VS.

Decline vs. Gradient

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Declinenoun

Downward movement, fall.en

Gradientnoun

A slope or incline.

Declinenoun

A sloping downward, e.g. of a hill or road.en

Gradientnoun

A rate of inclination or declination of a slope.

Declinenoun

A weakening.en

Gradientnoun

(calculus) Of a function y = f(x) or the graph of such a function, the rate of change of y with respect to x
that is, the amount by which y changes for a certain (often unit) change in x
equivalently, the inclination to the X axis of the tangent to the curve of the graph.

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Declinenoun

A reduction or diminution of activity.

Gradientnoun

(science) The rate at which a physical quantity increases or decreases relative to change in a given variable, especially distance.

Declinenoun

The act of declining or refusing something.

Gradientnoun

(analysis) A differential operator that maps each point of a scalar field to a vector pointed in the direction of the greatest rate of change of the scalar. Notation for a scalar field φ: ∇φ

Declineverb

(intransitive) To move downwards, to fall, to drop.

‘The dollar has declined rapidly since 2001.’;

Gradientnoun

A gradual change in color. A color gradient; gradation.

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Declineverb

(intransitive) To become weaker or worse.

‘My health declined in winter.’;

Gradientadjective

Moving by steps; walking.

‘gradient automata’;

Declineverb

(transitive) To bend downward; to bring down; to depress; to cause to bend, or fall.

Gradientadjective

Rising or descending by regular degrees of inclination.

‘the gradient line of a railroad’;

Declineverb

(transitive) To cause to decrease or diminish.

Gradientadjective

Adapted for walking, as the feet of certain birds.

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Declineverb

To turn or bend aside; to deviate; to stray; to withdraw.

‘a line that declines from straightness’; ‘conduct that declines from sound morals’;

Gradientadjective

Moving by steps; walking; as, gradient automata.

Declineverb

(transitive) To refuse, forbear.

‘On reflection I think I will decline your generous offer.’;

Gradientadjective

Rising or descending by regular degrees of inclination; as, the gradient line of a railroad.

Declineverb

To inflect for case, number and sometimes gender.

Gradientadjective

Adapted for walking, as the feet of certain birds.

Declineverb

(by extension) To run through from first to last; to repeat like a schoolboy declining a noun.

Gradientnoun

The rate of regular or graded ascent or descent in a road; grade.

Declineverb

To reject a penalty against the opposing team, usually because the result of accepting it would benefit the non-penalized team less than the preceding play.

Gradientnoun

A part of a road which slopes upward or downward; a portion of a way not level; a grade.

Declineverb

To bend, or lean downward; to take a downward direction; to bend over or hang down, as from weakness, weariness, despondency, etc.; to condescend.

‘He . . . would decline even to the lowest of his family.’; ‘Disdaining to decline,Slowly he falls, amidst triumphant cries.’; ‘The ground at length became broken and declined rapidly.’;

Gradientnoun

The rate of increase or decrease of a variable magnitude, or the curve which represents it; as, a thermometric gradient.

Declineverb

To tend or draw towards a close, decay, or extinction; to tend to a less perfect state; to become diminished or impaired; to fail; to sink; to diminish; to lessen; as, the day declines; virtue declines; religion declines; business declines.

‘That empire must declineWhose chief support and sinews are of coin.’; ‘And presume to know . . . Who thrives, and who declines.’;

Gradientnoun

The variation of the concentration of a chemical substance in solution through some linear path; also called concentration gradient; - usually measured in concentration units per unit distance. Concentration gradients are created naturally, e.g. by the diffusion of a substance from a point of high concentration toward regions of lower concentration within a body of liquid; in laboratory techniques they may be made artificially.

Declineverb

To turn or bend aside; to deviate; to stray; to withdraw; as, a line that declines from straightness; conduct that declines from sound morals.

‘Yet do I not decline from thy testimonies.’;

Gradientnoun

a graded change in the magnitude of some physical quantity or dimension

Declineverb

To turn away; to shun; to refuse; - the opposite of accept or consent; as, he declined, upon principle.

