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verb
- (mathematics) To calculate the differential of a function of multiple variables.
- To recognize as different or distinct.
- (transitive, intransitive, often in the passive voice, biology) To (cause to) go through a process of development called differentiation; to make or become different in form or function.
- To modify so as to create a difference or distinction.
- (mathematics) To calculate the derivative of a function.
- To show or be the difference or distinction between things.
- To perceive the difference between things; to discriminate.
- (education) To teach a lesson in multiple different ways in order to meet the needs of more or less advanced students.
- become distinct and acquire a different character
- evolve so as to lead to a new species or develop in a way most suited to the environment
- be a distinctive feature, attribute, or trait; sometimes in a very positive sense
- mark as different
- calculate a derivative; take the derivative
- become different during development
noun
noun
- (vector calculus) Divergence; a kind of differential operator.
- (UK, Eton College, school slang) A division; a lesson.
- (UK, Ireland, slang) A foolish person; an idiot.
- (military) A division.
- Alternative form of daeva.
- (UK, Winchester College) division; a subject with multidisciplinary scope.
- (UK, Ireland, uncountable, slang) Divinity, as a school subject.
- (web design) A section of a web page, or the div element that represents it in HTML code.
- (mathematics, computing) A function, implemented in many programming languages, that returns the result of a division of two integers.
verb
adj
- (mathematics, of a differential equation) Able to be brought to a form where all occurrences of the dependent and the independent variable are on opposite sides of the equal sign.
- (abstract algebra, of an algebra over a ring) Satisfying any of several technical conditions on the center of the algebra which generalize the situation of field extensions; see Separable algebra on Wikipedia.Wikipedia
- (of a polynomial) Having no repeated roots (where roots are considered in an algebraic closure)
- Able to be separated.
- (mathematical analysis, of a topological space) Having a countable dense subset.
- (Galois theory, of an algebraic field extension E/F) Such that the minimal polynomial of every element of E is a separable polynomial.
- capable of being divided or dissociated
noun
name
noun
- (mathematics) A binary function, written as δ with two subscripts, which evaluates to 1 when its arguments are equal, and 0 otherwise.
- (mathematics) A unary function, written as δ with a single index, which evaluates to 1 at zero, and 0 elsewhere.
- a function of two variables i and j that equals 1 when i=j and equals 0 otherwise
adj
- possessing a differential coefficient or derivative
- capable of being perceived as different
- (comparable, of multiple items) able to be differentiated; distinguishable, as for example by differing appearance or measurable characteristics.
- (calculus, not comparable) Having a derivative, said of a function whose domain and codomain are manifolds.
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.
adj
- (mathematics, of a function) Having the property that the same argument may yield multiple values, but different arguments never yield the same value.
- (mathematics, logic, of a relationship between two sets) Having the property that an element of one set may be assigned by the relationship to several elements in the other set, but that a given element in the second set can have only one member of the first set assigned to it.
- From a single source to multiple recipients.
adj
- (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.
- (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.
- (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.
- 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;.
- (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 two integers) having no common integer divisor except 1.
- Not able to be measured by the same standards as another term in the context.
- (mathematics, of two real numbers) having a ratio that is not expressible as a fraction of two integers.
- impossible to measure or compare in value or size or excellence
- not having a common factor
noun
adj
- (functional analysis, of a Hilbert space operator) Which commutes with its adjoint.
- (topology, of a topology or topological space) In which disjoint closed sets can be separated by disjoint neighborhoods.
- (linear algebra, of a matrix) Which commutes with its conjugate transpose.
- (complex analysis, of a family of continuous functions) Which is pre-compact.
- (commutative algebra, of a domain) Integrally closed: equal its own integral closure in its field of fractions.
- (probability theory, statistics, of a distribution, random variable, etc.) Which has a very specific bell curve shape; that is or has the qualities of a normal distribution.
- (physics, of a mode in an oscillating system) In which all parts of an object vibrate at the same frequency (a normal mode).
- (rail transport, of points) In the default position, set for the most frequently used route.
