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concavity

Definitions

  • WordNet 3.6
    • n concavity the property possessed by a concave shape
    • n concavity a shape that curves or bends inward
    • ***
Webster's Revised Unabridged Dictionary
    • n Concavity A concave surface, or the space bounded by it; the state of being concave.
    • ***
Century Dictionary and Cyclopedia
    • n concavity The state of being concave; hollowness.
    • n concavity A concave surface, or the space contained in it; the internal surface of a hollow curved body, or the space within such body; any hollow space which is more or less spherical.
    • ***
Chambers's Twentieth Century Dictionary
    • n Concavity the quality of being concave: the inner surface of a concave or hollow body
    • ***

Etymology

Webster's Revised Unabridged Dictionary
L. concavitas,: cf. F. concavité,. See Concave
Chambers's Twentieth Century Dictionary
L. concavus, from con, inten., and cavus, hollow. See Cave.

Usage

In literature:

Perhaps they are like the concave and convex curves of a dome, like the two sides of a shield.
"The Outline of Science, Vol. 1 (of 4)" by J. Arthur Thomson
Concave shading 74 127.
"Carpentry for Boys" by J. S. Zerbe
The gouge that is commonly used for cutting concave outlines on end grain, is the inside bevel gouge.
"Handwork in Wood" by William Noyes
The floor of the furnace F is somewhat concave and is made of iron covered with a layer of iron oxide.
"An Elementary Study of Chemistry" by William McPherson
I hit the concave ceiling, shoved down, and like a swimmer in water struck against the struggling bodies of Snap and the guard.
"Wandl the Invader" by Raymond King Cummings
Its general direction is east and west, but in contour it is slightly concave towards the south, whence the assailants came.
"Story of the War in South Africa" by Alfred T. Mahan
But on its concave aide where it flows more slowly it deposits material.
"Lessons on Soil" by E. J. Russell
I was standing obviously on a concave surface, on the inside, not the outside of the world.
"The Girl in the Golden Atom" by Raymond King Cummings
Our concavity, so to speak, answers to His convexity; our hollowness to His fulness; our emptiness to His all-sufficiency.
"Expositions of Holy Scripture" by Alexander Maclaren
RADIATING AND CONCAVE PEDAL BOARDS.
"The Recent Revolution in Organ Building" by George Laing Miller
And otherwise unlike a volcanic crater is the concavity itself.
"The Lone Ranche" by Captain Mayne Reid
The seat should slope downward a little toward the back, be slightly concave, and have rounded edges in front.
"Essays In Pastoral Medicine" by Austin ÓMalley
The sky was absolutely clear, not a mote on its whole concavity.
"The Columbia River" by William Denison Lyman
Petals numerous, small, 1-lipped, the concavity near the base.
"The Manual of the Botany of the Northern United States" by Asa Gray
The lower mandible half the depth of the upper, the sides concave, and the teeth less.
"Zoological Illustrations, Volume I" by William Swainson
Through this second door she had come out into a circular gallery just beneath the huge concave of the dome.
"Mrs. Thompson" by William Babington Maxwell
Convex slopes melt sooner than concave, steep slopes sooner than flats or gentle inclines.
"The Alps" by Martin Conway
The brass pieces have the convex side bright, the concave black.
"The American Indians" by Henry R. Schoolcraft
The brass pieces have the convex side bright, the concave black.
"Western Scenes and Reminiscences" by Henry Rowe Schoolcraft
They collected the rays of that luminary in a concave mirror, by which means they rekindled their fires.
"Traditions, Superstitions and Folk-lore" by Charles Hardwick
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In poetry:

Piled up by skillful smith or mason
With care in one great concave heap,
Those gory gyves would form a basin
Unnumbered fathoms wide and deep.
"The Black Man's Wrongs" by James Madison Bell
All ether burns: Chaos returns,
And blends, once more, the seas and skies:
No space between Thy bosom green,
O Deep! and the blue concave, lies.
"Ocean: An Ode. Concluding With A Wish." by Edward Young
Ye Mists and Vapours, Hail and Snow,
And you who through the Concave blow,
Swift Executors of his holy Word,
Whirlwinds and Tempest, praise th'Almighty Lord.
"A Paraphrase On The CXLVIIIth Psalm" by Wentworth Dillon
Must I no more on midnight-splendors gaze,
Nor woo fair Cynthia's sweetly-pensive beam;
Must, O ye stars! your thousand golden rays,
And heaven's blue concave vanish as a dream?
"Time: An Elegy. Written Near The Ruins Of Elgin Cathedral" by Robert Alves
And we, creation's princes, we,
The favourites of the Deity,
The wise—the strong—whose thoughts can soar
Heaven's brightest, highest concave o'er;
And hold, above created things,
Communion with the King of kings—
"Spring: Thursday Morning" by John Bowring
In the liquid vault of ether hung the starry gems of light,
Blazing with unwonted splendor on the ebon brow of night;
Far across the arching concave like a train of silver lay,
Nebulous, and white, and dreamy, heaven's star-wrought Milky Way.
"The Soul’s Destiny" by Effie Afton

