Parole in English per '(mathematics) complementary error function, i.e. 1 - erf(x)'
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noun
- (mathematics) A binary function, written as δ with two subscripts, which evaluates to 1 when its arguments are equal, and 0 otherwise.
- a function of two variables i and j that equals 1 when i=j and equals 0 otherwise
- (mathematics) A unary function, written as δ with a single index, which evaluates to 1 at zero, and 0 elsewhere.
adj
- (mathematics) an eigenvalue problem that would be a positone eigenvalue problem except that the nonlinear function is not positive when its argument is zero.
- for scriptstyle λ>0 under the assumption that scriptstyle f: ℝ→ ℝ is continuous, positive, monotone. For this reason such problems were named positone... If the nonlinearity scriptstyle f: ℝ→ ℝ is continuous, monotone and scriptstyle f(0)<0,...then the eigenvalue problem is called semipositone...
noun
- (complex analysis) The equivalent single equation (∂f)/(∂x)+i(∂f)/(∂y)=0.
- (mathematics, complex analysis, always plural) Given a complex-valued function f and real-valued functions u and v such that f(z) = u(z) + iv(z), either of the equations (∂u)/(∂x)=(∂v)/(∂y) or (∂u)/(∂y)=-(∂v)/(∂x), which together form part of the criteria that f be complex-differentiable.
adj
- The function f(x,y)#61;x²#43;x²ʸ#43;y² is not homogeneous on all of #92;mathbb#123;R#125;² because f(2,2)#61;16#92;neq 2ᵏ#42;3#61;2ᵏf(1,1) for any k, but f is homogeneous on the subspace of #92;mathbb#123;R#125;² spanned by (1,0) because f(#92;alphax,#92;alphay)#61;#92;alphax²#61;#92;alpha²f(x,y) for all (x,y)#92;in#92;operatorname#123;Span#125;#92;#123;(1,0)#92;#125;.
- (ring theory, of an element of a graded ring) Belonging to one of the summands of the grading (if the ring is graded over the natural numbers and the element is in the kth summand, it is said to be homogeneous of degree k; if the ring is graded over a commutative monoid I, and the element is an element of the ith summand, it is said to be of grade i)
- (of a linear differential equation) Having its degree-zero term equal to zero; admitting the trivial solution.
- (algebra, of a polynomial) Such that all its nonzero terms have the same degree.
- Having the same composition throughout; of uniform make-up.
- (probability theory, Fourier analysis, of a distribution S on Euclidean n-space (or on ℝⁿmathbf 0)) Informally: Determined by its restriction to the unit sphere. Formally: Such that, for all real t>0 and test functions ϕ( mathbf x), the equality S[t⁻ⁿϕ( mathbf x/t)]=t^(mS)[ϕ( mathbf x)] holds for some fixed real or complex m.
- Of the same kind; alike, similar.
- (of a linear map f between vector spaces graded by a commutative monoid I) Which respects the grading of its domain and codomain. Formally: Satisfying f(V_j)⊆W_i+j for fixed i (called the degree or grade of f), V_j the jth component of the grading of f 's domain, W_k the kth component of the grading of f 's codomain, and + representing the monoid operation in I.
- (geometry, of a space equipped with a group action) Informally: Everywhere the same, uniform, in the sense that any point can be moved to any other (via the group action) while respecting the structure of the space. Formally: Such that the group action is transitively and acts by automorphisms on the space (some authors also require that the action be faithful).
- (set theory, order theory, of a relation) Holding between a set and itself; being an endorelation.
- (of a first-order differential equation) Capable of being written in the form f(x,y) mathop dy=g(x,y) mathop dx where f and g are homogeneous functions of the same degree as each other.
- (linear algebra, by specialization, of a system of linear equations) Such that all the constant terms are zero.
- (mathematics) In any of several technical senses uniform; scalable; having its behavior or form determined by, or the same as, its behavior on or form at a smaller component (of its domain of definition, of itself, etc.).
- (geometry) Of or relating to homogeneous coordinates.
