'(calculus) A function whose derivative is a given function; an indefinite integral'的English词汇
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noun
- (calculus) The operation of finding the integral of a function.
- an operation used in the calculus whereby the integral of a function is determined
- (society) The process of fitting into a community, notably applied to minorities.
- The act or process of making whole or entire.
- (biology) In evolution, the process by which the manifold is compacted into the relatively simple and permanent; supposed to alternate with differentiation as an agent in species' development.
- (US) Ellipsis of racial integration.
- The process of combining with compatible elements in order to incorporate them.
- the action of incorporating a racial or religious group into a community
- the act of combining into an integral whole
noun
- (calculus) A function used to define an integral transform.
- (mathematics, category theory, of a morphism f:X→Y in a category with zero morphisms) The equalizer of f and the zero morphism from X to Y, denoted operatorname kerf.
- (botany, US) The stone of certain fruits, such as peaches or plums.
- (botany) A single seed of grain, especially of corn or wheat.
- (computing) The central part of many computer operating systems which manages the system's resources and the communication between hardware and software components.
- (slang) The human clitoris.
- (computing) The core engine of any complex software system.
- (programming) The simplified input to an algorithm that has undergone kernelization.
- A small mass around which other matter is concreted; a nucleus; a concretion or hard lump in the flesh.
- (chemistry) The nucleus and electrons of an atom excluding its valence electrons.
- (botany) The central (usually edible) part of a nut, especially once the hard shell has been removed.
- (mathematics, linear algebra, of a linear transformation f:M→N between modules or vector spaces) The set of elements of M which are mapped to the additive identity 0 of N.
- (mathematics, set theory, of a function f) The set of pairs of elements in the domain of f which are mapped to the same value; the equivalence relation x≡y⟺f(x)=f(y).
- (mathematics, group theory, of a group homomorphism f:G→H between groups) The set of elements of G which are mapped to the identity of H (usually written as 0 in an additive group and as 1 in a multiplicative group).
- (mathematics, fuzzy set theory) The set of members of a fuzzy set that are fully included (i.e., whose grade of membership is 1).
- (mathematics, ring theory, of a ring homomorphism f:R→S between rings) The set of elements of R which are mapped to the additive identity 0 of S.
- (mathematics, category theory) The source of operatorname kerf, denoted operatorname Kerf.
- The core, center, or essence of an object or system.
- a single whole grain of a cereal
- the choicest or most essential or most vital part of some idea or experience
- the inner and usually edible part of a seed or grain or nut or fruit stone
verb
noun
- (mathematics) An indefinite integral: the result of the application of such an operation onto a function together with an indefinite domain, yielding a function; a function's antiderivative;
- (mathematics) A definite integral: the result of the application of such an operation onto a function and a suitable subset of the function's domain: either a number or positive or negative infinity. In the former case, the integral is said to be finite or to converge; in the latter, the integral is said to diverge. In notation, the domain of integration is indicated either below the sign, or, if it is an interval, with its endpoints as sub- and super-scripts, and the function being integrated forming part of the integrand (or, generally, differential form) appearing in front of the integral sign.
- (mathematics) One of the two fundamental operations of calculus (the other being differentiation), whereby a function's displacement, area, volume, or other qualities arising from the study of infinitesimal change are quantified, usually defined as a limiting process on a sequence of partial sums. Denoted using a long s: ∫, or a variant thereof.
- (specifically) Any of several analytic formalizations of this operation: the Riemann integral, the Lebesgue integral, etc.
- the result of a mathematical integration; F(x) is the integral of f(x) if dF/dx = f(x)
adj
- Constituting a whole together with other parts or factors; not omittable or removable.
- (mathematics) Relating to integration (“the process of finding the integral [noun] of a function”).
- (algebra, commutative algebra, of a ring element in a ring B relative to a subring A) Being the root of some monic polynomial in A.
- (mathematics) Of, pertaining to, or being an integer.
- constituting the undiminished entirety; lacking nothing essential especially not damaged
- of or denoted by an integer
- existing as an essential constituent or characteristic
adj
- (calculus, not comparable) Having a derivative, said of a function whose domain and codomain are manifolds.
- (comparable, of multiple items) able to be differentiated; distinguishable, as for example by differing appearance or measurable characteristics.
- possessing a differential coefficient or derivative
- capable of being perceived as different
verb
- (mathematics) To calculate the derivative of a function.
- 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 differential of a function of multiple variables.
- 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
name
- (calculus) A generalization of the fundamental theorem of calculus to the two-dimensional plane, which states that given two scalar fields P and Q and a simply connected region R, the area integral of derivatives of the fields equals the line integral of the fields, or
- (calculus) Letting ⃑G=(P,Q) be a vector field, and d⃑l=(dx,dy) this can be restated as
adj
- (mathematics) Being an integral without specified limits.
- Without limit; forever, or until further notice; not definite.
- (linguistics) Designating an unspecified or unidentified person or thing or group of persons or things.
- Undecided or uncertain.
