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Using and tensor
Using the equivalence principle, this tensor is readily generalized to curved space-time.
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 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 calculus
Using a branch of mathematics known as tuple calculus, he demonstrated that such a system could support all the operations of normal databases ( inserting, updating etc.
Using these two examples, we can make some useful observations that motivate the major ideas in lambda calculus.
Using the techniques of differential calculus, the velocity and acceleration as a function of time can be found:
Using differential calculus, we can determine the limit, or the value that Δy / Δx approaches as Δy and Δx get closer to zero ; it follows that this limit is the exact slope of the tangent.
Using the probability calculus of Bayes Theorem, Salmon concludes that it is very improbable that the universe was created by the type of intelligent being theists argue for.
Using geometry and calculus, some simple combinations of sources are easily solved ; others are not.
Using a method called " calculus of statement ," Lentz helps the team to mitigate the pressure harming the plant operators.
Using the fundamental theorem of calculus often requires finding an antiderivative.
Using this in the sum, one can evaluate the remaining integral using the calculus of residues and arrive at the desired generating function.
Using the limit notation of calculus, the volume may be expressed as:
Using differential calculus we can obtain conditions on x under which this holds.
Using the parametrization of the hyperbola with hyperbolic angle, the theory of special relativity provided a calculus of relative motion with the one-parameter group indexed by rapidity.
* Using process calculus to model biological systems ( stochastic-calculus, BioAmbients, Beta Binders, BioPEPA, Brane calculus ).
Using calculus, Gershun could compute the irradiance falling on points () on a surface.
Using the functional calculus for larger classes of functions, we can for example define rigorously the " square root " of the ( negative ) Laplacian operator − Δ or the exponential
Using the bounded functional calculus, one can prove part of the Stone's theorem on one-parameter unitary groups:
Using typed lambda calculus to implement formal systems on a machine.
Using modern predicate calculus, we quickly discover that the statement is ambiguous.

Using and proper
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.
Using the concept of the impossibility of a gambling system, von Mises defined an infinite sequence of zeros and ones as random if it is not biased by having the frequency stability property i. e. the frequency of zeros goes to 1 / 2 and every sub-sequence we can select from it by a " proper " method of selection is also not biased.
Using comparative analysis of all the material available to him, Vollaerts was able to show the internal logic and coherence in the neumatic notation with regard to a proper articulation of the verbal-melodic line.
Using the 15-province system and the name of Kiang-nan Province indicates that the concept of China proper probably had appeared between 1645 and 1662 and this concept may reflect the idea that identifies China as the territory of the former Ming Dynasty after the Manchu conquest of Ming.
Using proper equipment is key in preventing injury.
Using the proper subset of hardware description language, a program called a synthesizer ( or synthesis tool ) can infer hardware logic operations from the language statements and produce an equivalent netlist of generic hardware primitives to implement the specified behaviour.
Using GDI, it is very easy to draw on multiple devices, such as a screen and a printer, and expect proper reproduction in each case.
Using his authority as Chief Scientific Adviser at the MOD he decided that the subject should not be dismissed without some proper, official investigation.
Using proper body movements when performing activities helps reduce strain on joints and thereby decrease pain and stiffness.
Using the results, as part of a proper examination or test protocol, practitioners screen for toxic exposure and heavy metal poisoning.
Using a variety of mechanical or electrical systems, the output of the selsyns could be read to ensure proper movement had occurred ( in other words, forming a closed-loop control system ).
Using split shots or other forms of weights, fishermen could easily zero into their fishing lures ' depth while running at the proper speed.
# Using proper technique to strike with greater force: As in other martial arts, students learn specific body mechanics with the intent to produce a more powerful strike.
Using proper posture of the mandible could guide the jaws to grow their proper form.
Using proper care, the server could be very secure.
Using the prevalent definition, " city proper " is not limited to a city, it can describe the complete area of any locality that fits the definition.
Using the patient's own stem cells with genetic correction should reduce or eliminate the complications of graft vs. host disease and provide a long term solution to proper ARSA expression in MLD patients.
Using a regular triangle and the factor 1 / 2 will result in the Sierpinski triangle, while creating the proper arrangement with four points and a factor 1 / 2 will create a display of a " Sierpinski Tetrahedron ", the three-dimensional analogue of the Sierpinski triangle.

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