English-Wörter für '(mathematics) A function whose codomain is equal to its domain.'
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noun
- (mathematics) Synonym of function (“a relation in which each element of the domain is associated with exactly one element of the codomain”).
- (mathematics) a mathematical relation such that each element of a given set (the domain of the function) is associated with an element of another set (the range of the function)
adj
- (mathematics, of a function) Associating to each element of the codomain exactly one element of the domain; establishing a perfect (one-to-one) correspondence between the elements of the domain and the codomain; (formally) both injective and surjective.
- (mathematics) Having a component that is (specified to be) a bijective map; that specifies a bijective map.
noun
- (mathematics) A relation in which each element of the domain is associated with exactly one element of the codomain.
- (mathematics) a mathematical relation such that each element of a given set (the domain of the function) is associated with an element of another set (the range of the function)
- (anthropology) The role of a social practice in the continued existence of the group.
- Something which is dependent on or stems from another thing; a result or concomitant.
- An official or social occasion.
- What something does or is used for.
- A professional or official position.
- (slang) A party.
- (chemistry) The characteristic behavior of a chemical compound.
- (biology) The physiological activity of an organ or body part.
- (computing) A routine that receives zero or more arguments and may return a result.
- A relation where one thing is dependent on another for its existence, value, or significance.
- a formal or official social gathering or ceremony
- the actions and activities assigned to or required or expected of a person or group
- a relation such that one thing is dependent on another
- a formal or official social gathering or ceremony of people
- what something is used for
- a set sequence of steps, part of larger computer program
verb
noun
- (mathematics) The subset of the codomain of a function comprising those elements that are the image of some element of its domain.
- A statue or idol.
- A mental picture of something not real or not present.
- (computing) A file that contains all information needed to produce a live working copy. (See disk image and image copy.)
- (mathematics) The value a function maps some argument to.
- A file on a computer containing a single frame; an image file.
- A visual or other representation of the external form of something in art.
- (radio) A form of interference: a weaker "copy" of a strong signal that occurs at a different frequency.
- A characteristic of a person, group or company etc., style, manner of dress, how one is or wishes to be perceived by others.
- someone who closely resembles a famous person (especially an actor)
- a standard or typical example
- the general impression that something (a person or organization or product) presents to the public
- a visual representation (of an object or scene or person or abstraction) produced on a surface
- language used in a figurative or nonliteral sense
- an iconic mental representation
- (mathematics) the set of values of the dependent variable for which a function is defined
- a representation of a person (especially in the form of sculpture)
- (Jungian psychology) a personal facade that one presents to the world
verb
prep
- (mathematics) Having as identical domain and codomain.
- To the account or detriment of; denoting imprecation or invocation, or coming to, falling, or resting upon.
- At or in (a geographical location or position).
- At (a relative spatial position).
- Engaged in or occupied with (an action or activity).
- Serving as a member of.
- Under the influence of (a drug, or something that is causing drug-like effects).
- Indicating the target of, or thing affected by, an event or action.
- (snooker) In a position of being able to pot (a given ball).
- (also often 'upon') Arrived or coming into the presence of.
- Toward; for; indicating the object of an emotion.
- At (an instant or cusp).
- Aboard (a mode of transport, especially public transport, or transport that one sits astride or uses while standing).
- Expressing figurative placement, burden, or attachment.
- At (a certain position within a sequence).
- Denoting performance or action by contact with the surface, upper part, or outside of anything By means of; with.
- Covering.
- (mathematics) Having Vⁿ as domain and V as codomain, for the specified set V and some integer n.
- In addition to; besides; indicating multiplication or succession in a series.
- (mathematics, uncommon) Divided by.
- (especially Ireland) Indicating the person experiencing an emotion, cold, thirst, hunger, etc.
- (UK) At (a certain value or level).
- With verbs describing an action of pushing, pulling, pressing, etc., designates the thing to which force is applied.
- (also often 'upon') At the time of (and often because of).
- (UK dialectal, Scotland) Without.
- Positioned at the upper surface of, touching from above.
- Because of; upon the basis of (something not yet confirmed as true).
- (informal) In the possession of.
- Positioned at or resting against the outer surface of; attached to.
- (philosophy, logic) According to, from the standpoint of; (expressing what must follow, whether accepted or not, if a given premise or system is assumed true).
- (UK, especially in sports reporting) At (a given time after the start of something).
- Near; adjacent to; alongside; just off.
- Paid for by.
- Regularly taking (a drug).
- (especially when numbers of combatants or competitors are specified) Against; in opposition to.
- At or during the date or day of.
- (nautical) In the direction of (some part of one's vessel), to within 45 degrees.
- Indicating dependence or reliance.
- Indicating a means of subsistence or sustenance.
- (mathematics) Generated by.
- By virtue of; with the pledge of.
- (informal, chiefly in set phrases) Ellipsis of I swear on: on my life, on God, on everything, etc.
- Indicating a means or medium.
- Dealing with the subject of; about; concerning.
- With verbs describing an action of hitting, rubbing, scratching, binding against, etc., designates the thing impacted or contacted.
- Supported by (the specified part of itself).
adj
- (euphemistic) Menstruating.
- (chiefly UK, informal, chiefly in the negative) Acceptable, appropriate.
- (snooker, postpositive) Of a ball, being the next in sequence to be potted, according to the rules of the game.
- In the state of being active, functioning or operating.
- Happening; taking place; being or due to be put into action.
- (informal) Of a person, used to express agreement to or acceptance of a proposal or challenge made by that person; most commonly with subject "you" (see you're on).
- (acting, drama, roleplaying games) Acting in character.
- (chiefly in the negative) Possible; capable of being successfully carried out.
- Fitted; covering or being worn.
- (cricket) Within the half of the field on the same side as the batsman's legs; the left side for a right-handed batsman.
- (baseball, informal) Having reached a base as a runner and being positioned there, awaiting further action from a subsequent batter.
- (informal, of a person) Performative or funny in a wearying manner.
- (e.g. of points in a game) Available; remaining.
- (postpositive) Of a stated part of something, oriented towards the viewer or other specified direction.
- in operation or operational
- (of events) planned or scheduled
adv
- (infrequent in the US) Later.
- In continuation, at length.
- So as to cover or be fitted.
- (snooker) Of a ball, into a pottable position.
- Of betting odds, denoting a better-than-even chance. See also odds-on.
