Palavras em English para 'Any solution to a differential equation.'
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noun
- (mathematics) Any of a set of constraints that limit the solutions of a differential equation
- (mathematics) a condition specified for the solution to a set of differential equations
- (quantum mechanics) either one of the conditions that the wave function must be continuous and that its derivative must be as well, except in the case of infinite potential
noun
name
noun
- (mathematics) A discontinuity arising in the solution of a partial differential equation.
- (figuratively) Something so surprising that it is stunning.
- (physics) A shock wave.
- (medicine) Circulatory shock, a medical emergency characterized by the inability of the circulatory system to supply enough oxygen to meet tissue requirements.
- A sudden, heavy impact.
- (psychology) A sudden or violent mental or emotional disturbance.
- An arrangement of sheaves for drying; a stook.
- A chemical added to a swimming pool to moderate the chlorine levels.
- (medicine) Electric shock, a sudden burst of electrical energy hitting a person or animal.
- (by extension) A tuft or bunch of something, such as hair or grass.
- (psychology) A state of distress following a mental or emotional disturbance, often caused by news or other stimuli.
- (automotive, mechanical engineering) A shock absorber (typically in the suspension of a vehicle).
- a sudden jarring impact
- (pathology) bodily collapse or near collapse caused by inadequate oxygen delivery to the cells; characterized by reduced cardiac output and rapid heartbeat and circulatory insufficiency and pallor
- an instance of agitation of the earth's crust
- an unpleasant or disappointing surprise
- the feeling of distress and disbelief that you have when something bad happens accidentally
- the violent interaction of individuals or groups entering into combat
- a reflex response to the passage of electric current through the body
- a pile of sheaves of grain set on end in a field to dry; stalks of Indian corn set up in a field
- a bushy thick mass (especially hair)
- a mechanical damper; absorbs energy of sudden impulses
adj
verb
- (transitive) To strike with disgust, to offend, scandalize.
- (transitive) To add a chemical to (a swimming pool) to moderate the chlorine levels.
- (transitive) To collect, or make up, into a shock or shocks; to stook.
- (transitive) To subject to a shock wave or violent impact.
- (transitive) To give an electric shock to.
- (transitive) To cause to be emotionally shocked; to cause (someone) to feel greatly surprised or upset.
- (geology, transitive) To deform the crystal structure of a stone by the application of extremely high pressure at moderate temperature, as produced only by hypervelocity impact events, lightning strikes, and nuclear explosions.
- strike with horror or terror
- strike with disgust or revulsion
- collide violently
- inflict a trauma upon
- collect or gather into shocks
- subject to electrical shocks
- surprise greatly; knock someone's socks off
adj
- (of a linear differential equation) Having its degree-zero term equal to zero; admitting the trivial solution.
- (of a general differential equation) Homogeneous as a function of the dependent variable and its derivatives.
- (of a first-order differential equation) Capable of being written in the form f(x,y) mathop dy=g(x,y) mathop dx where f and g are homogeneous functions of the same degree as each other.
- (ring theory, of an element of a graded ring) Belonging to one of the summands of the grading (if the ring is graded over the natural numbers and the element is in the kth summand, it is said to be homogeneous of degree k; if the ring is graded over a commutative monoid I, and the element is an element of the ith summand, it is said to be of grade i)
- (algebra, of a polynomial) Such that all its nonzero terms have the same degree.
- Having the same composition throughout; of uniform make-up.
- (probability theory, Fourier analysis, of a distribution S on Euclidean n-space (or on ℝⁿmathbf 0)) Informally: Determined by its restriction to the unit sphere. Formally: Such that, for all real t>0 and test functions ϕ( mathbf x), the equality S[t⁻ⁿϕ( mathbf x/t)]=t^(mS)[ϕ( mathbf x)] holds for some fixed real or complex m.
- Of the same kind; alike, similar.
- (of a linear map f between vector spaces graded by a commutative monoid I) Which respects the grading of its domain and codomain. Formally: Satisfying f(V_j)⊆W_i+j for fixed i (called the degree or grade of f), V_j the jth component of the grading of f 's domain, W_k the kth component of the grading of f 's codomain, and + representing the monoid operation in I.