- Vague or unclear.
- vague or not clearly defined or stated
- not decided or not known
noun
noun
- (mathematics) The value or range of values of a function for which a derivative does not exist.
- (physics) Ellipsis of gravitational singularity (“a point or region in spacetime in which gravitational forces cause matter to have an infinite density; associated with black holes”).
- Celibacy, singleness (as contrasted with marriage).
- A point where a measured variable reaches unmeasurable or infinite value.
- The state of being singular, distinct, peculiar, uncommon or unusual.
- (sometimes capitalized) Ellipsis of technological singularity (“a hypothetical turning point in the future, the culmination of ever-accelerating technological progress, when human history as we have known it ends, and a strange new era begins. For some writers, the catalyst is superhuman machine intelligence”).
- An unusual action or behaviour.
- A point where all parallel lines meet.
- strangeness by virtue of being remarkable or unusual
- the quality of being one of a kind
adj
- (mathematics, of a function) having a single derivative at a point
- producing offspring of only one sex, exhibiting monogeny
- of or relating to monogenesis or to monogenism
- (mathematics, of a semigroup) generated by a set containing only a single element
- (genetics) regulated by a single gene
- of or relating to an inheritable character that is controlled by a single pair of genes
noun
noun
- the set of functions F(x) + C, where C is any real number, such that F(x) is the integral of f(x)
- (mathematics) A function whose derivative is a given function; an antiderivative.
- (mathematics) The set of all functions whose derivative is a given function; the set of all antiderivatives of a given function.
noun
- (calculus) Of a function, another function, the value of which for any value of the independent variable is the instantaneous rate of change of the given function at that value of the independent variable.
- the result of mathematical differentiation; the instantaneous change of one quantity relative to another; df(x)/dx
adj
- (mathematics, of a function) Having a product of independent variables, or a variable with an exponent not equal to one.
- Erratic and unpredictable; tending to jump back and forth.
- (of a system) Whose output is not directly proportional to its input.
- (chemistry, of a molecule) Whose atoms do not lie in a straight line.
- (of a set of points) Not lying on a straight line.
- designating or involving an equation whose terms are not of the first degree
noun
- (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.
- (multivariable calculus) The Jacobian matrix of a function of several variables.
- 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
adj
noun
- (calculus) The operator which maps a function F=(F₁, ... Fₙ) from a n-dimensional vector space to itself to the function ∑ᵢ₌₁ⁿ(∂F_i)/(∂x_i).
- The process in which two or more populations accumulate genetic changes (mutations) through time.
- The state or degree of being divergent: of diverging.
- a difference between conflicting facts or claims or opinions
- an infinite series that has no limit
- a variation that deviates from the standard or norm
- the act of moving away in different direction from a common point
noun
- (mathematics, numerical analysis) The calculation of a definite integral by numerical means.
- (mathematics, mathematical analysis) The act or process of solving an indefinite integral by symbolic means.
- The process of making something square; squaring.
- (physics) The condition in which the phase angle between two alternating quantities is 90°.
- (mathematics) The act or process of constructing a square that has the same area as a given plane figure, or of computing that area.
- (art) A painting painted on a wooden panel.
- (astronomy) A situation in which the directions of two celestial bodies (or a celestial body and the Sun) form a right angle from the perspective of the observer.
- the construction of a square having the same area as some other figure
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
- Initialism of proportional integral derivative.
- Initialism of personal identification device.
- (medicine) Initialism of pelvic inflammatory disease.
- Initialism of piping and instrumentation diagram.
- Initialism of photoionization detector.
- (algebra) Initialism of principal ideal domain.
- (computing) Initialism of process identifier.
- inflammation of the female pelvic organs (especially the Fallopian tubes) caused by infection by any of several microorganisms (chiefly gonococci and chlamydia); symptoms are abdominal pain and fever and foul-smelling vaginal discharge
adj
- (mathematics, of a function) having an infinite number of derivatives at a point (otherwise it is monogenic)
- (genetics) controlled by the interaction of more than one gene
- of or relating to an inheritable character that is controlled by several genes at once; of or related to or determined by polygenes
name
- The definite integral of a continuous function f over a closed interval [a,,b] is equal to the net change of any antiderivative F over [a,,b], or: ∫ₐᵇf(x),dx=F(b)-F(a).
- For a continuous function f, an antiderivative or indefinite integral of F can be obtained as the integral of f over an interval with a variable upper bound, or: F(x)=∫ₐˣf(t),dt.
noun
- (calculus, of a function) The ratio of the rates of change of a dependent variable and an independent variable, the slope of a curve's tangent.
- A slope or incline.
- (sciences) The rate at which a physical quantity increases or decreases relative to change in a given variable, especially distance.
- (calculus) A differential operator that maps each point of a scalar field to a vector pointed in the direction of the greatest rate of change of the scalar. Notation for a scalar field φ: ∇φ
- A gradual change in color; a color gradient; gradation.
- A rate of inclination or declination of a slope.