- Along, forwards (continuing an action), onwards.
- To an operating state.
- indicates continuity or persistence or concentration
- in a state required for something to function or be effective
- with a forward motion
noun
verb
noun
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
- (specifically, mathematics) To consider (a function) as defined on a subset of its original domain.
- To restrain within boundaries; to limit; to confine
- place under restrictions; limit access to by law
- place limits on (extent or amount or access)
- prevent (information) from being circulated or disclosed
- place restrictions on
adj
- (mathematics) Which forms a surjection from the domain to every open subset of the codomain.
- (of wine) Having a slight lack of acidity; having mild sweetness.
- (of writing, etc.) overwrought.
- Yielding to the touch, and easily moved or shaken; hanging loose by its own weight; lacking firmness; flaccid.
- out of condition; not strong or robust; incapable of exertion or endurance
noun
- (mathematics) A function or other mapping that carries values defined on a domain into another value or set of values in a defined range.
- A telecommunications facilitator whose job is to connect or otherwise assist callers.
- (by ellipsis, mining) The company that operates a mine; often the same one that owns the mine.
- A person or organisation that operates a device, system, service, etc.
- (uncountable) The game of Chinese whispers.
- (linguistics) A kind of expression that enters into an a-bar movement dependency and is said to bind a variable.
- (computing) A symbol that represents a construct in a programming language and differs from a normal function in its syntax.
- A member of a military special operations unit.
- (informal) A person who is adept at making deals or getting results, especially one who uses questionable methods.
- (computing) The administrator of a channel or network on IRC.
- (slang) A thief or charlatan.
- (transport) A bus driver.
- (slang) A major criminal.
- an agent that operates some apparatus or machine
- (mathematics) a symbol or function representing a mathematical operation
- someone who owns or operates a business
- a shrewd or unscrupulous person who knows how to circumvent difficulties
- a speculator who trades aggressively on stock or commodity markets
noun
- (topology) A function derived, in a standard way, from another, such that the instant function’s domain and codomain are suspensions of the original function’s.
- (Scots law) A stay or postponement of the execution of a sentence, usually by letters of suspension granted on application to the Lord Ordinary.
- A temporary or conditional delay, interruption or discontinuation.
- Thus a kind of silt or sludge.
- The temporary barring of a person from a workplace, society, etc. pending investigation into alleged misconduct.
- (chemistry, physics) The state of a solid or substance produced when its particles are mixed with, but not dissolved in, a fluid, and are capable of separation by straining.
- (education) The process of barring a student from school grounds as a form of punishment (particularly out-of-school suspension).
- (music) The act of or discord produced by prolonging one or more tones of a chord into the chord which follows, thus producing a momentary discord, suspending the concord which the ear expects.
- (vehicles) The system of springs and shock absorbers connected to the wheels in an automobile, which allows the vehicle to move smoothly with reduced shock to its occupants.
- (topology) A topological space derived from another by taking the product of the original space with an interval and collapsing each end of the product to a point.
- The act of keeping a person who is listening in doubt and expectation of what is to follow.
- The act of suspending, or the state of being suspended.
- the act of suspending something (hanging it from above so it moves freely)
- a temporary debarment (from a privilege or position etc.)
- a mechanical system of springs or shock absorbers connecting the wheels and axles to the chassis of a wheeled vehicle
- a time interval during which there is a temporary cessation of something
- temporary cessation or suspension
- an interruption in the intensity or amount of something
- a mixture in which fine particles are suspended in a fluid where they are supported by buoyancy
noun
- (mathematics) a mathematical relation such that each element of a given set (the domain of the function) is associated with an element of another set (the range of the function)
- (mathematics) A function, especially a function satisfying a certain property (e.g. continuity, linearity, etc.; see Usage notes).
- a diagrammatic representation of the earth's surface (or part of it)
- (board games, video games) An imaginary or fictional area, often predefined and confined, where a game or a session thereof takes place.
- (entomology) Any of various nymphalid butterflies of the genera Araschnia (especially, Araschnia levana) and Cyrestis, having map-like markings on the wings.
- (computing) Synonym of associative array.
- A graphical or logical representation of any structure or system, showing the positions of or relationships between its components.
- A visual representation of an area, whether real or imaginary, showing the relative positions of places and other features.
verb
- depict as if on a map
- explore or survey for the purpose of making a map
- make a map of; show or establish the features of details of
- to establish a mapping (of mathematical elements or sets)
- plan, delineate, or arrange in detail
- locate within a specific region of a chromosome in relation to known DNA or gene sequences
- (transitive, computing) To assign a drive letter to a shared folder.
- (transitive) To create a map of; to examine or survey in order to gather information for a map.
- (mathematics, transitive, followed by a "to" phrase) To act as a function on something, taking it to something else.
- (intransitive, followed by a "to" phrase) To have a direct relationship; to correspond.
- (transitive) To represent by means of a map.
- (transitive, followed by a "to" phrase) To create a direct relationship to; to create a correspondence with.
noun
- (mathematics) a mathematical relation such that each element of a given set (the domain of the function) is associated with an element of another set (the range of the function)
- (mathematics) A function that maps every element of a given mathematical structure (eg: a set) to a unique element of another structure; a correspondence.
- (genetics) the process of locating genes on a chromosome
- the process of making maps
- (biology) The process of locating genes on a chromosome.
- The process of making maps.
- (object-oriented programming) conversion of data types between incompatible type systems.
- (computing) Assigning a PC to a shared drive or printer port on a network.
verb
noun
- (mathematical analysis) A function which is equal to 1 for all points in its domain which belong to a given set, and is equal to 0 for all points in the domain which do not belong to that given set.
- (mathematics, probability theory) A complex function completely defining the probability distribution of a real-valued random variable
- (electronics) graph showing how a particular characteristic of a device varies with other parameters
adj
- (mathematics, of a function) Being able to be locally represented by convergent power series around every point of the domain.
- Of, or relating to division into elements or principles.
- (mathematical analysis) Being defined in terms of objects of differential calculus such as derivatives.
- (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
verb
- (mathematics, transitive) To define a one-to-one function from one set to another so that certain properties of the domain are preserved when considering the image as a subset of the codomain.
- (transitive, by extension) To include (something) in surrounding matter.
- (transitive) To lay (something) as in a bed; to lay in surrounding matter; to bed.
