
	Where results make sense

Topic: Curvature form

Related Topics

Gem

In Death Ground

Scald

Southglenn, Colorado

Schoolhouse Blizzard

Eugene Wilson

Talos

In the News (Fri 1 Jun 12)

EXECUTIVE POWER

Iran

ANALYSIS

Pakistan

Family compact

	Roller forming of thermoplastic sheet material - Patent 4818460
		Where an application requires a form surface having a more complex curvature it may be desirable to use a pliable roller which can deform to aid in conforming the thermoplastic sheet to the shape of the form, or a specially shaped roller adapted to conform to unusual shapes.
		Forming assembly 10' is substantially identical to forming assembly 10 with the exception of the shape of form surface 14' and the construction of roller 16'.
		In forming assembly 10', outer cover 16b' of roller 16' deforms as the roller is moved across thermoplastic sheet 19', thereby causing the thermoplastic sheet to conform to the intricate curvature of form surface 14'.
	www.freepatentsonline.com /4818460.html (2450 words)

	Anti-fog goggle with foam frame - Patent 4707863
		To make the goggle, the support member is curved about a form having the generally desired curvature and the lens adhered to the curved support member with an adhesive to deform the lens and support member into the form curvature which is substantially maintained when the lens and support member are removed from the form.
		The air channels of the support member are formed in the upper and lower areas of the outer surface of the support member with the upper air channels being aligned with the lens apertures to allow air to enter the upper air channels through the apertures.
		The form 74 includes a block 76 attached thereto having a curved upper periphery to simulate the nose of a wearer and to maintain the goggle pieces 12, 14 and 15 in place on the form while the goggle is being made.
	www.freepatentsonline.com /4707863.html (4885 words)

	Curvature -- from Wolfram MathWorld
		Because Gaussian curvature is "intrinsic," it is detectable to two-dimensional "inhabitants" of the surface, whereas mean curvature and the Weingarten map are not detectable to someone who can't study the three-dimensional space surrounding the surface on which he resides.
		The simplest form of curvature and that usually first encountered in calculus is an extrinsic curvature.
		A signed version of the curvature of a circle appearing in the Descartes circle theorem for the radius of the fourth of four mutually tangent circles is called the bend.
	mathworld.wolfram.com /Curvature.html (576 words)

	Riemann curvature tensor - Wikipedia, the free encyclopedia
		In differential geometry, the Riemann curvature tensor is the most standard way to express curvature of Riemannian manifolds, or more generally, any manifold with an affine connection, torsionless or with torsion.
		the curvature tensor measures noncommutativity of the covariant derivative.
		Note that the Gauss curvature coincides with the sectional curvature of the surface.
	en.wikipedia.org /wiki/Curvature_tensor (399 words)

	SCOLIOSIS: Edgar Cayce Health Overview curvature of the spine
		Scoliosis is a curvature of the spinal column.
		In some cases the most serious aspect of the curvature is the rotational twisting of the spinal column toward the front of the body, in which the organs of the chest and/or abdomen may be affected.
		In evaluating spinal curvature, it is important to determine whether structural factors elsewhere in the body may be causing the spine to curve as a compensation.
	www.edgarcayce.org /health/database/health_resources/scoliosis.asp (1479 words)

	Curvature, Intrinsic and Extrinsic
		= -(1/R)sin(s/R). From this we have the magnitude of the curvature
		= 1/R and the signed curvature +1/R. The sign is based on the path direction being positive in the counter-clockwise direction. The center of curvature for every point on this curve is the origin (0,0).
		of the two principal extrinsic curvatures relative to a flat plane tangent to the surface at the point of interest. The reason this formula is so complicated is that it applies to any system of coordinates (rather than just projected tangent normal coordinates), and is based entirely on the intrinsic properties of the surface.
	www.mathpages.com /rr/s5-03/5-03.htm (2403 words)

	Curvature form
		In differential geometry, the curvature form describes curvature of principal bundle with connection.
		For example, the tangent bundle of a Riemannian manifold we have as the structure group and is the 2-form with values in (which can be thought of as antisymmetric matrices, given an orthonormal basis).
		In this case the form is an alternative description of the curvature tensor, namely in the stadard notation for curvatur tensor we have
	publicliterature.org /en/wikipedia/c/cu/curvature_form.html (303 words)

