms | This is a list of transforms in mathematics.
Integral transforms
Abel transform
Bateman transform
Fourier transform
Short-time Fourier transform
Gabor transform
Hankel transform
Hartley transform
Hermite transform
Hilbert transform
Hilbert–Schmidt integral operator
Jacobi transform
Laguerre transform
Laplace transform... |
https://en.wikipedia.org/wiki/Progression | Progression may refer to:
In mathematics:
Arithmetic progression, sequence of numbers such that the difference of any two successive members of the sequence is a constant
Geometric progression, sequence of numbers such that the quotient of any two successive members of the sequence is a constant
Harmonic progressio... |
https://en.wikipedia.org/wiki/Set-theoretic%20definition%20of%20natural%20numbers | In set theory, several ways have been proposed to construct the natural numbers. These include the representation via von Neumann ordinals, commonly employed in axiomatic set theory, and a system based on equinumerosity that was proposed by Gottlob Frege and by Bertrand Russell.
Definition as von Neumann ordinals
In... |
https://en.wikipedia.org/wiki/Illustration%20of%20the%20central%20limit%20theorem | In probability theory, the central limit theorem (CLT) states that, in many situations, when independent and identically distributed random variables are added, their properly normalized sum tends toward a normal distribution. This article gives two illustrations of this theorem. Both involve the sum of independent and... |
https://en.wikipedia.org/wiki/Hausdorff%20distance | In mathematics, the Hausdorff distance, or Hausdorff metric, also called Pompeiu–Hausdorff distance, measures how far two subsets of a metric space are from each other. It turns the set of non-empty compact subsets of a metric space into a metric space in its own right. It is named after Felix Hausdorff and Dimitrie Po... |
https://en.wikipedia.org/wiki/Probability%20amplitude | In quantum mechanics, a probability amplitude is a complex number used for describing the behaviour of systems. The modulus squared of this quantity represents a probability density.
Probability amplitudes provide a relationship between the quantum state vector of a system and the results of observations of that syste... |
https://en.wikipedia.org/wiki/Empirical%20orthogonal%20functions | In statistics and signal processing, the method of empirical orthogonal function (EOF) analysis is a decomposition of a signal or data set in terms of orthogonal basis functions which are determined from the data. The term is also interchangeable with the geographically weighted Principal components analysis in geophy... |
https://en.wikipedia.org/wiki/Earley | Earley ( ) is a town and civil parish in the Borough of Wokingham, Berkshire, England. Along with the neighbouring town of Woodley, the Office for National Statistics places Earley within the Reading/Wokingham Urban Area; for the purposes of local government it falls within the Borough of Wokingham, outside the area of... |
https://en.wikipedia.org/wiki/Cyclotomic%20identity | In mathematics, the cyclotomic identity states that
where M is Moreau's necklace-counting function,
and μ is the classic Möbius function of number theory.
The name comes from the denominator, 1 − z j, which is the product of cyclotomic polynomials.
The left hand side of the cyclotomic identity is the generating f... |
https://en.wikipedia.org/wiki/Woodbury%20matrix%20identity | In mathematics (specifically linear algebra), the Woodbury matrix identity, named after Max A. Woodbury, says that the inverse of a rank-k correction of some matrix can be computed by doing a rank-k correction to the inverse of the original matrix. Alternative names for this formula are the matrix inversion lemma, Sher... |
https://en.wikipedia.org/wiki/Truncated%20mean | A truncated mean or trimmed mean is a statistical measure of central tendency, much like the mean and median. It involves the calculation of the mean after discarding given parts of a probability distribution or sample at the high and low end, and typically discarding an equal amount of both. This number of points to b... |
https://en.wikipedia.org/wiki/Motive%20%28algebraic%20geometry%29 | In algebraic geometry, motives (or sometimes motifs, following French usage) is a theory proposed by Alexander Grothendieck in the 1960s to unify the vast array of similarly behaved cohomology theories such as singular cohomology, de Rham cohomology, etale cohomology, and crystalline cohomology. Philosophically, a "mot... |
https://en.wikipedia.org/wiki/Similarity%20transformation | Similarity transformation may refer to:
Similarity (geometry), for shape-preserving transformations
Matrix similarity, for matrix transformations of the form
See also
Similarity (disambiguation)
Transformation (disambiguation)
Affine transformation |
https://en.wikipedia.org/wiki/Necklace%20polynomial | In combinatorial mathematics, the necklace polynomial, or Moreau's necklace-counting function, introduced by , counts the number of distinct necklaces of n colored beads chosen out of α available colors. The necklaces are assumed to be aperiodic (not consisting of repeated subsequences), and counted up to rotation (ro... |
https://en.wikipedia.org/wiki/Integral%20transform | In mathematics, an integral transform is a type of transform that maps a function from its original function space into another function space via integration, where some of the properties of the original function might be more easily characterized and manipulated than in the original function space. The transformed fu... |
https://en.wikipedia.org/wiki/Singular%20homology | In algebraic topology, singular homology refers to the study of a certain set of algebraic invariants of a topological space X, the so-called homology groups Intuitively, singular homology counts, for each dimension n, the n-dimensional holes of a space. Singular homology is a particular example of a homology theory... |
https://en.wikipedia.org/wiki/220%20%28number%29 | 220 (two hundred [and] twenty) is the natural number following 219 and preceding 221.