- (transitive, computing) To encapsulate within another document or data file.
- fix or set securely or deeply
- attach to, as a journalist to a military unit when reporting on a war
noun
- An element of an advertisement, etc. serving as a subliminal message.
- (computing) A piece of computer hardware embedded within another physical object, which is often a larger IT device.
- (journalism) An embedded reporter or journalist, such as a war reporter assigned to and travelling with a military unit, or a political reporter assigned to follow and report on the campaign of a candidate.
- (computing) A digital object embedded within another, which is often a document.
noun
- (algebra, computing) Any function which maps all elements of its domain to themselves.
- The difference or character that marks off an individual or collective from the rest of the same kind; selfhood; the sense of who something or someone or oneself is, or the recurring characteristics that enable the recognition of such an individual or group by others or themselves.
- (Australia, New Zealand) A well-known or famous person.
- (mathematics) An equation which always holds true regardless of the choice of input variables.
- A name or persona—a mask or appearance one presents to the world—by which one is known.
- Sameness, identicalness; the quality or fact of (several specified things) being the same.
- (algebra) An element of an algebraic structure which, when applied to another element under an operation in that structure, yields this second element.
- the individual characteristics by which a thing or person is recognized or known
- an operator that leaves unchanged the element on which it operates
- exact sameness
- the distinct personality of an individual regarded as a persisting entity
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) A property of functions that have a rule describing how the function can be performed to the individual components of another operation.
- (logic) Assigning the species of a general term.
- Relating to distribution.
- Tending to distribute; serving to divide and assign in portions; dealing a proper share to each.
- (grammar) Expressing separation; denoting a taking singly, not collectively.
- serving to distribute or allot or disperse
noun
noun
- (functional analysis) The principle that functions are equal if and only if they operate on the same domain and for any given element of the domain the result of each of the functions is the same.
- (set theory) The principle, codified in the axiom of extensionality, that sets are equal if and only if they contain the same elements.
- (philosophy) The principle that objects are equal if and only if their observed properties are the same, regardless of internal processes that lead to those properties.
noun
- (mathematical analysis, of a function) The highest order of derivative (the differentiability class) over a given domain.
- (approximation theory, numerical analysis, of a function) The quantity measured by the modulus of smoothness.
- The condition of being smooth; the degree or measure of said condition.
- the quality of having a level and even surface
- the quality of being free from errors or interruptions
- powerful and effective language
- the quality of being bland and gracious or ingratiating in manner
- a texture without roughness; smooth to the touch
noun
- (mathematics, category theory) The codomain of a function; the object at which a morphism points.
- A butt or mark to shoot at, as for practice, or to test the accuracy of a firearm, or the force of a projectile.
- An object of criticism or ridicule.
- A person, place, or thing that is frequently attacked, criticized, or ridiculed.
- A kind of small shield or buckler, used as a defensive weapon in war.
- (sports) The pattern or arrangement of a series of hits made by a marksman on a butt or mark.
- (linguistics) The tenor of a metaphor.
- (heraldry) A bearing representing a buckler.
- A person (or group of people) that a person or organization is trying to employ or to have as a customer, audience etc.
- (surveying) The sliding crosspiece, or vane, on a leveling staff.
- A goal or objective.
- (cricket) the number of runs that the side batting last needs to score in the final innings in order to win
- (translation studies) The translated version of a document, or the language into which translation occurs.
- (rail transport) A conspicuous disk attached to a switch lever to show its position, or for use as a signal.
- a reference point to shoot at
- a person who is the aim of an attack (especially a victim of ridicule or exploitation) by some hostile person or influence
- the goal intended to be attained (and which is believed to be attainable)
- sports equipment consisting of an object set up for a marksman or archer to aim at
- the location of the target that is to be hit
verb
noun
- (mathematics) (of a function) defined for each point x in the domain of the function by inf diam(f(U))∣Uisaneighborhoodofx, and describes the difference (possibly ∞) between the limit superior and limit inferior of the function near that point.
- a single such cycle
- the act of oscillating or the state of being oscillated
- a regular periodic fluctuation in value about some mean
- (physics) a regular periodic variation in value about a mean
- the process of oscillating between states
- a single complete execution of a periodically repeated phenomenon
noun
- (mathematics) An equivalence class that includes a specified function defined in an open neighborhood.
- (figurative) The origin or earliest version of an idea or project.
- A pathogen: a pathogenic microorganism, such as a bacterium or virus.
- (biology) The small mass of cells from which a part of an organism develops, or a macroscopic but immature form of that part; a bud.
- The embryo of a seed, especially of a seed used as a cereal or grain. See Wikipedia article on cereal germ.
- a minute life form (especially a disease-causing bacterium); the term is not in technical use
- anything that provides inspiration for later work
- a small apparently simple structure (as a fertilized egg) from which new tissue can develop into a complete organism
verb
adj
- (of an encoding or function) Having multiple domain elements correspond to one element of the range.
- (physics) Having the same quantum energy level.
- Having lost functionality in general.
- (of qualities) Having deteriorated, degraded or fallen from normal, coherent, balanced and desirable to undesirable and typically abnormal.
- (mathematics, of an eigenvalue) Having multiple different (linearly independent) eigenvectors.
- (mathematics) Qualitatively different, usually simpler, than typical objects of its class.
- (of a person or system) Having lost good or desirable qualities; hence also having bad character or habits, base, immoral, corrupt. ABR
- unrestrained by convention or morality
noun
verb
adj
- (algebraic geometry) Of a function between varieties: acting as a morphism on an open subset of its domain.
- (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.
- (algebra) Of an algebraic expression in indeterminates, or more generally a function: capable of being expressed as the ratio of two polynomials.
- 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
noun
- (mathematics) A set of arguments where two or more functions have equal values; the solution set of an equation.
- A conductor of low resistance joining the armature ends of the series field coils of dynamos connected in parallel.
- A device, such as a bar, for operating two brakes, especially a pair of hub brakes for an automobile, with equal force.
- (category theory) A morphism whose codomain is the domain of a parallel pair of morphisms and which forms part of the limit of that parallel pair. Equivalently, a morphism which equalizes a parallel pair of morphisms in a limiting way, which is to say that any other morphism which equalizes that parallel pair factors through this limiting morphism; and moreover such factorization is unique.
- A sliding panel to preserve the lateral stability of an aeroplane.