- (geometry, of a space equipped with a group action) Informally: Everywhere the same, uniform, in the sense that any point can be moved to any other (via the group action) while respecting the structure of the space. Formally: Such that the group action is transitively and acts by automorphisms on the space (some authors also require that the action be faithful).
- (set theory, order theory, of a relation) Holding between a set and itself; being an endorelation.
- (linear algebra, by specialization, of a system of linear equations) Such that all the constant terms are zero.
- (mathematics) In any of several technical senses uniform; scalable; having its behavior or form determined by, or the same as, its behavior on or form at a smaller component (of its domain of definition, of itself, etc.).
- (geometry) Of or relating to homogeneous coordinates.
- The function f(x,y)#61;x²#43;x²ʸ#43;y² is not homogeneous on all of #92;mathbb#123;R#125;² because f(2,2)#61;16#92;neq 2ᵏ#42;3#61;2ᵏf(1,1) for any k, but f is homogeneous on the subspace of #92;mathbb#123;R#125;² spanned by (1,0) because f(#92;alphax,#92;alphay)#61;#92;alphax²#61;#92;alpha²f(x,y) for all (x,y)#92;in#92;operatorname#123;Span#125;#92;#123;(1,0)#92;#125;.
- (mathematical analysis, generalizing the case of polynomial functions, of a function f) Such that if each of f 's inputs are multiplied by the same scalar, f 's output is multiplied by the same scalar to some fixed power (called the degree of homogeneity or degree of f). (Formally and more generally, of a partial function f between vector spaces whose domain is a linear cone) Satisfying the equality f(s mathbf x)=sᵏᶠ(
- (chemistry) In the same state of matter.
- all of the same or similar kind or nature
adj
- (mathematics, of a differential equation) Able to be brought to a form where all occurrences of the dependent and the independent variable are on opposite sides of the equal sign.
- (abstract algebra, of an algebra over a ring) Satisfying any of several technical conditions on the center of the algebra which generalize the situation of field extensions; see Separable algebra on Wikipedia.Wikipedia
- (of a polynomial) Having no repeated roots (where roots are considered in an algebraic closure)
- Able to be separated.
- (mathematical analysis, of a topological space) Having a countable dense subset.
- (Galois theory, of an algebraic field extension E/F) Such that the minimal polynomial of every element of E is a separable polynomial.
- capable of being divided or dissociated
noun
- (mathematics) A method of finding an approximate solution of an ordinary differential equation L[y]=0 by determining coefficients in an expansion y(x)=y_0(x)+∑ₗ₌₀^qαₗy_l(x) so as to make L[y] vanish at prescribed points; the expansion with the coefficients thus found is the sought approximation.
- (uncountable) The grouping or juxtaposition of things, especially words or sounds.
- (countable) Such a specific grouping.
- (linguistics, translation studies) A sequence of words or terms that co-occur more often than would be expected by chance (i.e., the statistically significant placement of particular words in a language), often representing an established name for, or idiomatic way of conveying, a particular semantic concept.
- (computing) A service allowing multiple customers to locate network, server, and storage gear and connect them to a variety of telecommunications and network service providers, at a minimum of cost and complexity.
- the act of positioning close together (or side by side)
- a grouping of words in a sentence
noun
- (mathematics) A positive 1-soliton solution to the sine-Gordon equation.
- A difficulty or flaw that is likely to impede operation, as in a plan or system.
- (Scotland, dialect) A convulsive fit of coughing or laughter; a sonorous indraft of breath; a whoop; a gasp of breath caused by laughing, coughing, or crying.
- Any sexual preference outside normal or expected norms.
- An unreasonable notion; a crotchet; a whim; a caprice.
- A person with peculiar sexual tastes.
- Peculiarity or deviation in sexual behaviour or taste.
- A tight curl, twist, or bend in a length of thin material, hair etc.
- a difficulty or flaw in a plan or operation
- an eccentric idea
- a person with unusual sexual tastes
- a sharp bend in a line produced when a line having a loop is pulled tight
- a painful muscle spasm especially in the neck or back (‘rick’ and ‘wrick’ are British)
verb
verb
- (mathematics) To calculate the differential of a function of multiple variables.
