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Topic: Intrinsic metric

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	Gravity, Entropy, and Thermodynamics
		Gravitation is a local, temporal metric (gauged by the universal gravitational constant G), imposed upon (and derived from) a global, spatial metric (gauged by the electromagnetic constant c).
		The purpose of a metric, whether spatial and global (as gauged by c) or temporal and local (as gauged by G) is the conservation of energy and symmetry.
		Entropy is fundamentally expressed as the intrinsic motion c of free energy (the velocity of light - primary form), and as the intrinsic motion T of bound energy's time dimension (the metric equivalent of velocity c - secondary form).
	www.people.cornell.edu /pages/jag8/thermo.html (9654 words)

	Intrinsic metric - Wikipedia, the free encyclopedia
		If two objects are at a distance one mile from each other, it should be possible to construct a road of length one mile between them.
		That seems to be a reasonable expectation; but in mathematics it fails to be true for a general metric space.
		A metric space (M,d) is called length space or path metric space or equivalently the metric d is called intrinsic if the distance between any pair of points in M is equal to the infimum of lengths of curves connecting these points.
	en.wikipedia.org /wiki/Intrinsic_metric (280 words)

	CVSS v2 Complete Documentation
		The environmental metrics, however, are specified by users because they are best able to assess the potential impact of a vulnerability within their own environments.
		This metric does not gauge the strength or complexity of the authentication process, only that an attacker is required to provide credentials before an exploit may occur. The possible values for this metric are listed in Table 3.
		This metric measures the degree of confidence in the existence of the vulnerability and the credibility of the known technical details.
	www.first.org /cvss/cvss-guide.html (6303 words)

	Intrinsic Safety (Site not responding. Last check: 2007-11-04)
		Intrinsic and extrinsic properties 1: ''This article is not about the concepts of intrinsic and extrinsic properties in philosophy.'' 5: In physics and chemistry an '''intrinsic property''' (or '''intensive property''') of a sy 6: t of material in the system.
		Intrinsic value 1: l, is the argument that the value of a product is intrinsic within the product rather than dependent on the b 3: s intrinsic value, if it is in-the-money.
		The intrinsic value is the positive difference between the curr 5: e of USD 0.20.
	www.elusiveeye.com /side29191-intrinsic-safety.html (471 words)

	Analytical event horizons of merging black holes
		There is now an analytical expression for the intrinsic metric of the event horizon of merging eternal fl holes.
		In this case, the conformal metric of the null slice constitutes free data.
		is the pullback of the Minkowski metric to a self-intersecting hypersurface which is null with respect to the Minkowski metric.
	www.phys.lsu.edu /mog/mog13/node9.html (1106 words)

	Intrinsic metric -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-11-04)
		Equivalently is intrinsic if for any and any pair of points there is such that and are smaller than.
		Given any metric, one can define the induced intrinsic metric by saying is to be the infimum of lengths of paths connecting and (or if there is no (Click link for more info and facts about contractible) contractible path connecting and).
		(A space in which Euclid's axioms and definitions apply; a metric space that is linear and finite-dimensional) Euclidean space.
	www.absoluteastronomy.com /encyclopedia/I/In/Intrinsic_metric.htm (242 words)

	32a
		The discussion started off with some comments about Riemannian metrics and whether the set of metrics on tree space would be useful to study.
		Should the metric on tree space come from an intrinsic metric, or an extrinsic metric on a larger space in which tree space is embedded?
		Vert remarked that the ``average'' of trees with high likelihood may not be high likelihood with the intrinsic metric.
	www.aimath.org /WWN/geombio/articles/html/32a (661 words)

	Time Supplement [Internet Encyclopedia of Philosophy]
		For example, the natural metric between any two points in a one-dimensional (1-d) space, such as the time sub-space of spacetime, is the numerical difference between the coordinates of the two points.
		One happy feature of this metric is that the value of the interval is unaffected by changing to a new reference frame provided the new reference frame is not accelerating relative to the first.
		The metric for spacetime defines the spacetime interval between two spacetime locations, and it is more complicated than the metric for time alone.
	www.iep.utm.edu /ancillaries/time-sup.htm (12731 words)

