adj
(mathematics) Being an abundant number, i.e. less than the sum of all of its divisors except itself.
n
(obsolete, mathematics) A polynomial equation in two variables
adj
(mathematics) Assigning finite values to finite quantities.
n
(uncountable, mathematics, graph theory) The subbranch of graph theory in which algebraic methods are applied to problems about graphs.
n
(more formally) a mathematical object comprising a carrier set (aka underlying set or domain), an optional scalar set, a set of operations (typically binary operations, but otherwise each of finite arity) and a set of identities (axioms) which the operations must satisfy.
n
(mathematics) The result produced by the formula for the limit of a parameterized series applied to any parameter values in which the series is not convergent.
adj
(set theory, order theory, of a binary relation R on a set S) Having the property that, for any two distinct elements of S, at least one is not related to the other via R; equivalently, having the property that, for any x, y ∈ S, if both xRy and yRx then x=y.
n
A branch of chemical engineering that uses geometric and mathematical optimization concepts to assist in the design of networks of chemical reactors.
n
(mathematical analysis) Upper bound function; see big O notation.
n
(mathematics) The Maclaurin series expansion of the function f(x) = (1 + x)^α, for arbitrary complex α; the series ∑ₖ₌₀ ᪲𝛼 choose kxᵏ, where 𝛼 choose k=(𝛼(𝛼-1)(𝛼-2)…(𝛼-k+1))/(k!).
n
(mathematics) A summation method for divergent series, particularly useful for summing divergent asymptotic series, and in some sense giving the best possible sum for such series.
n
(algebra, order theory) Any lattice (type of partially ordered set) that has both a greatest and a least element.
n
(uncountable, often definite, the calculus) Differential calculus and integral calculus considered as a single subject; analysis.
n
(set theory) The set of all possible pairs of elements whose components are members of two sets. Notation: X⨯Y=(x,y)|x∈X∧y∈Y.
n
(mathematics, mathematical analysis) The target set into which a function is formally defined to map elements of its domain; the set denoted Y in the notation f : X → Y.
adj
(algebra, of a lattice) In which every set with a lower bound has a greatest lower bound.
n
(mathematics) The following axiom (applied to an ordered field): for any subset of the given ordered field, if there is any upper bound for this subset, then there is also a supremum for this subset, and this supremum is an element of the given ordered field (though not necessarily of the subset).
n
(mathematical analysis) A function whose domain is a σ-algebra, whose codomain is the set of complex numbers, and which is countably additive.
n
(complex analysis) A number of the form a + bi, where a and b are real numbers and i denotes the imaginary unit
adj
(mathematics) Having a difference divisible by a modulus.
adj
(mathematics) That uses congruency (division by a modulus)
adj
(mathematics) Composed of elements that are each expressible by a unary polynomial.
n
(mathematics, number theory) A compound numerical expression consisting of an integer plus a fraction whose numerator is a positive integer and whose denominator is a continued fraction (an integer plus a fraction), and so on, with finite or infinite recursion.
n
(set theory) The hypothesis which states that any infinite subset of ℝ must have the cardinality of either the set of natural numbers or of ℝ itself.
n
(calculus) Initialism of delay differential equation. [(calculus) a type of differential equation in which the derivative of the unknown function at a certain time is given in terms of the values of the function at previous times]
n
(mathematics) the symbol ∂, in the context of a partial differential
n
(calculus) a type of differential equation in which the derivative of the unknown function at a certain time is given in terms of the values of the function at previous times
adj
(mathematics) Of or pertaining to differentiation or the differential calculus.
n
(mathematics, mathematical analysis) The alternating sum of the Dirichlet series expansion of the Riemann zeta function: 𝜂(s)=∑ₙ₌₁ ᪲(-1)ⁿ⁻¹/nˢ=1/(1ˢ)-1/(2ˢ)+1/(3ˢ)-1/(4ˢ)+⋯.
n
(mathematics) The process of converting a discrete time-based function into its frequency-based representation.
n
(mathematics, set theory) The set of input (argument) values for which a function is defined.