- To recognize as different or distinct.
- (transitive, intransitive, often in the passive voice, biology) To (cause to) go through a process of development called differentiation; to make or become different in form or function.
- To modify so as to create a difference or distinction.
- (mathematics) To calculate the derivative of a function.
- To show or be the difference or distinction between things.
- To perceive the difference between things; to discriminate.
- (education) To teach a lesson in multiple different ways in order to meet the needs of more or less advanced students.
- become distinct and acquire a different character
- evolve so as to lead to a new species or develop in a way most suited to the environment
- be a distinctive feature, attribute, or trait; sometimes in a very positive sense
- mark as different
- calculate a derivative; take the derivative
- become different during development
noun
noun
- (mathematics) An equation upon whose solution the solution of a given problem depends.
- Any substance or material able to resolve the constituents of a mixture; a solvent.
- (medicine) That which has power to disperse inflammatory or other tumours; a discutient; anything which aids the absorption of effused products.
- a liquid substance capable of dissolving other substances
adj
noun
- (mathematics) The boundary separating two modes of behavior in a differential equation.
- (typography) The proofreader's mark resembling a slash ⟨ / ⟩ or vertical bar ⟨ | ⟩ placed after a note in the margin to indicate that it should replace the item(s) struckthrough in the running text or to separate it from other margin notes.
- A terminator: a line on a partially-illuminated surface separating the lit and shaded regions.
- (typography, historical) The ⟨L⟩ or pipe ⟨|⟩ mark formerly used to divide integers from decimals.
- (physics) The line between regions having different magnetic fields.
- a punctuation mark (‘/’) used to separate related items of information
adj
- possessing a differential coefficient or derivative
- capable of being perceived as different
- (comparable, of multiple items) able to be differentiated; distinguishable, as for example by differing appearance or measurable characteristics.
- (calculus, not comparable) Having a derivative, said of a function whose domain and codomain are manifolds.
noun
- root of an algebraic equation with rational coefficients
- (algebra, number theory) A complex number (more generally, an element of a number field) that is a root of a polynomial whose coefficients are integers; equivalently, a complex number (or element of a number field) that is a root of a monic polynomial whose coefficients are rational numbers.
noun
- (mathematics) Clipping of differential
- (climbing) A difficult route.
- (computing) The output of a diff program, a diff file.
- (slang) Clipping of difference
- (video games, slang) Used to trash-talk an opposing team at the end of a game by pointing out a skill difference between some role and the same role on the other team.
- (automotive) Abbreviation of differential: the differential gear in an automobile.
- (medicine) Abbreviation of differential: differential of types of white blood cell in a complete blood count.
- (computing) Any program which compares two files or sets of files and outputs a description of the differences between them.
- (fandom slang) Clipping of difficulty.
adj
name
verb
- (transitive, computing) To compare two files or other objects, manually or otherwise.
- (transitive, fandom slang) To win (or to be able to win) a fight against another, with a defined level of difficulty. Usually used when power scaling fictional characters.
- (transitive, computing) To run a diff program on (files or items) so as to produce a description of the differences between them, as for a patch file.
noun
- (mechanics) Initialism of limited-slip differential.
- (organic chemistry) Abbreviation of lysergic acid diethylamide.
- Initialism of Lake Shore Drive (freeway in Chicago).
- Initialism of long slow distance (training method of long-distance running).
- (geology) Initialism of longshore drift (geological process by which sediments move along a beach shore).
- (veterinary pathology) Initialism of lumpy skin disease.
- a powerful hallucinogenic drug manufactured from lysergic acid
verb
- (transitive, mathematics) To simplify an equation or formula without changing its value.
- (transitive) To bring to an inferior rank; to degrade, to demote.
- (intransitive) To lose weight.
- (transitive, Scots law) To annul by legal means.
- (transitive, military) To reform a line or column from (a square).
- (transitive) To be forced by circumstances (into something one considers unworthy).
- (transitive, metallurgy) To produce metal from ore by removing nonmetallic elements in a smelter.
