Using these commutation relations it can be shown that

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 this period-luminosity relation, in 1913 the distance to the SMC was first estimated by Ejnar Hertzsprung.

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 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 space exploration as a symbol of national prestige, he warned of a " missile gap " between the two nations, pledging to make the U. S. not " first but, first and, first if, but first period.

Using the traditional definition, the anode switches ends between charge and discharge cycles.

Using scientific knowledge from textbooks in the trunk of his 1973 Oldsmobile Delta 88, and enlisting the help of Duke Henry, Ash successfully leads the medieval soldiers to victory over the Deadites and Evil Ash, saving Sheila and bringing peace between Arthur and Henry in the process.

" Using this legal principle, many judges in Britain and the United States had voided, as an infringement of an individual's property rights, legislation that regulated common law bargains made in the marketplace between employers and their workers.

" Freedom of contract is a qualified and not an absolute right ...," Hughes declared in upholding an Iowa law that voided contracts limiting the legal rights of railroad workers: The state may " interfere where the parties do not stand upon an equality ...." Using similar reasoning, the associate justice upheld a California law that mandated a forty-eight-hour work-week for women in various industries and allowed a federal statute to override a contract between an interstate railroad and its employees.

* An Empirical Approach to Study the Relation between Ontogeny, Size and Using Geometric Morphometrics

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 sonar, the team encountered a kind of underwater disturbance ( called a seiche ) due to stored energy ( such as from a wind ) causing an imbalance between the loch's warmer and colder layers ( known as the thermocline ).

Using a similarity matrix, the algorithm delivered matches between meanings including a confidence factor.

Using triangulation he then measured a 137 km arc of meridian between Cape Town and Aurora.

Using periodic trends, the periodic table can help predict the properties of various elements and the relations between properties.

Using few props, they created dry and absurd television which lasted for three series between 1965 and 1970.

Using this setup, he discovered the direct proportionality between the intensity of light and the induced photo electric current ( the first law of photoeffect or Stoletov's law ).

Using this pump, Boyle and Hooke noticed a correlation between pressure, temperature, and volume.

Using the Greek numerical prefixes, these would be as follows for series with between two and ten entries:

Using Minkowski's spacetime formalism, Laue went on to demonstrate that the world lines of the inertially moving bodies maximize the proper time elapsed between two events.

The Chinese character s around the Taijitu symbol read: " Using no way as way " and " Having no limitation as limitation " The arrows represent the endless interaction between yang and yin.

Using the second definition of depression, most economists refer to the Great Depression, as the period between 1929 and 1941.

Using the above examples, Universal Grammar would be the property that the brain has that causes it to posit a difference between nouns and verbs whenever presented with linguistic data.

Using hybrids for bidirectional amplificationThe primary use of a voiceband hybrid coil is to convert between 2-wire and 4-wire operation in sequential sections of a communications circuit, for example in a four-wire terminating set.

In the United States, the Federal Communications Commission ( FCC ) regulates phone-to-phone connections, but says they do not plan to regulate connections between a phone user and an IP telephony service provider. Using the Internet, calls travel as packets of data on shared lines, avoiding the tolls of the PSTN.

Using old technology, this was often done with rubber ( or possibly cork ) stoppers inserted between the component glassware items.

Using the Dvorak technique, infrared satellite imagery can used to determine the temperature difference between the eye and the cloud top temperature of the central dense overcast of mature tropical cyclones to estimate their maximum sustained winds and their minimum central pressures.

Using it, he compiled the 1437 Zij-i-Sultani of 994 stars, generally considered the greatest star catalogue between those of Ptolemy and Brahe, a work that stands alongside Abd al-Rahman al-Sufi's Book of Fixed Stars.

Using the value 4 in this equation ( midway between 3 and 5 ) yields a " compromise " wavelength-frequency-neutral peak, which is given for x =