- (chemistry) Of, relating to, or being a solution containing one equivalent weight of solute per litre of solution.
- (category theory, of a category) Which contains only normal morphisms.
- (organic chemistry) Describing a straight chain isomer of an aliphatic hydrocarbon, or an aliphatic compound in which a substituent is in the 1- position of such a hydrocarbon.
- (fandom slang, sarcastic, with “about”) Fervently interested in a subject; obsessed.
- (algebraic geometry, of a variety or scheme) Such that the local ring at every point is an integrally closed domain.
- (category theory, of a morphism) Which is the kernel or cokernel of some morphism, respectively.
- (number theory, of a real number) In whose representation in a given base b ≥ 2, for every positive integer n, the bⁿ possible strings of n digits follow a uniform distribution.
- Usual, healthy; not sick or ill or unlike oneself.
- (set theory, of a function from the ordinals to the ordinals) Which is strictly monotonically increasing and continuous with respect to the order topology.
- (algebra, of a field extension of a field K) Which is the splitting field of a family of polynomials in K.
- (algebra, of a subgroup) With cosets which form a group.
- (commutative algebra, of a ring) Such that all of its localizations at prime ideals are integrally closed domains.
- (education, of a school) Teaching teachers how to teach; teaching teachers the norms of education.
- According to norms or rules or to a regular pattern.
- (geometry) Perpendicular to a tangent of a curve or tangent plane of a surface.
- in accordance with scientific laws
- conforming with or constituting a norm or standard or level or type or social norm; not abnormal
- forming a right angle
- being approximately average or within certain limits in e.g. intelligence and development
noun
- (geometry, countable) A line or vector that is perpendicular to another line, surface, or plane.
- (medicine, countable) A person who is healthy, normal, as opposed to one who is morbid.
- (slang, countable) A person who is normal, who fits into mainstream society, as opposed to those who live alternative lifestyles.
- (countable, uncountable) The usual state.
- something regarded as a normative example
adj
- (mathematics) Having a dual that is nonnegative.
- Partially positive in attitude etc.
- (materials engineering) A type of compression mold for plastics that allows for excess powder and flash, as in an open flash mold, but which allows for lower melt viscosities as in a fully positive mold.
- (mathematics) Having all elements nonnegative where at least one is positive.
adj
noun
- (multivariable calculus) The Jacobian matrix of a function of several variables.
- (calculus, of a univariate differentiable function f(x)) A function giving the change in the linear approximation of f at a point x over a small interval Δx or operatorname d!x, the function being called the differential of f and denoted operatorname d!f(x,Δx), operatorname d!f(x), or simply operatorname d!f.
- Any of several generalizations of this concept to functions of several variables or to higher orders: the partial differential, total differential, Gateaux differential, etc.
- One of two coils of conducting wire so related to one another or to a magnet or armature common to both, that one coil produces polar action contrary to that of the other.
- The differential gear in an automobile, etc.
- A form of conductor used for dividing and distributing the current to a series of electric lamps so as to maintain equal action in all.
- (differential geometry, of a smooth map ϕ between smooth manifolds) The pushforward or total derivative of ϕ: a linear map from the tangent space at a point x in ϕ's domain to the tangent space at ϕ(x) which is, in a technical sense, the best linear approximation of ϕ at x; denoted operatorname d!ϕₓ.
- (mathematics) Any of several generalizations of the concept(s) above: e.g. the Kähler differential in the setting of schemes, the quadratic differential in the theory of Riemann surfaces, etc.
- (calculus) A quantity representing an infinitesimal change in a variable, now only used as a heuristic aid except in nonstandard analysis but considered rigorous until the 20th century; a fluxion in Newtonian calculus, now usually written in Leibniz's notation as operatorname d!x.
- A qualitative or quantitative difference between similar or comparable things.
- a quality that differentiates between similar things
- a bevel gear that permits rotation of two shafts at different speeds; used on the rear axle of automobiles to allow wheels to rotate at different speeds on curves
- the result of mathematical differentiation; the instantaneous change of one quantity relative to another; df(x)/dx
noun
- (mathematics) Clipping of differential
- (climbing) A difficult route.
