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Using and equivalence

Using the principle of equivalence, Einstein concluded that the same thing holds in any gravitational field, that the rate of clocks R at different heights was altered according to the gravitational field g. When g is slowly varying, it gives the fractional rate of change of the ticking rate.

Using Einstein's mass-energy equivalence,, this can be rewritten as

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 equivalence above, the fact that φ is a contradiction may be derived, for example, from.

Using the intrinsic rotations equivalence, Tait – Bryan angles correspond with the three rotations with a different axis.

Using the equivalence between Euler angles and rotation composition, it is possible to change to and from matrix convention.

* D. Shannon and M. Sweedler " Using Groebner bases to determine algebra membership, split surjective algebra homomorphisms determine birational equivalence " Journal of Symbolic Computation v6 n2-3 pp267 – 273 ( 1988 )

Using a coarser notion of equivalence that also allows transposition, there are 4 inequivalent matrices of order 16, 3 of order 20, 36 of order 24, and 294 of order 28.

Using the axiom of choice, they select and memorize a representative sequence from each equivalence class.

There are various situations, where such a functor is an equivalence between the opposite category C op of C, and D. Using a duality of this type, every statement in the first theory can be translated into a " dual " statement in the second theory, where the direction of all arrows has to be reversed.

Using and principle

" 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.

Using these modelling techniques, Malthus ' population principle of growth was later transformed into a model known as the logistic equation:

Using Huygens ' theory and the principle of superposition of waves, the complex amplitude at a further point P is found by summing the contributions from each point on the sphere of radius r 0 .

) Using the customary international law principle of a nation's right to protect its natural resources, President Truman in 1945 extended United States control to all the natural resources of its continental shelf.

Using Le Chatelier's principle, we can predict that the amount of methanol will increase, decreasing the total change in CO.

The technology gained further public attention when a company announced in early 2008 that they were close to fielding a device called MEDUSA ( Mob Excess Deterrent Using Silent Audio ) based on the principle.

Using the Heisenberg uncertainty principle for position and momentum, the products of uncertainty in position and momentum become zero as ħ → 0:

Using the newly created cyclotron as a mass spectrometer, Lawrence and his colleagues developed the principle behind the electromagnetic enrichment of uranium, which was put to use in the calutrons ( named after the university ) at the massive Y-12 facility in Oak Ridge, Tennessee.

Using algebra, we may write this principle as an algebraic identity:

Using his newly-developed electromagnetic principle, Henry in 1831 created one of the first machines to use electromagnetism for motion.

Using the principle of locality, in a famous paper he and his co-authors articulated the Einstein-Podolsky-Rosen Paradox which showed that position and momentum were simultaneous " real " physical properties of a particle.

Using the sensory equipment available to the Culture, Minds can see inside solid objects ; in principle they can also read minds by examining the cellular processes inside a living brain, but Culture Minds regard such mindreading as taboo.

Using the principle that any function with a finite number of possible outputs placed in a feedback loop will cycle, one can use a relatively small amount of memory to store outputs with particular structures and use them as " markers " to better detect when a marker has been " passed " before.

* By Blade: Using essentially the same principle as communication by mirror, by applying blood and breath, communication between two people can be established by calling them by name.

Using this principle, the world's only commercial tunable nanopore-based particle detection system has been developed by Izon Science Ltd.

Using an alternative DNS root breaks the principle of universal resolvability, unless it is for a strictly private purpose.

Using the perimeter block development principle, city blocks are developed so that buildings are located along the perimeter of the block, with entrances facing the street, and semi-private courtyards in the rear of the buildings.

Using this principle, Progressive Creationist Alan Hayward cites Hebrews 4, which discusses in the context of the creation story, a continued Seventh Day of creation.

Using a modern direct ophthalmoscope gives a view of the optic disc using the principle of reversibility of light.

Using Boltzmann's principle, we conclude that

Using XAML to develop user interfaces also allows for separation of model and view, which is considered a good architectural principle.

( Using a character for the first sound of its name is the acrophonic principle.

