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Elliptic modular form Summary Modular_function In mathematics, a modular form is a (complex) analytic function on the upper half-plane that satisfies: a kind of functional equation with respect to the group action of the modular group, and a growth condition.The theory of modular forms therefore belongs to complex anal... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Elliptic modular form Summary Modular_function Modular form theory is a special case of the more general theory of automorphic forms, which are functions defined on Lie groups that transform nicely with respect to the action of certain discrete subgroups, generalizing the example of the modular group S L 2 ( Z ) ⊂ S L ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Modular invariant of a group Summary Modular_invariant_of_a_group In mathematics, a modular invariant of a group is an invariant of a finite group acting on a vector space of positive characteristic (usually dividing the order of the group). The study of modular invariants was originated in about 1914 by Dickson (2004)... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Right module Summary Module_(ring_theory) In mathematics, a module is a generalization of the notion of vector space in which the field of scalars is replaced by a ring. The concept of module generalizes also the notion of abelian group, since the abelian groups are exactly the modules over the ring of integers. Like a... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Countably generated module Summary Countably_generated_module In mathematics, a module over a (not necessarily commutative) ring is countably generated if it is generated as a module by a countable subset. The importance of the notion comes from Kaplansky's theorem (Kaplansky 1958), which states that a projective modul... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Fine moduli scheme Summary Fine_moduli_scheme In mathematics, a moduli scheme is a moduli space that exists in the category of schemes developed by Alexander Grothendieck. Some important moduli problems of algebraic geometry can be satisfactorily solved by means of scheme theory alone, while others require some extensi... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Moment matrix Summary Moment_matrix In mathematics, a moment matrix is a special symmetric square matrix whose rows and columns are indexed by monomials. The entries of the matrix depend on the product of the indexing monomials only (cf. Hankel matrices.) Moment matrices play an important role in polynomial fitting, po... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Moment problem Summary Moment_problem In mathematics, a moment problem arises as the result of trying to invert the mapping that takes a measure μ to the sequence of moments m n = ∫ − ∞ ∞ x n d μ ( x ) . {\displaystyle m_{n}=\int _{-\infty }^{\infty }x^{n}\,d\mu (x)\,.} More generally, one may consider m n = ∫ − ∞ ∞ M ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Monogenic field Summary Power_integral_basis In mathematics, a monogenic field is an algebraic number field K for which there exists an element a such that the ring of integers OK is the subring Z of K generated by a. Then OK is a quotient of the polynomial ring Z and the powers of a constitute a power integral basis. ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Monogenic semigroup Summary Periodic_semigroup In mathematics, a monogenic semigroup is a semigroup generated by a single element. Monogenic semigroups are also called cyclic semigroups. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Monoidal category of endofunctors Summary Monoidal_category In mathematics, a monoidal category (or tensor category) is a category C {\displaystyle \mathbf {C} } equipped with a bifunctor ⊗: C × C → C {\displaystyle \otimes :\mathbf {C} \times \mathbf {C} \to \mathbf {C} } that is associative up to a natural isomorphis... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Monoidal category of endofunctors Summary Monoidal_category Monoidal categories can be seen as a generalization of these and other examples. Every (small) monoidal category may also be viewed as a "categorification" of an underlying monoid, namely the monoid whose elements are the isomorphism classes of the category's ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Monoidal category of endofunctors Summary Monoidal_category The associativity up to isomorphism is then a way of expressing that different ways of aggregating the same data—such as ( ( a , b ) , c ) {\displaystyle ((a,b),c)} and ( a , ( b , c ) ) {\displaystyle (a,(b,c))} —store the same information even though the agg... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Monoidal category of endofunctors Summary Monoidal_category For type sum, the identity object is the void type, which stores no information and it is impossible to address an inhabitant. The concept of monoidal category does not presume that values of such aggregate types can be taken apart; on the contrary, it provide... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Monoidal category of endofunctors Summary Monoidal_category Monoidal categories have numerous applications outside of category theory proper. They are used to define models for the multiplicative fragment of intuitionistic linear logic. They also form the mathematical foundation for the topological order in condensed m... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Simple expression Summary Monomial In mathematics, a monomial is, roughly speaking, a polynomial which has only one term. Two definitions of a monomial may be encountered: A monomial, also called power product, is a product of powers of variables with nonnegative integer exponents, or, in other words, a product of vari... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Simple expression Summary Monomial If only a single variable x {\displaystyle x} is considered, this means that a monomial is either 1 {\displaystyle 1} or a power x n {\displaystyle x^{n}} of x {\displaystyle x} , with n {\displaystyle n} a positive integer. If several variables are considered, say, x , y , z , {\disp... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Simple expression Summary Monomial A monomial in the first sense is a special case of a monomial in the second sense, where the coefficient is 1 {\displaystyle 1} . For example, in this interpretation − 7 x 5 {\displaystyle -7x^{5}} and ( 3 − 4 i ) x 4 y z 13 {\displaystyle (3-4i)x^{4}yz^{13}} are monomials (in the sec... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Monomial ordering Summary Monomial_ordering In mathematics, a monomial order (sometimes called a term order or an admissible order) is a total order on the set of all (monic) monomials in a given polynomial ring, satisfying the property of respecting multiplication, i.e., If u ≤ v {\displaystyle u\leq v} and w {\displa... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Monopole (mathematics) Summary Monopole_(mathematics) In mathematics, a monopole is a connection over a principal bundle G with a section of the associated adjoint bundle. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Monothetic group Summary Monothetic_group In mathematics, a monothetic group is a topological group with a dense cyclic subgroup. They were introduced by Van Dantzig (1933). An example is the additive group of p-adic integers, in which the integers are dense. A monothetic group is necessarily abelian. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Monotonically non-decreasing Summary Strictly_increasing_function In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. This concept first arose in calculus, and was later generalized to the more abstract setting of order theory. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Moving frame Summary Moving_frame 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. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Integer multiple Summary Integer_multiple In mathematics, a multiple is the product of any quantity and an integer. In other words, for the quantities a and b, it can be said that b is a multiple of a if b = na for some integer n, which is called the multiplier. If a is not zero, this is equivalent to saying that b / a... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Multiplication tables Summary Times_table In mathematics, a multiplication table (sometimes, less formally, a times table) is a mathematical table used to define a multiplication operation for an algebraic system. The decimal multiplication table was traditionally taught as an essential part of elementary arithmetic ar... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Multiplicative cascade Summary Multiplicative_cascade In mathematics, a multiplicative cascade is a fractal/multifractal distribution of points produced via an iterative and multiplicative random process. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Multiplicative character Summary Multiplicative_character In mathematics, a multiplicative character (or linear character, or simply character) on a group G is a group homomorphism from G to the multiplicative group of a field (Artin 1966), usually the field of complex numbers. If G is any group, then the set Ch(G) of ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Multiplicative character Summary Multiplicative_character Dirichlet characters can be seen as a special case of this definition. Multiplicative characters are linearly independent, i.e. if χ 1 , χ 2 , … , χ n {\displaystyle \chi _{1},\chi _{2},\ldots ,\chi _{n}} are different characters on a group G then from a 1 χ 1 +... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Reciprocal value Summary Arithmetic_inverse In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x−1, is a number which when multiplied by x yields the multiplicative identity, 1. The multiplicative inverse of a fraction a/b is b/a. For the multiplicative inverse of a real number, di... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Reciprocal value Summary Arithmetic_inverse The reciprocal function, the function f(x) that maps x to 1/x, is one of the simplest examples of a function which is its own inverse (an involution). Multiplying by a number is the same as dividing by its reciprocal and vice versa. For example, multiplication by 4/5 (or 0.8)... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Reciprocal value Summary Arithmetic_inverse Therefore, multiplication by a number followed by multiplication by its reciprocal yields the original number (since the product of the number and its reciprocal is 1). The term reciprocal was in common use at least as far back as the third edition of Encyclopædia Britannica ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Reciprocal value Summary Arithmetic_inverse In these cases it can happen that ab ≠ ba; then "inverse" typically implies that an element is both a left and right inverse. The notation f −1 is sometimes also used for the inverse function of the function f, which is for most functions not equal to the multiplicative inver... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Multiplicative sequence Summary Multiplicative_sequence In mathematics, a multiplicative sequence or m-sequence is a sequence of polynomials associated with a formal group structure. They have application in the cobordism ring in algebraic topology. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Multiperfect number Summary Triperfect_number In mathematics, a multiply perfect number (also called multiperfect number or pluperfect number) is a generalization of a perfect number. For a given natural number k, a number n is called k-perfect (or k-fold perfect) if the sum of all positive divisors of n (the divisor f... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Series multisection Summary Series_multisection In mathematics, a multisection of a power series is a new power series composed of equally spaced terms extracted unaltered from the original series. Formally, if one is given a power series ∑ n = − ∞ ∞ a n ⋅ z n {\displaystyle \sum _{n=-\infty }^{\infty }a_{n}\cdot z^{n}... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Multiset Summary Multiset_coefficient In mathematics, a multiset (or bag, or mset) is a modification of the concept of a set that, unlike a set, allows for multiple instances for each of its elements. The number of instances given for each element is called the multiplicity of that element in the multiset. As a consequ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Multiset Summary Multiset_coefficient In the multiset {a, a, a, b, b, b}, a and b both have multiplicity 3.These objects are all different when viewed as multisets, although they are the same set, since they all consist of the same elements. As with sets, and in contrast to tuples, the order in which elements are liste... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Multiset Summary Multiset_coefficient For example, in the multiset {a, a, b, b, b, c} the multiplicities of the members a, b, and c are respectively 2, 3, and 1, and therefore the cardinality of this multiset is 6. Nicolaas Govert de Bruijn coined the word multiset in the 1970s, according to Donald Knuth. : 694 However... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Multiset Summary Multiset_coefficient Knuth himself attributes the first study of multisets to the Indian mathematician Bhāskarāchārya, who described permutations of multisets around 1150. Other names have been proposed or used for this concept, including list, bunch, bag, heap, sample, weighted set, collection, and su... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Multisymplectic integrator Summary Multisymplectic_integrator In mathematics, a multisymplectic integrator is a numerical method for the solution of a certain class of partial differential equations, that are said to be multisymplectic. Multisymplectic integrators are geometric integrators, meaning that they preserve t... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Many-valued function Summary Single-valued_function In mathematics, a multivalued function, also called multifunction and many-valued function, is a set-valued function with continuity properties that allow considering it locally as an ordinary function. Multivalued functions arise commonly in applications of the impli... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Many-valued function Summary Single-valued_function It cannot be considered as an ordinary function, since, when one follows one value of the logarithm along a circle centered at 0, one gets another value than the starting one after a complete turn. This phenomenon is called monodromy. Another common way for defining a... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Absolute irreducibility Summary Absolutely_irreducible In mathematics, a multivariate polynomial defined over the rational numbers is absolutely irreducible if it is irreducible over the complex field. For example, x 2 + y 2 − 1 {\displaystyle x^{2}+y^{2}-1} is absolutely irreducible, but while x 2 + y 2 {\displaystyle... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Isotope (Jordan algebra) Summary Mutation_(Jordan_algebra) In mathematics, a mutation, also called a homotope, of a unital Jordan algebra is a new Jordan algebra defined by a given element of the Jordan algebra. The mutation has a unit if and only if the given element is invertible, in which case the mutation is called... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Isotope (Jordan algebra) Summary Mutation_(Jordan_algebra) Their functorial properties allow an explicit construction of the corresponding Hermitian symmetric space of compact type as a compactification of a finite-dimensional complex semisimple Jordan algebra. The automorphism group of the compactification becomes a c... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Natural bundle Summary Natural_bundle In mathematics, a natural bundle is any fiber bundle associated to the s-frame bundle F s ( M ) {\displaystyle F^{s}(M)} for some s ≥ 1 {\displaystyle s\geq 1} . It turns out that its transition functions depend functionally on local changes of coordinates in the base manifold M {\... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bi-unitary divisor Summary Bi-unitary_divisor In mathematics, a natural number a is a unitary divisor (or Hall divisor) of a number b if a is a divisor of b and if a and b a {\displaystyle {\frac {b}{a}}} are coprime, having no common factor other than 1. Thus, 5 is a unitary divisor of 60, because 5 and 60 5 = 12 {\di... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bi-unitary divisor Summary Bi-unitary_divisor Equivalently, a divisor a of b is a unitary divisor if and only if every prime factor of a has the same multiplicity in a as it has in b. The sum-of-unitary-divisors function is denoted by the lowercase Greek letter sigma thus: σ*(n). The sum of the k-th powers of the unita... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Kaprekar number Summary Kaprekar_number In mathematics, a natural number in a given number base is a p {\displaystyle p} -Kaprekar number if the representation of its square in that base can be split into two parts, where the second part has p {\displaystyle p} digits, that add up to the original number. The numbers ar... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Blum integer Summary Blum_integer In mathematics, a natural number n is a Blum integer if n = p × q is a semiprime for which p and q are distinct prime numbers congruent to 3 mod 4. That is, p and q must be of the form 4t + 3, for some integer t. Integers of this form are referred to as Blum primes. This means that the... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Near polygon Summary Near_polygon In mathematics, a near polygon is an incidence geometry introduced by Ernest E. Shult and Arthur Yanushka in 1980. Shult and Yanushka showed the connection between the so-called tetrahedrally closed line-systems in Euclidean spaces and a class of point-line geometries which they called... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Near-field (mathematics) Summary Near-field_(mathematics) In mathematics, a near-field is an algebraic structure similar to a division ring, except that it has only one of the two distributive laws. Alternatively, a near-field is a near-ring in which there is a multiplicative identity and every non-zero element has a m... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Near-ring Summary Near-ring In mathematics, a near-ring (also near ring or nearring) is an algebraic structure similar to a ring but satisfying fewer axioms. Near-rings arise naturally from functions on groups. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Near-semiring Summary Near-semiring In mathematics, a near-semiring, also called a seminearring, is an algebraic structure more general than a near-ring or a semiring. Near-semirings arise naturally from functions on monoids. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Nearly Kähler manifold Summary Nearly_Kähler_manifold In mathematics, a nearly Kähler manifold is an almost Hermitian manifold M {\displaystyle M} , with almost complex structure J {\displaystyle J} , such that the (2,1)-tensor ∇ J {\displaystyle \nabla J} is skew-symmetric. So, ( ∇ X J ) X = 0 {\displaystyle (\nabla _... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Nearly Kähler manifold Summary Nearly_Kähler_manifold For example, the nearly Kähler six-sphere S 6 {\displaystyle S^{6}} is an example of a nearly Kähler manifold that is not Kähler. The familiar almost complex structure on the six-sphere is not induced by a complex atlas on S 6 {\displaystyle S^{6}} . Usually, non Kä... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Nearly Kähler manifold Summary Nearly_Kähler_manifold Nearly Kähler manifolds, also known as almost Tachibana manifolds, were studied by Shun-ichi Tachibana in 1959 and then by Alfred Gray from 1970 on. For example, it was proved that any 6-dimensional strict nearly Kähler manifold is an Einstein manifold and has vanis... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Nearly Kähler manifold Summary Nearly_Kähler_manifold In the 1980s, strict nearly Kähler manifolds obtained a lot of consideration because of their relation to Killing spinors: Thomas Friedrich and Ralf Grunewald showed that a 6-dimensional Riemannian manifold admits a Riemannian Killing spinor if and only if it is nea... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Nearly Kähler manifold Summary Nearly_Kähler_manifold Each of these admits such a unique nearly Kähler metric that is also homogeneous, and these examples are in fact the only compact homogeneous strictly nearly Kähler 6-manifolds. However, Foscolo and Haskins recently showed that S 6 {\displaystyle S^{6}} and S 3 × S ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Nearly Kähler manifold Summary Nearly_Kähler_manifold An almost Kähler manifold M {\displaystyle M} is an almost Hermitian manifold with a closed Kähler form: d ω = 0 {\displaystyle d\omega =0} . The Kähler form or fundamental 2-form ω {\displaystyle \omega } is defined by ω ( X , Y ) = g ( J X , Y ) , {\displaystyle \... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Negative number Summary Negative_numbers In mathematics, a negative number represents an opposite. In the real number system, a negative number is a number that is less than zero. Negative numbers are often used to represent the magnitude of a loss or deficiency. A debt that is owed may be thought of as a negative asse... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Negative number Summary Negative_numbers If a quantity, such as the charge on an electron, may have either of two opposite senses, then one may choose to distinguish between those senses—perhaps arbitrarily—as positive and negative. Negative numbers are used to describe values on a scale that goes below zero, such as t... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Negative number Summary Negative_numbers For example, −(−3) = 3 because the opposite of an opposite is the original value. Negative numbers are usually written with a minus sign in front. For example, −3 represents a negative quantity with a magnitude of three, and is pronounced "minus three" or "negative three". | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Negative number Summary Negative_numbers To help tell the difference between a subtraction operation and a negative number, occasionally the negative sign is placed slightly higher than the minus sign (as a superscript). Conversely, a number that is greater than zero is called positive; zero is usually (but not always)... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Negative number Summary Negative_numbers In general, the negativity or positivity of a number is referred to as its sign. Every real number other than zero is either positive or negative. The non-negative whole numbers are referred to as natural numbers (i.e., 0, 1, 2, 3...), while the positive and negative whole numbe... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Negative number Summary Negative_numbers (Some definitions of the natural numbers exclude zero.) In bookkeeping, amounts owed are often represented by red numbers, or a number in parentheses, as an alternative notation to represent negative numbers. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Negative number Summary Negative_numbers It has been proposed that negative numbers were used on the Greek counting table at Salamis, known as the Salamis Tablet, dated to 300 BC. Negative numbers were also used in the Nine Chapters on the Mathematical Art, which in its present form dates from the period of the Chinese... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Negative number Summary Negative_numbers Liu Hui (c. 3rd century) established rules for adding and subtracting negative numbers. By the 7th century, Indian mathematicians such as Brahmagupta were describing the use of negative numbers. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Negative number Summary Negative_numbers Islamic mathematicians further developed the rules of subtracting and multiplying negative numbers and solved problems with negative coefficients. Prior to the concept of negative numbers, mathematicians such as Diophantus considered negative solutions to problems "false" and eq... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Negligible set Summary Negligible_set In mathematics, a negligible set is a set that is small enough that it can be ignored for some purpose. As common examples, finite sets can be ignored when studying the limit of a sequence, and null sets can be ignored when studying the integral of a measurable function. Negligible... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Negligible set Summary Negligible_set For some purposes, we also need this ideal to be a sigma-ideal, so that countable unions of negligible sets are also negligible. If I and J are both ideals of subsets of the same set X, then one may speak of I-negligible and J-negligible subsets. The opposite of a negligible set is... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Nilcurve Summary Nilcurve In mathematics, a nilcurve is a pointed stable curve over a finite field with an indigenous bundle whose p-curvature is square nilpotent. Nilcurves were introduced by Mochizuki (1996) as a central concept in his theory of p-adic Teichmüller theory. The nilcurves form a stack over the moduli st... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Nil manifold Summary Nil_manifold In mathematics, a nilmanifold is a differentiable manifold which has a transitive nilpotent group of diffeomorphisms acting on it. As such, a nilmanifold is an example of a homogeneous space and is diffeomorphic to the quotient space N / H {\displaystyle N/H} , the quotient of a nilpot... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Nil manifold Summary Nil_manifold A Riemannian manifold is called a homogeneous nilmanifold if there exist a nilpotent group of isometries acting transitively on it. The requirement that the transitive nilpotent group acts by isometries leads to the following rigid characterization: every homogeneous nilmanifold is iso... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Non-Archimedean ordered field Summary Non-Archimedean_ordered_field In mathematics, a non-Archimedean ordered field is an ordered field that does not satisfy the Archimedean property. Examples are the Levi-Civita field, the hyperreal numbers, the surreal numbers, the Dehn field, and the field of rational functions with... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Non-Desarguesian plane Summary Non-Desarguesian_projective_plane In mathematics, a non-Desarguesian plane is a projective plane that does not satisfy Desargues' theorem (named after Girard Desargues), or in other words a plane that is not a Desarguesian plane. The theorem of Desargues is true in all projective spaces o... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Non-Euclidean crystallographic group Summary Non-Euclidean_crystallographic_group In mathematics, a non-Euclidean crystallographic group, NEC group or N.E.C. group is a discrete group of isometries of the hyperbolic plane. These symmetry groups correspond to the wallpaper groups in euclidean geometry. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Non-Euclidean crystallographic group Summary Non-Euclidean_crystallographic_group A NEC group which contains only orientation-preserving elements is called a Fuchsian group, and any non-Fuchsian NEC group has an index 2 Fuchsian subgroup of orientation-preserving elements. The hyperbolic triangle groups are notable NEC... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Relativistic system (mathematics) Summary Relativistic_system_(mathematics) In mathematics, a non-autonomous system of ordinary differential equations is defined to be a dynamic equation on a smooth fiber bundle Q → R {\displaystyle Q\to \mathbb {R} } over R {\displaystyle \mathbb {R} } . For instance, this is the case... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Relativistic system (mathematics) Summary Relativistic_system_(mathematics) Therefore, it is called the relativistic system. In particular, Special Relativity on the Minkowski space Q = R 4 {\displaystyle Q=\mathbb {R} ^{4}} is of this type. Since a configuration space Q {\displaystyle Q} of a relativistic system has n... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Relativistic system (mathematics) Summary Relativistic_system_(mathematics) The notion of jets of submanifolds generalizes that of jets of sections of fiber bundles which are utilized in covariant classical field theory and non-autonomous mechanics. A first order jet bundle J 1 1 Q → Q {\displaystyle J_{1}^{1}Q\to Q} i... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Relativistic system (mathematics) Summary Relativistic_system_(mathematics) Given coordinates ( q 0 , q i ) {\displaystyle (q^{0},q^{i})} on Q {\displaystyle Q} , a first order jet manifold J 1 1 Q {\displaystyle J_{1}^{1}Q} is provided with the adapted coordinates ( q 0 , q i , q 0 i ) {\displaystyle (q^{0},q^{i},q_{0... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Relativistic system (mathematics) Summary Relativistic_system_(mathematics) Then a generic equation of motion of a relativistic system in terms of relativistic velocities reads ( ∂ λ G μ α 2 … α 2 N 2 N − ∂ μ G λ α 2 … α 2 N ) q τ μ q τ α 2 ⋯ q τ α 2 N − ( 2 N − 1 ) G λ μ α 3 … α 2 N q τ τ μ q τ α 3 ⋯ q τ α 2 N + F λ μ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Delta-ring Summary Delta-ring In mathematics, a non-empty collection of sets R {\displaystyle {\mathcal {R}}} is called a δ-ring (pronounced "delta-ring") if it is closed under union, relative complementation, and countable intersection. The name "delta-ring" originates from the German word for intersection, "Durschnit... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Non-measurable set Summary Non-measurable_subset In mathematics, a non-measurable set is a set which cannot be assigned a meaningful "volume". The mathematical existence of such sets is construed to provide information about the notions of length, area and volume in formal set theory. In Zermelo–Fraenkel set theory, th... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Non-measurable set Summary Non-measurable_subset The notion of a non-measurable set has been a source of great controversy since its introduction. Historically, this led Borel and Kolmogorov to formulate probability theory on sets which are constrained to be measurable. The measurable sets on the line are iterated coun... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Non-measurable set Summary Non-measurable_subset These sets are rich enough to include every conceivable definition of a set that arises in standard mathematics, but they require a lot of formalism to prove that sets are measurable. In 1970, Robert M. Solovay constructed the Solovay model, which shows that it is consis... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Nonabelian sheaf cohomology Summary Nonabelian_sheaf_cohomology In mathematics, a nonabelian cohomology is any cohomology with coefficients in a nonabelian group, a sheaf of nonabelian groups or even in a topological space. If homology is thought of as the abelianization of homotopy (cf. Hurewicz theorem), then the non... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Non-commutative ring Summary Non-commutative_localization In mathematics, a noncommutative ring is a ring whose multiplication is not commutative; that is, there exist a and b in the ring such that ab and ba are different. Equivalently, a noncommutative ring is a ring that is not a commutative ring. Noncommutative alge... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Non-commutative ring Summary Non-commutative_localization Sometimes the term noncommutative ring is used instead of ring to refer to an unspecified ring which is not necessarily commutative, and hence may be commutative. Generally, this is for emphasizing that the studied properties are not restricted to commutative ri... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Noncommutative unique factorization domain Summary Noncommutative_unique_factorization_domain In mathematics, a noncommutative unique factorization domain is a noncommutative ring with the unique factorization property. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Noncototient Summary Noncototient In mathematics, a noncototient is a positive integer n that cannot be expressed as the difference between a positive integer m and the number of coprime integers below it. That is, m − φ(m) = n, where φ stands for Euler's totient function, has no solution for m. The cototient of n is d... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Noncototient Summary Noncototient {\displaystyle pq-\varphi (pq)=pq-(p-1)(q-1)=p+q-1=n-1.\,} It is expected that every even number larger than 6 is a sum of two distinct primes, so probably no odd number larger than 5 is a noncototient. The remaining odd numbers are covered by the observations 1 = 2 − ϕ ( 2 ) , 3 = 9 −... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Nonelementary Integral Summary Nonelementary_Integral In mathematics, a nonelementary antiderivative of a given elementary function is an antiderivative (or indefinite integral) that is, itself, not an elementary function (i.e. a function constructed from a finite number of quotients of constant, algebraic, exponential... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Sigma-ring Summary Sigma-ring In mathematics, a nonempty collection of sets is called a 𝜎-ring (pronounced sigma-ring) if it is closed under countable union and relative complementation. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Symmetric set Summary Symmetric_set In mathematics, a nonempty subset S of a group G is said to be symmetric if it contains the inverses of all of its elements. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Nonhypotenuse number Summary Nonhypotenuse_number In mathematics, a nonhypotenuse number is a natural number whose square cannot be written as the sum of two nonzero squares. The name stems from the fact that an edge of length equal to a nonhypotenuse number cannot form the hypotenuse of a right angle triangle with int... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Nonhypotenuse number Summary Nonhypotenuse_number The first fifty nonhypotenuse numbers are: 1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 14, 16, 18, 19, 21, 22, 23, 24, 27, 28, 31, 32, 33, 36, 38, 42, 43, 44, 46, 47, 48, 49, 54, 56, 57, 59, 62, 63, 64, 66, 67, 69, 71, 72, 76, 77, 79, 81, 83, 84 (sequence A004144 in the OEIS)Althou... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Polynomial eigenvalue problem Summary Nonlinear_eigenproblem In mathematics, a nonlinear eigenproblem, sometimes nonlinear eigenvalue problem, is a generalization of the (ordinary) eigenvalue problem to equations that depend nonlinearly on the eigenvalue. Specifically, it refers to equations of the form M ( λ ) x = 0 ,... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Dynamic systems theory Nonlinear system Dynamical_systems_theory > Concepts > Nonlinear system In mathematics, a nonlinear system is a system that is not linear—i.e., a system that does not satisfy the superposition principle. Less technically, a nonlinear system is any problem where the variable(s) to solve for cannot... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
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