- (computing) The output of a diff program, a diff file.
- (slang) Clipping of difference
- (video games, slang) Used to trash-talk an opposing team at the end of a game by pointing out a skill difference between some role and the same role on the other team.
- (automotive) Abbreviation of differential: the differential gear in an automobile.
- (medicine) Abbreviation of differential: differential of types of white blood cell in a complete blood count.
- (computing) Any program which compares two files or sets of files and outputs a description of the differences between them.
- (fandom slang) Clipping of difficulty.
adj
name
verb
- (transitive, computing) To compare two files or other objects, manually or otherwise.
- (transitive, fandom slang) To win (or to be able to win) a fight against another, with a defined level of difficulty. Usually used when power scaling fictional characters.
- (transitive, computing) To run a diff program on (files or items) so as to produce a description of the differences between them, as for a patch file.
noun
adj
prep
verb
noun
noun
- (mathematics) a condition specified for the solution to a set of differential equations
- (mathematics) Any of a set of constraints that limit the solutions of a differential equation
- (quantum mechanics) either one of the conditions that the wave function must be continuous and that its derivative must be as well, except in the case of infinite potential
noun
- an arithmetic operation that is the inverse of division; the product of two numbers is computed
- a multiplicative increase
- the act of producing offspring or multiplying by such production
- The process of multiplying or increasing in number; increase.
- (countable, arithmetic) A calculation involving multiplication.
- (uncountable, arithmetic) The process of computing the sum of an addition with one and the same number a specified number of times (i.e. 4 times 5 = [0 +] 5 + 5 + 5 + 5 = 20) or any other analogous binary operation that combines other mathematical objects.
noun
prep
verb
noun
adj
adj
noun
noun
- the derivative of a function of two or more variables with respect to a single variable while the other variables are considered to be constant
- a harmonic with a frequency that is a multiple of the fundamental frequency
- (dentistry) dentures that replace only some of the natural teeth
- (bodybuilding) The condition of not exhausting the amplitude during the repetition of an exercise.
- (forensics) An incomplete fingerprint
- (furry fandom) A fursuit that does not fully cover the wearer's body.
- (programming, Internet) A fragment of a template containing markup.
- (mathematics) A partial derivative: a derivative with respect to one independent variable of a function in multiple variables while holding the other variables constant.
- (music) Any of the sine waves which make up a complex tone; often an overtone or harmonic of the fundamental.
adj
- (followed by ‘of’ or ‘to’) having a strong preference or liking for
- being or affecting only a part; not total
- constituting or comprising a part or fraction of a possible whole or entirety
- showing favoritism
- (botany) Subordinate.
- Biased in favor of a person, side, or point of view, especially when dealing with a competition or dispute.
- (crosswording, of a clue) Having a wordplay element, but no definition.
- (followed by the preposition to) Having a predilection for something.
- (computer science) Describing a property that holds only when an algorithm terminates.
- Existing as a part or portion; incomplete.
- (mathematics) Of or relating to a partial derivative or partial differential.
verb
noun
- (logic) The proposition resulting from the combination of two or more propositions using the ∧ ( and ) operator.
- (astrology) An aspect in which planets are in close proximity to one another.
- (grammar) A word used to join other words, phrases, or clauses together into sentences. (The specific conjunction used shows how the two joined parts are related semantically.)
- The act of joining, or condition of being joined.
- (astronomy) The alignment of two bodies in the solar system such that they have the same longitude when seen from Earth.
- A place where multiple things meet.
- Cooccurrence; coincidence.
- the state of being joined together
- something that joins or connects
- the grammatical relation between linguistic units (words or phrases or clauses) that are connected by a conjunction
- the temporal property of two things happening at the same time
- an uninflected function word that serves to conjoin words or phrases or clauses or sentences
- (astronomy) apparent meeting or passing of two or more celestial bodies in the same degree of the zodiac
noun
- (vector calculus) Divergence; a kind of differential operator.