Using the action principle, a Lagrangian can be constructed from the trace of a polynomial function of these matrices, leading to Hamiltonian equations of motion.

Using and tensor

Using conditions 1 and the symmetry of the metric tensor g we find:

Using diffusion tensor sequences on MRI machines, the rate that molecules diffuse in and out of a specific area of tissue, directionality or anisotropy, and rates of metabolism can be measured.

Using index notation, the Hodge dual is obtained by contracting the indices of a k-form with the n-dimensional completely antisymmetric Levi-Civita tensor.

Using tensor calculus, proper time is more rigorously defined in general relativity as follows: Given a spacetime which is a pseudo-Riemannian manifold mapped with a coordinate system and equipped with a corresponding metric tensor, the proper time experienced in moving between two events along a timelike path P is given by the line integral

Using these properties, the Navier – Stokes equations of motion, expressed in tensor notation, are ( for an incompressible Newtonian fluid ):

Using Newton's identities, this condition can be re-expressed in terms of the traces of the powers of the Einstein tensor as

Using and is

Using Edgerton's method, the fast-closing action is obtained from the blackening of a window by exploding a series of parallel lead wires.

Using the F-distribution is a natural candidate because the test statistic is the ratio of two scaled sums of squares each of which follows a scaled chi-squared distribution.

Using visual imagery of a soroban, one can arrive at the answer in the same time as, or even faster than, is possible with a physical instrument.

Using a byte-oriented approach, it is possible to combine the < tt > SubBytes </ tt >, < tt > ShiftRows </ tt >, and < tt > MixColumns </ tt > steps into a single round operation.

Using two anchors set approximately 45 ° apart, or wider angles up to 90 °, from the bow is a strong mooring for facing into strong winds.

Using the same techniques they calculated the length of the Nile as, which is longer than previous estimates but still shorter than the Amazon.

Using the biblical Book of Revelation as a point of departure, Caesar Antichrist presents a parallel world of extreme formal symbolism in which Christ is resurrected not as an agent of spirituality but as an agent of the Roman Empire that seeks to dominate spirituality.

Using archery to take game animals is known as bow hunting.

Using a bow and arrow to take fish is known as bow fishing.

Using this criterion of falsifiability, astrology is a pseudoscience.

Using the formula, the overall speed boost is 1 / 0. 4575

Using this binding mechanism, an antibody can tag a microbe or an infected cell for attack by other parts of the immune system, or can neutralize its target directly ( for example, by blocking a part of a microbe that is essential for its invasion and survival ).

* Using a suitable catalyst ( e. g. Wilkinson's catalyst ), it is possible to reduce just one of the double bonds of an allene.

Using Zorn's lemma, it can be shown that every field has an algebraic closure, and that the algebraic closure of a field K is unique up to an isomorphism that fixes every member of K. Because of this essential uniqueness, we often speak of the algebraic closure of K, rather than an algebraic closure of K.

Using the above theorem it is easy to see that the original Borsuk Ulam statement is correct since if we take a map f: S n → ℝ n that does not equalize on any antipodes then we can construct a map g: S n → S n-1 by the formula

Using an existing language to bootstrap a new language is one way to solve the " chicken or the egg " causality dilemma.

Using ballpoint pens to create artwork is not without limitations.

Using the familiar cartesian basis, a vector A is written ;

Using programs or proofs of bounded lengths, it is possible to construct an analogue of the Berry expression in a formal mathematical language, as has been done by Gregory Chaitin.

Using terms from formal language theory, the precise mathematical definition of this concept is as follows: Let S and T be two finite sets, called the source and target alphabets, respectively.

Using numeric references that refer to permanently undefined characters and control characters is forbidden, with the exception of the linefeed, tab, and carriage return characters.

Using a three-digit Julian day number saves one byte of computer storage over a two-digit month plus two-digit day, for example, " January 17 " is 017 in Julian versus 0117 in month-day format.

Using color this way, the darkness and intensity ( or value ) of the color is evaluated by the eye as a measure of intensity or concentration.

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