In mathematics
It is a composite number, with its proper divisors being 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110, making it an amicable number with 284. Every number up to 220 may be expressed as a sum of its divisors, making 220 a... |
https://en.wikipedia.org/wiki/Covariant%20derivative | In mathematics, the covariant derivative is a way of specifying a derivative along tangent vectors of a manifold. Alternatively, the covariant derivative is a way of introducing and working with a connection on a manifold by means of a differential operator, to be contrasted with the approach given by a principal conne... |
https://en.wikipedia.org/wiki/Deviance%20%28statistics%29 | In statistics, deviance is a goodness-of-fit statistic for a statistical model; it is often used for statistical hypothesis testing. It is a generalization of the idea of using the sum of squares of residuals (SSR) in ordinary least squares to cases where model-fitting is achieved by maximum likelihood. It plays an imp... |
https://en.wikipedia.org/wiki/List%20of%20English%20districts%20by%20population | This is a list of the 314 districts of England ordered by population, according to estimated figures for from the Office for National Statistics.
The list consists of 188 non-metropolitan districts, 32 London boroughs, 36 metropolitan boroughs, 66 unitary authorities, and three sui generis authorities (the City of Lo... |
https://en.wikipedia.org/wiki/Mann%E2%80%93Whitney%20U%20test | In statistics, the Mann–Whitney U test (also called the Mann–Whitney–Wilcoxon (MWW/MWU), Wilcoxon rank-sum test, or Wilcoxon–Mann–Whitney test) is a nonparametric test of the null hypothesis that, for randomly selected values X and Y from two populations, the probability of X being greater than Y is equal to the probab... |
https://en.wikipedia.org/wiki/Derived%20functor | In mathematics, certain functors may be derived to obtain other functors closely related to the original ones. This operation, while fairly abstract, unifies a number of constructions throughout mathematics.
Motivation
It was noted in various quite different settings that a short exact sequence often gives rise to a... |
https://en.wikipedia.org/wiki/Catastrophe%20theory | In mathematics, catastrophe theory is a branch of bifurcation theory in the study of dynamical systems; it is also a particular special case of more general singularity theory in geometry.