- One who makes equal; a balancer.
- (Canada, US, slang) A weapon, usually a blackjack or gun.
- (music, electronics) An electronic audio device for altering the frequencies of sound recordings.
- (sports) A goal, run, point, etc. that equalizes the score.
- A device that balances various quantities.
- Any device for equalizing the pull of electromagnets.
- electronic equipment that reduces frequency distortion
- a score that makes the match even
- a weight that balances another weight
noun
- (mathematics) Applying a function to the result of another.
- (printing) Typesetting.
- (linguistics) The formation of compound words from separate words.
- Synthesis as opposed to analysis.
- A mixture or compound; the result of composing.
- A work of music, literature or art.
- The general makeup of a thing or person.
- The proportion of different parts to make a whole.
- (law) an agreement or compromise by which a creditor or group of creditors accepts partial payment from a debtor.
- (object-oriented programming) Way to combine simple objects or data types into more complex ones.
- The act of putting together; assembly.
- (physics) The compounding of two velocities or forces into a single equivalent velocity or force.
- (painting, photography) The arrangement and flow of elements in a picture.
- (chess) A puzzle created by the composer using chess pieces on a chessboard, which presents the solver with a particular task.
- An essay.
- an essay (especially one written as an assignment)
- something that is created by arranging several things to form a unified whole
- musical creation
- the act of creating written works
- art and technique of printing with movable type
- the way in which someone or something is composed
- the spatial property resulting from the arrangement of parts in relation to each other and to the whole
- a mixture of ingredients
- a musical work that has been created
adj
- (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.).
- (ring theory, of an element of a graded ring) Belonging to one of the summands of the grading (if the ring is graded over the natural numbers and the element is in the kth summand, it is said to be homogeneous of degree k; if the ring is graded over a commutative monoid I, and the element is an element of the ith summand, it is said to be of grade i)
- (of a linear differential equation) Having its degree-zero term equal to zero; admitting the trivial solution.
- (algebra, of a polynomial) Such that all its nonzero terms have the same degree.
- Having the same composition throughout; of uniform make-up.
- (probability theory, Fourier analysis, of a distribution S on Euclidean n-space (or on ℝⁿmathbf 0)) Informally: Determined by its restriction to the unit sphere. Formally: Such that, for all real t>0 and test functions ϕ( mathbf x), the equality S[t⁻ⁿϕ( mathbf x/t)]=t^(mS)[ϕ( mathbf x)] holds for some fixed real or complex m.
- Of the same kind; alike, similar.
- (of a linear map f between vector spaces graded by a commutative monoid I) Which respects the grading of its domain and codomain. Formally: Satisfying f(V_j)⊆W_i+j for fixed i (called the degree or grade of f), V_j the jth component of the grading of f 's domain, W_k the kth component of the grading of f 's codomain, and + representing the monoid operation in I.
- (geometry, of a space equipped with a group action) Informally: Everywhere the same, uniform, in the sense that any point can be moved to any other (via the group action) while respecting the structure of the space. Formally: Such that the group action is transitively and acts by automorphisms on the space (some authors also require that the action be faithful).
- (set theory, order theory, of a relation) Holding between a set and itself; being an endorelation.
- (of a first-order differential equation) Capable of being written in the form f(x,y) mathop dy=g(x,y) mathop dx where f and g are homogeneous functions of the same degree as each other.
- (linear algebra, by specialization, of a system of linear equations) Such that all the constant terms are zero.
- (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
- of or relating to the multiplicative inverse of a quantity or function
- concerning each of two or more persons or things; especially given or done in return
- Done, given, felt, or owed in return.
- Mutually interchangeable.
- (grammar) Expressing mutual action, applied to pronouns and verbs; also in a broad sense: reflexive.
- Of a feeling, action or such: mutual, uniformly felt or done by each party towards the other or others; two-way.
- (mathematics) Used to denote different kinds of mutual relation; often with reference to the substitution of reciprocals for given quantities.
noun
- something (a term or expression or concept) that has an inverse relation to something else
- (mathematics) one of a pair of numbers whose product is 1: the reciprocal of 2/3 is 3/2; the multiplicative inverse of 7 is 1/7
- hybridization involving a pair of crosses that reverse the sexes associated with each genotype
- (grammar) A construction expressing mutual action.
- (arithmetic) The number obtained by dividing 1 by another given number; the result of exchanging the numerator and the denominator of a fraction.
adj
- (commutative algebra, of a domain) Integrally closed: equal its own integral closure in its field of fractions.
- (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.
- (functional analysis, of a Hilbert space operator) Which commutes with its adjoint.
- (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) Relating to the corresponding elements of an equivalence relation.
- (cartography) Of a map, equal-area.
- (geometry) Equal in measure but not admitting of superposition; applied to magnitudes.
- (mathematics, category theory) Of two categories, (informally) such that one is essentially a relabeling of the other; (formally) related by a pair of functors such the composition of the one with the other is naturally isomorphic to the identity functor.
- (chemistry) Having the equal ability to combine.
- Similar or identical in value, meaning or effect; virtually equal.
- (mathematics) Of two sets, having a one-to-one correspondence.
- being essentially equal to something
noun
- Anything that is virtually equal to something else, or has the same value, force, etc.
- (chemistry) An equivalent weight.
- a person or thing equal to another in value or measure or force or effect or significance etc
- the atomic weight of an element that has the same combining capacity as a given weight of another element; the standard is 8 for oxygen
verb
noun
- (topology) A continuous map which is also a homeomorphism between its domain and its image (considered with the subspace topology induced by its codomain).
- (differential topology) An immersion which is also a topological embedding; equivalently, a diffeomorphism whose image is a submanifold of its codomain.
- (machine learning, artificial intelligence) A representation of a unit of text (such as a word or token) as a vector, which encodes the context in which it is used.
- (mathematical analysis) A map between metric spaces which preserves distances up to some scaling factor (called the distortion).
- The act or process by which one thing is embedded in another.
- (category theory) An injective morphism in a concrete category which is also initial.
- (field theory, Galois theory) A ring homomorphism between fields (the name deriving from the fact that all such maps are injective).
verb
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
noun
- (mathematics, category theory) The domain of a function; the object which a morphism points from.
- A reporter's informant.
- Spring; fountainhead; wellhead; any collection of water on or under the surface of the ground in which a stream originates.