- the property possessed by a line or surface that departs from the horizontal
- a graded change in the magnitude of some physical quantity or dimension
adj
noun
- (mathematics, calculus) The process of applying the derivative operator to a function; of calculating a function's derivative.
- the mathematical process of obtaining the derivative of a function
- (biology) The process by which the components of multicellular life (cells, organs, etc.) are produced and acquire function, as when a seed develops the root and stem, and the initial stem develops the leaf, branches, and flower buds.
- (biology, evolution) The evolutionary process by which one taxonomic group (species, genus, variety, etc.) becomes distinct from another, or acquires distinct features; the result of such a process: distinctness.
- The act of treating one thing as distinct from another, or of creating such a distinction; of separating a class of things into categories; of describing a thing by illustrating how it is different from something else.
- (geology) The process of separation of cooling magma into various rock types.
- The process of developing distinct components.
- (biology) the structural adaptation of some body part for a particular function
- a discrimination between things as different and distinct on the basis of their characteristics or attributes
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
adj
- (mathematics, of a function) Having derivatives of all finite orders at all points within the function’s domain.
- (of muscles, medicine) Involuntary and non-striated.
- (of an action) Natural; unconstrained.
- Bland; glib.
- (mathematics, of a number) That factors completely into small prime numbers.
- Having a texture that lacks friction. Not rough.
- (of a motion) Unbroken.
- (linguistics, classical studies, of a vowel) Lacking marked aspiration.
- (of food or drink) Not grainy; having an even texture.
- (of an edge) Lacking projections or indentations; not serrated.
- Without difficulty, problems, or unexpected consequences or incidents.
- (of a beverage) Having a pleasantly rounded flavor; neither rough nor astringent.
- Flowing or uttered without check, obstruction, or hesitation; not harsh; fluent.
- Suave; sophisticated.
- (chiefly of water) Placid, calm.
- smooth and unconstrained in movement
- of the margin of a leaf shape; not broken up into teeth
- smoothly agreeable and courteous with a degree of sophistication
- lacking obstructions or difficulties
- (of a body of water) free from disturbance by heavy waves
- having a surface free from roughness or bumps or ridges or irregularities
- of motion that runs or flows or proceeds without jolts or turbulence
- (music) without breaks between notes; smooth and connected
adv
noun
verb
- (transitive) To make straightforward or easy.
- (transitive) To make smooth or even.
- (West Country) To stroke; especially to stroke an animal's fur.
- (transitive) To calm or palliate.
- (transitive) To reduce to a particular shape or form by pressure; to press, to flatten.
- (statistics, image processing, digital audio) To capture important patterns in the data, while leaving out noise.
- free from obstructions
- make smooth or smoother, as if by rubbing
- make (a surface) shine
noun
- (mathematics) A function of a function.
- (chiefly law enforcement) A drawing, photograph, etc. that combines several separate pictures or images.
- A mixture of different components.
- (fraternities) A framed photo board composed of many individual photos of fraternity or sorority members.
- (school yearbook) The separate pages of individual student photos that form the main section.
- A structural material that gains its strength from a combination of complementary materials.
- (mathematics) Clipping of composite number.
- (uncommon) A segment, subset.
- (botany) A plant belonging to the family Asteraceae, syn. Compositae.
- (rail transport, UK) A railway carriage with compartments for two different classes of travel; see Composite Corridor.
- a conceptual whole made up of complicated and related parts
- considered the most highly evolved dicotyledonous plants, characterized by florets arranged in dense heads that resemble single flowers
adj
- (botany) Belonging to the Asteraceae family (formerly known as Compositae), bearing involucrate heads of many small florets.
- (mathematics) Having factors other than itself and one; not prime and not one.
- (architecture) Being a mixture of Ionic and Corinthian styles.
- (photography, historical) Employing multiple exposures on a single plate, so as to create an average view of something, such as faces in physiognomy.
- Made up of multiple components; compound or complex.
- of or relating to or belonging to the plant family Compositae
- consisting of separate interconnected parts
verb
noun
adj
- (mathematics) Characterised by a rate of change that is proportional to the value of the varying quantity, or, equivalently, by a doubling or halving over successive fixed intervals of time or other parameter, described as exponential growth or exponential decay.
- Relating to an exponent.
- (loosely) Characterised by a very rapid rate of change, especially increase, or merely a very large amount or degree.
- (mathematics) Expressed in terms of an exponent (power of a base), the base often being 10 or e.
- of or involving exponents
adj
- (mathematics) Of or relating to a function or functions.
- Optimized for all-around physiological benefit.
- Useful; serving a purpose, fulfilling a function.
- (computing theory) Having semantics defined purely in terms of mathematical functions, without side-effects.
- Of or relating to one's role or office; official.
- Only for functional purposes, notably in architecture.
- In good working order.
- (physiology, psychology) Characterizing functioning in environment, being symptoms that do not presuppose alteration of organic structure.