	[No title] (Site not responding. Last check: 2007-10-13)
		One line of curvature passes for the lemon type umbilical point whereas three pass throught the umbilical point of monstar or star types.
		The criterion distinguishing between monstar and star types is that all three directions of lines of curvature through a monstar umbilic are contained in a right angle, whereas in the star type umbilical point case, they are not enclosed in a right angle [12].
		Under the intermediate test for the maximum principal curvature with a tolerance 0.03, the similarity value between two surfaces is 91.25%.
	deslab.mit.edu /DesignLab/Watermarking/NSF.htm (5477 words)

	[No title]
		The volume form for the metric inherited from $U(2)$ is $\cos(\theta) d\alpha\wedge d\gamma\wedge d\theta, \label{volume2}$ and the curvature form is now $\Omega = {-2} \sin(\theta)\cos(\theta) d\theta \wedge d\alpha$.
		The joint distribution of curvature, $\omega$, and conductance, $g= {1\over 2\pi}\, t^2$ is given by the probability density \be {\pi \over 2 C}\ e^{-\omega/2C} d\omega\, dg \label{NoTRI2} \ee with $\omega$ ranging from $-\infty$ to $\infty$ and $g$ from 0 to $1\over 2\pi$.
		The volume form indicates that $\sqrt g$, and not $g$, is uniformly distributed.
	www.ma.utexas.edu /mp_arc/html/papers/00-72 (3160 words)

	A.R.E. Health & Rejuvenation Research Center - The Cayce Health Database
		It should also be noted that the curvature of scoliosis does not occur just in the left-right plane, but also from back to front.
		Similarly, if there is a pelvic tilt causing the body to form a compensatory curvature, then chiropractic or osteopathic manipulation of the pelvic area is needed to create the necessary, balanced foundation.
		This is consistent with the basic theories of osteopathy and chiropractic, which place strong emphasis on the interplay between the spine and the internal organs.
	www.edgarcayce.org /health/database/chdata/data/prscol3.html (1480 words)

	Curvature of Riemannian manifolds - Wikipedia, the free encyclopedia
		It is the Gauss curvature of the σ-section at p; here σ-section is a locally-defined piece of surface which has the plane σ as a tangent plane at p, obtained from geodesics which start at p in the directions of the image of σ under the exponential map at p.
		It is possible to do this precisely because of the symmetries of the curvature tensor (namely antisymmetry in the first and last pairs of indices, and block-symmetry of those pairs).
		For a manifold of constant curvature, the Weyl tensor is zero.
	en.wikipedia.org /wiki/Curvature_of_Riemannian_manifolds (962 words)

	Contribution of DNA Conformation and Topology in Right-handed DNA Wrapping by the Bacillus subtilis LrpC Protein -- ...
		The DNA corresponding to the C7 curved region is indicated (410 to 750 bp in the 1444-bp TaqI-TaqI fragment that corresponds to 2986 to 3301 bp in pBR322).
		The maximum of the major curvature (650 bp) is indicated by the thick arrow, whereas the maximum of the minor curvature (550 bp) is indicated by the thin arrow.
		B' form structure of A tracts and B form (29).
	www.jbc.org /cgi/content/full/278/7/5333 (5934 words)

	Spontaneous-Curvature Theory of Clathrin-Coated Membranes -- Mashl and Bruinsma 74 (6): 2862 -- Biophysical Journal
		The unbinding of a dislocation by spontaneous curvature
		The equations of elasticity governing the strain tensor and the curvature of tethered surfaces are discussed in the Appendix.
		A6, and we use the cosine form of Eq.
	www.biophysj.org /cgi/content/full/74/6/2862 (6137 words)

	Are We Cruising a Hypothesis Space?
		This is in fact a differential form [] that provides a notion of surface area for the manifold \cal H and it is naturally interpreted as the uniform distribution over \cal H.
		Curvature seems to be well understood only in physics, specially from the point of view of gauge theories where the curvature form associated to a connection has been shown to encode field strengths for all the four fundamental forces of nature [].
		In statistics, on the other hand, the only thing we know (so far) about the role of curvature is that the higher the scalar curvature is at a given point of the model, the more difficult it is to do estimation at that point.
	omega.albany.edu:8008 /cruise.html (2657 words)