- The person, place, or thing from which something (information, goods, etc.) comes or is acquired.
- (electronics) The name of one terminal of a field effect transistor (FET).
- (computing) Source code.
- (graph theory) A node in a directed graph whose edges all go out from it; one with no entering edges.
- a facility where something is available
- the place where something begins, where it springs into being
- a publication (or a passage from a publication) that is referred to
- anything (a person or animal or plant or substance) in which an infectious agent normally lives and multiplies
- someone who originates or causes or initiates something
- a document (or organization) from which information is obtained
- anything that provides inspiration for later work
- (technology) a process by which energy or a substance enters a system
- a person who supplies information
verb
noun
- (set theory) A function that maps distinct x in the domain to distinct y in the codomain; formally, a f: X → Y such that f(a) = f(b) implies a = b for any a, b in the domain.
- (internal combustion engines) Fuel injection: the pressurized introduction of fuel into a cylinder.
- (computer security) The insertion of program code into an application, URL, hardware, etc.; especially when malicious or when the target is not designed for such insertion.
- (space science) The act of putting a spacecraft into a particular orbit, especially for changing a stable orbit into a transfer orbit, e.g. trans-lunar injection.
- The act of injecting, or something that is injected.
- (construction) The act of inserting materials like concrete grout or gravel by using high pressure pumps.
- (mathematics) A relation on sets (X,Y) that associates each element of Y with at most one element of X.
- (category theory) A morphism from either one of the two components of a coproduct to that coproduct.
- (figuratively) The supply of additional funding to a person or a business.
- (steam engines) The act of throwing cold water into a condenser to produce a vacuum.
- A specimen prepared by injection.
- (medicine) Congestion (of a body part, with blood or other fluid), such as hyperemia.
- (steam engines) The cold water thrown into a condenser to produce a vacuum.
- (medicine) Something injected subcutaneously, intravenously, or intramuscularly by use of a syringe and a needle.
- the forceful insertion of a substance under pressure
- any solution that is injected (as into the skin)
- the act of putting a liquid into the body by means of a syringe
noun
- (mathematics) Synonym of function (“a relation in which each element of the domain is associated with exactly one element of the codomain”).
- (mathematics) a mathematical relation such that each element of a given set (the domain of the function) is associated with an element of another set (the range of the function)
noun
- (mathematics) A relation in which each element of the domain is associated with exactly one element of the codomain.
- (mathematics) a mathematical relation such that each element of a given set (the domain of the function) is associated with an element of another set (the range of the function)
- (anthropology) The role of a social practice in the continued existence of the group.
- Something which is dependent on or stems from another thing; a result or concomitant.
- An official or social occasion.
- What something does or is used for.
- A professional or official position.
- (slang) A party.
- (chemistry) The characteristic behavior of a chemical compound.
- (biology) The physiological activity of an organ or body part.
- (computing) A routine that receives zero or more arguments and may return a result.
- A relation where one thing is dependent on another for its existence, value, or significance.
- a formal or official social gathering or ceremony
- the actions and activities assigned to or required or expected of a person or group
- a relation such that one thing is dependent on another
- a formal or official social gathering or ceremony of people
- what something is used for
- a set sequence of steps, part of larger computer program
verb
noun
- (mathematics) The subset of the codomain of a function comprising those elements that are the image of some element of its domain.
- A statue or idol.
- A mental picture of something not real or not present.
- (computing) A file that contains all information needed to produce a live working copy. (See disk image and image copy.)
- (mathematics) The value a function maps some argument to.
- A file on a computer containing a single frame; an image file.
- A visual or other representation of the external form of something in art.
- (radio) A form of interference: a weaker "copy" of a strong signal that occurs at a different frequency.
- A characteristic of a person, group or company etc., style, manner of dress, how one is or wishes to be perceived by others.
- someone who closely resembles a famous person (especially an actor)
- a standard or typical example
- the general impression that something (a person or organization or product) presents to the public
- a visual representation (of an object or scene or person or abstraction) produced on a surface
- language used in a figurative or nonliteral sense
- an iconic mental representation
- (mathematics) the set of values of the dependent variable for which a function is defined
- a representation of a person (especially in the form of sculpture)
- (Jungian psychology) a personal facade that one presents to the world
verb
noun
noun
- (mathematics) A function or other mapping that carries values defined on a domain into another value or set of values in a defined range.
- A telecommunications facilitator whose job is to connect or otherwise assist callers.
- (by ellipsis, mining) The company that operates a mine; often the same one that owns the mine.
- A person or organisation that operates a device, system, service, etc.
- (uncountable) The game of Chinese whispers.
- (linguistics) A kind of expression that enters into an a-bar movement dependency and is said to bind a variable.
- (computing) A symbol that represents a construct in a programming language and differs from a normal function in its syntax.
- A member of a military special operations unit.
- (informal) A person who is adept at making deals or getting results, especially one who uses questionable methods.
- (computing) The administrator of a channel or network on IRC.
- (slang) A thief or charlatan.
- (transport) A bus driver.
- (slang) A major criminal.
- an agent that operates some apparatus or machine
- (mathematics) a symbol or function representing a mathematical operation
- someone who owns or operates a business
- a shrewd or unscrupulous person who knows how to circumvent difficulties
- a speculator who trades aggressively on stock or commodity markets
noun
- (topology) A function derived, in a standard way, from another, such that the instant function’s domain and codomain are suspensions of the original function’s.
- (Scots law) A stay or postponement of the execution of a sentence, usually by letters of suspension granted on application to the Lord Ordinary.
- A temporary or conditional delay, interruption or discontinuation.
- Thus a kind of silt or sludge.
- The temporary barring of a person from a workplace, society, etc. pending investigation into alleged misconduct.
- (chemistry, physics) The state of a solid or substance produced when its particles are mixed with, but not dissolved in, a fluid, and are capable of separation by straining.
- (education) The process of barring a student from school grounds as a form of punishment (particularly out-of-school suspension).
- (music) The act of or discord produced by prolonging one or more tones of a chord into the chord which follows, thus producing a momentary discord, suspending the concord which the ear expects.
- (vehicles) The system of springs and shock absorbers connected to the wheels in an automobile, which allows the vehicle to move smoothly with reduced shock to its occupants.
- (topology) A topological space derived from another by taking the product of the original space with an interval and collapsing each end of the product to a point.
