Using a separate statistical evaluation than used above for interventions, civil wars that included pro-or anti-communist forces lasted 141 % longer than the average non-Cold War conflict, while a Cold War civil war that attracted superpower intervention resulted in wars typically lasting over three times as long as other civil wars.

Using the DPV formula above ( FV =$ 150, 000, i = 0. 05, n = 3 ), that means that the value of $ 150, 000 received in three years actually has a present value of $ 129, 576 ( rounded off ).

Using now the power series definition from above we see that for real values of x

Using the conventions above,

Using their data on the time occupied by travel to work, Table 2 below shows the absolute number of people who responded with travel times " at least 15 but less than 20 minutes " is higher than the numbers for the categories above and below it.

Using the example above, the disjunction expresses that it is either raining outside or there is a cold front over Kansas.

* 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 values above 128 conflicts with using the 8th bit as a checksum, but the checksum usage gradually died out.

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 the formula above, we can calculate the amount of power that needs to be generated, at least given extremely efficient heat transfer: P =

Using the example of a solution of two liquids, A and B, if no other gases are present, then the total vapor pressure p above the solution is equal to the weighted sum of the " pure " vapor pressures of the two components, p < sub > A </ sub > and p < sub > B </ sub >.

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 coils with parallel capacitors will form a filter with the topology of an m-derived filter and a band of frequencies above the cut-off will also be passed.

Using the above definition, it is useful to think of the function as a matrix ( called the input matrix ) where each row of the matrix corresponds to X and each column corresponds to Y.

Using these coefficients gives the Taylor polynomial of f. The Taylor polynomial of degree d is the polynomial of degree d which best approximates f, and its coefficients can be found by a generalization of the above formulas.

Using the pseudocode above, the Cray did:

Using the above given notation, suppose that some infinite cardinal.

Using the Boltzmann expression for the mean electron velocity given above with and setting the ion current to zero, the electron saturation current density would be

Using equation in the set above, we have:

Using the above rule, we can complete the proof of Fermat's little theorem quite easily, as follows.

Using the above authorities one then will see whether the property is eligible for the National Register.

Using the equation above, the probability of exactly two tosses out of four total tosses resulting in a heads is given by:

Using Kuratowski's representation for an ordered pair, the second definition above can be reformulated in terms of pure set theory:

Using a marine sextant to measure the altitude of the sun above the horizon

Using Wick theorem on the terms of the Dyson series, all the terms of the S-matrix for quantum electrodynamics can be computed through the technique of Feynman diagrams.

Using a uniqueness theorem and showing that a potential satisfies Laplace's equation ( second derivative of V should be zero i. e. in free space ) and the potential has the correct values at the boundaries, the potential is then uniquely defined.

Using the parallel axis theorem, the radius of gyration L of a rigid pendulum can be shown to be

Using the formula for Bayes ' theorem, we have:

Using the disintegration theorem we can define a restriction of Lebesgue measure to the-dimensional affine subspace of where the Gaussian distribution is supported, i. e..

Using Fibonacci numbers, he proved that when finding the greatest common divisor of integers a and b, the algorithm runs in no more than 5k steps, where k is the number of ( decimal ) digits of b. He also proved a special case of Fermat's last theorem.

Using Bayes ' theorem, we write

Using Noether's theorem, the types of Lagrangians that conserve X through a continuous symmetry may be determined, and their fitness judged by further criteria.

Using the fundamental theorem of calculus often requires finding an antiderivative.

Using the Pythagorean theorem twice, b < sup > 2 </ sup > =

Using Dirichlet's theorem on primes in arithmetic progressions, the law of quadratic reciprocity, and the Chinese remainder theorem ( CRT ) it is easy to see that for any M > 0 there are primes p such that the numbers 1, 2, …, M are all residues modulo p.

Using Gauss's theorem and Poisson's equation gives

Using the close correspondence between divisors and holomorphic line bundles on a Riemann surface, the theorem can also be stated in a different, yet equivalent way: let L be a holomorphic line bundle on X.

Using topological cobordism and K-homology one may provide a full statement of an index theorem on quasiconformal manifolds ( see page 678 of ).

Using the compactness theorem, the resulting theory is easily seen to be consistent.

This theorem was never published by Desargues ( 1591 – 1661 ), but appeared in an appendix entitled Universal Method of M. Desargues for Using Perspective ( Maniére universelle de M. Desargues pour practiquer la perspective ) of a practical book on the use of perspective published in 1648 by his friend and pupil Abraham Bosse ( 1602 – 1676 ).

Using the theorem we can treat every abelian category as if it is the category of R-modules concerning theorems about existence of morphisms in a diagram and commutativity and exactness of diagrams.

Using Bloch's theorem, we only need to find a solution for a single period, make sure it is continuous and smooth, and to make sure the function u ( x ) is also continuous and smooth.

Using case 3 of the master theorem ( with ε = 1 and c = 2 / 3 ), we know that T ( n ) = Θ ( n ).

Using a theorem of Schwartz on compact operators in Frechet spaces, Cartan and Serre proved that compact complex manifolds have the property that their sheaf cohomology for any coherent sheaf consists of vector spaces of finite dimension.

Using Taylor's theorem,

Using the Riesz representation theorem, one can show that there exists a unique continuous linear operator