	Intrinsic metric - Definition up Erdmond.Com (Site not responding. Last check: 2007-11-04)
		A metric_space (M,d) is called length space or path metric_space or equivalently the metric d is called intrinsic if the distance between any pair of points in M is equal to the infimum of lengths of curves connecting these points.
		Equivalently d is intrinsic if for any \epsilon>0 and any pair of points x,y\in M there is c\in M such that 2d(x,c) and 2d(c,y) are smaller then d(x,y)+\epsilon.
		Given any metric d, one can define the induced intrinsic metric by saying \hat d(x,y) is to be the infimum of lengths of paths connecting x and y (or \infty if there is no contractible path connecting x and y).
	www.erdmond.com /Intrinsic_metric.html (306 words)

	The SMIL Media Object Modules
		The interpretation of this attribute is specific to the media type of the media object, and is only applicable to those media types for which there is a definition of a repeat value found in the media type format specification.
		The metric specifier is "npt", and the syntax of the time value is identical to the syntax of SMIL clock values.
		A new metric called "marker" can be used to define a clip using marked time points in a media object, rather than using clock values or SMPTE values.
	www.w3.org /TR/2005/REC-SMIL2-20050107/extended-media-object.html (4096 words)

	Intrinsic metric (Site not responding. Last check: 2007-11-04)
		If two objects are at a distance one mile from each other, it should be possible to construct a road of length one mile betweenthem.
		That seems to be a reasonable expectation; but in mathematics it failsto be true for a general metric space.
		A metric space (M,d) iscalled length space or path metric space or equivalently the metric d is called intrinsic if the distance between any pair of points in M is equal to the infimum of lengths of curves connectingthese points.
	www.therfcc.org /intrinsic-metric-220535.html (261 words)

	Intrinsic Safety -- Recommendations and Resources (Site not responding. Last check: 2007-11-04)
		Intrinsics (also know as Xt, for X toolkit), provides a friendly (object-oriented-looking) API to develop X11 softwares with graphical widgets.
		Since by definition intrinsic motivation does not rely on financial incentives, it is cheap.
		For instance, additional extrinsic motivation is known to have a negative impact on intrinsic motivation in many cases, perceived injustice in awarding such external incentives even more so.
	www.becomingapediatrician.com /health/80/intrinsic-safety.html (573 words)

	Riemannian manifold
		To pass from a linear algebraic concept to a differential geometric one, the smoothness requirement is important, in many instances.
		In particular one could define Riemannian manifold as a metric space which is isometric to a smooth submanifold of R
		With this definition of length, every connected Riemannian manifold M becomes a metric space (and even a length metric space) in a natural fashion: the distance d(x, y) between the points x and y of M is defined as
	www.brainyencyclopedia.com /encyclopedia/r/ri/riemannian_manifold.html (560 words)

	[No title]
		In general, I define the \emph{intrinsic metricity} to be the projected intrinsic derivative \[ Q_{H}^{HH}{}^{\mu \nu }{}_{\delta }{}=-\hat{D}_{H\delta }{}g^{HH}{}^{\mu \nu }{} \]% and, to complete the decomposition of the metricity, I define \emph{% cross-projected metricities} \[ Q_{H}^{XY}{}^{\mu \nu }{}_{\delta }{}=-\hat{D}_{H\delta }{}g^{XY}{}^{\mu \nu }{} \]% as well as the complements of these objects.
		If the connection is metric compatible, one might suspect that the intrinsic and cross-projected metricities would automatically vanish as a consequence of equation (\ref% {prjctn.compat}).
		One might use the fact that a metric exists or assume that the projection tensor field is normal, but the actual metric tensor components do not enter into any of the arguments.
	www.people.vcu.edu /~rgowdy/phys691/rap/pt.rap (4454 words)

	Koranyi Abstract UGA Math (Site not responding. Last check: 2007-11-04)
		The natural candidates for "Riemann maps" are the maps that are qc with respect to the real part of this metric and preserve its imaginary part ("symplectic qc maps").
		The boundaries of the domains also have an intrinsic metric which is highly non-isotropic and is defined with the aid of the Levi form.
		The main technique is to find qc maps of the boundaries onto each other that are qc with respect to this metric and then try to extend them to the interior as symplectic qc maps.
	www.math.uga.edu /~wag/colloquium/abst-koranyi.html (163 words)