- The act of keeping a person who is listening in doubt and expectation of what is to follow.
- The act of suspending, or the state of being suspended.
- the act of suspending something (hanging it from above so it moves freely)
- a temporary debarment (from a privilege or position etc.)
- a mechanical system of springs or shock absorbers connecting the wheels and axles to the chassis of a wheeled vehicle
- a time interval during which there is a temporary cessation of something
- temporary cessation or suspension
- an interruption in the intensity or amount of something
- a mixture in which fine particles are suspended in a fluid where they are supported by buoyancy
noun
- (mathematics) a mathematical relation such that each element of a given set (the domain of the function) is associated with an element of another set (the range of the function)
- (mathematics) A function, especially a function satisfying a certain property (e.g. continuity, linearity, etc.; see Usage notes).
- a diagrammatic representation of the earth's surface (or part of it)
- (board games, video games) An imaginary or fictional area, often predefined and confined, where a game or a session thereof takes place.
- (entomology) Any of various nymphalid butterflies of the genera Araschnia (especially, Araschnia levana) and Cyrestis, having map-like markings on the wings.
- (computing) Synonym of associative array.
- A graphical or logical representation of any structure or system, showing the positions of or relationships between its components.
- A visual representation of an area, whether real or imaginary, showing the relative positions of places and other features.
verb
- depict as if on a map
- explore or survey for the purpose of making a map
- make a map of; show or establish the features of details of
- to establish a mapping (of mathematical elements or sets)
- plan, delineate, or arrange in detail
- locate within a specific region of a chromosome in relation to known DNA or gene sequences
- (transitive, computing) To assign a drive letter to a shared folder.
- (transitive) To create a map of; to examine or survey in order to gather information for a map.
- (mathematics, transitive, followed by a "to" phrase) To act as a function on something, taking it to something else.
- (intransitive, followed by a "to" phrase) To have a direct relationship; to correspond.
- (transitive) To represent by means of a map.
- (transitive, followed by a "to" phrase) To create a direct relationship to; to create a correspondence with.
noun
- (mathematics) a mathematical relation such that each element of a given set (the domain of the function) is associated with an element of another set (the range of the function)
- (mathematics) A function that maps every element of a given mathematical structure (eg: a set) to a unique element of another structure; a correspondence.
- (genetics) the process of locating genes on a chromosome
- the process of making maps
- (biology) The process of locating genes on a chromosome.
- The process of making maps.
- (object-oriented programming) conversion of data types between incompatible type systems.
- (computing) Assigning a PC to a shared drive or printer port on a network.
verb
noun
- (mathematical analysis) A function which is equal to 1 for all points in its domain which belong to a given set, and is equal to 0 for all points in the domain which do not belong to that given set.
- (mathematics, probability theory) A complex function completely defining the probability distribution of a real-valued random variable
- (electronics) graph showing how a particular characteristic of a device varies with other parameters
noun
- (algebra, computing) Any function which maps all elements of its domain to themselves.
- The difference or character that marks off an individual or collective from the rest of the same kind; selfhood; the sense of who something or someone or oneself is, or the recurring characteristics that enable the recognition of such an individual or group by others or themselves.
- (Australia, New Zealand) A well-known or famous person.
- (mathematics) An equation which always holds true regardless of the choice of input variables.
- A name or persona—a mask or appearance one presents to the world—by which one is known.
- Sameness, identicalness; the quality or fact of (several specified things) being the same.
- (algebra) An element of an algebraic structure which, when applied to another element under an operation in that structure, yields this second element.
- the individual characteristics by which a thing or person is recognized or known
- an operator that leaves unchanged the element on which it operates
- exact sameness
- the distinct personality of an individual regarded as a persisting entity
noun
- (functional analysis) The principle that functions are equal if and only if they operate on the same domain and for any given element of the domain the result of each of the functions is the same.
- (set theory) The principle, codified in the axiom of extensionality, that sets are equal if and only if they contain the same elements.
- (philosophy) The principle that objects are equal if and only if their observed properties are the same, regardless of internal processes that lead to those properties.
noun
- (mathematical analysis, of a function) The highest order of derivative (the differentiability class) over a given domain.
- (approximation theory, numerical analysis, of a function) The quantity measured by the modulus of smoothness.
- The condition of being smooth; the degree or measure of said condition.
- the quality of having a level and even surface
- the quality of being free from errors or interruptions
- powerful and effective language
- the quality of being bland and gracious or ingratiating in manner
- a texture without roughness; smooth to the touch
noun
- (mathematics, category theory) The codomain of a function; the object at which a morphism points.
- A butt or mark to shoot at, as for practice, or to test the accuracy of a firearm, or the force of a projectile.
- An object of criticism or ridicule.
- A person, place, or thing that is frequently attacked, criticized, or ridiculed.
- A kind of small shield or buckler, used as a defensive weapon in war.
- (sports) The pattern or arrangement of a series of hits made by a marksman on a butt or mark.
- (linguistics) The tenor of a metaphor.
- (heraldry) A bearing representing a buckler.
- A person (or group of people) that a person or organization is trying to employ or to have as a customer, audience etc.
- (surveying) The sliding crosspiece, or vane, on a leveling staff.
- A goal or objective.
- (cricket) the number of runs that the side batting last needs to score in the final innings in order to win
- (translation studies) The translated version of a document, or the language into which translation occurs.
- (rail transport) A conspicuous disk attached to a switch lever to show its position, or for use as a signal.
- a reference point to shoot at
- a person who is the aim of an attack (especially a victim of ridicule or exploitation) by some hostile person or influence
- the goal intended to be attained (and which is believed to be attainable)
- sports equipment consisting of an object set up for a marksman or archer to aim at
- the location of the target that is to be hit
verb
noun
- (mathematics) (of a function) defined for each point x in the domain of the function by inf diam(f(U))∣Uisaneighborhoodofx, and describes the difference (possibly ∞) between the limit superior and limit inferior of the function near that point.
- a single such cycle
- the act of oscillating or the state of being oscillated
- a regular periodic fluctuation in value about some mean
- (physics) a regular periodic variation in value about a mean
- the process of oscillating between states
- a single complete execution of a periodically repeated phenomenon
noun
- (mathematics) An equivalence class that includes a specified function defined in an open neighborhood.
- (figurative) The origin or earliest version of an idea or project.