- designed for or adapted to a function or use
- involving or affecting function rather than physiology
- (of e.g. a machine) performing or capable of performing
- relating to or based on function especially as opposed to structure
- designed for or capable of a particular function or use
- fit or ready for use or service
noun
- (mathematics) A function that takes a function as its argument; more precisely, a function whose argument varies in a space of (real or complex valued) functions and whose value belongs to a monodimensional space.
- (computing) An object encapsulating a function pointer (or equivalent).
- (mathematics, functional analysis) A scalar-valued linear function on a vector space.
noun
- a function expressed as a sum or product of terms
- a discussion that provides additional information
- adding information or detail
- the act of increasing (something) in size or volume or quantity or scope
- (geometry) Stretching of geometric objects with flat sides.
- The string of text thus substituted.
- (algebra) The rewriting of an expression as a longer but equivalent sum of terms.
- The fractional change in unit length per unit length per unit temperature change.
- (steam engines) The operation of steam in a cylinder after its communication with the boiler has been cut off, by which it continues to exert pressure upon the moving piston.
- (building) A new addition.
- An act, process, or instance of expanding.
- (economics) An increase in the market value of an economy over time.
- The replacement of a short name (e.g., acronym, initialism, alphanumeric symbol, abbreviation) with the longer name that is synonymous with it, as when spelling out acronyms to ensure clarity for a general audience.
- That which is expanded; expanse; extended surface.
- A product to be used with a previous product.
- (video games) Ellipsis of expansion pack.
adj
- (mathematical analysis) Being defined in terms of objects of differential calculus such as derivatives.
- Of, or relating to division into elements or principles.
- (mathematics, of a function) Being able to be locally represented by convergent power series around every point of the domain.
- (mathematics) Of, or relating to algebra or a similar method of analysis.
- (logic, of a proposition) that follows necessarily by definition; tautologous.
- Of, or relating to any form of analysis, or to analytics.
- (linguistics) Of a language, having a grammar principally dependent on the arrangement of uninflected function words within sentences to indicate meaning.
- Having the ability to analyse.
- using or skilled in using analysis (i.e., separating a whole — intellectual or substantial — into its elemental parts or basic principles)
- using or subjected to a methodology using algebra and calculus
- expressing a grammatical category by using two or more words rather than inflection
- of a proposition that is necessarily true independent of fact or experience
adj
- (algebra) Of an algebraic expression in indeterminates, or more generally a function: capable of being expressed as the ratio of two polynomials.
- (algebraic geometry) Of a point on an algebraic variety over a field: whose coordinates belong to the field in question (in contrast to those points of the variety which are only defined over the algebraic closure of the base field).
- Logically sound; not self-contradictory or otherwise absurd.
- (of a person or personal characteristics) Healthy or balanced intellectually; exhibiting reasonableness.
- (arithmetic) Of a number, capable of being expressed as the ratio of two integers.
- (algebraic geometry) Of a variety: (informally) geometrically simple almost everywhere; (formally) birationally equivalent to projective space
- Capable of reasoning.
- (algebraic geometry) Of a function between varieties: acting as a morphism on an open subset of its domain.
- of or associated with or requiring the use of the mind
- having its source in or being guided by the intellect (as distinguished from experience or emotion)
- capable of being expressed as a quotient of integers
- consistent with or based on or using reason
noun
verb
- (mathematics, sciences, transitive) To subject to the operation of integration; to find the integral of an equation.
- (transitive) To include as a constituent part or functionality.
- (transitive) To form into one whole; to make entire; to complete; to renew; to restore; to perfect.
- (mathematics, sciences, transitive) To give the sum or total of a varying quantity over an interval such as a period of time or an area.
- (transitive) To desegregate, as a school or neighborhood.
- (usually intransitive, sometimes reflexive) To join a group or an environment harmoniously; to make oneself fit in.
- (genetics, transitive) To combine compatible elements in order to incorporate them.
- become one; become integrated
- open (a place) to members of all races and ethnic groups
- calculate the integral of; calculate by integration
- make into a whole or make part of a whole
noun
- (mathematics) A function whose derivative is a given function; an antiderivative.
- (linguistics) An original or primary word; a word not derived from another, as opposed to derivative.
- A simple-minded person.
- Primitive or primeval nature; the innate, instinctive element within a person; the deep, instinctive, precultural layer of human nature.
- Natural or premodern environment or conditions; life lacking modern technology and society.
- A member of a primitive society.
- (programming) A data type that is built into the programming language, as opposed to more complex structures.
- (programming) Any of the simplest elements (instructions, statements, etc.) available in a programming language.
- A basic geometric shape from which more complex shapes can be constructed.
- a mathematical expression from which another expression is derived
- a person who belongs to an early stage of civilization
- a word serving as the basis for inflected or derived forms
adj
- Relating to an art style characterized by asymmetrical shapes and faded colors.
- Crude, obsolete.
- (mathematics) Not derived from another of the same type
- (grammar) Original; primary; radical; not derived.
- (biology) Occurring in or characteristic of an early stage of development or evolution.