n
(mathematics) Any function that is composed of algebraic functions, trigonometric functions, exponential functions and/or logarithmic functions, combined using addition, subtraction, multiplication and/or division
v
(mathematics, transitive) To define a one-to-one function from one set to another so that certain properties of the domain are preserved when considering the image as a subset of the codomain.
n
(mathematics) A function whose domain is the empty set.
n
(set theory) Any one of the subsets into which an equivalence relation partitions a set, each of these subsets containing all the elements of the set that are equivalent under the equivalence relation.
n
(differential equations) A method for numerically approximating the solution to an ordinary differential equation with a given initial value.
n
Alternative form of Euler method [(differential equations) A method for numerically approximating the solution to an ordinary differential equation with a given initial value.]
n
(mathematics) A formal power series with one indeterminate, whose coefficients are fractions with factorial denominators (of index corresponding to the power of the indeterminate) and numerators which represent a sequence of numbers that is to be studied.
n
(mathematics) One of the variables of a quantic as distinguished from a coefficient.
n
(mathematics) An identity that generalizes the chain rule to higher derivatives.
n
(mathematics) A set which is unchanged by a function or other mapping. Formally: a set, S, is a fixed set of a function, f, if and only if for all x in S, f(x)=x.
n
(mathematics) A function that maps a real number to the largest integer that is not greater than it.
n
(mathematics, obsolete) A continuous variable, especially one with respect to time in Newton's Method of Fluxions.
n
(mathematics, algebra) Any finite or infinite series of the form a_0+a_1x+a_2x²…=∑ᵢa_ixⁱ, where the aᵢ are numbers, but it is understood that no value is assigned to x.
n
(mathematics) A field of study concerned with the representation or approximation of general functions, such as arbitrary waveforms, by sums of trigonometric functions.
n
(mathematics) A relation in which each element of the domain is associated with exactly one element of the codomain.
n
(mathematics, functional analysis) A scalar-valued linear function on a vector space.
n
(mathematics) The branch of mathematics dealing with infinite-dimensional vector spaces, whose elements are actually functions, as well as generalizations such as Banach spaces and Hilbert spaces.
n
(mathematics) A generalized continued fraction.
n
(mathematics) A sequence of natural numbers generated from an initial value m, starting with that value, and proceeding by performing certain operations on it. Although such sequences rapidly produce very large numbers, they always terminate at zero.
n
(uncountable, mathematics) The branch of mathematics dealing with the properties of graphs (networks of vertices and edges).
n
(mathematics) a type of function used in the analysis of inhomogeneous differential equations.
n
(numerical analysis) A root-finding algorithm used for functions of one real variable with a continuous second derivative.
n
(mathematics) The function whose value is zero if its independent variable is negative, and one otherwise.
n
(mathematics) Any function of a real variable whose value increases (or is constant) as the variable increases.
n
(mathematics) A variable with no value assigned to it; for example the variables in a polynomial.
adj
Alternative spelling of integrodifferential [(mathematics) Describing an equation (or other entity) containing both derivatives and integrals]
n
(set theory) The set containing all the elements that are common to two or more sets.
n
(numerical analysis) An algorithm that significantly reduces the numerical error in the total obtained by adding a sequence of finite-precision floating-point numbers, compared to the obvious approach, by tracking the accumulated small errors in a separate variable.
n
(mathematics) An infinite sequence of symbols {1,2} that is its own run-length encoding and the prototype for an infinite family of related sequences.
adj
(set theory) Relating to a generalized variant of the notion of fuzzy sets, with membership functions taking values in a (fixed or variable) algebra or structure L of a given kind, usually at least a poset or lattice.
n
(algebra, order theory) A partially ordered set in which every pair of elements has a unique supremum and a unique infimum.
n
(mathematics, uncountable) The branch of mathematics concerned with lattices (partially ordered sets).
n
(mathematics) A pair which is a member of a mapping.
n
(algebra) The greatest lower bound, an operation between pairs of elements in a lattice, denoted by the symbol ∧.
adj
(mathematics) Of a set, containing at least one element, thereby being distinct from the empty set.