Bifurcation theory studies and classifies phenomena characterized by sudden shifts in behavior arising from small changes in circu... |
https://en.wikipedia.org/wiki/DN | DN, dN, or dn may refer to:
Science, technology, and mathematics
Computing and telecommunications
Digital number, the discrete of an analog value sampled by an analog-to-digital converter
Directory number in a phone system
Distinguished Name, an identifier type in the LDAP protocol
Domain name, an identification... |
https://en.wikipedia.org/wiki/Cyclic%20order | In mathematics, a cyclic order is a way to arrange a set of objects in a circle. Unlike most structures in order theory, a cyclic order is not modeled as a binary relation, such as "". One does not say that east is "more clockwise" than west. Instead, a cyclic order is defined as a ternary relation , meaning "after , o... |
https://en.wikipedia.org/wiki/Finite%20Fourier%20transform |
In mathematics the finite Fourier transform may refer to either
another name for discrete-time Fourier transform (DTFT) of a finite-length series. E.g., F.J.Harris (pp. 52–53) describes the finite Fourier transform as a "continuous periodic function" and the discrete Fourier transform (DFT) as "a set of samples of t... |
https://en.wikipedia.org/wiki/Category%20of%20topological%20spaces | In mathematics, the category of topological spaces, often denoted Top, is the category whose objects are topological spaces and whose morphisms are continuous maps. This is a category because the composition of two continuous maps is again continuous, and the identity function is continuous. The study of Top and of pr... |
https://en.wikipedia.org/wiki/Urn%20problem | In probability and statistics, an urn problem is an idealized mental exercise in which some objects of real interest (such as atoms, people, cars, etc.) are represented as colored balls in an urn or other container. One pretends to remove one or more balls from the urn; the goal is to determine the probability of drawi... |
https://en.wikipedia.org/wiki/Conditional%20expectation | In probability theory, the conditional expectation, conditional expected value, or conditional mean of a random variable is its expected value – the value it would take "on average" over an arbitrarily large number of occurrences – given that a certain set of "conditions" is known to occur. If the random variable can t... |
https://en.wikipedia.org/wiki/Birch%20and%20Swinnerton-Dyer%20conjecture | In mathematics, the Birch and Swinnerton-Dyer conjecture (often called the Birch–Swinnerton-Dyer conjecture) describes the set of rational solutions to equations defining an elliptic curve. It is an open problem in the field of number theory and is widely recognized as one of the most challenging mathematical problems.... |
https://en.wikipedia.org/wiki/Khinchin%27s%20constant | In number theory, Aleksandr Yakovlevich Khinchin proved that for almost all real numbers x, coefficients ai of the continued fraction expansion of x have a finite geometric mean that is independent of the value of x and is known as Khinchin's constant.
That is, for
it is almost always true that
where is Khinchin's ... |
https://en.wikipedia.org/wiki/Common%20cause%20and%20special%20cause%20%28statistics%29 | Common and special causes are the two distinct origins of variation in a process, as defined in the statistical thinking and methods of Walter A. Shewhart and W. Edwards Deming. Briefly, "common causes", also called natural patterns, are the usual, historical, quantifiable variation in a system, while "special causes" ... |
https://en.wikipedia.org/wiki/Daniel%20Quillen | Daniel Gray "Dan" Quillen (June 22, 1940 – April 30, 2011) was an American mathematician. He is known for being the "prime architect" of higher algebraic K-theory, for which he was awarded the Cole Prize in 1975 and the Fields Medal in 1978.
From 1984 to 2006, he was the Waynflete Professor of Pure Mathematics at Magd... |
https://en.wikipedia.org/wiki/Mertens%20function | In number theory, the Mertens function is defined for all positive integers n as
where is the Möbius function. The function is named in honour of Franz Mertens. This definition can be extended to positive real numbers as follows:
Less formally, is the count of square-free integers up to x that have an even nu... |
https://en.wikipedia.org/wiki/Vysochanskij%E2%80%93Petunin%20inequality | In probability theory, the Vysochanskij–Petunin inequality gives a lower bound for the probability that a random variable with finite variance lies within a certain number of standard deviations of the variable's mean, or equivalently an upper bound for the probability that it lies further away. The sole restrictions... |
https://en.wikipedia.org/wiki/WZ | WZ may refer to:
WZ sex-determination system, also known as the ZW sex-determination system
WZ theory, a technique for simplifying certain combinatorial summations in mathematics
Eswatini (FIPS 10-4 country code WZ)
Westdeutsche Zeitung, a German newspaper
Wetzlar, Germany
WinZip, a computer file compression sof... |
https://en.wikipedia.org/wiki/Lee%20Harwood | Lee Harwood (6 June 1939 – 26 July 2015) was an English poet associated with the British Poetry Revival.
Life
Travers Rafe Lee Harwood was born in Leicester to maths teacher Wilfred Travers Lee-Harwood and Grace Ladkin Harwood, who were then living in Chertsey, Surrey. His father was an army reservist and called up as... |
https://en.wikipedia.org/wiki/K.%20G.%20Ramanathan | Kollagunta Gopalaiyer Ramanathan (13 November 1920 – 10 May 1992) was an Indian mathematician known for his work in number theory. His contributions are also to the general development of mathematical research and teaching in India.