- (transitive) To bring down the size, quantity, quality, value or intensity of something; to diminish, to lower.
- (transitive, medicine) To perform a reduction; to restore a fracture or dislocation to the correct alignment.
- (transitive, law) To convert to written form. (Usage note: this verb almost always appears as "reduce to writing".)
- (transitive) To humble; to conquer; to subdue; to capture.
- (transitive) To bring to an inferior state or condition.
- (transitive, computer science) To express the solution of a problem in terms of another (known) algorithm.
- (transitive, military) To strike off the payroll.
- (transitive, phonetics, phonology) To pronounce (a sound or word) with less effort.
- (transitive, chemistry) To add electrons / hydrogen or to remove oxygen.
- (transitive, cooking) To decrease the liquid content of (a food) by boiling much of its water off.
- (transitive, logic) To convert a syllogism to a clearer or simpler form.
- to remove oxygen from a compound, or cause to react with hydrogen or form a hydride, or to undergo an increase in the number of electrons
- cook until very little liquid is left
- lessen and make more modest
- be cooked until very little liquid is left
- reduce in size; reduce physically
- lessen the strength or flavor of a solution or mixture
- reposition (a broken bone after surgery) back to its normal site
- reduce in scope while retaining essential elements
- be the essential element
- cut down on; make a reduction in
- make smaller
- lower in grade or rank or force somebody into an undignified situation
- make less complex
- simplify the form of a mathematical equation of expression by substituting one term for another
- narrow or limit
- undergo meiosis
- put down by force or intimidation
- bring to humbler or weaker state or condition
- destress and thus weaken a sound when pronouncing it
- take off weight
noun
- a variable whose values are solutions of an equation
- an unknown and unexplored region
- anyone who does not belong in the environment in which they are found
- A person of no identity; a nonentity.
- (algebra) A variable (usually x, y or z) whose value is to be found.
- Any thing, place, or situation about which nothing is known; an unknown fact or piece of information.
adj
verb
noun
- (complex analysis) The equivalent single equation (∂f)/(∂x)+i(∂f)/(∂y)=0.
- (mathematics, complex analysis, always plural) Given a complex-valued function f and real-valued functions u and v such that f(z) = u(z) + iv(z), either of the equations (∂u)/(∂x)=(∂v)/(∂y) or (∂u)/(∂y)=-(∂v)/(∂x), which together form part of the criteria that f be complex-differentiable.
noun
- (mathematics) A differential form whose exterior derivative is zero.
- (poetry) A type of poetry with regular structure, such as meter or a rhyming pattern.
- (poetry) Trobar clus.
- (mathematics) A form (expression) that does not use limits, implicitly or explicitly.
- Used other than figuratively or idiomatically: see closed, form.
noun
- (mathematics) A set of equations involving the same variables, which are to be solved simultaneously.
- (multiplicity) A set of alters of a person, or the multiple (“an individual with multiple personalities”) who contains them.
- A group or set of related things that operate together as a complex whole.
- (physiology) A set of body organs having a particular function.
- (politics) A socioeconomic formation.
- (music) A set of staves linked by a brace that indicate instruments or sounds that are to be played simultaneously.
- (computing) A set of hardware and software operating in a computer.
- (derogatory, preceded by the, often capitalized) The mainstream culture, controlled by the elites or government of a state, or a combination of them, seen as oppressive to the individual.
- (astronomy) A system in which two or more objects are bound to each other by gravity.
- (roleplaying games) A set of rules for a tabletop roleplaying game.
- (countable, uncountable) A method or way of organizing or planning.
- (philosophy) A comprehensive and logically organized set of propositions or philosophical beliefs.
- an ordered manner; orderliness by virtue of being methodical and well organized
- a group of physiologically or anatomically related organs or parts
- a procedure or process for obtaining an objective
- an organized structure for arranging or classifying
- a complex of methods or rules governing behavior
- the living body considered as made up of interdependent components forming a unified whole
- instrumentality that combines interrelated interacting artifacts designed to work as a coherent entity
- (physical chemistry) a sample of matter in which substances in different phases are in equilibrium
- a group of independent but interrelated elements comprising a unified whole
noun
- (mathematics) Any of a set of constraints that limit the solutions of a differential equation
- (mathematics) a condition specified for the solution to a set of differential equations
- (quantum mechanics) either one of the conditions that the wave function must be continuous and that its derivative must be as well, except in the case of infinite potential
noun
name
noun
- (mathematics) A discontinuity arising in the solution of a partial differential equation.