	Ken Richardson's Publications and Preprints
		I consider the basic heat operator on forms of a Riemannian foliation on a compact manifold with a bundle--like metric, and I show that the trace T(t) of this operator has a particular asymptotic expansion as t approaches 0.
		Cheng's eigenvalue comparison theorems assume bounds on the curvature of the manifold and then compare a specific eigenvalue to that of a ball in a constant curvature space form.
		Surprisingly, the condition for a critical point is not a local condition (like constant scalar curvature) in any higher dimension, and I exhibit examples of manifolds of all possible higher dimensions with locally homogeneous metrics that are not critical points for the determinant functional.
	faculty.tcu.edu /richardson/pubs.htm (2094 words)

	Publications by F.-E. Wolter et al.
		The curvature method is based on the Gaussian and the mean curvatures to establish correspondence between two objects.
		For objects with piecewise C² boundaries, relationships between the curvature of the boundary and the position of the medial axis are developed.
		To compute curvatures at a point q in S where the surface representation is degenerate one has to assume that the point set S has a tangent plane and well defined curvatures at the point q where the curvatures are to be computed.
	www.lems.brown.edu /vision/people/leymarie/Refs/CompGeom/Wolter.html (4192 words)

	Inquire Face Curvature
		You are prompted for a base surface, a point on the surface, and a point which determines the direction to slice the surface for curvature calculations.
		The Inquire Face Curvature Form appears which shows the max/min curvature and the max/min radius of curvature at the selected point.
		The form also shows the curvature, radius of curvature, and center of circle of curvature, in the direction of the second point.
	www.vx.com /help/4374.htm (151 words)

	[No title] (Site not responding. Last check: 2007-10-13)
		Our main Theorem 4.4 says that if for example the sectional curvature K is less than K0, then an enclosure of small volume V has at least as much perimeter P as a round sphere of the same volume in the model space form of curvature K0.
		First one estimates the mean curvature H of a minimizer by an application of the Gauss-Bonnet-Chern theorem with boundary.
		(In the conclusion for the case of equality, M has constant scalar curvature.) The assumption of positive Ricci curvature, needed to guarantee at one point in the argument that ¶R is connected, is not necessary for small volumes by Theorem 2.2.
	www.lehigh.edu /~dlj0/courses/IsopSph7=28=00.doc (3467 words)

	The Male Health Center - Peyronie's Disease
		Peyronie's disease is a severe curvature of the erect penis.
		Although the cause of Peyronie's disease isn’t known for sure, some physicians theorize that the curvature may form as a result of trauma to the penis.
		During healing, certain growth factors are upregulated, causing an abnormal amount of scar tissue (or plaque) to form.
	www.malehealthcenter.com /c_peyronie.html (1622 words)

	[No title] (Site not responding. Last check: 2007-10-13)
		Subject: The Joy of Forms Date: 18 Jun 2000 00:00:00 GMT Newsgroups: sci.physics.relativity Let's begin with the R^2, thought of as a real topological manifold, but not yet endowed with a metric or even an affine connection (if you know what these are).
		Newsgroups: sci.physics.relativity Subject: The Joy of Forms: E^(1,1) In this post, I continue my attempt to bring exterior calculus to the masses, showing by example how to compute the volume form, the connection one-forms, the curvature two forms, and the Laplace-Beltrami operator on both flat and curved spacetimes.
		It is simply this: in order to describe geodesics and curvature in terms of forms, we will need to somehow extend the exterior derivative to a "covariant exterior derivative" which can act on vectors or tensors in addition to forms.
	math.ucr.edu /home/baez/PUB/joy (9937 words)

	2.1 Geometry (Site not responding. Last check: 2007-10-13)
		The curvature tensors arise because the covariant derivative is not commutative and obeys the Ricci identity:
		From both affine curvature tensors we may form two different tensorial traces each.
		is the covariant derivative formed with the Christoffel symbol.
	relativity.livingreviews.org /Articles/lrr-2004-2/articlesu3.html (2680 words)

