* The rational numbers, expressed as the quotient of two integers a and b, b not equal to zero, satisfy the above definition because is the root of.

Prisms and antiprisms, whose symmetry groups are the dihedral groups, are generally not considered to be Archimedean solids, despite meeting the above definition.

In fact anode polarity depends on the device type, and sometimes even in which mode it operates, as per the above electric current direction-based universal definition.

From the above, it is possible to reformulate the definition to either of the following:

There is a larger class of number-theoretic functions that do not fit the above definition, e. g. the prime-counting functions.

According to the definition above, two relations with the same graph may be different, if they differ in the sets and.

Because this range of non-zero amplitude may be very broad or infinite, this definition is typically relaxed so that the bandwidth is defined as the range of frequencies in which the signal's spectral density is above a certain threshold relative to its maximum.

Although sometimes referred to as a coalition government, according to the definition above, it was not.

The above definition imposes no constraints on η ( 0 ), even though it is assumed that η ( k ) tends to zero as k tends to zero.

Because the above expression is equal to the difference, by the definition of the derivative is differentiable at a and its derivative is f ′( g ( a )) g ′( a ).

In practice, the above definition is rarely used because in virtually all cases, the curl operator can be applied using some set of curvilinear coordinates, for which simpler representations have been derived.

The informal definition above is subject to a rounding problem called the table-maker's dilemma whereas the modern definition is not.

First, State coercion may very easily be arbitrary – indeed technically very specific, according to the above definition.

Given the definition of above, we might fix ( or ' bind ') the first argument, producing a function of type.

The above definition of the commutator is used by some group theorists.

A nominal definition is the definition explaining what a word means, i. e. which says what the ' nominal essence ' is, and is definition in the classical sense as given above.

The four definitions given above are special cases of a more general definition.

Famine is classified by Rummel as democide if it fits the definition above.

In this case the definition above has no explicit instructions, so in both languages access to the slots and methods is considered, meaning they can be used only by subclasses.

In addition to the definition above, there is an equivalent definition.

If < math > c ^ 2 < 4km </ math > there are two complex conjugate roots a ± ib, and the solution ( with the above boundary conditions ) will look like this:

If pH is above the pKa value, the concentration of the conjugate base is greater than the concentration of the acid, and the color associated with the conjugate base dominates.

One example of this notion is the conjugate transpose operation of complex matrices defined above.

As above, let f and g denote measurable real-or complex-valued functions defined on S. If || fg ||< sub > 1 </ sup > is finite, then the products of f with g and its complex conjugate function, respectively, are μ-integrable, the estimates

Notice that the set of natural variables for the above four potentials are formed from every combination of the T-S and P-V variables, excluding any pairs of conjugate variables.

The above expression yields the poles of the gain G. For each complex pole, there is another which is the complex conjugate, and for each conjugate pair there are two more that are the negatives of the pair.

* U < sub > 3 </ sub >( 5 ): 2 – conjugate to class above in HS: 2

* M < sub > 11 </ sub > – conjugate to class above in HS: 2

The conjugate spinor plays a role similar to that of θ < sup >*</ sup > in the superspace R < sup > 1 | 2 </ sup >, except that the Majorana condition, as manifested in the above equation, imposes that θ and θ < sup >*</ sup > are not independent.

The above expression of the first law in terms of entropy change defines the conjugate variables of and, which are and and are intensive quantities analogous to potential energies ; their gradients of are called thermodynamic forces as they cause flows of the corresponding extensive variables as expressed in the following equations.

For example, in the example above, let the likelihood be a Poisson distribution, and let the prior now be specified by the conjugate prior, which is a Gamma distribution () ( where ):

The above algorithm gives the most straightforward explanation of the conjugate gradient method.

The above formulation is equivalent to applying the conjugate gradient method without preconditioning to the system

b < sup > q </ sup >/ q with q such that 1 / p + 1 / q = 1, and thus Young's inequality for conjugate Hölder exponents mentioned above is a special case.

The definition of the complex molecular multipole moment given above is the complex conjugate of the definition given in this article, which follows the definition of the standard textbook on classical electrodynamics by Jackson, except for the normalization.

There was an artificial lake just out of sight in the first stand of trees, fed by a half dozen springs that popped out of the ground above the hillside orchard.

only the counter at one end was lighted by a long fluorescent tube suspended directly above it.

By now Harmony could see that most of the adults in the train were winded and resting, or else siphoned off from the games by the challenging lure of the great cliff towering above them.

Beyond the two basic tasks mentioned above, no attention was paid by statesman or scholar to an idea of state responsibility, either internally or externally.

In both the farmer's tale in Ralph Ellison's Invisible Man and in Thomas Mann's The Holy Sinner, the incest hero rises above the myth by accepting the wish as motive ; ;

The Negro composer Hall Johnson studied the American-Negro Suite and said of it, `` Of all the many songs written by white composers and employing what claims to be a Negroid idiom in both words and music, these six songs by Harold Arlen and Ted Koehler easily stand far out above the rest.

This is what was meant, above, by describing history as inferential.

`` Tact '', by its very derivation, implies that its possessor keeps in touch with other people, but the author of Clericis Laicos and Unam Sanctam, the wielder of the two swords, the papal sun of which the imperial moon was but a dim reflection, the peer of Caesar and vice-regent of Christ, was so high above other human beings that he had forgotten what they were like.

The credit provdied by the first two services in the system outlined above is primarily for general agricultural purposes.

recommend to the Congress from time to time authorization for construction and operation, or for participation in the construction and operation, of a demonstration plant for any process which he determines, on the basis of subsections ( A ) and ( B ) above, has great promise of accomplishing the purposes of this Act, such recommendation to be accompanied by a report on the size, location, and cost of the proposed plant and the engineering and economic details with respect thereto ; ;

This work gave a heat of formation of aluminum fluoride which closely substantiates a value which had been determined by a less direct method, and raises this property to 15 percent above that accepted a few years ago.

Determine the ratio of 50% to the average per capita income of the U. S. ( Divide 50 by the result obtained in item 2 above.

( Multiply the result obtained in item 3 above by the result obtained for each State in item 1 above.

In all other States it is the difference obtained by subtracting from 100 the result obtained in item 4 above ; ;

( Multiply result obtained in item 7 above, by result obtained in item 6 above.

( Divide the amount being allotted by the result obtained in item 9 above.

( Multiply the State product in item 8 above by the result obtained in item 10 above.

The funds recouped by reductions in item 12 above are used: first, to increase the unadjusted allotments to the specified minimum in those States where the unadjusted allotment is less than the minimum allotment ( item 13 above ) ; ;

( Divide 40 by the amount used in item 2 above.

( Multiply the result obtained in item 3 above by the amount used for each State in item 1 above.