metric function การใช้

• For a plan, a value can now be computed using a metric function, which is specified with : metric:
• It then needs to learn a similarity function ( or a distance metric function ) that can predict if new objects are similar.
• Therefore, one solution is obtained from the other by actively dragging the metric function over the spacetime manifold into the new configuration.
• These metrics function similarly to the 13A, which used a 120 mm ( 4.7 in ) rotor radius and 17.5 mm ( 0.7 in ) crankshaft offset.
• All other quantities that are of interest in geometry, such as the length of any given curve, or the angle at which two curves meet, can be computed from this metric function.
• The metric function and its rate of change from point to point can be used to define a geometrical quantity called the Riemann curvature tensor, which describes exactly how the space or spacetime is curved at each point.
• Where we use \ lambda in Eq ( 22 ) as the single metric function in place of \ psi in Eq ( 1 ) to emphasize that they are different by axial symmetry ( \ phi-dependence ).
• The aforementioned equivalence of metric functions remains valid if } } is replaced with, where is any convex positive homogeneous function of degree 1, i . e . a vector norm ( see Minkowski distance for useful examples ).
• This diffeomorphism invariance has an important implication : canonical quantum gravity will be manifestly finite as the ability to ` drag'the metric function over the bare manifold means that small and large ` distances'between abstractly defined coordinate points are gauge-equivalent!
• Where the metric functions \ { F, G ^ A \ } are independent of the coordinate r, \ hat { h } _ { AB } denotes the intrinsic metric of the horizon, and y ^ A are isothermal coordinates on the horizon.
• This implies that as soon as one finds a metric function in the x coordinate system that solves the field equations, one can simply write down the very same function but replace all the x's with y's, which solves the field equations in the y coordinate system.
• This example metric function specifies that the calculated value of the plan should be minimized ( i . e ., a plan with value " v1 " and a plan with value " v2 " such that " v1 " < " v2 ", the former plan is strictly preferred ).
• Considering the interplay between spacetime geometry and energy-matter distributions, it is natural to assume that in Eqs ( 7 . a-7 . e ) the metric function \ psi ( \ rho, z ) relates with the electrostatic scalar potential \ Phi ( \ rho, z ) via a function \ psi = \ psi ( \ Phi ) ( which means geometry depends on energy ), and it follows that