In news:

The one-square-inch cutter has a quarter-inch-thick body that encloses a concaved circle, which has another circle at its center.
HOW TO Create Soft Concave Layers by Angelo Pacente.
A racy concave grille with quad lamps snarls at the pavement before it.
Many of today's roller camshafts have a re-entrant (concave) profile in the flank areas.
The Concave Cylindrical 5mm (T1-3/4) Discrete LEDs from LEDtronics®, the manufacturer and designer of LED products such as panel mount LEDs and PCB LEDs, emit light that is as bright at its edges as it is in the center.
China's Chic Waistline: Convex to Concave .
China's Chic Waistline: Convex to Concave.
The A2 employs all new Variable Concave Technology for maximum speed and angle with safety to match.
China's Chic Waistline : Convex to Concave.
With the concave shape of the asphalt lanes, the path of the ball can be unpredictable.
I think the weirdest one was a concave tube that required users to stick their heads inside the enclosure while an image was projected all around.
Photo courtesy of Tewksbury Township police Note the round concave indentation to the left.
The get the full experience, watch this on a giant concave screen.
A Matt Manzari-inspired creation Three-layer sandwich EVA innovation ABS-wrapped bottom deck 3D concave top deck EVA creates rebound and snap.
Virtually everything said and done in a presidential election year distorts the truth, much like concave and convex mirrors in a carnival attraction alter one's true reflection.
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In science:

This is related to the fact that the states on the concave parts of the envelope of the shaded region are not reachable by any field history because of the jump in the ma jor hysteresis loop.
Metastable states and T=0 hysteresis in the random-field Ising model on random graphs
Harg´e, G. A convex/log-concave correlation inequality for Gaussian measure and an application to abstract Wiener spaces.
Combinatorial aspects of matrix models
Quantitative versions with refinements for the rate of concentration in the case of log-concave random vectors X were obtained in (year?), (year?); see also (year?), (year?), (year?).
Concentration of normalized sums and a central limit theorem for noncorrelated random variables
Let Φ denote the class of functions φ which are continuous and convex on R+, twice differentiable on R∗+, and such that either φ is affine or φ′′ is strictly positive and 1/φ′′ is concave.
Moment inequalities for functions of independent random variables
Assuming this time that φ is differentiable on R and twice differentiable on R \ {0}, the proof of the duality formula above can be easily adapted to cover this case provided that 1/φ′′ can be extended to a concave function on R.
Moment inequalities for functions of independent random variables
This means that the tensorization inequality for the φ-entropy also holds for convex functions φ on R under the condition that 1/φ′′ is the restriction to R \ {0} of a concave function on R. 3.2.
Moment inequalities for functions of independent random variables
As pointed out in, provided that φ′′ is strictly positive, the condition 1/φ′′ concave is necessary for the tensorization property to hold.
Moment inequalities for functions of independent random variables
If Hφ is convex on L+ ∞(Ω, A, P), then φ′′ (x) > 0 for every x > 0 and 1/φ′′ is concave on R∗+ .
Moment inequalities for functions of independent random variables
Letting λ tend to 1, we derive from the above inequality that φ′′ is nonincreasing, that is, φ′ is concave.
Moment inequalities for functions of independent random variables
Furthermore, by the concavity of Σ(µ), it suffices to prove (2.6) for (1 − ε)µ + εm for each 0 < ε < 1, where m is the uniform measure on an interval including the support supp µ.
Large deviations for functions of two random projection matrices
The statement follows by Jensen’s inequality (x 7→ xb is concave) if t obeyes t ≥ δ, implying M ≥ 1.
An interlacing technique for spectra of random walks and its application to finite percolation clusters
Fig. B.10 shows a smoothly increasing concave curve without any sharp cutoff or signi ficant in flection poin t as seen in Figs. 3 & 4 of Zackrisson et al. (2003).
Rates and Progenitors of Type Ia Supernovae
We also prove that for an isotropic log-concave random vector, we only need ⌊np/2 log n⌋ sample points so that the empirical p-th moments of the linear functionals are almost isometrically the same as the exact ones.
L_p moments of random vectors via majorizing measures
Let p ≥ 1 and let µ be an isotropic log-concave measure satisfying the ψα condition for scalar products with some α ∈ [1, 2].
L_p moments of random vectors via majorizing measures
We apply Theorem 1 to isotropic log-concave random vectors.
L_p moments of random vectors via majorizing measures
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