Using this relation, it is possible to construct a partial order on the quotient set of the equivalence, S / ~, the set of all equivalence classes of ~.

Using the corresponding strict relation "<", one can also define the interval ( a, b ) as the set of points x satisfying a < x and x < b, also written a < x < b. An open interval may be empty even if a < b.

Using this, we can get the relation, again choosing the right sign:

where the reference variables may be functions of the number of particles N. Using the definition of the heat capacity at constant volume for the first differential and the appropriate Maxwell relation for the second we have:

Using this etymology, scholar John Lindow gives the meanings " in-law-relationship ", scholar Andy Orchard provides " relation ", and scholar Rudolf Simek gives " relation by marriage ".

The position of Bradman's left foot in relation to the stumps is an example of how he Crease ( cricket )# Using the crease | used the crease when batting.

Using the Gibbs – Duhem relation it is possible to translate the change in solvent vapor pressures with concentration into activities for the solute.

Using freezing point depression techniques, it is possible to calculate the activity of a weak acid from the relation,

Using the ideal properties, it is not difficult to check that ~ is a congruence relation.

Using the orthogonality relation where is the Kronecker delta, we simplify the above three terms for each to see

** Protective Coating: Bearing the Weight of Pynchon Using the Spectrum of Freud's Insight An analysis of Pynchon's use of parody in relation to Freudian theory

Using the accessibility relation we can translate this scenario as follows: At all of the worlds accessible to our own world, it is not the case that humans can travel faster than the speed of light, but at one of these accessible worlds there is another world accessible from those worlds but not accessible from our own at which humans can travel faster than the speed of light.

Using a reciprocity relation for on this equation and reordering gives a cyclic relation ( the triple product rule ),

Using this relation, putting ( 7 ) into ( 6 ) and transforming to one gets

Using the notation for the relation of being infinitely close as above,

Using generating functionals, the relation is expressed as

Using his mastery of the Quran and his innovative subject-based approach to Quranic exegesis, Al-Sadr extracted two concepts from the Holy text in relation to governance: khilafat al-insan ( Man as heir or trustee of God ) and shahadat al-anbiya ( Prophets as witnesses ).

Using the assumption that the cross-shore velocity v is zero at the coast, v = 0, one may solve a frequency relation for the phase speed of coastal Kelvin waves, which are among the class of waves called boundary waves, edge waves, trapped waves, or surface waves ( similar to the Lamb waves ).

Using the above recurrence relation, all higher can be expressed as polynomials in and.

Using the commutation relation between and we obtain:

Using the relativistic relation between momentum and energy, when Δp exceeds mc then the uncertainty in energy is greater than mc < sup > 2 </ sup >, which is enough energy to create another particle of the same type.

Using this relation we see that for itself.

Using the VNP's funds, more than 30 km² of heathland were purchased or rented by 1913.

Using the Historical Consumer Price Index for Jan 1913 ( 9. 8 ) and Jan 2009 ( 211. 143 ), the rate of inflation change is 2, 067 %.

Using this distance and other photographs, more information about the object, including its orbital elements, can be obtained .< ref >

Using the data collected by Vesto Slipher and his ( Hubble's ) assistant Milton Humason ( a former mule-driver and janitor ), Hubble and Humason found a direct relationship between a galaxy's distance and its relative speed away from the solar system.

Using this and the known moment of inertia of the flywheel, the computer is able to calculate speed, power, distance and energy usage.

Using its dichromatic color vision, it can detect predators from a great distance and then alert other prairie dogs to the danger with a special, high-pitched call.

Using the above equation, it is known that if an average speed is 80 kilometers per hour on a 4-hour trip, the distance covered is 320 kilometers.

Using this improved calibration, they find an absolute distance modulus of 18. 41, or 48 kpc (~ 157, 000 light years ).

Using a McMillan long-range TAC-50. 50-calibre rifle, he killed a Taliban fighter armed with an RPK machine gun at a confirmed distance of 2, 430 metres ( 1. 51 miles ).

Using metric units and taking the radius of the Earth as 6371 km, the distance to the horizon is

Using imperial units, the distance to the horizon is

Using newer and more powerful infrared telescope technology, able to detect brown dwarfs as cool as 150 kelvins out to a distance of 10 light-years from the Sun, preliminary results from the Wide-field Infrared Survey Explorer ( WISE survey ) have not, to date, detected Nemesis, although the analysis of the full survey is not yet complete.

Using this measurement and the latitudes of the two cities they could calculate the distance between the North Pole and the Equator in classical French units of length and hence produce the first prototype metre which was defined as being one ten millionth of that distance.

Using the same measurements for the distance from Ninety-Six to the Savannah River,

Using more modern techniques than had been available to the older major railroads during the 19th century, and the Rogers fortune to build to the highest standards and acquire the finest equipment and rolling stock, it was widely considered an engineering marvel of the times when completed all the way from Deepwater to reach a port near Norfolk, Virginia on Hampton Roads in 1909, a distance of about 450 miles.

" Critic Howard Halle said of it that " Using distance and attendant shifts of scale within the very fabric of the city, Horizon creates a metaphor for urban life and all the contradictory associations – alienation, ambition, anonymity, fame – it entails.

Using the two transit times and and the distance between receiving and transmitting transducers and the inclination angle one can write the equations:

Using kinetic depth perception enables the brain to calculate time to crash distance ( aka time to collision or time to contact-TTC ) at a particular velocity.

Using a novel and simple astrophysical method, he determined the distance as 450 kpc.

* Using positive curvature ( magnifying ) lenses, the focus point of the image is changed from its short distance ( about 30 to 40 cm ) to a virtual distance at infinity.

* Using MeshLab to measure difference between two surfaces A short tutorial on how to compute and visualize the Hausdorff distance between two triangulated 3D surfaces using the open source tool MeshLab.

Using the average swimming speed, Kooyman estimated the distance travelled to foraging areas at.

" 3 "> Using the tape measure, measure the horizontal distance ( d ) from the middle of the pile to the edge.

Using your scientific calculator, divide height ( h calculated in Step 2 ) by the distance ( d calculated in Step 3 ).