K. G. Ramanathan's early life and his family
K. G. Ramanathan was born in Hyderabad in... |
https://en.wikipedia.org/wiki/Infinitesimal%20generator | In mathematics, the term infinitesimal generator may refer to:
an element of the Lie algebra, associated to a Lie group
Infinitesimal generator (stochastic processes), of a stochastic process
infinitesimal generator matrix, of a continuous time Markov chain, a class of stochastic processes
Infinitesimal generator ... |
https://en.wikipedia.org/wiki/Effect%20size | In statistics, an effect size is a value measuring the strength of the relationship between two variables in a population, or a sample-based estimate of that quantity. It can refer to the value of a statistic calculated from a sample of data, the value of a parameter for a hypothetical population, or to the equation th... |
https://en.wikipedia.org/wiki/Matrix%20normal%20distribution | In statistics, the matrix normal distribution or matrix Gaussian distribution is a probability distribution that is a generalization of the multivariate normal distribution to matrix-valued random variables.
Definition
The probability density function for the random matrix X (n × p) that follows the matrix normal di... |
https://en.wikipedia.org/wiki/Midpoint | In geometry, the midpoint is the middle point of a line segment. It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints. It bisects the segment.
Formula
The midpoint of a segment in n-dimensional space whose endpoints are and is given by
That is, the ith coordinate o... |
https://en.wikipedia.org/wiki/Statistics%20Sweden | Statistics Sweden ( ; SCB, ) is the Swedish government agency operating under the Ministry of Finance and responsible for producing official statistics for decision-making, debate and research. The agency's responsibilities include:
developing, producing and disseminating statistics;
active participation in internati... |
https://en.wikipedia.org/wiki/Moving%20frame | In mathematics, a moving frame is a flexible generalization of the notion of an ordered basis of a vector space often used to study the extrinsic differential geometry of smooth manifolds embedded in a homogeneous space.
Introduction
In lay terms, a frame of reference is a system of measuring rods used by an observer... |
https://en.wikipedia.org/wiki/Glenwood%2C%20Newfoundland%20and%20Labrador | Glenwood is a town in northeastern Newfoundland, Newfoundland and Labrador, Canada. It is in Division No. 6 on Gander Lake.
Demographics
In the 2021 Census of Population conducted by Statistics Canada, Glenwood had a population of living in of its total private dwellings, a change of from its 2016 population of .... |
https://en.wikipedia.org/wiki/Division%20No.%206%2C%20Subdivision%20D%2C%20Newfoundland%20and%20Labrador | Division No. 6, Subd. D is an unorganized subdivision in northeastern Newfoundland, Newfoundland and Labrador, Canada. It is in Division No. 6 on the Bay of Exploits.
According to the 2016 Statistics Canada Census:
Population: 682
% Change (2011-2016): 131.2
Dwellings: 769
Area (km2): 4,228.2
Density (persons per km2)... |
https://en.wikipedia.org/wiki/1706%20in%20science | The year 1706 in science and technology involved some significant events.
Mathematics
William Jones publishes Synopsis palmariorum matheseos or, A New Introduction to the Mathematics, Containing the Principles of Arithmetic and Geometry Demonstrated in a Short and Easie Method ... Designed for ... Beginners in which ... |
https://en.wikipedia.org/wiki/Modular%20equation | In mathematics, a modular equation is an algebraic equation satisfied by moduli, in the sense of moduli problems. That is, given a number of functions on a moduli space, a modular equation is an equation holding between them, or in other words an identity for moduli.
The most frequent use of the term modular equation ... |
https://en.wikipedia.org/wiki/Oscar%20Buneman | Oscar Buneman (28 September 1913 – 24 January 1993) made advances in science, engineering, and mathematics. Buneman was a pioneer of computational plasma physics and plasma simulation.
