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Page "Curvature" ¶ 79
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intrinsic and definition
Take good and evil for example: goodness is biblically defined as that which is of God ; it is intrinsic to his being and is revealed most prominently through his provision of Old Testament Law, the keeping of which is the very definition of goodness and the neglecting of which ( on even the slightest of grounds ), is the epitome of evil.
More precisely, matrices are tensors of type ( 1, 1 ), having one row index and one column index, also called covariant order 1 and contravariant order 1 ; see Tensor ( intrinsic definition ) for details.
Although it is possible to show that transformation laws indeed ensure independence from the basis, sometimes a more intrinsic definition is preferred.
In algebraic geometry, in contrast, there is an intrinsic definition of tangent space at a point P of a variety V, that gives a vector space of dimension at least that of V. The points P at which the dimension is exactly that of V are called the non-singular points ; the others are singular points.
( Indeed, a relative intrinsic values is a self-contradictory term ; intrinsic values are also absolute or else they are by definition in intrinsive ).
After the discovery of the intrinsic definition of curvature, which is closely connected with non-Euclidean geometry, many mathematicians and scientists questioned whether ordinary physical space might be curved, although the success of Euclidean geometry up to that time meant that the radius of curvature must be astronomically large.
By this definition, the field variations δφ < sup > A </ sup > result from two factors: intrinsic changes in the field themselves and changes in coordinates, since the transformed field α < sup > A </ sup > depends on the transformed coordinates ξ < sup > μ </ sup >.
* Tensor ( intrinsic definition )
As of December 22, 2010, it takes ₱ 2, 933. 07 modern pesos to equal the intrinsic purchasing power parity of the 1903 – 1949 Philippine Commonwealth peso, as per its legal definition: 12. 9 grains of pure gold ( or 0. 026875 XAU ).
The Levi-Civita notions of intrinsic derivative and parallel displacement of a vector along a curve make sense on an abstract Riemannian manifold, even though the original motivation relied on a specific embedding, since the definition of the Christoffel symbols make sense in any Riemannian manifold.
# REDIRECT Tensor ( intrinsic definition )
For a more general definition of Eta or intrinsic impedance,.
The " remarkable ", and surprising, feature of this theorem is that although the definition of the Gaussian curvature of a surface S in R < sup > 3 </ sup > certainly depends on the way in which the surface is located in space, the end result, the Gaussian curvature itself, is determined by the inner metric of the surface without any further reference to the ambient space: it is an intrinsic invariant.
# REDIRECT Tensor ( intrinsic definition )
# REDIRECT Tensor ( intrinsic definition )
* Tensor ( intrinsic definition )
The intrinsic definition had been published only a few years earlier in the work of Oswald Veblen and J. H. C.
However, the energy-momentum four-vector is a genuine Minkowski four-vector, and the intrinsic origin of the square-root in the definition of the relativistic mass is the distinction between dτ and dt .</ ref > Relativistic mass depends on the motion of the object, so that different observers in relative motion see different values for it.
There is an intrinsic definition of an embedded submanifold which is often useful.
Norman's 1988 definition makes the concept of affordance relational rather than subjective or intrinsic.
In relation to the meaning of a construct, quantity involves two semantic dimensions: 1. extension or extent ( determining the specific classes or individual instances indicated by the construct ) 2. intension ( content or comprehension or definition ) measuring all the implications ( relationships and associations involved in a construct, its intrinsic, inherent, internal, built-in, and constitutional implicit meanings and relations ).
The Business Round Table has also argued that the RMA contains core concepts, such as sustainable management, intrinsic values, Treaty principles, kaitiakitanga and the definition of the environment, which are ' hopelessly fuzzy '.
These definitions shall prove to be useful later on during the intrinsic definition of the jet of a function between two manifolds.

intrinsic and Gaussian
Gaussian curvature is however in fact an intrinsic property of the surface, meaning it does not depend on the particular embedding of the surface ; intuitively, this means that ants living on the surface could determine the Gaussian curvature.
Thus the Gaussian curvature is an intrinsic invariant of a surface.
Theorema egregium of Gauss states that the Gaussian curvature of a surface can be expressed solely in terms of the first fundamental form and its derivatives, so that K is in fact an intrinsic invariant of the surface.
# The luminosity function can be approximated as a Gaussian function, centered on an intrinsic mean absolute magnitude M < sub > 0 </ sub >.