- A pathogen: a pathogenic microorganism, such as a bacterium or virus.
- (biology) The small mass of cells from which a part of an organism develops, or a macroscopic but immature form of that part; a bud.
- The embryo of a seed, especially of a seed used as a cereal or grain. See Wikipedia article on cereal germ.
- a minute life form (especially a disease-causing bacterium); the term is not in technical use
- anything that provides inspiration for later work
- a small apparently simple structure (as a fertilized egg) from which new tissue can develop into a complete organism
verb
noun
- (mathematics) A set of arguments where two or more functions have equal values; the solution set of an equation.
- A conductor of low resistance joining the armature ends of the series field coils of dynamos connected in parallel.
- A device, such as a bar, for operating two brakes, especially a pair of hub brakes for an automobile, with equal force.
- (category theory) A morphism whose codomain is the domain of a parallel pair of morphisms and which forms part of the limit of that parallel pair. Equivalently, a morphism which equalizes a parallel pair of morphisms in a limiting way, which is to say that any other morphism which equalizes that parallel pair factors through this limiting morphism; and moreover such factorization is unique.
- A sliding panel to preserve the lateral stability of an aeroplane.
- One who makes equal; a balancer.
- (Canada, US, slang) A weapon, usually a blackjack or gun.
- (music, electronics) An electronic audio device for altering the frequencies of sound recordings.
- (sports) A goal, run, point, etc. that equalizes the score.
- A device that balances various quantities.
- Any device for equalizing the pull of electromagnets.
- electronic equipment that reduces frequency distortion
- a score that makes the match even
- a weight that balances another weight
noun
- (mathematics) Applying a function to the result of another.
- (printing) Typesetting.
- (linguistics) The formation of compound words from separate words.
- Synthesis as opposed to analysis.
- A mixture or compound; the result of composing.
- A work of music, literature or art.
- The general makeup of a thing or person.
- The proportion of different parts to make a whole.
- (law) an agreement or compromise by which a creditor or group of creditors accepts partial payment from a debtor.
- (object-oriented programming) Way to combine simple objects or data types into more complex ones.
- The act of putting together; assembly.
- (physics) The compounding of two velocities or forces into a single equivalent velocity or force.
- (painting, photography) The arrangement and flow of elements in a picture.
- (chess) A puzzle created by the composer using chess pieces on a chessboard, which presents the solver with a particular task.
- An essay.
- an essay (especially one written as an assignment)
- something that is created by arranging several things to form a unified whole
- musical creation
- the act of creating written works
- art and technique of printing with movable type
- the way in which someone or something is composed
- the spatial property resulting from the arrangement of parts in relation to each other and to the whole
- a mixture of ingredients
- a musical work that has been created
noun
- (topology) A continuous map which is also a homeomorphism between its domain and its image (considered with the subspace topology induced by its codomain).
- (differential topology) An immersion which is also a topological embedding; equivalently, a diffeomorphism whose image is a submanifold of its codomain.
- (machine learning, artificial intelligence) A representation of a unit of text (such as a word or token) as a vector, which encodes the context in which it is used.
- (mathematical analysis) A map between metric spaces which preserves distances up to some scaling factor (called the distortion).
- The act or process by which one thing is embedded in another.
- (category theory) An injective morphism in a concrete category which is also initial.
- (field theory, Galois theory) A ring homomorphism between fields (the name deriving from the fact that all such maps are injective).
verb
noun
- (mathematics, category theory) The domain of a function; the object which a morphism points from.
- A reporter's informant.
- Spring; fountainhead; wellhead; any collection of water on or under the surface of the ground in which a stream originates.
- The person, place, or thing from which something (information, goods, etc.) comes or is acquired.
- (electronics) The name of one terminal of a field effect transistor (FET).
- (computing) Source code.
- (graph theory) A node in a directed graph whose edges all go out from it; one with no entering edges.
- a facility where something is available
- the place where something begins, where it springs into being
- a publication (or a passage from a publication) that is referred to
- anything (a person or animal or plant or substance) in which an infectious agent normally lives and multiplies
- someone who originates or causes or initiates something
- a document (or organization) from which information is obtained
- anything that provides inspiration for later work
- (technology) a process by which energy or a substance enters a system
- a person who supplies information
verb
noun
- (set theory) A function that maps distinct x in the domain to distinct y in the codomain; formally, a f: X → Y such that f(a) = f(b) implies a = b for any a, b in the domain.
- (internal combustion engines) Fuel injection: the pressurized introduction of fuel into a cylinder.
- (computer security) The insertion of program code into an application, URL, hardware, etc.; especially when malicious or when the target is not designed for such insertion.
- (space science) The act of putting a spacecraft into a particular orbit, especially for changing a stable orbit into a transfer orbit, e.g. trans-lunar injection.
- The act of injecting, or something that is injected.
- (construction) The act of inserting materials like concrete grout or gravel by using high pressure pumps.
- (mathematics) A relation on sets (X,Y) that associates each element of Y with at most one element of X.
- (category theory) A morphism from either one of the two components of a coproduct to that coproduct.
- (figuratively) The supply of additional funding to a person or a business.
- (steam engines) The act of throwing cold water into a condenser to produce a vacuum.
- A specimen prepared by injection.
- (medicine) Congestion (of a body part, with blood or other fluid), such as hyperemia.
- (steam engines) The cold water thrown into a condenser to produce a vacuum.
- (medicine) Something injected subcutaneously, intravenously, or intramuscularly by use of a syringe and a needle.
- the forceful insertion of a substance under pressure
- any solution that is injected (as into the skin)
- the act of putting a liquid into the body by means of a syringe
verb
- (specifically, mathematics) To consider (a function) as defined on a subset of its original domain.
- To restrain within boundaries; to limit; to confine
- place under restrictions; limit access to by law
- place limits on (extent or amount or access)
- prevent (information) from being circulated or disclosed
- place restrictions on
verb
- (mathematics, transitive) To define a one-to-one function from one set to another so that certain properties of the domain are preserved when considering the image as a subset of the codomain.
- (transitive, by extension) To include (something) in surrounding matter.
- (transitive) To lay (something) as in a bed; to lay in surrounding matter; to bed.
- (transitive, computing) To encapsulate within another document or data file.
- fix or set securely or deeply
- attach to, as a journalist to a military unit when reporting on a war
noun
- An element of an advertisement, etc. serving as a subliminal message.
