convexity

Definitions

  • WordNet 3.6
    • n convexity the property possessed by a convex shape
    • n convexity a shape that curves or bulges outward
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Webster's Revised Unabridged Dictionary
    • n Convexity The state of being convex; the exterior surface of a convex body; roundness. "A smooth, uniform convexity and rotundity of a globe."
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Century Dictionary and Cyclopedia
    • n convexity The character or state of being convex; roundness; sphericity. Also sometimes convexness, convexedness.
    • n convexity The exterior surface or form of a convex body.
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Chambers's Twentieth Century Dictionary
    • ns Convexity roundness of form on the outside
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Etymology

Webster's Revised Unabridged Dictionary
L. convexitas,: cf. F. convexité,
Chambers's Twentieth Century Dictionary
L. convexusconveh-ĕrecon, together, and vehĕre, to carry.

Usage

In literature:

For example, the vertical curvature may be more convex than the horizontal.
"The Science of Human Nature" by William Henry Pyle
The rest of his face forcibly suggested the idea of a convex edge.
"Arthur Mervyn" by Charles Brockden Brown
Disk of sandstone, slightly convex in the centre; used in games.
"Illustrated Catalogue Of The Collections Obtained From The Indians Of New Mexico And Arizona In 1879" by James Stevenson
Disk usually convex, commonly on wood 10.
"Ohio Biological Survey, Bull. 10, Vol. 11, No. 6" by Bruce Fink and Leafy J. Corrington
The convexity of the disc was sharply defined.
"Brigands of the Moon" by Ray Cummings
There, two lenses were made, one plano-convex, and the other plano-concave, and these were placed in a tube made of sheet copper.
"Little Journeys to the Homes of the Great - Volume 12" by Elbert Hubbard
Grooved ax, 8 inches in length, 3-1/2 in width, and about 1 in thickness; one side is quite flat, the other convex.
"Illustrated Catalogue of a Portion of the Collections Made" by William H. Holmes
No beak or rostrum; snout short and convex; numerous teeth in both jaws.
"Natural History of the Mammalia of India and Ceylon" by Robert A. Sterndale
She is too bulky for a flower bed, too convex for a bench.
"Modern American Prose Selections" by Various
On the convex side were slight ridges with gentle forward slopes; on the concave were steep escarpments.
"With the British Army in The Holy Land" by Henry Osmond Lock
The work should be held in convex fashion over the fingers of the left hand.
"Embroidery and Tapestry Weaving" by Grace Christie
It had a nearly cylindrical body, covered with exceptionally large scales, and its head above convex.
"The Wonder Island Boys: The Mysteries of the Caverns" by Roger Thompson Finlay
Wings rather broad; fore wings rectangular at the tips; costa hardly convex; exterior border rather oblique.
"Journal of the Proceedings of the Linnean Society - Vol. 3" by Various
Convex shading 74 128.
"Carpentry for Boys" by J. S. Zerbe
The convex one, fig.
"Encyclopedia of Needlework" by Thérèse de Dillmont
Then the convex side is exposed and the board may straighten thus: Fig.
"Handwork in Wood" by William Noyes
I gazed down at the convex North Atlantic with the reddening coastline of North America spread like a map.
"Wandl the Invader" by Raymond King Cummings
On its convex side, Fig.
"Lessons on Soil" by E. J. Russell
In the early stages of its development, especially if in unconsolidated material, the slopes are normally convex inward.
"The Geography of the Region about Devils Lake and the Dalles of the Wisconsin" by Rollin D. Salisbury
The lower extremity of the neck of the uterus is irregularly convex and tumid.
"Fruits of Philosophy" by Charles Knowlton
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In poetry:

So when on earth the god of day
Obliquely sheds his tempered ray,
Through convex orbs the beams transmit,
The beams that gently warmed before,
Collected, gently warm no more,
But glow with more prevailing heat.
"A Song : The Sparkling Eye" by William Cowper
My aunt! my poor deluded aunt! Her hair is almost gray;
Why will she train that winter curl
In such a spring-like way? How can she lay her glasses down,
And say she reads as well,
When through a double convex lens
She just makes out to spell?
"My Aunt" by Oliver Wendell Holmes

In news:

