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Stephen Smale - Wikipedia

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

Bali myna - Wikipedia

https://en.wikipedia.org/wiki/Bali_myna
[1] In 2018, there were three locations on Bali where the birds existed in the wild: the West Bali National Park; Bali's small island of Nusa Penida and Begawan Foundation's breeding and release site at Melinggih Kelod, Payangan

Theorem - Wikipedia

https://en.wikipedia.org/wiki/Theorem
Moreover, many authors qualify as theorems only the most important results, and use the terms lemma, proposition and corollary for less important theorems

Saul Kripke - Wikipedia

https://en.wikipedia.org/wiki/Saul_Kripke
|edition=Fall 2016 |language=en}}</ref> [[direct reference theory]], criticism of the [[Frege–Russell view]])<br />[[Admissible ordinal]]<br />[[Kripke structure]]<br />[[Rigid designator|Rigid]] vs

Markov chain - Wikipedia

https://en.wikipedia.org/wiki/Markov_chain
Markov chains have many applications as statistical models of real-world processes

Tragedy of the commons - Wikipedia

https://en.wikipedia.org/wiki/Tragedy_of_the_commons
He postulated that if a herder put more than his allotted number of cattle on the common, overgrazing could result

Nicolaus Copernicus - Wikipedia

https://en.wikipedia.org/wiki/Nicolaus_Copernicus
Jump to content Main menu Main menu move to sidebar hide Navigation Main page Contents Current events Random article About Wikipedia Contact us Contribute Help Learn to edit Community portal Recent changes Upload file Special pages

Chrysler PT Cruiser

https://en.wikipedia.org/wiki/Chrysler_PT_Cruiser
com/chrysler/pt-cruiser/2004/ |publisher=Kelly Blue Book |access-date=3 January 2021}}</ref>"},"platform":{"wt":"Chrysler PT platform"},"related":{"wt":"[[Dodge SRT4]]<br/>[[Dodge Neon]]"},"predecessor":{"wt":"[[Dodge Neon]] (Japan)"},"successor":{"wt":"[[Dodge Caliber]] (Japan)"},"layout":{"wt":"[[Front-engine, front

Role-playing video game

https://en.wikipedia.org/wiki/Role-playing_video_game
Players explore a game world, while solving puzzles and engaging in combat

Nakayama's lemma - Wikipedia

https://en.wikipedia.org/wiki/Nakayama's_lemma
Informally, the lemma immediately gives a precise sense in which finitely generated modules over a commutative ring behave like vector spaces over a field

Boolean prime ideal theorem - Wikipedia

https://en.wikipedia.org/wiki/Boolean_prime_ideal_theorem
A variation of this statement for filters on sets is known as the ultrafilter lemma

Prime ideal - Wikipedia

https://en.wikipedia.org/wiki/Prime_ideal
This generalizes the following property of prime numbers, known as Euclid's lemma: if p is a prime number and if p divides a product ab of two integers, then p divides a or p divides b

Basis (linear algebra) - Wikipedia

https://en.wikipedia.org/wiki/Basis_(linear_algebra)
: bases) if every element of V can be written in a unique way as a finite linear combination of elements of B

Stochastic calculus - Wikipedia

https://en.wikipedia.org/wiki/Stochastic_calculus
This field was created and started by the Japanese mathematician Kiyosi Itô during World War II

Integral element - Wikipedia

https://en.wikipedia.org/wiki/Integral_extension
over a subring A of B if b is a root of some monic polynomial over A

Division ring - Wikipedia

https://en.wikipedia.org/wiki/Skew-field
In general, if R is a ring and S is a simple module over R, then, by Schur's lemma, the endomorphism ring of S is a division ring;[6] every division ring arises in this fashion from some simple module

Consistent estimator - Wikipedia

https://en.wikipedia.org/wiki/Consistent_estimator
If the sequence of estimates can be mathematically shown to converge in probability to the true value θ0, it is called a consistent estimator; otherwise the estimator is said to be inconsistent

Noether's second theorem

https://en.wikipedia.org/wiki/Noether's_second_theorem
Specifically, the theorem says that if the action has an infinite-dimensional Lie algebra of infinitesimal symmetries parameterized linearly by k arbitrary functions and their derivatives up to order m, then the functional derivatives of L satisfy a system of k differential equations