intrinsic and curvature
Taken as a physical description of space, postulate 2 ( extending a line ) asserts that space does not have holes or boundaries ( in other words, space is homogeneous and unbounded ); postulate 4 ( equality of right angles ) says that space is isotropic and figures may be moved to any location while maintaining congruence ; and postulate 5 ( the parallel postulate ) that space is flat ( has no intrinsic curvature ).
The concept enabled an alternative formulation of the intrinsic differential geometry of a manifold in the form of the Riemann curvature tensor.
A full 360 ° rotation is not needed because of a symmetry intrinsic to the Fourier transforms of real functions ( such as the electron density ), but " slightly more " than 180 ° is needed to cover all of reciprocal space within a given resolution because of the curvature of the Ewald sphere.
There is a key distinction between extrinsic curvature, which is defined for objects embedded in another space ( usually a Euclidean space ) in a way that relates to the radius of curvature of circles that touch the object, and intrinsic curvature, which is defined at each point in a Riemannian manifold.
In contrast to curves, which do not have intrinsic curvature, but do have extrinsic curvature ( they only have a curvature given an embedding ), surfaces can have intrinsic curvature, independent of an embedding.
The intrinsic and extrinsic curvature of a surface can be combined in the second fundamental form.
The curvature is intrinsic in the sense that it is a property defined at every point in the space, rather than a property defined with respect to a larger space that contains it.
There are ways of describing curves without coordinates, using intrinsic equations that use invariant quantities such as curvature and arc length.
* Theorema Egregium − The " remarkable theorem " discovered by Gauss which showed there is an intrinsic notion of curvature for surfaces.
This is used by Riemann to generalize the ( intrinsic ) notion of curvature to higher dimensional spaces.
Bernhard Riemann extended Gauss's theory to higher dimensional spaces called manifolds in a way that also allows distances and angles to be measured and the notion of curvature to be defined, again in a way that was intrinsic to the manifold and not dependent upon its embedding in higher-dimensional spaces.

intrinsic and at
Angular momenta of a classical object .< p > Left: intrinsic " spin " angular momentum S is really orbital angular momentum of the object at every point ,</ p >< p > right: extrinsic orbital angular momentum L about an axis ,</ p >< p > top: the moment of inertia tensor | moment of inertia tensor I and angular velocity ω ( L is not always parallel to ω )</ p >< p > bottom: momentum p and it's radial position r from the axis .</ p > The total angular momentum ( spin + orbital ) is J.
Consilience has its roots in the ancient Greek concept of an intrinsic orderliness that governs our cosmos, inherently comprehensible by logical process, a vision at odds with mystical views in many cultures that surrounded the Hellenes.
Since the nominal values of these new issues were lower than their intrinsic worth as metals, the state was minting these coins at a loss.
Thus in Hippolytus, a love-sick queen rationalizes her position and arrives at this comment on intrinsic merit while reflecting on adultery:
Research has indicated that learners who are better at goal-setting and self-monitoring tend to have greater intrinsic task interest and self-efficacy ; and that teaching learning strategies can increase academic achievement.
Fluorescence in the life sciences is used generally as a non-destructive way of tracking or analysis of biological molecules by means of the fluorescent emission at a specific frequency where there is no background from the excitation light, as relatively few cellular components are naturally fluorescent ( called intrinsic or autofluorescence ).
In addition to their other properties all particles possess a quantity, which has no correspondence at all in conventional physics, namely the spin, which is some kind of intrinsic angular momentum ( therefore the name ).
Both Ge ( Li ) and HPGe detectors have excellent sensitivity and resolution, but Ge ( Li ) detectors are unstable at room temperature, with the lithium drifting into the intrinsic region ruining the detector.
For instance, if limited onboard power fed to its engine was the dominant limitation on how much payload a hypothetical spacecraft could shuttle ( such as if intrinsic propellant economic cost was minor from usage of extraterrestrial soil or ice ), ideal exhaust velocity would rather be around 62. 75 % of total mission delta v if operating at constant specific impulse, except greater optimization could come from varying exhaust velocity during the mission profile ( as possible with some thruster types, including mass drivers and variable specific impulse magnetoplasma rockets ).
Increasing the dimensions of the intrinsic region ( and its stored charge ) allows the diode to look like a resistor at lower frequencies.
Pinker ’ s research on visual cognition, begun in collaboration with his thesis adviser Stephen Kosslyn, showed that mental images represent scenes and objects as they appear from a specific vantage point ( rather than capturing their intrinsic three-dimensional structure ), and thus correspond to the neuroscientist David Marr ’ s theory of a “ two-and-a-half-dimensional sketch .” He also showed that this level of representation is used in visual attention, and in object recognition ( at least for asymmetrical shapes ), contrary to Marr ’ s theory that recognition uses viewpoint-independent representations.
Other metrics are absolute magnitude, which is an object's intrinsic brightness at visible wavelengths, irrespective of distance, while bolometric magnitude is the total power output across all wavelengths.
Also one intrinsic attribute of HTS is that it can withstand much higher magnetic fields than LTS, so HTS at liquid helium temperatures are being explored for very high-field inserts inside LTS magnets.
The Leconfield Head ( a head of the Aphrodite of Cnidus type, included in the 2007 exhibition at the Louvre ) in the Red Room, Petworth House, West Sussex, UK, was claimed by Adolf Furtwängler to be an actual work of Praxiteles, based on its style and its intrinsic quality.
" David Roberts continues that " the secrecy that lies at the heart of Puebloan Hopi life ... long predates European contact, forming an intrinsic feature of the culture.
" One of the most ancient of these rites of reconciliation, the Kiss of Peace as a sign of reconciliation between communicants as an intrinsic part of these communicants ' preparation for Communion has been restored to all the faithful and no longer limited to clerics at High Mass.
An economic bubble ( sometimes referred to as a speculative bubble, a market bubble, a price bubble, a financial bubble, a speculative mania or a balloon ) is " trade in high volumes at prices that are considerably at variance with intrinsic values ".
To isolate the intrinsic changes, the field variation at a single point x < sup > μ </ sup > may be defined

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