- (mathematical analysis, generalizing the case of polynomial functions, of a function f) Such that if each of f 's inputs are multiplied by the same scalar, f 's output is multiplied by the same scalar to some fixed power (called the degree of homogeneity or degree of f). (Formally and more generally, of a partial function f between vector spaces whose domain is a linear cone) Satisfying the equality f(s mathbf x)=sᵏᶠ(
- (of a general differential equation) Homogeneous as a function of the dependent variable and its derivatives.
- (chemistry) In the same state of matter.
- all of the same or similar kind or nature
noun
- a mathematical statement that two expressions are equal
- the act of regarding as equal
- a state of being essentially equal or equivalent; equally balanced
- (astronomy) A small correction to observed values to remove the effects of systematic errors in an observation.
- The act or process of equating two or more things, or the state of those things being equal (that is, identical).
- (mathematics) An assertion that two expressions are equal, expressed by writing the two expressions separated by an equal sign; in mathematical problems, equations describe various essential aspects of the problem, each of which contributes to the resolution of the problem in part.
noun
- (mathematics) For a given function f, another function, denoted f⁻¹, that reverses the mapping action of f; (formally) given a function f:X→Y, a function g:Y→X such that, ∀x∈X,f(x)=y⟹g(y)=x.
- a function obtained by expressing the dependent variable of one function as the independent variable of another; f and g are inverse functions if f(x)=y and g(y)=x
adj
- (mathematics, of an eigenvalue) Having multiple different (linearly independent) eigenvectors.
- (physics) Having the same quantum energy level.
- Having lost functionality in general.
- (of an encoding or function) Having multiple domain elements correspond to one element of the range.
- (of qualities) Having deteriorated, degraded or fallen from normal, coherent, balanced and desirable to undesirable and typically abnormal.
- (mathematics) Qualitatively different, usually simpler, than typical objects of its class.
- (of a person or system) Having lost good or desirable qualities; hence also having bad character or habits, base, immoral, corrupt. ABR
- unrestrained by convention or morality
noun
verb
name
- (mathematics education) A rule stating that, if two ratios are equal, then the denominator of the second equals its numerator times the reciprocal of the first ratio: if a/b=c/d then d=(bc)/a.
- (writing, rhetoric, comedy) Specifically, the technique of having a setup in advance, a reminder to keep it fresh in the audience's memory, and then a payoff.
- (medicine) A rule for clinical trials used for determining the rate of adverse side effects when no such side effects present during the course of the trial.
- (writing, rhetoric, comedy) A rule which states that things which come in groups of three are inherently funnier or more effective than things which come in groups of other sizes.
- (programming) A rule of thumb in the C++ programming language, stating that any class that defines a destructor, a copy constructor, or a copy assignment operator should define all three of them.
- (religion, Wicca) A religious tenet stating that the energy a person puts out into the world, positive or negative, will be returned to that person threefold.
noun
- (mathematics) An additive inverse.
- Something opposite or contrary to something else.
- An antonym.
- An opponent.
- A person or thing that is entirely different from or the reverse of someone or something else; used to show contrast between two people or two things.
- a relation of direct opposition
- something inverted in sequence or character or effect
- a contestant that you are matched against
- a word that expresses a meaning opposed to the meaning of another word, in which case the two words are antonyms of each other
adj
- Facing in the other direction.
- Located directly across from something else, or from each other.
- Of either of two complementary or mutually exclusive things.
- (botany) Of leaves and flowers, positioned directly across from each other on a stem.
- Extremely different; inconsistent; contrary; repugnant; antagonistic.
- characterized by opposite extremes; completely opposed
- the other one of a complementary pair
- moving or facing away from each other
- altogether different in nature or quality or significance
- being directly across from each other; facing
- of leaves etc.; growing in pairs on either side of a stem
adv
prep
noun
- (calculus) A function f : X→R (where X is a subset of R, possibly a discrete set) that either never decreases or never increases as its independent variable increases; that is, either x ≤ y implies f(x) ≤ f(y) or x ≤ y implies f(y) ≤ f(x).