Measurable function - Wikipedia

https://en.wikipedia.org/wiki/Measurable_function
} A function f : X → Y {\displaystyle f:X\to Y} is said to be measurable if for every E ∈ T {\displaystyle E\in \mathrm {T} } the pre-image of E {\displaystyle E} under f {\displaystyle f} is in Σ {\displaystyle \Sigma } ; that is, for all E ∈ T {\displaystyle E\in \mathrm {T} } f − 1 ( E ) := { x ∈ X ∣ f

Local ring - Wikipedia

https://en.wikipedia.org/wiki/Local_ring
1 ≠ 0 and if x is any element of R, then x or 1 − x is a unit

Module homomorphism - Wikipedia

https://en.wikipedia.org/wiki/Module_homomorphism
Explicitly, if M and N are left modules over a ring R, then a function f : M → N {\displaystyle f:M\to N} is called an R-module homomorphism or an R-linear map if for any x, y in M and r in R, f ( x + y ) = f ( x ) + f ( y ) , {\displaystyle f(x+y)=f(x)+f(y),} f ( r x ) = r f ( x )

Annihilator (ring theory) - Wikipedia

https://en.wikipedia.org/wiki/Faithful_module
For example, if R {\displaystyle R} is a commutative ring and I {\displaystyle I} is an ideal of R {\displaystyle R} , we can consider the quotient ring R / I {\displaystyle R/I} to be an R {\displaystyle R} -module

Commutator - Wikipedia

https://en.wikipedia.org/wiki/Commutator_(ring_theory)
[1] This element is equal to the group's identity if and only if g and h commute (that is, if and only if gh = hg)

Euclidean division - Wikipedia

https://en.wikipedia.org/wiki/Euclidean_division
This can be confirmed using multiplication, the inverse of division: if each of the 4 people received 2 slices, then 4 × 2 = 8 slices were given out in total

Ideal (order theory) - Wikipedia

https://en.wikipedia.org/wiki/Ideal_(order_theory)
In this case, the following equivalent definition can be given: a subset I of a lattice ( P , ≤ ) {\displaystyle (P,\leq )} is an ideal if and only if it is a lower set that is closed under finite joins (suprema); that is, it is nonempty and for all x, y in I, the element x ∨ y {\displaystyle x\vee y} of P is also

Korean verbs

https://en.wikipedia.org/wiki/Korean_verbs
If the verbal root ends in a vowel, the two vowels may merge or contract

Cohen–Macaulay ring - Wikipedia

https://en.wikipedia.org/wiki/Unmixed_ideal
finitely generated) R-module M ≠ 0 {\displaystyle M\neq 0} is a Cohen–Macaulay module if d e p t h ( M ) = d i m ( M ) {\displaystyle \mathrm {depth} (M)=\mathrm {dim} (M)} (in general we have: d e p t h ( M ) ≤ d i m ( M ) {\displaystyle \mathrm {depth} (M)\leq \mathrm {dim} (M)} , see Auslander–Buchsbaum

Discrete space - Wikipedia

https://en.wikipedia.org/wiki/Discrete_space
X {\displaystyle X} is defined by letting every superset of the diagonal { ( x , x ) : x ∈ X } {\displaystyle \{(x,x):x\in X\}} in X × X {\displaystyle X\times X} be an entourage, and X {\displaystyle X} is a discrete uniform space if it is equipped with its discrete uniformity

Embedding - Wikipedia

https://en.wikipedia.org/wiki/Embedding
[3] More explicitly, an injective continuous map f : X → Y {\displaystyle f:X\to Y} between topological spaces X {\displaystyle X} and Y {\displaystyle Y} is a topological embedding if f {\displaystyle f} yields a homeomorphism between X {\displaystyle X} and f ( X ) {\displaystyle f(X)} (where f ( X ) {\displaystyle

Projective module - Wikipedia

https://en.wikipedia.org/wiki/Projective_dimension
However, every projective module is a free module if the ring is a principal ideal domain such as the integers, or a (multivariate) polynomial ring over a field (this is the Quillen–Suslin theorem)