Gradientnoun

the property possessed by a line or surface that departs from the horizontal;

‘a five-degree gradient’;

Declineverb

To bend downward; to bring down; to depress; to cause to bend, or fall.

‘In melancholy deep, with head declined.’; ‘And now fair Phoebus gan decline in hasteHis weary wagon to the western vale.’;

Gradient

In vector calculus, the gradient of a scalar-valued differentiable function f of several variables is the vector field (or vector-valued function) ∇ f {\displaystyle \nabla f} whose value at a point p {\displaystyle p} is the vector whose components are the partial derivatives of f {\displaystyle f} at p {\displaystyle p} . That is, for f : R n → R {\displaystyle f\colon \mathbb {R} ^{n}\to \mathbb {R} } , its gradient ∇ f : R n → R n {\displaystyle \nabla f\colon \mathbb {R} ^{n}\to \mathbb {R} ^{n}} is defined at the point p = ( x 1 , … , x n ) {\displaystyle p=(x_{1},\ldots ,x_{n})} in n-dimensional space as the vector: ∇ f ( p ) = [ ∂ f ∂ x 1 ( p ) ⋮ ∂ f ∂ x n ( p ) ] .

Declineverb

To cause to decrease or diminish.

‘He knoweth his error, but will not seek to decline it.’;

Declineverb

To put or turn aside; to turn off or away from; to refuse to undertake or comply with; reject; to shun; to avoid; as, to decline an offer; to decline a contest; he declined any participation with them.

‘Could IDecline this dreadful hour?’;

Declineverb

To inflect, or rehearse in order the changes of grammatical form of; as, to decline a noun or an adjective.

‘After the first declining of a noun and a verb.’;

Declineverb

To run through from first to last; to repeat like a schoolboy declining a noun.

Declinenoun

A falling off; a tendency to a worse state; diminution or decay; deterioration; also, the period when a thing is tending toward extinction or a less perfect state; as, the decline of life; the decline of strength; the decline of virtue and religion.

‘Their fathers lived in the decline of literature.’;

Declinenoun

That period of a disorder or paroxysm when the symptoms begin to abate in violence; as, the decline of a fever.

Declinenoun

A gradual sinking and wasting away of the physical faculties; any wasting disease, esp. pulmonary consumption; as, to die of a decline.

Declinenoun

change toward something smaller or lower

Declinenoun

a condition inferior to an earlier condition; a gradual falling off from a better state

Declinenoun

a gradual decrease; as of stored charge or current

Declinenoun

a downward slope or bend

Declineverb

grow worse;

‘Conditions in the slum worsened’;

Declineverb

refuse to accept;

‘He refused my offer of hospitality’;

Declineverb

show unwillingness towards;

‘he declined to join the group on a hike’;

Declineverb

grow smaller;

‘Interest in the project waned’;

Declineverb

go down;

‘The roof declines here’;

Declineverb

go down in value;

‘the stock market corrected’; ‘prices slumped’;

Declineverb

inflect for number, gender, case, etc.,

‘in many languages, speakers decline nouns, pronouns, and adjectives’;

Declineverb

(typically of something regarded as good) become smaller, fewer, or less; decrease

‘the birth rate continued to decline’;

Declineverb

diminish in strength or quality; deteriorate

‘her health began to decline’;

Declineverb

politely refuse (an invitation or offer)

‘the company declined to comment’; ‘Caroline declined the coffee’;

Declineverb

(especially of the sun) move downwards

‘the sun began to creep round to the west and to decline’;

Declineverb

bend down; droop

‘the wearisome creatures of the world declining to their rest’;

Declineverb

(in the grammar of Latin, Greek, and certain other languages) state the forms of (a noun, pronoun, or adjective) corresponding to case, number, and gender.

Declinenoun

a gradual and continuous loss of strength, numbers, quality, or value

‘a serious decline in bird numbers’; ‘a civilization in decline’;

Declinenoun

the sun's gradual setting

‘this Evening from the Sun's decline arriv'd’;

Declinenoun

a disease in which the bodily strength gradually fails, especially tuberculosis

‘he died at his brother's of a deep decline’;

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