- (Boolean algebra) A Boolean function with the property that switching any one input variable from 0 to 1 results either in no change in output or a change from 0 to 1.
- (order theory, mathematical analysis) A function f : X→Y (where X and Y are posets with partial order "≤") with either: (1) the property that x ≤ y implies f(x) ≤ f(y), or (2) the property that x ≤ y implies f(y) ≤ f(x).
noun
- (countable, mathematics) An equivalence relation; ≡; ~
- (translation studies) The degree to which a term or text in one language is semantically similar to its translated counterpart.
- (uncountable, logic) The relationship between two propositions that are either both true or both false.
- (mathematics) A Boolean operation that is TRUE when both input variables are TRUE or both input variables are FALSE, but otherwise FALSE; the XNOR function.
- (geometry) A number in intersection theory. A positive-dimensional variety sometimes behaves formally as if it were a finite number of points; this number is its equivalence.
- (chemistry) The quantity of the combining power of an atom, expressed in hydrogen units; the number of hydrogen atoms can combine with, or be exchanged for; valency.
- (uncountable) The condition of being equivalent or essentially equal.
- qualities that are comparable
- a state of being essentially equal or equivalent; equally balanced
- essential equality and interchangeability
verb
adj
- Of a mathematical expression containing e.g. x⁴.
- Of fourth rank or order.
- (inorganic chemistry) Composed of four elements.
- Relating to or in number base four.
- (organic chemistry) quaternary ammonium.
- consisting of or especially arranged in sets of four
- coming next after the third and just before the fifth in position or time or degree or magnitude
noun
noun
- (mathematics) one of a pair of numbers whose product is 1: the reciprocal of 2/3 is 3/2; the multiplicative inverse of 7 is 1/7
- something (a term or expression or concept) that has an inverse relation to something else
- hybridization involving a pair of crosses that reverse the sexes associated with each genotype
- (grammar) A construction expressing mutual action.
- (arithmetic) The number obtained by dividing 1 by another given number; the result of exchanging the numerator and the denominator of a fraction.
adj
- concerning each of two or more persons or things; especially given or done in return
- of or relating to the multiplicative inverse of a quantity or function
- Done, given, felt, or owed in return.
- Mutually interchangeable.
- (grammar) Expressing mutual action, applied to pronouns and verbs; also in a broad sense: reflexive.
- Of a feeling, action or such: mutual, uniformly felt or done by each party towards the other or others; two-way.
- (mathematics) Used to denote different kinds of mutual relation; often with reference to the substitution of reciprocals for given quantities.
noun
- (mathematics) A binary function, written as δ with two subscripts, which evaluates to 1 when its arguments are equal, and 0 otherwise.
- a function of two variables i and j that equals 1 when i=j and equals 0 otherwise
- (mathematics) A unary function, written as δ with a single index, which evaluates to 1 at zero, and 0 elsewhere.
noun
- (complex analysis) The equivalent single equation (∂f)/(∂x)+i(∂f)/(∂y)=0.
- (mathematics, complex analysis, always plural) Given a complex-valued function f and real-valued functions u and v such that f(z) = u(z) + iv(z), either of the equations (∂u)/(∂x)=(∂v)/(∂y) or (∂u)/(∂y)=-(∂v)/(∂x), which together form part of the criteria that f be complex-differentiable.
noun
- a mathematical statement that two expressions are equal
- the act of regarding as equal
- a state of being essentially equal or equivalent; equally balanced
- (astronomy) A small correction to observed values to remove the effects of systematic errors in an observation.
- The act or process of equating two or more things, or the state of those things being equal (that is, identical).
- (mathematics) An assertion that two expressions are equal, expressed by writing the two expressions separated by an equal sign; in mathematical problems, equations describe various essential aspects of the problem, each of which contributes to the resolution of the problem in part.
noun
- (mathematics) For a given function f, another function, denoted f⁻¹, that reverses the mapping action of f; (formally) given a function f:X→Y, a function g:Y→X such that, ∀x∈X,f(x)=y⟹g(y)=x.
