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Alternatively and corresponding
Alternatively, one may say that the predicted values corresponding to the above model, namely
: Alternatively we multiply by an orthogonal matrix with determinant − 1 ( corresponding to a reflection in a line through the origin ), followed by a translation.
Alternatively, the 162 cards could be three regular decks of playing cards, including the jokers, with ace to queen corresponding to 1 to 12 and the kings and jokers corresponding to the SKIP-BO cards.

Alternatively and map
Alternatively, a Jordan curve is the image of a continuous map φ: → R < sup > 2 </ sup > such that φ ( 0 ) = φ ( 1 ) and the restriction of φ to
Alternatively we can define the subspace topology for a subset of as the coarsest topology for which the inclusion map
Alternatively one can consider the set of homomorphisms onto the two element Boolean algebra and form complexes by associating each element of the Boolean algebra with the set of such homomorphisms that map it to the top element.
Alternatively one can define the Grothendieck group using a similar universal property: An abelian group G together with a mapping is called the Grothendieck group of iff every " additive " map from into an abelian group X (" additive " in the above sense, i. e. for every exact sequence we have ) factors uniquely through φ.

Alternatively and T
e. Alternatively, T is also injective since, if g * x = g * x implies g = g ' ( by post-multiplying with the inverse of x, which exists because G is a group ).
Alternatively, the development of " T " budding now permits the grafting of a different grape variety onto existing rootstock in the vineyard, making it possible to switch varieties within a two year period.
Alternatively, it has been suggested that they should be considered subspecies of T. maximus, but they differ in structure, voice and the appearance of the eye-ring.
Alternatively, an inker may do the basic layout of the page, give the work to another artist to do more detailed pencil work, and then ink the page himself ( as Joe Simon often did when inking Jack Kirby, or when Michael T. Gilbert collaborated with penciller P. Craig Russell on the Elric of Melniboné series ).
" Alternatively, a reconstructed Altaic etymology from * T ` aŋgiri (" oath " or " god ") would emphasize the god's divinity rather than his domain over the sky.
Alternatively, Walter Schuck-who followed the R / T exchange over the loudspeaker in the ops room-recalled Ehrler's last words as: " Theo, Heinrich here.
Alternatively the term fax server is sometimes used to describe a program that enables a computer to send and receive fax messages, set of software running on a server computer which is equipped with one or more fax-capable modems ( or dedicated fax boards ) attached to telephone lines or, more recently, software modem emulators which use T. 38 (" Fax over IP ") technology to transmit the signal over an IP network.

Alternatively and <
Alternatively a therm is used representing 100, 000 or 10 < sup > 5 </ sup > Btu, and a quad as 10 < sup > 15 </ sup > Btu.
( Alternatively, for a preorder "", a relation "<" can be defined as a < b if and only if ( a b and a ≠ b ).
Alternatively, it follows from () that if the polar coordinates of the point p are ( r < sub > 1 </ sub >, θ < sub > 1 </ sub >) and those of q are ( r < sub > 2 </ sub >, θ < sub > 2 </ sub >), then the distance between the points is
Alternatively, an analytic function is an infinitely differentiable function such that the Taylor series at any point x < sub > 0 </ sub > in its domain
Alternatively, the mother may prefer to be known as " The Dowager Lady < Bloggs >".
Alternatively, linear independence can be directly defined as follows: a set of vectors is linearly independent if and only if the only representations of the zero vector as linear combinations of its elements are trivial solutions, i. e., whenever a < sub > 1 </ sub >, a < sub > 2 </ sub >, ..., a < sub > n </ sub > are scalars such that
Alternatively a dilute solution of ammonium fluoride ( NH < sub > 4 </ sub > F ) can be used.
Alternatively, the energy source can be another chemical gradient already in place, as in the Ca < sup > 2 +</ sup >/ Na < sup >+</ sup > antiporter.
Alternatively, the right-hand side expression can be justified by multiplying the power series on the left by 1 − x, and checking that the result is the constant power series 1, in other words that all coefficients except the one of x < sup > 0 </ sup > vanish.
Alternatively, some materials with the formula MTiO < sub > 3 </ sub > crystallize in the motif known as Perovskite ( structure ), which is also the name of the mineral form of calcium titanate ( CaTiO < sub > 3 </ sub >).
Alternatively in terms of free current, the line integral of the magnetic H-field ( in ampere per metre, Am < sup >− 1 </ sup >) around closed curve C equals the free current I < sub > f, enc </ sub > through a surface S:
Alternatively, one can work entirely in a local coordinate system ( x < sup > 1 </ sup >, ..., x < sup > n </ sup >).
Alternatively, if f < sub > r </ sub > is reduced by a factor of 40 to compensate, it becomes 312. 5 Hz, which is much too low to give good filtering and lock performance characteristics.
Alternatively, an uncountable cardinal κ is supercompact if for every A such that | A | ≥ κ there exists a normal measure over < sup >< κ </ sup >.

Alternatively and sup
Alternatively, they can all be divided out at once: for example the linear factors x – r and x – s can be multiplied together to obtain the quadratic factor x < sup > 2 </ sup >( r + s ) x + rs, which can then be divided into the original polynomial P ( x ) to obtain a quotient of degree n – 2.

Alternatively and >
Alternatively, 5 ml from a neutron star of radius 20 km radius ( average density ) has a mass of about 400 million metric tons, or about the mass of all humans .</ ref > The resulting force of gravity is so strong that if an object were to fall from a height of one meter it would only take one microsecond to hit the surface of the neutron star, and would do so at around 2000 kilometers per second, or 7. 2 million kilometers per hour.

Alternatively and 2
Alternatively, the clinic may stop dosage at 80 mg, then allow the patient to move up by 5 mg or 10 mg every 2 or 3 days, until they are free from withdrawal symptoms and intense cravings.
Alternatively, it can be defined in terms of the Euler characteristic χ, via the relationship χ = 2 − 2g for closed surfaces, where g is the genus.
Alternatively, it can be defined for a closed surface in terms of the Euler characteristic χ, via the relationship χ = 2 − k, where k is the non-orientable genus.
Alternatively, the word chance could be used as in: " the chance of picking a blue marble is 2 in 15 ".
Alternatively Person 2 can redefine X in way that instead concludes all things are not X.
Alternatively, dividing the votes numbers by 0. 33, 1. 33, 2. 33, 3. 33 etc.
Alternatively, a graph is outerplanar if and only if it does not contain K < sub > 4 </ sub > or K < sub > 2, 3 </ sub > as a minor, a graph obtained from it by deleting and contracting edges.
Alternatively, the 7 points of the plane correspond to the 7 non-identity elements of the group ( Z < sub > 2 </ sub >)< sup > 3 </ sup > = Z < sub > 2 </ sub > × Z < sub > 2 </ sub > × Z < sub > 2 </ sub >.
Alternatively, as for the magnitude of the term is less than 1 / 2, is the closest integer to or, equivalently, the integer part of, also written as.
Alternatively, it has enough output to drive up to 2 standard integrated circuit RTL " buffers ", each of which can drive up to 25 other standard RTL NOR gates.

Alternatively and </
Alternatively, if the mail user agent supports it, < tt > sa-learn </ tt > can be called for individual emails.
Alternatively, the quantum group U < sub > q </ sub >( G ) can be regarded as an algebra over the field C ( q ), the field of all rational functions of an indeterminate q over C.

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