Career
In 1940 upon completion of his PhD with Douglas Hartree, Buneman joined Hartree's magnetron research group assisting the develo... |
https://en.wikipedia.org/wiki/Smarandache%E2%80%93Wellin%20number | In mathematics, a Smarandache–Wellin number is an integer that in a given base is the concatenation of the first n prime numbers written in that base. Smarandache–Wellin numbers are named after Florentin Smarandache and Paul R. Wellin.
The first decimal Smarandache–Wellin numbers are:
2, 23, 235, 2357, 235711, 235711... |
https://en.wikipedia.org/wiki/Genichi%20Taguchi | was an engineer and statistician. From the 1950s on, Taguchi developed a methodology for applying statistics to improve the quality of manufactured goods. Taguchi methods have been controversial among some conventional Western statisticians, but others have accepted many of the concepts introduced by him as valid exten... |
https://en.wikipedia.org/wiki/Risk-neutral%20measure | In mathematical finance, a risk-neutral measure (also called an equilibrium measure, or equivalent martingale measure) is a probability measure such that each share price is exactly equal to the discounted expectation of the share price under this measure.
This is heavily used in the pricing of financial derivatives du... |
https://en.wikipedia.org/wiki/Axiom%20of%20dependent%20choice | In mathematics, the axiom of dependent choice, denoted by , is a weak form of the axiom of choice () that is still sufficient to develop most of real analysis. It was introduced by Paul Bernays in a 1942 article that explores which set-theoretic axioms are needed to develop analysis.
Formal statement
A homogeneous re... |
https://en.wikipedia.org/wiki/List%20of%20census%20divisions%20of%20Ontario | The Province of Ontario has 51 first-level administrative divisions, which collectively cover the whole province. With two exceptions, their areas match the 49 census divisions Statistics Canada has for Ontario.
The Province has four types of first-level division: single-tier municipalities, regional municipalities, c... |
https://en.wikipedia.org/wiki/Interaction%20%28statistics%29 | In statistics, an interaction may arise when considering the relationship among three or more variables, and describes a situation in which the effect of one causal variable on an outcome depends on the state of a second causal variable (that is, when effects of the two causes are not additive). Although commonly thoug... |
https://en.wikipedia.org/wiki/Simple%20ring | In abstract algebra, a branch of mathematics, a simple ring is a non-zero ring that has no two-sided ideal besides the zero ideal and itself. In particular, a commutative ring is a simple ring if and only if it is a field.
The center of a simple ring is necessarily a field. It follows that a simple ring is an associa... |
https://en.wikipedia.org/wiki/Parallelogram%20of%20force | The parallelogram of forces is a method for solving (or visualizing) the results of applying two forces to an object.
When more than two forces are involved, the geometry is no longer parallelogrammatic, but the same principles apply. Forces, being vectors are observed to obey the laws of vector addition, and so the ... |
https://en.wikipedia.org/wiki/Borel%E2%80%93Kolmogorov%20paradox | In probability theory, the Borel–Kolmogorov paradox (sometimes known as Borel's paradox) is a paradox relating to conditional probability with respect to an event of probability zero (also known as a null set). It is named after Émile Borel and Andrey Kolmogorov.
A great circle puzzle
Suppose that a random variable ... |
https://en.wikipedia.org/wiki/Simon%20Newcomb | Simon Newcomb (March 12, 1835 – July 11, 1909) was a Canadian–American astronomer, applied mathematician, and autodidactic polymath. He served as Professor of Mathematics in the United States Navy and at Johns Hopkins University. Born in Nova Scotia, at the age of 19 Newcomb left an apprenticeship to join his father in... |
https://en.wikipedia.org/wiki/Weierstrass%20function | In mathematics, the Weierstrass function is an example of a real-valued function that is continuous everywhere but differentiable nowhere. It is an example of a fractal curve. It is named after its discoverer Karl Weierstrass.
The Weierstrass function has historically served the role of a pathological function, being ... |
https://en.wikipedia.org/wiki/Piecewise%20linear%20function | In mathematics and statistics, a piecewise linear, PL or segmented function is a real-valued function of a real variable, whose graph is composed of straight-line segments.