- a function obtained by expressing the dependent variable of one function as the independent variable of another; f and g are inverse functions if f(x)=y and g(y)=x
noun
- (mathematics) An additive inverse.
- Something opposite or contrary to something else.
- An antonym.
- An opponent.
- A person or thing that is entirely different from or the reverse of someone or something else; used to show contrast between two people or two things.
- a relation of direct opposition
- something inverted in sequence or character or effect
- a contestant that you are matched against
- a word that expresses a meaning opposed to the meaning of another word, in which case the two words are antonyms of each other
adj
- Facing in the other direction.
- Located directly across from something else, or from each other.
- Of either of two complementary or mutually exclusive things.
- (botany) Of leaves and flowers, positioned directly across from each other on a stem.
- Extremely different; inconsistent; contrary; repugnant; antagonistic.
- characterized by opposite extremes; completely opposed
- the other one of a complementary pair
- moving or facing away from each other
- altogether different in nature or quality or significance
- being directly across from each other; facing
- of leaves etc.; growing in pairs on either side of a stem
adv
prep
noun
- (calculus) A function f : X→R (where X is a subset of R, possibly a discrete set) that either never decreases or never increases as its independent variable increases; that is, either x ≤ y implies f(x) ≤ f(y) or x ≤ y implies f(y) ≤ f(x).
- (Boolean algebra) A Boolean function with the property that switching any one input variable from 0 to 1 results either in no change in output or a change from 0 to 1.
- (order theory, mathematical analysis) A function f : X→Y (where X and Y are posets with partial order "≤") with either: (1) the property that x ≤ y implies f(x) ≤ f(y), or (2) the property that x ≤ y implies f(y) ≤ f(x).
noun
- (countable, mathematics) An equivalence relation; ≡; ~
- (translation studies) The degree to which a term or text in one language is semantically similar to its translated counterpart.
- (uncountable, logic) The relationship between two propositions that are either both true or both false.
- (mathematics) A Boolean operation that is TRUE when both input variables are TRUE or both input variables are FALSE, but otherwise FALSE; the XNOR function.
- (geometry) A number in intersection theory. A positive-dimensional variety sometimes behaves formally as if it were a finite number of points; this number is its equivalence.
- (chemistry) The quantity of the combining power of an atom, expressed in hydrogen units; the number of hydrogen atoms can combine with, or be exchanged for; valency.
- (uncountable) The condition of being equivalent or essentially equal.
- qualities that are comparable
- a state of being essentially equal or equivalent; equally balanced
- essential equality and interchangeability
verb
noun
- (mathematics) one of a pair of numbers whose product is 1: the reciprocal of 2/3 is 3/2; the multiplicative inverse of 7 is 1/7
- something (a term or expression or concept) that has an inverse relation to something else
- hybridization involving a pair of crosses that reverse the sexes associated with each genotype
- (grammar) A construction expressing mutual action.
- (arithmetic) The number obtained by dividing 1 by another given number; the result of exchanging the numerator and the denominator of a fraction.
adj
- concerning each of two or more persons or things; especially given or done in return
- of or relating to the multiplicative inverse of a quantity or function
- Done, given, felt, or owed in return.
- Mutually interchangeable.
- (grammar) Expressing mutual action, applied to pronouns and verbs; also in a broad sense: reflexive.
- Of a feeling, action or such: mutual, uniformly felt or done by each party towards the other or others; two-way.
- (mathematics) Used to denote different kinds of mutual relation; often with reference to the substitution of reciprocals for given quantities.
adj
- (mathematics) an eigenvalue problem that would be a positone eigenvalue problem except that the nonlinear function is not positive when its argument is zero.
- for scriptstyle λ>0 under the assumption that scriptstyle f: ℝ→ ℝ is continuous, positive, monotone. For this reason such problems were named positone... If the nonlinearity scriptstyle f: ℝ→ ℝ is continuous, monotone and scriptstyle f(0)<0,...then the eigenvalue problem is called semipositone...
adj
- The function f(x,y)#61;x²#43;x²ʸ#43;y² is not homogeneous on all of #92;mathbb#123;R#125;² because f(2,2)#61;16#92;neq 2ᵏ#42;3#61;2ᵏf(1,1) for any k, but f is homogeneous on the subspace of #92;mathbb#123;R#125;² spanned by (1,0) because f(#92;alphax,#92;alphay)#61;#92;alphax²#61;#92;alpha²f(x,y) for all (x,y)#92;in#92;operatorname#123;Span#125;#92;#123;(1,0)#92;#125;.