- (UK, Eton College, school slang) A division; a lesson.
- (UK, Ireland, slang) A foolish person; an idiot.
- (military) A division.
- Alternative form of daeva.
- (UK, Winchester College) division; a subject with multidisciplinary scope.
- (UK, Ireland, uncountable, slang) Divinity, as a school subject.
- (web design) A section of a web page, or the div element that represents it in HTML code.
- (mathematics, computing) A function, implemented in many programming languages, that returns the result of a division of two integers.
verb
noun
name
noun
- (mathematics) A binary function, written as δ with two subscripts, which evaluates to 1 when its arguments are equal, and 0 otherwise.
- (mathematics) A unary function, written as δ with a single index, which evaluates to 1 at zero, and 0 elsewhere.
- a function of two variables i and j that equals 1 when i=j and equals 0 otherwise
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) Clipping of differential
- (climbing) A difficult route.
- (computing) The output of a diff program, a diff file.
- (slang) Clipping of difference
- (video games, slang) Used to trash-talk an opposing team at the end of a game by pointing out a skill difference between some role and the same role on the other team.
- (automotive) Abbreviation of differential: the differential gear in an automobile.
- (medicine) Abbreviation of differential: differential of types of white blood cell in a complete blood count.
- (computing) Any program which compares two files or sets of files and outputs a description of the differences between them.
- (fandom slang) Clipping of difficulty.
adj
name
verb
- (transitive, computing) To compare two files or other objects, manually or otherwise.
- (transitive, fandom slang) To win (or to be able to win) a fight against another, with a defined level of difficulty. Usually used when power scaling fictional characters.
- (transitive, computing) To run a diff program on (files or items) so as to produce a description of the differences between them, as for a patch file.
noun
adj
prep
verb
noun
noun
- (mathematics) a condition specified for the solution to a set of differential equations
- (mathematics) Any of a set of constraints that limit the solutions of a differential equation
- (quantum mechanics) either one of the conditions that the wave function must be continuous and that its derivative must be as well, except in the case of infinite potential
noun
- an arithmetic operation that is the inverse of division; the product of two numbers is computed
- a multiplicative increase
- the act of producing offspring or multiplying by such production
- The process of multiplying or increasing in number; increase.
- (countable, arithmetic) A calculation involving multiplication.
- (uncountable, arithmetic) The process of computing the sum of an addition with one and the same number a specified number of times (i.e. 4 times 5 = [0 +] 5 + 5 + 5 + 5 = 20) or any other analogous binary operation that combines other mathematical objects.
noun
prep
verb
noun
adj
noun
- the derivative of a function of two or more variables with respect to a single variable while the other variables are considered to be constant
- a harmonic with a frequency that is a multiple of the fundamental frequency
- (dentistry) dentures that replace only some of the natural teeth
- (bodybuilding) The condition of not exhausting the amplitude during the repetition of an exercise.
- (forensics) An incomplete fingerprint
- (furry fandom) A fursuit that does not fully cover the wearer's body.
- (programming, Internet) A fragment of a template containing markup.
- (mathematics) A partial derivative: a derivative with respect to one independent variable of a function in multiple variables while holding the other variables constant.
- (music) Any of the sine waves which make up a complex tone; often an overtone or harmonic of the fundamental.
adj
- (followed by ‘of’ or ‘to’) having a strong preference or liking for
- being or affecting only a part; not total
- constituting or comprising a part or fraction of a possible whole or entirety
- showing favoritism
- (botany) Subordinate.
- Biased in favor of a person, side, or point of view, especially when dealing with a competition or dispute.
- (crosswording, of a clue) Having a wordplay element, but no definition.
- (followed by the preposition to) Having a predilection for something.
- (computer science) Describing a property that holds only when an algorithm terminates.
- Existing as a part or portion; incomplete.
- (mathematics) Of or relating to a partial derivative or partial differential.
verb
noun
- (logic) The proposition resulting from the combination of two or more propositions using the ∧ ( and ) operator.