- Of or pertaining to the beginning or origin, or to early times; original; primordial; primeval; first.
- Of or pertaining to or harking back to a former time; old-fashioned; characterized by simplicity.
- used of preliterate or tribal or nonindustrial societies
- little evolved from or characteristic of an earlier ancestral type
- of or created by one without formal training; simple or naive in style
- belonging to an early stage of technical development; characterized by simplicity and (often) crudeness
noun
- (calculus) The operation of finding the integral of a function.
- an operation used in the calculus whereby the integral of a function is determined
- (society) The process of fitting into a community, notably applied to minorities.
- The act or process of making whole or entire.
- (biology) In evolution, the process by which the manifold is compacted into the relatively simple and permanent; supposed to alternate with differentiation as an agent in species' development.
- (US) Ellipsis of racial integration.
- The process of combining with compatible elements in order to incorporate them.
- the action of incorporating a racial or religious group into a community
- the act of combining into an integral whole
noun
- (calculus) A function used to define an integral transform.
- (mathematics, category theory, of a morphism f:X→Y in a category with zero morphisms) The equalizer of f and the zero morphism from X to Y, denoted operatorname kerf.
- (botany, US) The stone of certain fruits, such as peaches or plums.
- (botany) A single seed of grain, especially of corn or wheat.
- (computing) The central part of many computer operating systems which manages the system's resources and the communication between hardware and software components.
- (slang) The human clitoris.
- (computing) The core engine of any complex software system.
- (programming) The simplified input to an algorithm that has undergone kernelization.
- A small mass around which other matter is concreted; a nucleus; a concretion or hard lump in the flesh.
- (chemistry) The nucleus and electrons of an atom excluding its valence electrons.
- (botany) The central (usually edible) part of a nut, especially once the hard shell has been removed.
- (mathematics, linear algebra, of a linear transformation f:M→N between modules or vector spaces) The set of elements of M which are mapped to the additive identity 0 of N.
- (mathematics, set theory, of a function f) The set of pairs of elements in the domain of f which are mapped to the same value; the equivalence relation x≡y⟺f(x)=f(y).
- (mathematics, group theory, of a group homomorphism f:G→H between groups) The set of elements of G which are mapped to the identity of H (usually written as 0 in an additive group and as 1 in a multiplicative group).
- (mathematics, fuzzy set theory) The set of members of a fuzzy set that are fully included (i.e., whose grade of membership is 1).
- (mathematics, ring theory, of a ring homomorphism f:R→S between rings) The set of elements of R which are mapped to the additive identity 0 of S.
- (mathematics, category theory) The source of operatorname kerf, denoted operatorname Kerf.
- The core, center, or essence of an object or system.
- a single whole grain of a cereal
- the choicest or most essential or most vital part of some idea or experience
- the inner and usually edible part of a seed or grain or nut or fruit stone
verb
noun
- (mathematics) An indefinite integral: the result of the application of such an operation onto a function together with an indefinite domain, yielding a function; a function's antiderivative;
- (mathematics) A definite integral: the result of the application of such an operation onto a function and a suitable subset of the function's domain: either a number or positive or negative infinity. In the former case, the integral is said to be finite or to converge; in the latter, the integral is said to diverge. In notation, the domain of integration is indicated either below the sign, or, if it is an interval, with its endpoints as sub- and super-scripts, and the function being integrated forming part of the integrand (or, generally, differential form) appearing in front of the integral sign.
- (mathematics) One of the two fundamental operations of calculus (the other being differentiation), whereby a function's displacement, area, volume, or other qualities arising from the study of infinitesimal change are quantified, usually defined as a limiting process on a sequence of partial sums. Denoted using a long s: ∫, or a variant thereof.
- (specifically) Any of several analytic formalizations of this operation: the Riemann integral, the Lebesgue integral, etc.
- the result of a mathematical integration; F(x) is the integral of f(x) if dF/dx = f(x)
adj
- Constituting a whole together with other parts or factors; not omittable or removable.
- (mathematics) Relating to integration (“the process of finding the integral [noun] of a function”).
- (algebra, commutative algebra, of a ring element in a ring B relative to a subring A) Being the root of some monic polynomial in A.
- (mathematics) Of, pertaining to, or being an integer.
- constituting the undiminished entirety; lacking nothing essential especially not damaged
- of or denoted by an integer
- existing as an essential constituent or characteristic
noun
- (mathematics) The value or range of values of a function for which a derivative does not exist.
- (physics) Ellipsis of gravitational singularity (“a point or region in spacetime in which gravitational forces cause matter to have an infinite density; associated with black holes”).
- Celibacy, singleness (as contrasted with marriage).
- A point where a measured variable reaches unmeasurable or infinite value.
- The state of being singular, distinct, peculiar, uncommon or unusual.
- (sometimes capitalized) Ellipsis of technological singularity (“a hypothetical turning point in the future, the culmination of ever-accelerating technological progress, when human history as we have known it ends, and a strange new era begins. For some writers, the catalyst is superhuman machine intelligence”).
