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https://en.wikipedia.org/wiki/Semigroup
If the semigroup operation is commutative, then the semigroup is called a commutative semigroup or (less often than in the analogous case of groups) it may be called an abelian semigroup
https://en.wikipedia.org/wiki/Theory_of_knots
Two mathematical knots are equivalent if one can be transformed into the other via a deformation of R 3 {\displaystyle \mathbb {R} ^{3}} upon itself (known as an ambient isotopy); these transformations correspond to manipulations of a knotted string that do not involve cutting it or passing it through itself
https://en.wikipedia.org/wiki/Autoregressive_conditional_heteroskedasticity
The ARCH model is appropriate when the error variance in a time series follows an autoregressive (AR) model; if an autoregressive moving average (ARMA) model is assumed for the error variance, the model is a generalized autoregressive conditional heteroskedasticity (GARCH) model
https://en.wikipedia.org/wiki/Projective_varieties
A projective variety is a projective curve if its dimension is one; it is a projective surface if its dimension is two; it is a projective hypersurface if its dimension is one less than the dimension of the containing projective space; in this case it is the set of zeros of a single homogeneous polynomial
https://en.wikipedia.org/wiki/Autoregressive_model
It can be used to describe time-varying processes from many natural and artificial sources
https://en.wikipedia.org/wiki/Mathematical_descriptions_of_the_electromagnetic_field
If only the electric field (E) is non-zero, and is constant in time, the field is said to be an electrostatic field
https://en.wikipedia.org/wiki/P-adic_number
as a slice of a solenoid
In number theory, given a prime number p,[a] the p-adic numbers form an extension of the rational numbers that is distinct from the real numbers, though with some similar properties; p-adic numbers can be written in a form similar to (possibly infinite) decimals, but with digits based on a
https://en.wikipedia.org/wiki/Excess_kurtosis
Different measures of kurtosis can yield varying interpretations
https://en.wikipedia.org/wiki/Formal_power_series_ring
Find sources: "Formal power series" – news · newspapers · books · scholar · JSTOR (December 2009) (Learn how and when to remove this message)
In mathematics, a formal series is an infinite sum that is considered independently from any notion of convergence, and can be manipulated with the usual algebraic
https://en.wikipedia.org/wiki/Inference_rule
If an argument with true premises follows a rule of inference then the conclusion cannot be false
https://en.wikipedia.org/wiki/Affine_connection
In differential geometry, an affine connection[a] is a geometric object on a smooth manifold which connects nearby tangent spaces, so it permits tangent vector fields to be differentiated as if they were functions on the manifold with values in a fixed vector space
https://en.wikipedia.org/wiki/Mathematical_logic
However, it can also include usage of logic to characterize correct mathematical reasoning or to establish foundations of mathematics
https://en.wikipedia.org/wiki/Hypothesis_test
In general, any statement about the parameters describing a population can be a hypothesis (but not a statement about the sample)
https://en.wikipedia.org/wiki/Spam_(food)
It was introduced in the United States in 1937 and gained popularity worldwide after its use during World War II
https://en.wikipedia.org/wiki/Hypothesis_testing
In general, any statement about the parameters describing a population can be a hypothesis (but not a statement about the sample)
https://en.wikipedia.org/wiki/Poisson_distribution
z-1\right)\right]}
Fisher information 1 λ {\displaystyle {\frac {1}{\lambda }}}
In probability theory and statistics, the Poisson distribution (/ˈpwɑːsɒn/) is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time if these events
https://en.wikipedia.org/wiki/Group_(mathematics)
In addition to their abstract properties, group theorists also study the different ways in which a group can be expressed concretely, both from a point of view of representation theory (that is, through the representations of the group) and of computational group theory
https://en.wikipedia.org/wiki/Child_development
Parents play a large role in a child's activities, socialization, and development; having multiple parents can add stability to a child's life and therefore encourage healthy development
https://en.wikipedia.org/wiki/List_of_general_topology_topics
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https://en.wikipedia.org/wiki/List_of_set_theory_topics
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https://en.wikipedia.org/wiki/List_of_representation_theory_topics
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https://en.wikipedia.org/wiki/List_of_topology_topics
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https://en.wikipedia.org/wiki/List_of_commutative_algebra_topics
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https://en.wikipedia.org/wiki/Elliott_H._Lieb
entropy principle]]<br>[[AKLT model|Affleck-Kennedy-Lieb-Tasaki model]]<br>[[Borell–Brascamp–Lieb inequality]]<br>[[Brascamp–Lieb inequality]]<br>[[Brezis–Lieb lemma]]<br>[[Strong subadditivity of quantum entropy#Carlen-Lieb Extension|Carlen–Lieb extension]]<br>[[Temperley–Lieb algebra]]<br>[[Dicke model]
https://en.wikipedia.org/wiki/Perfected_Spelling
for lemma entries in its dictionary)
https://en.wikipedia.org/wiki/Stephen_Smale
]]<br>[[Morse–Smale system]]<br>[[Morse–Smale diffeomorphism]]<br>[[Palais–Smale compactness condition]]<br>[[Blum–Shub–Smale machine]]<br>[[Smale–Williams attractor]]<br>[[Morse–Palais lemma]]<br>[[Regular homotopy]]<br>[[Sard's theorem]]<br>[[Sphere eversion]]<br>[[Structural stability]]<br>[[Whitehead
https://en.wikipedia.org/wiki/Lexicographer
Lexicographers are tasked with defining simple words as well as figuring out how compound or complex words or words with many meanings can be clearly explained
https://en.wikipedia.org/wiki/Operator_algebra
From this point of view, operator algebras can be regarded as a generalization of spectral theory of a single operator
https://en.wikipedia.org/wiki/Riemann%E2%80%93Stieltjes_integral
[2]
On the other hand, a classical result[3] shows that the integral is well-defined if f is α-Hölder continuous and g is β-Hölder continuous with 1"}},"i":0}}]}'>α + β > 1
https://en.wikipedia.org/wiki/Metalanguage
For example, to say that the word "noun" can be used as a noun in a sentence, one could write "noun" is a <noun>