adj
(mathematics) Of an expression, especially a function, being nonzero at a value, everywhere on a specified set, or on the entire domain.
n
(mathematics) A cone of nullforms
adj
(mathematics) In one to one correspondence with the set of natural integers.
n
(mathematical analysis) Initialism of ordinary differential equation. [(calculus) An equation involving the derivatives of a function of only one independent variable.]
adj
(mathematics, of a function) Having the property that the same argument may yield multiple values, but different arguments never yield the same value.
adj
(mathematics, logic, of a formula) Having a free variable.
n
(mathematics) A process to uniquely encode two natural numbers into a single natural number.
n
(mathematics, countable) A set with the property of having all of its elements belonging to one of two disjoint subsets, especially a set of integers split in subsets of even and odd elements.
n
(mathematical analysis) A set which is equal to its set of limit points. That is, a set A is perfect if A'=A.
n
(mathematics) Partial ordered multiset.
n
A coefficient which precedes a given quantity in a mathematical formula
adj
(mathematics) Able to be expressed as the convolution ratio of distributions with compact support.
n
(mathematics) By analogy, the result of any process that is the inverse of multiplication as defined for any mathematical entities other than numbers.
n
(mathematics, given some set and an equivalence relation on that set) the set consisting of all equivalence classes
n
for a power series ∑ₙ₌₀ ᪲c_n(z-a)ⁿ, the unique number R=[0,∞] such that the sum is convergent for |z-a|R
n
(mathematics) A function whose range is a subset of the set of real numbers.
n
(mathematics) A simple continued fraction.
n
(mathematics, numerical analysis) Any of an important family of implicit and explicit iterative methods for the approximation of solutions of ordinary differential equations.
n
(calculus) Initialism of stochastic differential equation. [(calculus) a type of differential equation in which one or more of the terms is a stochastic process resulting in a solution which is itself a stochastic process]
adj
(set theory) Such that there exists a nonempty intersection (with another set) that is low.
adj
(mathematics) Relating to semiprimes
n
(mathematics) The sequence of partial sums ∑ᵢ₌₁ⁿa_i of a given sequence aᵢ.
n
(computer science) A mathematical function whose input is a set (usually of real numbers or a set of points in the Euclidean or some measure space), and whose output is usually a number.
n
(game theory) A real number determined for the player i as
n
(mathematics, sciences) A cascade that originates from a member of another
adj
(mathematics) (of a sequence of nonnegative integers) such that the value of each term is less than the position of that term in the sequence (e.g. the first term is less than 1, the second term is less than 2, etc.)
n
(mathematics) A pair of subgroups
n
(computer science) A mathematical expression which is fully bound and self-contained. It may be either a constant or a combinator where all the subexpressions are supercombinators.
adj
(set theory) Describing a transitive set that contains all subsets of all its elements
n
(fuzzy logic) A mathematical function T: [0, 1] × [0, 1] → [0, 1] that is commutative, associative, monotonic, and the number 1 acts as identity element, that is T(a, 1) = a.
n
(mathematical analysis) Any function that is algebraically independent of its variable(s); a function which does not satisfy a polynomial equation whose coefficients are themselves polynomials.
n
(number theory) An absolute value (or norm) for a field which is defined to be equal to one for any element of the field other than the field's zero, for which it is defined to be equal to zero.
n
(mathematics) A set, containing infinite number of elements, whose elements can not be mapped one-to-one to the natural numbers. A set with a cardinality greater than that of the set of natural numbers.
n
(mathematics) An upper set; a subset (X,≤) of a partially ordered set with the property that, if x is in U and x≤y, then y is in U.
n
(set theory) A mathematical object which is not a set but which can be an element of a set.
n
(mathematics) A special kind of integral equation, having applications in demography, the study of viscoelastic materials, and actuarial science.
n
(mathematics) In harmonic analysis, any of a complete orthogonal set of functions that can be used to represent any discrete function.
n
(linear algebra) a vector 0 in a vector space V such that for any v∈V, 0+v=v
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