- An unusual action or behaviour.
- A point where all parallel lines meet.
- strangeness by virtue of being remarkable or unusual
- the quality of being one of a kind
noun
- the set of functions F(x) + C, where C is any real number, such that F(x) is the integral of f(x)
- (mathematics) A function whose derivative is a given function; an antiderivative.
- (mathematics) The set of all functions whose derivative is a given function; the set of all antiderivatives of a given function.
noun
- (calculus) Of a function, another function, the value of which for any value of the independent variable is the instantaneous rate of change of the given function at that value of the independent variable.
- the result of mathematical differentiation; the instantaneous change of one quantity relative to another; df(x)/dx
noun
- (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.
- (multivariable calculus) The Jacobian matrix of a function of several variables.
- 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
adj
noun
- (calculus) The operator which maps a function F=(F₁, ... Fₙ) from a n-dimensional vector space to itself to the function ∑ᵢ₌₁ⁿ(∂F_i)/(∂x_i).
- The process in which two or more populations accumulate genetic changes (mutations) through time.
- The state or degree of being divergent: of diverging.
- a difference between conflicting facts or claims or opinions
- an infinite series that has no limit
- a variation that deviates from the standard or norm
- the act of moving away in different direction from a common point
noun
- (mathematics, numerical analysis) The calculation of a definite integral by numerical means.
- (mathematics, mathematical analysis) The act or process of solving an indefinite integral by symbolic means.
- The process of making something square; squaring.
- (physics) The condition in which the phase angle between two alternating quantities is 90°.
- (mathematics) The act or process of constructing a square that has the same area as a given plane figure, or of computing that area.
- (art) A painting painted on a wooden panel.
- (astronomy) A situation in which the directions of two celestial bodies (or a celestial body and the Sun) form a right angle from the perspective of the observer.
- the construction of a square having the same area as some other figure
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
- Initialism of proportional integral derivative.
- Initialism of personal identification device.
- (medicine) Initialism of pelvic inflammatory disease.
- Initialism of piping and instrumentation diagram.
- Initialism of photoionization detector.
- (algebra) Initialism of principal ideal domain.
- (computing) Initialism of process identifier.
- inflammation of the female pelvic organs (especially the Fallopian tubes) caused by infection by any of several microorganisms (chiefly gonococci and chlamydia); symptoms are abdominal pain and fever and foul-smelling vaginal discharge
noun
- (calculus, of a function) The ratio of the rates of change of a dependent variable and an independent variable, the slope of a curve's tangent.
- A slope or incline.
- (sciences) The rate at which a physical quantity increases or decreases relative to change in a given variable, especially distance.
- (calculus) A differential operator that maps each point of a scalar field to a vector pointed in the direction of the greatest rate of change of the scalar. Notation for a scalar field φ: ∇φ
- A gradual change in color; a color gradient; gradation.
- A rate of inclination or declination of a slope.
- the property possessed by a line or surface that departs from the horizontal
- a graded change in the magnitude of some physical quantity or dimension
adj
noun
- (mathematics, calculus) The process of applying the derivative operator to a function; of calculating a function's derivative.
- the mathematical process of obtaining the derivative of a function
- (biology) The process by which the components of multicellular life (cells, organs, etc.) are produced and acquire function, as when a seed develops the root and stem, and the initial stem develops the leaf, branches, and flower buds.
- (biology, evolution) The evolutionary process by which one taxonomic group (species, genus, variety, etc.) becomes distinct from another, or acquires distinct features; the result of such a process: distinctness.
- The act of treating one thing as distinct from another, or of creating such a distinction; of separating a class of things into categories; of describing a thing by illustrating how it is different from something else.
- (geology) The process of separation of cooling magma into various rock types.
- The process of developing distinct components.
- (biology) the structural adaptation of some body part for a particular function
- a discrimination between things as different and distinct on the basis of their characteristics or attributes
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
- (mathematics) A function of a function.
- (chiefly law enforcement) A drawing, photograph, etc. that combines several separate pictures or images.
- A mixture of different components.
- (fraternities) A framed photo board composed of many individual photos of fraternity or sorority members.
- (school yearbook) The separate pages of individual student photos that form the main section.
- A structural material that gains its strength from a combination of complementary materials.
- (mathematics) Clipping of composite number.
- (uncommon) A segment, subset.
- (botany) A plant belonging to the family Asteraceae, syn. Compositae.
- (rail transport, UK) A railway carriage with compartments for two different classes of travel; see Composite Corridor.
- a conceptual whole made up of complicated and related parts
- considered the most highly evolved dicotyledonous plants, characterized by florets arranged in dense heads that resemble single flowers
adj
- (botany) Belonging to the Asteraceae family (formerly known as Compositae), bearing involucrate heads of many small florets.
- (mathematics) Having factors other than itself and one; not prime and not one.
- (architecture) Being a mixture of Ionic and Corinthian styles.
- (photography, historical) Employing multiple exposures on a single plate, so as to create an average view of something, such as faces in physiognomy.