	561 Course Syllabus
		Normal and geodesic curvature of a curve on a surface.
		Its relation with the Curvature of curves on a surface is in §6.2.
		The second fundamental form of the graph of a function, in particular near points with a horizontal tangent.
	www.math.wisc.edu /~angenent/561/oldindex.html (460 words)

	CVSSP: multi-scale free-form surface description and curvature estimation
		The theory described above is the generalization of the curvature scale space method to 3-D surfaces, and has been applied to a number of 3-D triangulated meshes.
		Curvature values are then mapped to colours or greyscales, using the Visualization ToolKit (VTK), and displayed directly on the surface.
		Once curvature values have been estimated, curvature zero-crossing contours can be detected and also displayed on the surface using VTK.
	www.ee.surrey.ac.uk /Research/VSSP/demos/css3d/index.html (626 words)

	Categorified Gauge Theory
		In particular, we define a "Lie 2-group" to be a category C where the set of objects and the set of morphisms are Lie groups, and source, target, identity and composition maps are homomorphisms of Lie groups.
		Following ideas of Breen and Messing, we give formulas defining the curvature of such a connection, which consists of a Lie(G)-valued 2-form together with a Lie(H)-valued 3-form.
		We write down the obvious generalization of the Yang-Mills action for a connection on a trivial C-2-bundle, and derive the "categorified Yang-Mills equations" from this action.
	math.ucr.edu /home/baez/gauge (604 words)

	Freed, Moore, Segal on p-Form Gauge Theory, I \| The String Coffee Table
		The fact, mentioned above, that the image in deRham cohomology of curvature and characteristic class coincide can hence be expressed by the commutativity of the following diagram [Gom II, (4)]
		Notice that these characteristic classes correspond to the curvature of our connection, which measures the magnetic flux.
		Hence this is a grading by magnetic flux.
	golem.ph.utexas.edu /string/archives/000868.html (1957 words)

	Curvature form - Education - Information - Educational Resources - Encyclopedia - Music (Site not responding. Last check: 2007-10-13)
		Curvature form - Education - Information - Educational Resources - Encyclopedia - Music
		denotes the connection form, a 1-form on E with values in g.
		is an alternative description of the curvature tensor, namely in the stadard notation for curvatur tensor we have
	education.music.us /C/Curvature-form.htm (430 words)

	CiteULike: Tag curvature (Site not responding. Last check: 2007-10-13)
		A sampling framework for accurate curvature estimation in discrete surfaces
		Membrane Proteins Modulate the Bilayer Curvature in the Bacterial Virus Bam35.
		Endstopped neurons in the visual cortex as a substrate for calculating curvature
	www.citeulike.org /tag/curvature (322 words)

	Mathematical Sciences Research Institute - Geometric Evolution Equations and Related Topics (Site not responding. Last check: 2007-10-13)
		Many such flows are driven by some form of curvature such as the mean, inverse mean, Gauss, and Willmore flows of submanifolds, the Ricci, Kähler-Ricci, and Calabi flows of manifolds, the Yang-Mills and Hermitian-Einstein flows of connections and metrics on vector bundles, and the Yamabe and other conformal flows of metrics.
		Mean curvature flow, which is the gradient flow for the area functional, and its variants are related to material science.
		Inverse mean curvature has been applied to solve fundamental problems in general relativity, such as the Penrose inequality.
	www.msri.org /calendar/programs/ProgramInfo/242/show_program (664 words)

	Math 401: Differential Geometry*, Fall 2003
		the index of a vectorfield or the curvature of a surface at a point) with a global quantity such as the number of handles of a closed surface.
		For example the Poincare-Hopf theorem implies that any continuous vectorfield tangent to the sphere must vanish somewhere, or the Gauss-Bonnet theorem implies that the integral of the curvature over any topological donut, however lumpy, must be zero.
		A shorter proof involves showing that the corresponding principal curvatures of the parallel surface are k1/(1-ak1), k2/(1-ak2).)
	math.rice.edu /~hardt/401F03 (1024 words)

Try your search on: Qwika (all wikis)