	Geometry-Algebra-Singularities-Combinatorics Seminar Talk (Site not responding. Last check: 2007-11-04)
		Each connected set of these types can be considered as a metric space with different natural metrics.
		The most interesting metrics are induced (euclidian) metric and intrinsic metric.
		We present an example of a complex analytic set which is not intrinsically bi-Lipschitz equivalent to any normally embedded complex analytic set.
	www.math.neu.edu /GASC/GAS/birbrair.html (109 words)

	laub04a.html (Site not responding. Last check: 2007-11-04)
		This occurs either due to noise, fallible estimates, or due to intrinsic non-metric features such as they arise from human judgments.
		So far the problem of non-metric pairwise data has been tackled by essentially omitting the negative eigenvalues or shifting the spectrum of the associated (pseudo-)covariance matrix for a subsequent embedding.
		The information hidden in the negative eigenvalue part of the spectrum is illustrated and discussed for three data sets, namely USPS handwritten digits, text-mining and data from cognitive psychology.
	jmlr.csail.mit.edu /papers/v5/laub04a.html (165 words)

	Intrinsic metric - Enpsychlopedia (Site not responding. Last check: 2007-11-04)
		A metric space $(M,d)$ is called length space or path metric space or equivalently the metric $d$ is called intrinsic if the distance between any pair of points in $M$ is equal to the infimum of lengths of curves connecting these points.
		Equivalently $d$ is intrinsic if for any $\epsilon>0$ and any pair of points $x,y\in M$ there is $c\in M$ such that $2d(x,c)$ and $2d(c,y)$ are smaller than $d(x,y)+\epsilon$ .
		Given any metric $d$ , one can define the induced intrinsic metric $\hat d$ by saying $\hat d(x,y)$ is to be the infimum of lengths of paths connecting $x$ and $y$ (or $\infty$ if there is no contractible path connecting $x$ and $y$ ).
	www.grohol.com /psypsych/Intrinsic_metric (356 words)

	Mathematics 265: Differential Geometry Assignments (Site not responding. Last check: 2007-11-04)
		We gave the integers Z the p-adic metric d(m,n)=p^{-k} if the highest power of p that m-n is divisible by is k.
		Extend this metric to the rational numbers Q. Let d(x,y) be the "straight-line" distance between points on the unit sphere discussed in lecture in connection with the set of lines passing through the origin in R^3, and let d'(x,y) be the visual angle distance on the same set of lines, also discussed in class.
		A torus in R^3 with the intrinsic metric
	zimmer.csufresno.edu /~cleary/math265/hw.html (462 words)

	Amazon.de: English Books: A.D. Alexandrov: Selected Works: Intrinsic Geometry of Convex Surfaces (Site not responding. Last check: 2007-11-04)
		Proof of some of the general properties of the intrinsic metric of convex surfaces follows.
		The study then splits into two almost independent lines: further exploration of the intrinsic geometry of convex surfaces and proof of the existence of a surface with a given metric.
		The final chapter reviews the generalization of the whole theory to convex surfaces in the Lobachevskii space and in the spherical space, concluding with an outline of the theory of nonconvex surfaces.Alexandrov's work was both original and extremely influential.
	www.amazon.de /exec/obidos/ASIN/0415298024/ilectricinf0d-21 (434 words)

	Self-Calibration and Metric Reconstruction in spite of Varying and Unknown Intrinsic Camera Parameters - Pollefeys, Van ... (Site not responding. Last check: 2007-11-04)
		Abstract: In this paper the theoretical and practical feasibility of self-calibration in the presence of varying intrinsic camera parameters is under investigation.
		The paper's main contribution is to propose a self-calibration method which efficiently deals with all kinds of constraints on the intrinsic camera parameters.
		Self-calibration and metric reconstruction in spite of varying and unknown internal camera parameters.
	citeseer.lcs.mit.edu /pollefeys98selfcalibration.html (597 words)

	Curvature, Intrinsic and Extrinsic
		. The quantities in the numerator of the right hand expression are the coefficients of the "second groundform" of the surface, and the metric line element is called the first groundform. Hence the curvature is simply the ratio of the determinants of the two groundforms.
		, neither of which is an intrinsic metrical property of the surface, but the product of these two numbers is an intrinsic metrical property.
		The inverse of the metric tensor is denoted by g
	www.mathpages.com /rr/s5-03/5-03.htm (2403 words)