- (ring theory, of an element of a graded ring) Belonging to one of the summands of the grading (if the ring is graded over the natural numbers and the element is in the kth summand, it is said to be homogeneous of degree k; if the ring is graded over a commutative monoid I, and the element is an element of the ith summand, it is said to be of grade i)
- (of a linear differential equation) Having its degree-zero term equal to zero; admitting the trivial solution.
- (algebra, of a polynomial) Such that all its nonzero terms have the same degree.
- Having the same composition throughout; of uniform make-up.
- (probability theory, Fourier analysis, of a distribution S on Euclidean n-space (or on ℝⁿmathbf 0)) Informally: Determined by its restriction to the unit sphere. Formally: Such that, for all real t>0 and test functions ϕ( mathbf x), the equality S[t⁻ⁿϕ( mathbf x/t)]=t^(mS)[ϕ( mathbf x)] holds for some fixed real or complex m.
- Of the same kind; alike, similar.
- (of a linear map f between vector spaces graded by a commutative monoid I) Which respects the grading of its domain and codomain. Formally: Satisfying f(V_j)⊆W_i+j for fixed i (called the degree or grade of f), V_j the jth component of the grading of f 's domain, W_k the kth component of the grading of f 's codomain, and + representing the monoid operation in I.
- (geometry, of a space equipped with a group action) Informally: Everywhere the same, uniform, in the sense that any point can be moved to any other (via the group action) while respecting the structure of the space. Formally: Such that the group action is transitively and acts by automorphisms on the space (some authors also require that the action be faithful).
- (set theory, order theory, of a relation) Holding between a set and itself; being an endorelation.
- (of a first-order differential equation) Capable of being written in the form f(x,y) mathop dy=g(x,y) mathop dx where f and g are homogeneous functions of the same degree as each other.
- (linear algebra, by specialization, of a system of linear equations) Such that all the constant terms are zero.
- (mathematics) In any of several technical senses uniform; scalable; having its behavior or form determined by, or the same as, its behavior on or form at a smaller component (of its domain of definition, of itself, etc.).
- (geometry) Of or relating to homogeneous coordinates.
- (mathematical analysis, generalizing the case of polynomial functions, of a function f) Such that if each of f 's inputs are multiplied by the same scalar, f 's output is multiplied by the same scalar to some fixed power (called the degree of homogeneity or degree of f). (Formally and more generally, of a partial function f between vector spaces whose domain is a linear cone) Satisfying the equality f(s mathbf x)=sᵏᶠ(
- (of a general differential equation) Homogeneous as a function of the dependent variable and its derivatives.
- (chemistry) In the same state of matter.
- all of the same or similar kind or nature
adj
- (mathematics, of an eigenvalue) Having multiple different (linearly independent) eigenvectors.
- (physics) Having the same quantum energy level.
- Having lost functionality in general.
- (of an encoding or function) Having multiple domain elements correspond to one element of the range.
- (of qualities) Having deteriorated, degraded or fallen from normal, coherent, balanced and desirable to undesirable and typically abnormal.
- (mathematics) Qualitatively different, usually simpler, than typical objects of its class.
- (of a person or system) Having lost good or desirable qualities; hence also having bad character or habits, base, immoral, corrupt. ABR
- unrestrained by convention or morality
noun
verb
adj
- Of a mathematical expression containing e.g. x⁴.
- Of fourth rank or order.
- (inorganic chemistry) Composed of four elements.
- Relating to or in number base four.
- (organic chemistry) quaternary ammonium.
- consisting of or especially arranged in sets of four
- coming next after the third and just before the fifth in position or time or degree or magnitude