Murray Carter on Convex Edges.
17th Generation Yoshimoto Bladesmith/ABS Master Bladesmith Murray Carter discusses convex edges.
All Videos Tagged Convex BLADE magazine is the World's Number One Knife Publication.
Here's an entry from the annals of "things I've always wondered about but never had the energy to bother checking on": Why don't cars in the United States have convex driver's side mirrors.
We study properties of programs with monotone and convex constraints.
Marked by convexity or swelling.
ERGO 's handmade ER500 scissors, featuring the "precision convex" blade, take advantage of new alloy tempering technologies.
Self-Portrait in a Convex Mirror by John Ashbery Viking, 83 pp.
Irritant or contact diaper dermatitis (DD) presents maximally on areas of skin in consistent contact with the irritant or allergen, ie, the convex areas of the groin but not the folds.
What are the parameters of the Great Convexity.
A simple magnifying glass with a convex lens.
Patty pans are disk-shaped, convex on both sides with a scalloped border, giving them the appearance of a plate or a flying saucer - an odd, fun, UFO shape kids find fascinating.
The 51st annual convention of the Petroleum Equipment Institute ( PEI ) will head for Dallas, Texas, when Convex 2001 opens in October.
Ram trucks can be outfitted with features to make towing jobs easier: an integrated trailer brake controller supplied by Continental and bigger 7"x11" trailer mirrors with full convex spotter mirror, twice the size of previous models.
The CapMax Convex Cap Printer from Workhorse Products (www.workhorseproducts.com) features a curved platen and screen that follow the natural shape of the cap.
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In science:

Apart from the product property given by the previous lemma, if one assumes additionally that the set of inputs is convex, then in the query model Q′ each part of the partition is a convex set.
Dispersion of Mass and the Complexity of Randomized Geometric Algorithms
Since the function f is convex by the H¨older inequality, the sets f −1 ((−∞, a]) for a ∈ R are also convex.
Coincidence of Lyapunov exponents for random walks in weak random potentials
We investigate lattices that can be represented as sublattices of the lattice of all convex subsets of a linearly ordered set (X, ≤) and as lattices of convex subsets of (X, ≤).
Lattices which can be represented as lattices of intervals
Polytopes, cones, and fans. A convex polytope P is the convex hull of a finite collection of points in Rn .
Faces of Generalized Permutohedra
If we take our metric d to be the Euclidean metric d2 or the ℓ1 -metric d1 (and take P to be a Poisson process on R3 ), then the cells Vz are two-dimensional sections of (bounded) convex sets (in fact polyhedra) in R3 , and hence convex.
Percolation on random Johnson-Mehl tessellations and related models
We prove: “If M is a compact hypersurface of the hyperbolic space, convex by horospheres and evolving by the volume preserving mean curvature flow, then it flows for all time, convexity by horospheres is preserved and the flow converges, exponentially, to a geodesic sphere”.
Volume preserving mean curvature flow in the Hyperbolic space
In fact, Huisken illustrated this by showing a way to obtain examples of convex hypersurfaces in the sphere S n+1 which could lose convexity along the flow.
Volume preserving mean curvature flow in the Hyperbolic space
The set of all nonnegative solutions is a compact convex set with the property that every its point has a unique representation as convex mixture of the extremes (Choquet simplex).
Coherent random permutations with record statistics
A V -polyhedron C is said open convex in V (or just open convex when V is implicitly known) if it is equal to a finite intersection of open V -half spaces (in particular V is an open convex).
Least Significant Digit First Presburger Automata
Hence, ARCCC maximizes a concave function over a convex set; so, it is convex.
Sensor Networks with Random Links: Topology Design for Distributed Consensus
Convex functions Let f be a proper convex function on Rk .
Conditional large and moderate deviations for sums of discrete random variables. Combinatoric applications
Note that it implies that ψX is strictly convex and that X (n) is not essentially constant and that ψX (n) is strictly convex for n large enough.
Conditional large and moderate deviations for sums of discrete random variables. Combinatoric applications
Hence, k(s) = 1 b ρ(s) ∈ (0, ∞] for all s and is log-convex, as the limit of a log-convex function is log-convex.
Random environment on coloured trees
Combining these three gives an approximate identification of a compact convex polyhedron in Rn−1 with a codimension one face of a compact convex polyhedron in Rn .
Kuranishi homology and Kuranishi cohomology
Lefschetz shows that we can choose a triangulation T of Y by convex polyhedra, with a dual triangulation T ∗ , such that if P, P ∗ are polyhedra in T , T ∗ of dimensions k , l then P, P ∗ intersect transversely in a convex polyhedron of dimension k + l − n, or P ∩ P ∗ =
Kuranishi homology and Kuranishi cohomology
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