- (computing) A piece of computer hardware embedded within another physical object, which is often a larger IT device.
- (journalism) An embedded reporter or journalist, such as a war reporter assigned to and travelling with a military unit, or a political reporter assigned to follow and report on the campaign of a candidate.
- (computing) A digital object embedded within another, which is often a document.
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
adj
- (mathematics, of a function) Associating to each element of the codomain exactly one element of the domain; establishing a perfect (one-to-one) correspondence between the elements of the domain and the codomain; (formally) both injective and surjective.
- (mathematics) Having a component that is (specified to be) a bijective map; that specifies a bijective map.
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) Which forms a surjection from the domain to every open subset of the codomain.
- (of wine) Having a slight lack of acidity; having mild sweetness.
- (of writing, etc.) overwrought.
- Yielding to the touch, and easily moved or shaken; hanging loose by its own weight; lacking firmness; flaccid.
- out of condition; not strong or robust; incapable of exertion or endurance
adj
- (mathematics, of a function) Being able to be locally represented by convergent power series around every point of the domain.
- Of, or relating to division into elements or principles.
- (mathematical analysis) Being defined in terms of objects of differential calculus such as derivatives.
- (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
- (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) A property of functions that have a rule describing how the function can be performed to the individual components of another operation.
- (logic) Assigning the species of a general term.
- Relating to distribution.
- Tending to distribute; serving to divide and assign in portions; dealing a proper share to each.
- (grammar) Expressing separation; denoting a taking singly, not collectively.
- serving to distribute or allot or disperse
noun
adj
- (of an encoding or function) Having multiple domain elements correspond to one element of the range.
- (physics) Having the same quantum energy level.
- Having lost functionality in general.
- (of qualities) Having deteriorated, degraded or fallen from normal, coherent, balanced and desirable to undesirable and typically abnormal.
- (mathematics, of an eigenvalue) Having multiple different (linearly independent) eigenvectors.
- (mathematics) Qualitatively different, usually simpler, than typical objects of its class.
- (of a person or system) Having lost good or desirable qualities; hence also having bad character or habits, base, immoral, corrupt. ABR
- unrestrained by convention or morality
noun
verb
adj
- (algebraic geometry) Of a function between varieties: acting as a morphism on an open subset of its domain.
- (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.
- (algebra) Of an algebraic expression in indeterminates, or more generally a function: capable of being expressed as the ratio of two polynomials.
- 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
adj
- (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.).
- (ring theory, of an element of a graded ring) Belonging to one of the summands of the grading (if the ring is graded over the natural numbers and the element is in the kth summand, it is said to be homogeneous of degree k; if the ring is graded over a commutative monoid I, and the element is an element of the ith summand, it is said to be of grade i)
- (of a linear differential equation) Having its degree-zero term equal to zero; admitting the trivial solution.
- (algebra, of a polynomial) Such that all its nonzero terms have the same degree.
- Having the same composition throughout; of uniform make-up.
- (probability theory, Fourier analysis, of a distribution S on Euclidean n-space (or on ℝⁿmathbf 0)) Informally: Determined by its restriction to the unit sphere. Formally: Such that, for all real t>0 and test functions ϕ( mathbf x), the equality S[t⁻ⁿϕ( mathbf x/t)]=t^(mS)[ϕ( mathbf x)] holds for some fixed real or complex m.
- Of the same kind; alike, similar.
- (of a linear map f between vector spaces graded by a commutative monoid I) Which respects the grading of its domain and codomain. Formally: Satisfying f(V_j)⊆W_i+j for fixed i (called the degree or grade of f), V_j the jth component of the grading of f 's domain, W_k the kth component of the grading of f 's codomain, and + representing the monoid operation in I.
- (geometry, of a space equipped with a group action) Informally: Everywhere the same, uniform, in the sense that any point can be moved to any other (via the group action) while respecting the structure of the space. Formally: Such that the group action is transitively and acts by automorphisms on the space (some authors also require that the action be faithful).
- (set theory, order theory, of a relation) Holding between a set and itself; being an endorelation.
- (of a first-order differential equation) Capable of being written in the form f(x,y) mathop dy=g(x,y) mathop dx where f and g are homogeneous functions of the same degree as each other.
- (linear algebra, by specialization, of a system of linear equations) Such that all the constant terms are zero.
- (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
- of or relating to the multiplicative inverse of a quantity or function
- concerning each of two or more persons or things; especially given or done in return
- Done, given, felt, or owed in return.
- Mutually interchangeable.
- (grammar) Expressing mutual action, applied to pronouns and verbs; also in a broad sense: reflexive.
- Of a feeling, action or such: mutual, uniformly felt or done by each party towards the other or others; two-way.
- (mathematics) Used to denote different kinds of mutual relation; often with reference to the substitution of reciprocals for given quantities.
noun
- something (a term or expression or concept) that has an inverse relation to something else
- (mathematics) one of a pair of numbers whose product is 1: the reciprocal of 2/3 is 3/2; the multiplicative inverse of 7 is 1/7
- hybridization involving a pair of crosses that reverse the sexes associated with each genotype
- (grammar) A construction expressing mutual action.
- (arithmetic) The number obtained by dividing 1 by another given number; the result of exchanging the numerator and the denominator of a fraction.
adj
- (commutative algebra, of a domain) Integrally closed: equal its own integral closure in its field of fractions.
- (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.
- (functional analysis, of a Hilbert space operator) Which commutes with its adjoint.
- (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) Relating to the corresponding elements of an equivalence relation.
- (cartography) Of a map, equal-area.
- (geometry) Equal in measure but not admitting of superposition; applied to magnitudes.
- (mathematics, category theory) Of two categories, (informally) such that one is essentially a relabeling of the other; (formally) related by a pair of functors such the composition of the one with the other is naturally isomorphic to the identity functor.
- (chemistry) Having the equal ability to combine.
- Similar or identical in value, meaning or effect; virtually equal.
- (mathematics) Of two sets, having a one-to-one correspondence.
- being essentially equal to something
noun
- Anything that is virtually equal to something else, or has the same value, force, etc.
- (chemistry) An equivalent weight.
- a person or thing equal to another in value or measure or force or effect or significance etc
- the atomic weight of an element that has the same combining capacity as a given weight of another element; the standard is 8 for oxygen