- (figuratively) Something so surprising that it is stunning.
- (physics) A shock wave.
- (medicine) Circulatory shock, a medical emergency characterized by the inability of the circulatory system to supply enough oxygen to meet tissue requirements.
- A sudden, heavy impact.
- (psychology) A sudden or violent mental or emotional disturbance.
- An arrangement of sheaves for drying; a stook.
- A chemical added to a swimming pool to moderate the chlorine levels.
- (medicine) Electric shock, a sudden burst of electrical energy hitting a person or animal.
- (by extension) A tuft or bunch of something, such as hair or grass.
- (psychology) A state of distress following a mental or emotional disturbance, often caused by news or other stimuli.
- (automotive, mechanical engineering) A shock absorber (typically in the suspension of a vehicle).
- a sudden jarring impact
- (pathology) bodily collapse or near collapse caused by inadequate oxygen delivery to the cells; characterized by reduced cardiac output and rapid heartbeat and circulatory insufficiency and pallor
- an instance of agitation of the earth's crust
- an unpleasant or disappointing surprise
- the feeling of distress and disbelief that you have when something bad happens accidentally
- the violent interaction of individuals or groups entering into combat
- a reflex response to the passage of electric current through the body
- a pile of sheaves of grain set on end in a field to dry; stalks of Indian corn set up in a field
- a bushy thick mass (especially hair)
- a mechanical damper; absorbs energy of sudden impulses
adj
verb
- (transitive) To strike with disgust, to offend, scandalize.
- (transitive) To add a chemical to (a swimming pool) to moderate the chlorine levels.
- (transitive) To collect, or make up, into a shock or shocks; to stook.
- (transitive) To subject to a shock wave or violent impact.
- (transitive) To give an electric shock to.
- (transitive) To cause to be emotionally shocked; to cause (someone) to feel greatly surprised or upset.
- (geology, transitive) To deform the crystal structure of a stone by the application of extremely high pressure at moderate temperature, as produced only by hypervelocity impact events, lightning strikes, and nuclear explosions.
- strike with horror or terror
- strike with disgust or revulsion
- collide violently
- inflict a trauma upon
- collect or gather into shocks
- subject to electrical shocks
- surprise greatly; knock someone's socks off
noun
- (mathematics) A method of finding an approximate solution of an ordinary differential equation L[y]=0 by determining coefficients in an expansion y(x)=y_0(x)+∑ₗ₌₀^qαₗy_l(x) so as to make L[y] vanish at prescribed points; the expansion with the coefficients thus found is the sought approximation.
- (uncountable) The grouping or juxtaposition of things, especially words or sounds.
- (countable) Such a specific grouping.
- (linguistics, translation studies) A sequence of words or terms that co-occur more often than would be expected by chance (i.e., the statistically significant placement of particular words in a language), often representing an established name for, or idiomatic way of conveying, a particular semantic concept.
- (computing) A service allowing multiple customers to locate network, server, and storage gear and connect them to a variety of telecommunications and network service providers, at a minimum of cost and complexity.
- the act of positioning close together (or side by side)
- a grouping of words in a sentence
noun
- (mathematics) A positive 1-soliton solution to the sine-Gordon equation.
- A difficulty or flaw that is likely to impede operation, as in a plan or system.
- (Scotland, dialect) A convulsive fit of coughing or laughter; a sonorous indraft of breath; a whoop; a gasp of breath caused by laughing, coughing, or crying.
- Any sexual preference outside normal or expected norms.
- An unreasonable notion; a crotchet; a whim; a caprice.
- A person with peculiar sexual tastes.
- Peculiarity or deviation in sexual behaviour or taste.
- A tight curl, twist, or bend in a length of thin material, hair etc.