- Made up of multiple components; compound or complex.
- of or relating to or belonging to the plant family Compositae
- consisting of separate interconnected parts
verb
noun
adj
- (mathematics) Characterised by a rate of change that is proportional to the value of the varying quantity, or, equivalently, by a doubling or halving over successive fixed intervals of time or other parameter, described as exponential growth or exponential decay.
- Relating to an exponent.
- (loosely) Characterised by a very rapid rate of change, especially increase, or merely a very large amount or degree.
- (mathematics) Expressed in terms of an exponent (power of a base), the base often being 10 or e.
- of or involving exponents
noun
- a function expressed as a sum or product of terms
- a discussion that provides additional information
- adding information or detail
- the act of increasing (something) in size or volume or quantity or scope
- (geometry) Stretching of geometric objects with flat sides.
- The string of text thus substituted.
- (algebra) The rewriting of an expression as a longer but equivalent sum of terms.
- The fractional change in unit length per unit length per unit temperature change.
- (steam engines) The operation of steam in a cylinder after its communication with the boiler has been cut off, by which it continues to exert pressure upon the moving piston.
- (building) A new addition.
- An act, process, or instance of expanding.
- (economics) An increase in the market value of an economy over time.
- The replacement of a short name (e.g., acronym, initialism, alphanumeric symbol, abbreviation) with the longer name that is synonymous with it, as when spelling out acronyms to ensure clarity for a general audience.
- That which is expanded; expanse; extended surface.
- A product to be used with a previous product.
- (video games) Ellipsis of expansion pack.
noun
- (mathematics) A function whose derivative is a given function; an antiderivative.
- (linguistics) An original or primary word; a word not derived from another, as opposed to derivative.
- A simple-minded person.
- Primitive or primeval nature; the innate, instinctive element within a person; the deep, instinctive, precultural layer of human nature.
- Natural or premodern environment or conditions; life lacking modern technology and society.
- A member of a primitive society.
- (programming) A data type that is built into the programming language, as opposed to more complex structures.
- (programming) Any of the simplest elements (instructions, statements, etc.) available in a programming language.
- A basic geometric shape from which more complex shapes can be constructed.
- a mathematical expression from which another expression is derived
- a person who belongs to an early stage of civilization
- a word serving as the basis for inflected or derived forms
adj
- Relating to an art style characterized by asymmetrical shapes and faded colors.
- Crude, obsolete.
- (mathematics) Not derived from another of the same type
- (grammar) Original; primary; radical; not derived.
- (biology) Occurring in or characteristic of an early stage of development or evolution.
- Of or pertaining to the beginning or origin, or to early times; original; primordial; primeval; first.
- Of or pertaining to or harking back to a former time; old-fashioned; characterized by simplicity.
- used of preliterate or tribal or nonindustrial societies
- little evolved from or characteristic of an earlier ancestral type
- of or created by one without formal training; simple or naive in style
- belonging to an early stage of technical development; characterized by simplicity and (often) crudeness
verb
- (mathematics) To calculate the derivative of a function.
- 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 differential of a function of multiple variables.
- 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
verb
- (mathematics, sciences, transitive) To subject to the operation of integration; to find the integral of an equation.
- (transitive) To include as a constituent part or functionality.
- (transitive) To form into one whole; to make entire; to complete; to renew; to restore; to perfect.
- (mathematics, sciences, transitive) To give the sum or total of a varying quantity over an interval such as a period of time or an area.
- (transitive) To desegregate, as a school or neighborhood.
- (usually intransitive, sometimes reflexive) To join a group or an environment harmoniously; to make oneself fit in.
- (genetics, transitive) To combine compatible elements in order to incorporate them.
- become one; become integrated
- open (a place) to members of all races and ethnic groups
- calculate the integral of; calculate by integration
- make into a whole or make part of a whole
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adj
- (calculus, not comparable) Having a derivative, said of a function whose domain and codomain are manifolds.
- (comparable, of multiple items) able to be differentiated; distinguishable, as for example by differing appearance or measurable characteristics.
- possessing a differential coefficient or derivative
- capable of being perceived as different
adj
- (mathematics) Being an integral without specified limits.
- Without limit; forever, or until further notice; not definite.
- (linguistics) Designating an unspecified or unidentified person or thing or group of persons or things.
- Undecided or uncertain.
- Vague or unclear.
- vague or not clearly defined or stated
- not decided or not known
noun
adj
- (mathematics, of a function) having a single derivative at a point
- producing offspring of only one sex, exhibiting monogeny
- of or relating to monogenesis or to monogenism
- (mathematics, of a semigroup) generated by a set containing only a single element
- (genetics) regulated by a single gene
- of or relating to an inheritable character that is controlled by a single pair of genes
noun
adj
- (mathematics, of a function) Having a product of independent variables, or a variable with an exponent not equal to one.
- Erratic and unpredictable; tending to jump back and forth.
- (of a system) Whose output is not directly proportional to its input.
