By choosing widely separated keys, one could employ one dimple as a ' shift ' key to allow both letters and numbers to be produced.

By conceiving a timeless setting — " a vanished age " — and by carefully choosing names that resembled human history, Howard shrewdly avoided the problem of historical anachronisms and the need for lengthy exposition.

By adopting the name Chung-cheng (" central uprightness "), he was choosing a name very similar to the name of Sun Yat-sen, who was ( and still is ) known among Chinese as Zhongshan ( 中山 — meaning " central mountain "), thus establishing a link between the two.

By the terms of the agreement, the election of bishops and abbots in Germany was to take place in the emperor's presence as judge between potentially disputing parties, free of bribes, thus retaining to the emperor a crucial role in choosing these great territorial magnates of the Empire.

By choosing the angle of bank to match the car's speed around the curve, the car seat transmits only a perpendicular force to the passengers, and the passengers no longer feel a need to lean nor feel a sideways push by the car seats or doors.

By 2000, almost no major vendor produced its own EDIF tools, choosing instead to OEM third-party tools.

The award is named for Alice B. Sheldon, who wrote under the pseudonym James Tiptree, Jr. By choosing a masculine nom de plume, having her stories accepted under that name and winning awards with them, Sheldon helped demonstrate that the division between male and female science fiction writing was illusory.

By choosing different values for the parameter m, the following types of means are obtained:

By choosing conditions such that ω =

By choosing an appropriate mapping, the analyst can transform the inconvenient geometry into a much more convenient one.

By choosing porous graphitic carbon as a stationary phase for liquid chromatography, even non derivatized glycans can be analyzed.

By the advice of the cacique Colocolo, the Araucanians united their efforts choosing as toqui ( general-in-chief ) the famous warrior Caupolicán.

By shifting between shadows, one can appear to alter reality by choosing which elements of which shadows to keep, and which to move between.

By choosing a, b, c, d in A appropriately, A can represent a variety of transformations such as rotations, scaling and reflections, shears, of a geometric shape in space.

By choosing Anthemius, Leo obtained three results: he sent a possible candidate to the Eastern throne far away ; he repulsed Gaiseric's attempt to put a puppet of his on the Western throne ; and he put a capable and proven general with a trained army in Italy, ready to fight the Vandals.

By choosing a mass of 0. 78 and an estimated inclination of 30 °, this yields the frequently cited value of Jupiter masses for the planet's mass.

By 1996, VH1 was heading down the same path as its sister channel, MTV, choosing to focus more on music-related shows than on music videos.

By choosing another basis, the Newton basis, we get a system of linear equations with a much simpler lower triangular matrix which can be solved faster.

By choosing another basis, the Lagrange basis, we get the much simpler identity matrix = δ < sub > i, j </ sub > which we can solve instantly: the Lagrange basis inverts the Vandermonde matrix.

By choosing any point as " origin ", the points are in one-to-one correspondence with the vectors, but there is no preferred choice for the origin ; thus this approach can be characterized as obtaining the affine space from its associated vector space by " forgetting " the origin ( zero vector ).

By choosing an origin,, one can thus identify with, hence turn into a vector space.

By choosing an appropriate length-scale, one can thus assume, without loss of generality, that K =- 1.

By the 1920s this was felt to be undemocratic and undesirable, so in 1933 the method of choosing members of the Council was changed by referendum.

By choosing different values of p, it is possible to trade search costs against storage costs.

* HBP = times Hit By a Pitch

The intersection of the periodic orbit with the Poincaré section is a fixed point of the Poincaré map F. By a translation, the point can be assumed to be at x = 0.

Let f and g be any two elements of G. By virtue of the definition of G, = and =, so that =.

By reversing the steps in the Euclidean algorithm, the GCD can be expressed as a sum of the two original numbers each multiplied by a positive or negative integer, e. g., 21 = × 105 + × 252.

By definition, a and b can be written as multiples of c: a = mc and b = nc, where m and n are natural numbers.

( By modern convention, the sequence begins with F < sub > 0 </ sub > = 0.

By setting K = ker ( f ) we immediately get the first isomorphism theorem.

By the age of eleven, Basquiat could fluently speak, read, and write French, Spanish, and English .< ref name = ARTINFO >

By this rule, the average number of days per year will be 365 + 1 / 4 − 1 / 100 + 1 / 400 = 365. 2425, which is 365 days, 5 hours, 49 minutes, and 12 seconds.

By convention, the carbon atoms are numbered from 1 to x along the backbone, starting from the end that is closest to the C =

By construction, d * e = 1 mod φ ( n ).

By then, the dates of the Early Stone Age, or Paleolithic, and Late Stone Age, or Neolithic ( neo = new ), were fairly solid and were regarded by Goodwin as absolute.

By contrast, a Cosmological Constant is static, with a fixed energy density and w < sub > q </ sub > = − 1.

By the rank-nullity theorem, a system of n vectors in k dimensions ( where all dimensions are necessary ) satisfies a ( p = n − k )- dimensional space of relations.

On the other hand, if T is written as a unary number ( a string of n ones, where n = T ), then it only takes time n. By writing T in unary rather than binary, we have reduced the obvious sequential algorithm from exponential time to linear time.

By the end of 1848, some 6, 000 Argonauts | archivedate = 2006-10-10

By replacing n with m / M, and subsequently introducing density ρ = m / V, we get:

By assuming that the satellite is spherical,, Q = 100, and it is sensible to guess one revolution every 12 hours in the initial non-locked state ( most asteroids have rotational periods between about 2 hours and about 2 days )

By associating the element a in G with the inner automorphism ƒ ( x ) = x < sup > a </ sup > in Inn ( G ) as above, one obtains an isomorphism between the quotient group G / Z ( G ) ( where Z ( G ) is the center of G ) and the inner automorphism group:

By Euler's rotation theorem, we may replace the vector with where is a 3x3 rotation matrix and is the position of the particle at some fixed point in time, say t = 0.

By the 3rd century ( during the Three Kingdoms Period ), the Chinese had termed the device as the ' jì lĭ gŭ chē ' ( 記里鼓車 ), or ' li-recording drum carriage ' ( Note: the modern measurement of li = 500 m / 1640 ft ).