Definition
A piecewise linear function is a function defined on a (possibly unbounded) interval of real numbers, such that there is a collection o... |
https://en.wikipedia.org/wiki/Weierstrass%20M-test | In mathematics, the Weierstrass M-test is a test for determining whether an infinite series of functions converges uniformly and absolutely. It applies to series whose terms are bounded functions with real or complex values, and is analogous to the comparison test for determining the convergence of series of real or co... |
https://en.wikipedia.org/wiki/Plural%20quantification | In mathematics and logic, plural quantification is the theory that an individual variable x may take on plural, as well as singular, values. As well as substituting individual objects such as Alice, the number 1, the tallest building in London etc. for x, we may substitute both Alice and Bob, or all the numbers between... |
https://en.wikipedia.org/wiki/Icosagon | In geometry, an icosagon or 20-gon is a twenty-sided polygon. The sum of any icosagon's interior angles is 3240 degrees.
Regular icosagon
The regular icosagon has Schläfli symbol , and can also be constructed as a truncated decagon, , or a twice-truncated pentagon, .
One interior angle in a regular icosagon is 162°,... |
https://en.wikipedia.org/wiki/Locally%20cyclic%20group | In mathematics, a locally cyclic group is a group (G, *) in which every finitely generated subgroup is cyclic.
Some facts
Every cyclic group is locally cyclic, and every locally cyclic group is abelian.
Every finitely-generated locally cyclic group is cyclic.
Every subgroup and quotient group of a locally cyclic gr... |
https://en.wikipedia.org/wiki/Pi%20function | In mathematics, three different functions are known as the pi or Pi function:
(pi function) – the prime-counting function
(Pi function) – the gamma function when offset to coincide with the factorial
Rectangular function
You might also be looking for:
– the Infinite product of a sequence
Capital pi notation |
https://en.wikipedia.org/wiki/Polylogarithmic%20function | In mathematics, a polylogarithmic function in is a polynomial in the logarithm of ,
The notation is often used as a shorthand for , analogous to for .
In computer science, polylogarithmic functions occur as the order of time or memory used by some algorithms (e.g., "it has polylogarithmic order"), such as in th... |
https://en.wikipedia.org/wiki/Von%20Neumann%20universe | In set theory and related branches of mathematics, the von Neumann universe, or von Neumann hierarchy of sets, denoted by V, is the class of hereditary well-founded sets. This collection, which is formalized by Zermelo–Fraenkel set theory (ZFC), is often used to provide an interpretation or motivation of the axioms of ... |
https://en.wikipedia.org/wiki/Constructible%20set | In mathematics, constructible set may refer to either:
a notion in Gödel's constructible universe.
a union of locally closed set in a topological space. See constructible set (topology). |
https://en.wikipedia.org/wiki/Decision%20theory | Decision theory (or the theory of choice; not to be confused with choice theory) is a branch of applied probability theory and analytic philosophy concerned with the theory of making decisions based on assigning probabilities to various factors and assigning numerical consequences to the outcome.
There are three branc... |
https://en.wikipedia.org/wiki/360%20%28number%29 | 360 (three hundred sixty) is the natural number following 359 and preceding 361.
In mathematics
360 is a highly composite number and one of only seven numbers such that no number less than twice as much has more divisors; the others are 1, 2, 6, 12, 60, and 2520 .
360 is also a superior highly composite number, a c... |
https://en.wikipedia.org/wiki/Dedekind%20eta%20function | In mathematics, the Dedekind eta function, named after Richard Dedekind, is a modular form of weight 1/2 and is a function defined on the upper half-plane of complex numbers, where the imaginary part is positive. It also occurs in bosonic string theory.
Definition
For any complex number with , let ; then the eta func... |
https://en.wikipedia.org/wiki/Dirichlet%20eta%20function | In mathematics, in the area of analytic number theory, the Dirichlet eta function is defined by the following Dirichlet series, which converges for any complex number having real part > 0:
This Dirichlet series is the alternating sum corresponding to the Dirichlet series expansion of the Riemann zeta function, ζ(s) — ... |
https://en.wikipedia.org/wiki/Statistics%20Belgium | Statistics Belgium (formerly known as the NSI) is part of the Federal Public Service Economy, SMEs, Self-Employed and Energy.
