If the exponent r is even, then the inequality is valid for all real numbers x.

The statistical scale-invariance implies that the scaling of velocity increments should occur with a unique scaling exponent, so that when r is scaled by a factor,

In particular, any prime larger than can enter at most once in this decomposition ( that is, with an exponent r = 1 ).

The exponent is r / q when ( α, β ) is on the line and higher when it is above and to the right.

( We put the " r " in brackets to avoid confusion with an exponent.

A traditional RSA signature is computed by raising the message m to the secret exponent d modulo the public modulus N. The blind version uses a random value r, such that r is relatively prime to N ( i. e. gcd ( r, N )

In this case it happens to be that this is the rth coefficient but, it is possible for the lowest possible exponent to be r − 2, r − 1 or, something else depending on the given differential equation.

Finally, it can be noted that Carl Gustav Jung can be seen as an exponent of esotericism: his writings concern esoteric subject matter such as alchemy, and rephrased the concept of correspondences in a modern, psychologizing terminology in his theory of synchronicity.

Since the inverse DFT is the same as the DFT, but with the opposite sign in the exponent and a 1 / N factor, any FFT algorithm can easily be adapted for it.

If p is a non-zero real number, we can define the generalized mean with exponent p ( or power mean with exponent p ) of the positive real numbers as:

The definition in general is somewhat technical, but in the case of real matrix groups, it can be formulated via the exponential map, or the matrix exponent.

The equivalence of power laws with a particular scaling exponent can have a deeper origin in the dynamical processes that generate the power-law relation.

For positive a, the principal square root can also be written in exponent notation, as a < sup > 1 / 2 </ sup >.

In the study of wireless communications, path loss can be represented by the path loss exponent, whose value is normally in the range of 2 to 4 ( where 2 is for propagation in free space, 4 is for relatively lossy environments and for the case of full specular reflection from the earth surface — the so-called flat-earth model ).

In some environments, such as buildings, stadiums and other indoor environments, the path loss exponent can reach values in the range of 4 to 6.

One may observe that the above computation can be repeated plainly in more general settings than: a generalization of the Lagrange inversion formula is already available working in the-modules, where is a complex exponent.

The origins of Celtic metal can be traced to the earliest known exponent of folk metal, the English band Skyclad.

In binary floating-point arithmetic, division by two can be performed by decreasing the exponent by one ( as long as the result is not a subnormal number ).

Or an exponent of a weak form of solipsism might say that harming others is imprudent because the solipsist can only be uncertain of their real existence rather than certain of their non-existence.

Exponentiation is a mathematical operation, written as b < sup > n </ sup >, involving two numbers, the base b and the exponent ( or index or power ) n. When n is a positive integer, exponentiation corresponds to repeated multiplication ; in other words, a product of n factors, each of which is equal to b ( the product itself can also be called power ):

The exponentiation b < sup > n </ sup > can be read as: b raised to the n-th power, b raised to the power of n, or b raised by the exponent of n, most briefly as b to the n. Some exponents have their own pronunciation: for example, b < sup > 2 </ sup > is usually read as b squared and b < sup > 3 </ sup > as b cubed.

In a denormal number, since the exponent is the least that it can be, zero is the lead significand digit ( 0. m < sub > 1 </ sub > m < sub > 2 </ sub > m < sub > 3 </ sub >... m < sub > p-2 </ sub > m < sub > p-1 </ sub >) in order to represent numbers closer to zero than the smallest normal number.

One can prove that the power rule is valid for any exponent, that is

Thus if G is any finitely generated group of exponent n, then G a homomorphic image of B ( m, n ), where m is the number of generators of G. Burnside's problem can now be restated as follows:

: If it is known that a group G with m generators and exponent n is finite, can one conclude that the order of G is bounded by some constant depending only on m and n?

This variant of the Burnside problem can also be stated in terms of certain universal groups with m generators and exponent n. By basic results of group theory, the intersection of two subgroups of finite index in any group is itself a subgroup of finite index.

The maximal Lyapunov exponent can be defined as follows:

Similarly k = g < sup >– p </ sup > ( mod N ) for any non-zero index k and for a unique p in 0 ,..., N – 2, where the negative exponent denotes the multiplicative inverse of g < sup > p </ sup > modulo N. That means that we can rewrite the DFT using these new indices p and q as:

Under ideal ( adiabatic ) conditions, the exponent would be 1. 4, but a lower value, generally between 1. 2 and 1. 3 is used, since the amount of heat lost will vary among engines based on design, size and materials used, but provides useful results for purposes of comparison.

* " Treacherous Ruhi Afnan, not content with previous disobedience, correspondence with Mirza Ahmad Sohrab, contact with old Covenant-breakers, sale, in conjunction with other members of family, of sacred property purchased by Founder of Faith, and allowing his sister to marry son of ` Abdu ' l-Bahá's enemy, is now openly lecturing on Bahá ' í movement, claiming to be its exponent and is misrepresenting the teachings and deliberately causing confusion in minds of authorities and the local population.

The major exponent of esotericism in the latter part of the 19th century is the Theosophy of H. P. Blavatsky, not to be confused with the Christian Theosophy mentioned above.

The book proved to be an enormous success and established Wyndham as an important exponent of science fiction.

Some definitions of Mersenne numbers require that the exponent p be prime, since the associated number must be composite if p is composite.

A basic theorem about Mersenne numbers states that in order for M < sub > p </ sub > to be a Mersenne prime, the exponent p itself must be a prime number.

In its most common usage, the amount being scaled is 10 and the scale is the ( base 10 ) exponent being applied to this amount ( therefore, to be an order of magnitude greater is to be 10 times as large ).

Structuralism was a broad philosophical movement that developed particularly in France in the 1950s, partly in response to French Existentialism, but is considered by many to be an exponent of High-Modernism, though its categorization as either a Modernist or Postmodernist trend is contested.

If anything, if a part of objective reality, theorization and systemization to Post-structuralists was an exponent of larger, more nebulous patterns of control in social orders – patterns that could not be encapsulated in theory without simultaneously conditioning it.

Thus a is considered to be a parameter: it is less variable than the variable x or y, but it is not an explicit constant like the exponent 2.

The public key consists of the modulus n and the public ( or encryption ) exponent e. The private key consists of the modulus n and the private ( or decryption ) exponent d which must be kept secret.

" Talking bullshit " is thus a lesser form of lying, and is likely to elicit a correspondingly weaker emotional response: whereas an obvious liar may be greeted with derision, outrage, or anger, an exponent of bullshit tends to be dismissed with an indifferent sneer.

Decimal prefixes are a characteristic of the metric system ; conversions between units of different magnitudes is accomplished by shifting the decimal point or changing an exponent ; for example, the speed of light may be expressed as km / s or.