- a difficulty or flaw in a plan or operation
- an eccentric idea
- a person with unusual sexual tastes
- a sharp bend in a line produced when a line having a loop is pulled tight
- a painful muscle spasm especially in the neck or back (‘rick’ and ‘wrick’ are British)
verb
noun
- (mathematics) An equation upon whose solution the solution of a given problem depends.
- Any substance or material able to resolve the constituents of a mixture; a solvent.
- (medicine) That which has power to disperse inflammatory or other tumours; a discutient; anything which aids the absorption of effused products.
- a liquid substance capable of dissolving other substances
adj
noun
- (mathematics) The boundary separating two modes of behavior in a differential equation.
- (typography) The proofreader's mark resembling a slash ⟨ / ⟩ or vertical bar ⟨ | ⟩ placed after a note in the margin to indicate that it should replace the item(s) struckthrough in the running text or to separate it from other margin notes.
- A terminator: a line on a partially-illuminated surface separating the lit and shaded regions.
- (typography, historical) The ⟨L⟩ or pipe ⟨|⟩ mark formerly used to divide integers from decimals.
- (physics) The line between regions having different magnetic fields.
- a punctuation mark (‘/’) used to separate related items of information
noun
- root of an algebraic equation with rational coefficients
- (algebra, number theory) A complex number (more generally, an element of a number field) that is a root of a polynomial whose coefficients are integers; equivalently, a complex number (or element of a number field) that is a root of a monic polynomial whose coefficients are rational numbers.
noun
- (mathematics) Clipping of differential
- (climbing) A difficult route.
- (computing) The output of a diff program, a diff file.
- (slang) Clipping of difference
- (video games, slang) Used to trash-talk an opposing team at the end of a game by pointing out a skill difference between some role and the same role on the other team.
- (automotive) Abbreviation of differential: the differential gear in an automobile.
- (medicine) Abbreviation of differential: differential of types of white blood cell in a complete blood count.
- (computing) Any program which compares two files or sets of files and outputs a description of the differences between them.
- (fandom slang) Clipping of difficulty.
adj
name
verb
- (transitive, computing) To compare two files or other objects, manually or otherwise.
- (transitive, fandom slang) To win (or to be able to win) a fight against another, with a defined level of difficulty. Usually used when power scaling fictional characters.
- (transitive, computing) To run a diff program on (files or items) so as to produce a description of the differences between them, as for a patch file.
noun
- (mechanics) Initialism of limited-slip differential.
- (organic chemistry) Abbreviation of lysergic acid diethylamide.
- Initialism of Lake Shore Drive (freeway in Chicago).
- Initialism of long slow distance (training method of long-distance running).
- (geology) Initialism of longshore drift (geological process by which sediments move along a beach shore).
- (veterinary pathology) Initialism of lumpy skin disease.
- a powerful hallucinogenic drug manufactured from lysergic acid
noun
- a variable whose values are solutions of an equation
- an unknown and unexplored region
- anyone who does not belong in the environment in which they are found
- A person of no identity; a nonentity.
- (algebra) A variable (usually x, y or z) whose value is to be found.
- Any thing, place, or situation about which nothing is known; an unknown fact or piece of information.
adj
verb
noun
- (complex analysis) The equivalent single equation (∂f)/(∂x)+i(∂f)/(∂y)=0.
- (mathematics, complex analysis, always plural) Given a complex-valued function f and real-valued functions u and v such that f(z) = u(z) + iv(z), either of the equations (∂u)/(∂x)=(∂v)/(∂y) or (∂u)/(∂y)=-(∂v)/(∂x), which together form part of the criteria that f be complex-differentiable.
noun
- (mathematics) A differential form whose exterior derivative is zero.
- (poetry) A type of poetry with regular structure, such as meter or a rhyming pattern.
- (poetry) Trobar clus.
- (mathematics) A form (expression) that does not use limits, implicitly or explicitly.
- Used other than figuratively or idiomatically: see closed, form.
noun
- (mathematics) A set of equations involving the same variables, which are to be solved simultaneously.
- (multiplicity) A set of alters of a person, or the multiple (“an individual with multiple personalities”) who contains them.