Statistics Belgium conducts surveys among households and enterprises in Belgium. It uses and processes existing administrative databases (the national register) and provides data to Belgian and... |
https://en.wikipedia.org/wiki/Weierstrass%20elliptic%20function | In mathematics, the Weierstrass elliptic functions are elliptic functions that take a particularly simple form. They are named for Karl Weierstrass. This class of functions are also referred to as ℘-functions and they are usually denoted by the symbol ℘, a uniquely fancy script p. They play an important role in the the... |
https://en.wikipedia.org/wiki/Algebraic%20function%20field | In mathematics, an algebraic function field (often abbreviated as function field) of n variables over a field k is a finitely generated field extension K/k which has transcendence degree n over k. Equivalently, an algebraic function field of n variables over k may be defined as a finite field extension of the field K =... |
https://en.wikipedia.org/wiki/Ernst%20Schr%C3%B6der%20%28mathematician%29 | Friedrich Wilhelm Karl Ernst Schröder (25 November 1841 in Mannheim, Baden, Germany – 16 June 1902 in Karlsruhe, Germany) was a German mathematician mainly known for his work on algebraic logic. He is a major figure in the history of mathematical logic, by virtue of summarizing and extending the work of George Boole, A... |
https://en.wikipedia.org/wiki/Almost%20disjoint%20sets | In mathematics, two sets are almost disjoint if their intersection is small in some sense; different definitions of "small" will result in different definitions of "almost disjoint".
Definition
The most common choice is to take "small" to mean finite. In this case, two sets are almost disjoint if their intersection i... |
https://en.wikipedia.org/wiki/Heisenberg%20group | In mathematics, the Heisenberg group , named after Werner Heisenberg, is the group of 3×3 upper triangular matrices of the form
under the operation of matrix multiplication. Elements a, b and c can be taken from any commutative ring with identity, often taken to be the ring of real numbers (resulting in the "continuou... |
https://en.wikipedia.org/wiki/Pardo%20Brazilians | In Brazil, Pardo () is an ethnic and skin color category used by the Brazilian Institute of Geography and Statistics (IBGE) in the Brazilian censuses. The term "pardo" is a complex one, more commonly used to refer to Brazilians of mixed ethnic ancestries.
Pardo Brazilians represent a diverse range of skin colors and e... |
https://en.wikipedia.org/wiki/Cyclic%20permutation | In mathematics, and in particular in group theory, a cyclic permutation is a permutation consisting of a single cycle. In some cases, cyclic permutations are referred to as cycles; if a cyclic permutation has k elements, it may be called a k-cycle. Some authors widen this definition to include permutations with fixed p... |
https://en.wikipedia.org/wiki/Horseshoe%20map | In the mathematics of chaos theory, a horseshoe map is any member of a class of chaotic maps of the square into itself. It is a core example in the study of dynamical systems. The map was introduced by Stephen Smale while studying the behavior of the orbits of the van der Pol oscillator. The action of the map is define... |
https://en.wikipedia.org/wiki/Bilinear%20form | In mathematics, a bilinear form is a bilinear map on a vector space (the elements of which are called vectors) over a field K (the elements of which are called scalars). In other words, a bilinear form is a function that is linear in each argument separately:
and
and
The dot product on is an example of a... |
https://en.wikipedia.org/wiki/%E2%88%921 | In mathematics, −1 (negative one or minus one) is the additive inverse of 1, that is, the number that when added to 1 gives the additive identity element, 0. It is the negative integer greater than negative two (−2) and less than 0.
Algebraic properties
Multiplication
Multiplying a number by −1 is equivalent to chan... |
https://en.wikipedia.org/wiki/Fixed%20point%20%28mathematics%29 | {{hatnote|1=Fixed points in mathematics are not to be confused with other uses of "fixed point", or stationary points where {{math|1=f(x) = 0}}.}}
In mathematics, a fixed point (sometimes shortened to fixpoint), also known as an invariant point, is a value that does not change under a given transformation. Specificall... |
https://en.wikipedia.org/wiki/Theta%20function | In mathematics, theta functions are special functions of several complex variables. They show up in many topics, including Abelian varieties, moduli spaces, quadratic forms, and solitons. As Grassmann algebras, they appear in quantum field theory.
The most common form of theta function is that occurring in the theory ... |
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