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Using the periodicity of the trajectory, we can split the radiation integral into a sum over terms.
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Using and periodicity
:" Using more than 200 redshifts in Coma, Perseus, and A2199, the presence of a distinct band-related periodicity in redshifts is indicated.
Using and trajectory
Using this coordinate system in the inertial frame, it is easy to identify the force normal to the trajectory as the centripetal force and that parallel to the trajectory as the tangential force.
Using a root finder on these sixty functions produces the exact collision times for the two given triangles and the two given trajectory.
Using only the Principle of Least Action and the Lagrangian we can deduce the correct trajectory, by trial and error or the Calculus of Variations.
Using a semi-active laser homing guidance method, the LAHAT can be guided by the tank's crew or by teams on the ground, while the missile's trajectory can be selected to either attack from the top ( to defeat enemy armor ) or direct attack ( to engage enemy helicopters ).
Using and we
Using launch systems presently available, we are developing satellites to scout the world's weather ; ;
Hence S breaks up into uncountably many orbits under G. Using the axiom of choice, we could pick a single point from each orbit, obtaining an uncountable subset X of S with the property that all of its translates by G are disjoint from X.
Using the identity, we have
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 < sup > n </ sup > → ℝ < sup > n </ sup > that does not equalize on any antipodes then we can construct a map g: S < sup > n </ sup > → S < sup > n-1 </ sup > by the formula
Using the right-hand rule, we expect the curl to be into the page.
Using the product rule in reverse, we get:
Using now the power series definition from above we see that for real values of x
Using the composition of functions we can rewrite this statement as follows:
Using these two examples, we can make some useful observations that motivate the major ideas in lambda calculus.
Using the definition of free variables, we may now define a capture-avoiding substitution.
Using our senses of sight, hearing, touch, smell, and taste, we perceive colors, sounds, textures, etc.
* Using the above methods for simple polygons, we discover that particular regions within the polygon may have their area multiplied by a factor which we call the density of the region.
Using this information we can perform a series of exchanges on the input array that puts it in order, moving items only once.
Using =, we find that the period of precession is given by:
Using relativistic relations for energy and momentum, we have
Using the chosen basis, we may write
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 previous example, we would get the following:
Using this, we can get the relation, again choosing the right sign:
Using this Carnapian approach, Maher identifies a proposition which we intuitively ( and correctly ) know to be false, but which we easily confuse with the paradoxical conclusion.
Using Le Chatelier's principle, we can predict that the amount of methanol will increase, decreasing the total change in CO.
Using and can
Using a Batista man to screen refugees represented a total misunderstanding of the democratic forces which alone can effectively oppose Castro.
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 this distance and other photographs, more information about the object, including its orbital elements, can be obtained .< ref >
Using these formulas, the area of any polygon can be found by dividing the polygon into triangles.
Using the " lock and key " metaphor, the antigen itself can be seen as a string of keys-any epitope being a " key "-each of which can match a different lock.
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 these inhibitors it was discovered that cells can die while displaying a morphology similar to apoptosis without caspase activation.
Using modern full capacity firearms, a shooter can fire more shots with greater accuracy using a single gun in a two-handed grip than two guns with one-handed grips.
Using a solar roof, solar cells can provide electric power.
Using various modifiers, the activity of the enzyme can be regulated, enabling control of the biochemistry of the cell as a whole.
Using these tools, one can write a more complex text editor, and a simple compiler for a higher-level language and so on, until one can have a graphical IDE and an extremely high-level programming language.
Using pharmacogenomics, pharmaceutical companies can create drugs based on the proteins, enzymes and RNA molecules that are associated with specific genes and diseases.
Using braille translation software, a document can be embossed with relative ease, making braille production much more efficient and cost-effective.
Using summation notation, it can be written as
Using the previous relationships they can be expressed as:
Using the extension of the code, the encoded string 0011001011 can be grouped into codewords as 0 – 011 – 0 – 01 – 011, and these in turn can be decoded to the sequence of source symbols acabc.
Using the language of category theory, many areas of mathematical study can be cast into appropriate categories, such as the categories of all sets, groups, topologies, and so on.
Using the one-point compactification, one can also easily construct compact spaces which are not Hausdorff, by starting with a non-Hausdorff space.
Using Cartesian coordinates, it can be shown that
0.255 seconds.