- A group or set of related things that operate together as a complex whole.
- (physiology) A set of body organs having a particular function.
- (politics) A socioeconomic formation.
- (music) A set of staves linked by a brace that indicate instruments or sounds that are to be played simultaneously.
- (computing) A set of hardware and software operating in a computer.
- (derogatory, preceded by the, often capitalized) The mainstream culture, controlled by the elites or government of a state, or a combination of them, seen as oppressive to the individual.
- (astronomy) A system in which two or more objects are bound to each other by gravity.
- (roleplaying games) A set of rules for a tabletop roleplaying game.
- (countable, uncountable) A method or way of organizing or planning.
- (philosophy) A comprehensive and logically organized set of propositions or philosophical beliefs.
- an ordered manner; orderliness by virtue of being methodical and well organized
- a group of physiologically or anatomically related organs or parts
- a procedure or process for obtaining an objective
- an organized structure for arranging or classifying
- a complex of methods or rules governing behavior
- the living body considered as made up of interdependent components forming a unified whole
- instrumentality that combines interrelated interacting artifacts designed to work as a coherent entity
- (physical chemistry) a sample of matter in which substances in different phases are in equilibrium
- a group of independent but interrelated elements comprising a unified whole
verb
- (mathematics) To calculate the differential of a function of multiple variables.
- To recognize as different or distinct.
- (transitive, intransitive, often in the passive voice, biology) To (cause to) go through a process of development called differentiation; to make or become different in form or function.
- To modify so as to create a difference or distinction.
- (mathematics) To calculate the derivative of a function.
- To show or be the difference or distinction between things.
- To perceive the difference between things; to discriminate.
- (education) To teach a lesson in multiple different ways in order to meet the needs of more or less advanced students.
- become distinct and acquire a different character
- evolve so as to lead to a new species or develop in a way most suited to the environment
- be a distinctive feature, attribute, or trait; sometimes in a very positive sense
- mark as different
- calculate a derivative; take the derivative
- become different during development
noun
verb
- (transitive, mathematics) To simplify an equation or formula without changing its value.
- (transitive) To bring to an inferior rank; to degrade, to demote.
- (intransitive) To lose weight.
- (transitive, Scots law) To annul by legal means.
- (transitive, military) To reform a line or column from (a square).
- (transitive) To be forced by circumstances (into something one considers unworthy).
- (transitive, metallurgy) To produce metal from ore by removing nonmetallic elements in a smelter.
- (transitive) To bring down the size, quantity, quality, value or intensity of something; to diminish, to lower.
- (transitive, medicine) To perform a reduction; to restore a fracture or dislocation to the correct alignment.
- (transitive, law) To convert to written form. (Usage note: this verb almost always appears as "reduce to writing".)
- (transitive) To humble; to conquer; to subdue; to capture.
- (transitive) To bring to an inferior state or condition.
- (transitive, computer science) To express the solution of a problem in terms of another (known) algorithm.
- (transitive, military) To strike off the payroll.
- (transitive, phonetics, phonology) To pronounce (a sound or word) with less effort.
- (transitive, chemistry) To add electrons / hydrogen or to remove oxygen.
- (transitive, cooking) To decrease the liquid content of (a food) by boiling much of its water off.
- (transitive, logic) To convert a syllogism to a clearer or simpler form.
- to remove oxygen from a compound, or cause to react with hydrogen or form a hydride, or to undergo an increase in the number of electrons
- cook until very little liquid is left
- lessen and make more modest
- be cooked until very little liquid is left
- reduce in size; reduce physically
- lessen the strength or flavor of a solution or mixture
- reposition (a broken bone after surgery) back to its normal site
- reduce in scope while retaining essential elements
- be the essential element
- cut down on; make a reduction in
- make smaller
- lower in grade or rank or force somebody into an undignified situation
- make less complex
- simplify the form of a mathematical equation of expression by substituting one term for another
- narrow or limit
- undergo meiosis
- put down by force or intimidation
- bring to humbler or weaker state or condition
- destress and thus weaken a sound when pronouncing it
- take off weight
adj
- (of a linear differential equation) Having its degree-zero term equal to zero; admitting the trivial solution.