- (astrology) An aspect in which planets are in close proximity to one another.
- (grammar) A word used to join other words, phrases, or clauses together into sentences. (The specific conjunction used shows how the two joined parts are related semantically.)
- The act of joining, or condition of being joined.
- (astronomy) The alignment of two bodies in the solar system such that they have the same longitude when seen from Earth.
- A place where multiple things meet.
- Cooccurrence; coincidence.
- the state of being joined together
- something that joins or connects
- the grammatical relation between linguistic units (words or phrases or clauses) that are connected by a conjunction
- the temporal property of two things happening at the same time
- an uninflected function word that serves to conjoin words or phrases or clauses or sentences
- (astronomy) apparent meeting or passing of two or more celestial bodies in the same degree of the zodiac
verb
- (mathematics) To calculate the differential of a function of multiple variables.
- To recognize as different or distinct.
- (transitive, intransitive, often in the passive voice, biology) To (cause to) go through a process of development called differentiation; to make or become different in form or function.
- To modify so as to create a difference or distinction.
- (mathematics) To calculate the derivative of a function.
- To show or be the difference or distinction between things.
- To perceive the difference between things; to discriminate.
- (education) To teach a lesson in multiple different ways in order to meet the needs of more or less advanced students.
- become distinct and acquire a different character
- evolve so as to lead to a new species or develop in a way most suited to the environment
- be a distinctive feature, attribute, or trait; sometimes in a very positive sense
- mark as different
- calculate a derivative; take the derivative
- become different during development
noun
adj
- (mathematics, of a differential equation) Able to be brought to a form where all occurrences of the dependent and the independent variable are on opposite sides of the equal sign.
- (abstract algebra, of an algebra over a ring) Satisfying any of several technical conditions on the center of the algebra which generalize the situation of field extensions; see Separable algebra on Wikipedia.Wikipedia
- (of a polynomial) Having no repeated roots (where roots are considered in an algebraic closure)
- Able to be separated.
- (mathematical analysis, of a topological space) Having a countable dense subset.
- (Galois theory, of an algebraic field extension E/F) Such that the minimal polynomial of every element of E is a separable polynomial.
- capable of being divided or dissociated
adj
- possessing a differential coefficient or derivative
- capable of being perceived as different
- (comparable, of multiple items) able to be differentiated; distinguishable, as for example by differing appearance or measurable characteristics.
- (calculus, not comparable) Having a derivative, said of a function whose domain and codomain are manifolds.
adj
- (mathematics, of a function) Having the property that the same argument may yield multiple values, but different arguments never yield the same value.
- (mathematics, logic, of a relationship between two sets) Having the property that an element of one set may be assigned by the relationship to several elements in the other set, but that a given element in the second set can have only one member of the first set assigned to it.
- From a single source to multiple recipients.
adj
- (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.
- (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.
- (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.
- 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;.
- (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 two integers) having no common integer divisor except 1.
- Not able to be measured by the same standards as another term in the context.
- (mathematics, of two real numbers) having a ratio that is not expressible as a fraction of two integers.
- impossible to measure or compare in value or size or excellence
- not having a common factor
noun
adj
- (functional analysis, of a Hilbert space operator) Which commutes with its adjoint.
- (topology, of a topology or topological space) In which disjoint closed sets can be separated by disjoint neighborhoods.
- (linear algebra, of a matrix) Which commutes with its conjugate transpose.
- (complex analysis, of a family of continuous functions) Which is pre-compact.
- (commutative algebra, of a domain) Integrally closed: equal its own integral closure in its field of fractions.
- (probability theory, statistics, of a distribution, random variable, etc.) Which has a very specific bell curve shape; that is or has the qualities of a normal distribution.
- (physics, of a mode in an oscillating system) In which all parts of an object vibrate at the same frequency (a normal mode).
- (rail transport, of points) In the default position, set for the most frequently used route.
- (chemistry) Of, relating to, or being a solution containing one equivalent weight of solute per litre of solution.