	Destiny Matrix (Site not responding. Last check: 2007-11-04)
		Any gravitational field is just a change in the metric of spacetime as determined by the quantities gik." In ADM's canonical method gik splits into a spacelike 3-geometry with 3 shift and 1 lapse function (from local gauging of the translations) to push the time evolution of the geometrodynamic field 3-geometry forward.
		The whole idea of the practical metric engineering the fabric of spacetime to reverse engineer the alleged alien time travel ships from our future through the Star Gate(s) is to control the flying saucer's timelike geodesic from inside the saucer using tiny amounts of power.
		That is, Lp^2(Macro-Quantum Coherent Goldstone Phase),u is the distortion of the fabric of spacetime whose strain tensor is the curved part of the Einstein metric tensor in a given local coordinate patch, i.e.
	destinymatrix.blogspot.com /2004_12_01_destinymatrix_archive.html (17839 words)

	[No title] (Site not responding. Last check: 2007-11-04)
		Sender: owner-mcg-talk@laser.cps.softex.br Status: RO X-Status: Following some requests, this e-mail advances material which is being prepared for publication, on the formal methods used in intrinsic certification, when viewed as intrinsic metric.
		It is not neccessary to follow the proofs in order to apply the concepts, because the end results are rather intuitive from simple geometry -- when the geometry analogy of certification is followed, as done in the intrinsic.txt msg.
		This msg proves that certification defines a metric, by construction -- ie, by presenting a function on the set of certificates which obeys all four conditions of metric-functions AND which allows a certificate to be correctly either accepted or rejected.
	sv2.quimbik.com /mcg-mirror/certmt.txt (706 words)

	E. N. Sosov's publications (Site not responding. Last check: 2007-11-04)
		MR1286177 (95e:54022) Sosov, E. On the metric space of weakly bounded mappings of metric spaces.
		MR1832592 (2002c:41049) Sosov, E. On the continuity and connectedness of the metric $\delta$-projection in a uniformly convex geodesic space.
		MR1896431 (2003c:54058) Sosov, E. On the continuity of the metric $\delta$-projection onto a convex set in a special metric space.
	www.kcn.ru /tat_en/university/departments/niimm/geometry_department/sosov/publ.html (352 words)

	Experimental Damage Mechanics of Microelectronic Solder Joints under Fatigue Loading (Site not responding. Last check: 2007-11-04)
		Herein damage is defined as the gradual degradation of material strength due to growth and coalescence of smeared microvoids or microcracks to initiate a single crack in the representative volume element (RVE) under continuous load application.
		As an intrinsic material property, damage variable can be readily determined experimentally at the microscale, such as dislocation density or micro-crack density.
		Using elastic modulus degradation as a damage metric, is very well established in the continuum damage mechanics literature, Kachanov, 1986; Lemaitre, 1991.
	www.packaging.buffalo.edu /newsletters/summer03/article1.html (4754 words)

	SemErgence: TypeKey and the Trust Web (Site not responding. Last check: 2007-11-04)
		Note that a blog posting trust metric would be different than a "take care of my grandma" trust metric, so there must be a distinction there.
		As users, once authenticated, post to blogs without generating (subjectively measured) negative feedback, their intrinsic trust metric increases.
		For instance, if a user that has posted 10000 posts across the web with no spam, then that user can relatively be trusted to post to your blog without harm.
	www.picklematrix.net /semergence/archives/000926.html (701 words)

	Metric Structures of Inviscid Flows (ResearchIndex) (Site not responding. Last check: 2007-11-04)
		Abstract: An intrinsic metric tensor, a flat connexion and the corresponding distance-like function are constructed in the configuration space formed by the velocity field and the thermodynamic variables of an inviscid fluid.
		1 Metric geometry of equilibrium thermodynamics (context) - Weinhold - 1975
		1 Thermodynamic geometry and the metrics of Weinhold and Gilmo..
	citeseer.ist.psu.edu /123505.html (526 words)

	Seminar Abstract (Site not responding. Last check: 2007-11-04)
		Intrinsic Metrics on Graphs, Graph Invariants, and Graph Geometry
		Naturally there is a question of an intrinsic metric on graphs, independently of whether the graphs are used to represent molecules.
		Though it seems there is little mention in the mathematical graph-theory literature beyond the shortest-path metric, it may be surmised that there might be other natural intrinsic metrics on graphs.
	www.math.uh.edu /~josic/colloquium/abstracts/120303.html (265 words)

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