- (of a general differential equation) Homogeneous as a function of the dependent variable and its derivatives.
- (of a first-order differential equation) Capable of being written in the form f(x,y) mathop dy=g(x,y) mathop dx where f and g are homogeneous functions of the same degree as each other.
- (ring theory, of an element of a graded ring) Belonging to one of the summands of the grading (if the ring is graded over the natural numbers and the element is in the kth summand, it is said to be homogeneous of degree k; if the ring is graded over a commutative monoid I, and the element is an element of the ith summand, it is said to be of grade i)
- (algebra, of a polynomial) Such that all its nonzero terms have the same degree.
- Having the same composition throughout; of uniform make-up.
- (probability theory, Fourier analysis, of a distribution S on Euclidean n-space (or on ℝⁿmathbf 0)) Informally: Determined by its restriction to the unit sphere. Formally: Such that, for all real t>0 and test functions ϕ( mathbf x), the equality S[t⁻ⁿϕ( mathbf x/t)]=t^(mS)[ϕ( mathbf x)] holds for some fixed real or complex m.
- Of the same kind; alike, similar.
- (of a linear map f between vector spaces graded by a commutative monoid I) Which respects the grading of its domain and codomain. Formally: Satisfying f(V_j)⊆W_i+j for fixed i (called the degree or grade of f), V_j the jth component of the grading of f 's domain, W_k the kth component of the grading of f 's codomain, and + representing the monoid operation in I.
- (geometry, of a space equipped with a group action) Informally: Everywhere the same, uniform, in the sense that any point can be moved to any other (via the group action) while respecting the structure of the space. Formally: Such that the group action is transitively and acts by automorphisms on the space (some authors also require that the action be faithful).
- (set theory, order theory, of a relation) Holding between a set and itself; being an endorelation.
- (linear algebra, by specialization, of a system of linear equations) Such that all the constant terms are zero.
- (mathematics) In any of several technical senses uniform; scalable; having its behavior or form determined by, or the same as, its behavior on or form at a smaller component (of its domain of definition, of itself, etc.).
- (geometry) Of or relating to homogeneous coordinates.
- The function f(x,y)#61;x²#43;x²ʸ#43;y² is not homogeneous on all of #92;mathbb#123;R#125;² because f(2,2)#61;16#92;neq 2ᵏ#42;3#61;2ᵏf(1,1) for any k, but f is homogeneous on the subspace of #92;mathbb#123;R#125;² spanned by (1,0) because f(#92;alphax,#92;alphay)#61;#92;alphax²#61;#92;alpha²f(x,y) for all (x,y)#92;in#92;operatorname#123;Span#125;#92;#123;(1,0)#92;#125;.
- (mathematical analysis, generalizing the case of polynomial functions, of a function f) Such that if each of f 's inputs are multiplied by the same scalar, f 's output is multiplied by the same scalar to some fixed power (called the degree of homogeneity or degree of f). (Formally and more generally, of a partial function f between vector spaces whose domain is a linear cone) Satisfying the equality f(s mathbf x)=sᵏᶠ(
- (chemistry) In the same state of matter.
- all of the same or similar kind or nature
adj
- (mathematics, of a differential equation) Able to be brought to a form where all occurrences of the dependent and the independent variable are on opposite sides of the equal sign.
- (abstract algebra, of an algebra over a ring) Satisfying any of several technical conditions on the center of the algebra which generalize the situation of field extensions; see Separable algebra on Wikipedia.Wikipedia
- (of a polynomial) Having no repeated roots (where roots are considered in an algebraic closure)
- Able to be separated.
- (mathematical analysis, of a topological space) Having a countable dense subset.
- (Galois theory, of an algebraic field extension E/F) Such that the minimal polynomial of every element of E is a separable polynomial.
- capable of being divided or dissociated
adj
- possessing a differential coefficient or derivative
- capable of being perceived as different
- (comparable, of multiple items) able to be differentiated; distinguishable, as for example by differing appearance or measurable characteristics.
- (calculus, not comparable) Having a derivative, said of a function whose domain and codomain are manifolds.