Crossword clues for gradient
Longman Dictionary of Contemporary English
The Collaborative International Dictionary
del \del\ n. (Math.) a differential operator which, operating on a function of several variables, gives the sum of the partial derivatives of the function with respect to the three orthogonal spatial coordinates; -- also called the gradient or grad. It is represented by an inverted Greek capital delta ([nabla]), and is thus because of its shape also called nabla, meaning harp in Hebrew.
Douglas Harper's Etymology Dictionary
a. 1 Moving by steps; walking. 2 Rising or descending by regular degrees of inclination. 3 Adapted for walking, as the feet of certain birds. n. 1 A slope or incline. 2 A rate of inclination or declination of a slope. 3 (context calculus English) 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. 4 (context science English) The rate at which a physical quantity increases or decreases relative to change in a given variable, especially distance. 5 (context analysis English) 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
n. a graded change in the magnitude of some physical quantity or dimension
the property possessed by a line or surface that departs from the horizontal; "a five-degree gradient" [syn: slope]
The Gradient is the rate of variation of a numerical quantity. It may refer to:
- Slope or grade, referring to the inclination of a road or other geographic features
Image gradient, a gradual change or blending of color
- Color gradient
- Texture gradient
- Spatial gradient
In mathematics, the gradient is a generalization of the usual concept of derivative to functions of several variables. If is a differentiable, real-valued function of several variables, its gradient is the vector whose components are the n partial derivatives of f. It is thus a vector-valued function.
Similarly to the usual derivative, the gradient represents the slope of the tangent of the graph of the function. More precisely, the gradient points in the direction of the greatest rate of increase of the function, and its magnitude is the slope of the graph in that direction. The components of the gradient in coordinates are the coefficients of the variables in the equation of the tangent space to the graph. This characterizing property of the gradient allows it to be defined independently of a choice of coordinate system, as a vector field whose components in a coordinate system will transform when going from one coordinate system to another.
The Jacobian is the generalization of the gradient for vector-valued functions of several variables and differentiable maps between Euclidean spaces or, more generally, manifolds. A further generalization for a function between Banach spaces is the Fréchet derivative.
Usage examples of "gradient".
Baths of salt and percolating streams of micro-elements, genomic plug-ins, bilayer diffusion circuits and protein gradients, syncretic information systems.
En route, traveling the gradient of bombykol, he notes the presence of other males, heading in the same direction, all in a good mood, inclined to race for the sheer sport of it.
Happily there was not much of this exhausting work, for, just as higher and darker ranges, densely wooded with cryptomeria, began to close us in, we emerged upon a fine new road, broad enough for a carriage, which, after crossing two ravines on fine bridges, plunges into the depths of a magnificent forest, and then by a long series of fine zigzags of easy gradients ascends the pass of Yadate, on the top of which, in a deep sandstone cutting, is a handsome obelisk marking the boundary between Akita and Aomori ken.
The isobar pattern shows the pressure gradient growing ever steeper, sucking in gale-force winds behind and fuelling the system with energy.
The steam ploughs had, however, kept the railroad open, and the evening train which connects the long line of coal-mining and iron-working settlements was slowly groaning its way up the steep gradients which lead from Stagville on the plain to Vermissa, the central township which lies at the head of Vermissa Valley.
Yull and Omber dismissed such shows as trivial, and paid far more attention to experiments with a practical application: gradient separation of similar organic molecules, for instance, and the use of rotating pull-stones to prove that the fields they generated were intimately related to sparkforce, though as yet nobody had satisfactorily explained how.
I could talk for twenty minutes on portal-pressure gradients, on the various benefits and disadvantages of the surgical approach by forming a portal-vein-to-inferior-venacava anastomosis, end to end or end to side.
That they are somehow uncoupled from the entropy gradient of the Universe?
This space, intended to contain a few comfortable lounge chairs and perhaps a wet bar, was stuffed with meteorological equipment: dropsonde console, anemometer, barometer, gradient thermometer, three separate radar screens, and real-time satellite monitoring gear.
He was boring away toward the east, toward the Mozambican border, deviating only slightly from his course to take a gap in a line of hills or to climb the easier gradient when there was no pass.
The terrain of the seafloor is for the most part a gently sloping gradient, though some canyons up to one-thousand feet could be encountered.
Within an hour of the seismographic reading, crews will have drilled the holes through strata of incipient stress, pumped the supercooled polymer-treated water back into them at the proper temperature for the local gradient, and gone on to the next.
Cars passed us, headlights almost unnecessary as the sky began to alter in gradients from steel gray to dove.
The gentle pressure released the neurons and glia into suspension, and by choosing a combination of gradients and centrifugation speeds, I ended up with two fractions, each enriched in one of the two types of cells.
Vlad and Ursula were scoffing at Sax’s model—temperature gradients between biotically defrosted soil and the remaining frosted areas would be greater than ever, and the winds between the two regions correspondingly fiercer, so that when they finally hit loose fines, off they would go.