- (category theory, of a category) Which contains only normal morphisms.
- (organic chemistry) Describing a straight chain isomer of an aliphatic hydrocarbon, or an aliphatic compound in which a substituent is in the 1- position of such a hydrocarbon.
- (fandom slang, sarcastic, with “about”) Fervently interested in a subject; obsessed.
- (algebraic geometry, of a variety or scheme) Such that the local ring at every point is an integrally closed domain.
- (category theory, of a morphism) Which is the kernel or cokernel of some morphism, respectively.
- (number theory, of a real number) In whose representation in a given base b ≥ 2, for every positive integer n, the bⁿ possible strings of n digits follow a uniform distribution.
- Usual, healthy; not sick or ill or unlike oneself.
- (set theory, of a function from the ordinals to the ordinals) Which is strictly monotonically increasing and continuous with respect to the order topology.
- (algebra, of a field extension of a field K) Which is the splitting field of a family of polynomials in K.
- (algebra, of a subgroup) With cosets which form a group.
- (commutative algebra, of a ring) Such that all of its localizations at prime ideals are integrally closed domains.
- (education, of a school) Teaching teachers how to teach; teaching teachers the norms of education.
- According to norms or rules or to a regular pattern.
- (geometry) Perpendicular to a tangent of a curve or tangent plane of a surface.
- in accordance with scientific laws
- conforming with or constituting a norm or standard or level or type or social norm; not abnormal
- forming a right angle
- being approximately average or within certain limits in e.g. intelligence and development
noun
- (geometry, countable) A line or vector that is perpendicular to another line, surface, or plane.
- (medicine, countable) A person who is healthy, normal, as opposed to one who is morbid.
- (slang, countable) A person who is normal, who fits into mainstream society, as opposed to those who live alternative lifestyles.
- (countable, uncountable) The usual state.
- something regarded as a normative example
adj
- (mathematics) Having a dual that is nonnegative.
- Partially positive in attitude etc.
- (materials engineering) A type of compression mold for plastics that allows for excess powder and flash, as in an open flash mold, but which allows for lower melt viscosities as in a fully positive mold.
- (mathematics) Having all elements nonnegative where at least one is positive.
adj
noun
- (multivariable calculus) The Jacobian matrix of a function of several variables.
- (calculus, of a univariate differentiable function f(x)) A function giving the change in the linear approximation of f at a point x over a small interval Δx or operatorname d!x, the function being called the differential of f and denoted operatorname d!f(x,Δx), operatorname d!f(x), or simply operatorname d!f.
- Any of several generalizations of this concept to functions of several variables or to higher orders: the partial differential, total differential, Gateaux differential, etc.
- One of two coils of conducting wire so related to one another or to a magnet or armature common to both, that one coil produces polar action contrary to that of the other.
- The differential gear in an automobile, etc.
- A form of conductor used for dividing and distributing the current to a series of electric lamps so as to maintain equal action in all.
- (differential geometry, of a smooth map ϕ between smooth manifolds) The pushforward or total derivative of ϕ: a linear map from the tangent space at a point x in ϕ's domain to the tangent space at ϕ(x) which is, in a technical sense, the best linear approximation of ϕ at x; denoted operatorname d!ϕₓ.
- (mathematics) Any of several generalizations of the concept(s) above: e.g. the Kähler differential in the setting of schemes, the quadratic differential in the theory of Riemann surfaces, etc.
- (calculus) A quantity representing an infinitesimal change in a variable, now only used as a heuristic aid except in nonstandard analysis but considered rigorous until the 20th century; a fluxion in Newtonian calculus, now usually written in Leibniz's notation as operatorname d!x.
- A qualitative or quantitative difference between similar or comparable things.
- a quality that differentiates between similar things
- a bevel gear that permits rotation of two shafts at different speeds; used on the rear axle of automobiles to allow wheels to rotate at different speeds on curves
- the result of mathematical differentiation; the instantaneous change of one quantity relative to another; df(x)/dx