- (chemistry, of a molecule) Whose atoms do not lie in a straight line.
- (of a set of points) Not lying on a straight line.
- designating or involving an equation whose terms are not of the first degree
adj
- (mathematics, of a function) having an infinite number of derivatives at a point (otherwise it is monogenic)
- (genetics) controlled by the interaction of more than one gene
- of or relating to an inheritable character that is controlled by several genes at once; of or related to or determined by polygenes
adj
- (mathematics, of a function) Having derivatives of all finite orders at all points within the function’s domain.
- (of muscles, medicine) Involuntary and non-striated.
- (of an action) Natural; unconstrained.
- Bland; glib.
- (mathematics, of a number) That factors completely into small prime numbers.
- Having a texture that lacks friction. Not rough.
- (of a motion) Unbroken.
- (linguistics, classical studies, of a vowel) Lacking marked aspiration.
- (of food or drink) Not grainy; having an even texture.
- (of an edge) Lacking projections or indentations; not serrated.
- Without difficulty, problems, or unexpected consequences or incidents.
- (of a beverage) Having a pleasantly rounded flavor; neither rough nor astringent.
- Flowing or uttered without check, obstruction, or hesitation; not harsh; fluent.
- Suave; sophisticated.
- (chiefly of water) Placid, calm.
- smooth and unconstrained in movement
- of the margin of a leaf shape; not broken up into teeth
- smoothly agreeable and courteous with a degree of sophistication
- lacking obstructions or difficulties
- (of a body of water) free from disturbance by heavy waves
- having a surface free from roughness or bumps or ridges or irregularities
- of motion that runs or flows or proceeds without jolts or turbulence
- (music) without breaks between notes; smooth and connected
adv
noun
verb
- (transitive) To make straightforward or easy.
- (transitive) To make smooth or even.
- (West Country) To stroke; especially to stroke an animal's fur.
- (transitive) To calm or palliate.
- (transitive) To reduce to a particular shape or form by pressure; to press, to flatten.
- (statistics, image processing, digital audio) To capture important patterns in the data, while leaving out noise.
- free from obstructions
- make smooth or smoother, as if by rubbing
- make (a surface) shine
adj
- (mathematics) Of or relating to a function or functions.
- Optimized for all-around physiological benefit.
- Useful; serving a purpose, fulfilling a function.
- (computing theory) Having semantics defined purely in terms of mathematical functions, without side-effects.
- Of or relating to one's role or office; official.
- Only for functional purposes, notably in architecture.
- In good working order.
- (physiology, psychology) Characterizing functioning in environment, being symptoms that do not presuppose alteration of organic structure.
- designed for or adapted to a function or use
- involving or affecting function rather than physiology
- (of e.g. a machine) performing or capable of performing
- relating to or based on function especially as opposed to structure
- designed for or capable of a particular function or use
- fit or ready for use or service
noun
- (mathematics) A function that takes a function as its argument; more precisely, a function whose argument varies in a space of (real or complex valued) functions and whose value belongs to a monodimensional space.
- (computing) An object encapsulating a function pointer (or equivalent).
- (mathematics, functional analysis) A scalar-valued linear function on a vector space.
adj
- (mathematical analysis) Being defined in terms of objects of differential calculus such as derivatives.
- Of, or relating to division into elements or principles.
- (mathematics, of a function) Being able to be locally represented by convergent power series around every point of the domain.
- (mathematics) Of, or relating to algebra or a similar method of analysis.
- (logic, of a proposition) that follows necessarily by definition; tautologous.
- Of, or relating to any form of analysis, or to analytics.
- (linguistics) Of a language, having a grammar principally dependent on the arrangement of uninflected function words within sentences to indicate meaning.
- Having the ability to analyse.
- using or skilled in using analysis (i.e., separating a whole — intellectual or substantial — into its elemental parts or basic principles)
- using or subjected to a methodology using algebra and calculus
- expressing a grammatical category by using two or more words rather than inflection
- of a proposition that is necessarily true independent of fact or experience
adj
- (algebra) Of an algebraic expression in indeterminates, or more generally a function: capable of being expressed as the ratio of two polynomials.
- (algebraic geometry) Of a point on an algebraic variety over a field: whose coordinates belong to the field in question (in contrast to those points of the variety which are only defined over the algebraic closure of the base field).
- Logically sound; not self-contradictory or otherwise absurd.
- (of a person or personal characteristics) Healthy or balanced intellectually; exhibiting reasonableness.
- (arithmetic) Of a number, capable of being expressed as the ratio of two integers.
- (algebraic geometry) Of a variety: (informally) geometrically simple almost everywhere; (formally) birationally equivalent to projective space
- Capable of reasoning.
- (algebraic geometry) Of a function between varieties: acting as a morphism on an open subset of its domain.
- of or associated with or requiring the use of the mind
- having its source in or being guided by the intellect (as distinguished from experience or emotion)
- capable of being expressed as a quotient of integers
- consistent with or based on or using reason