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where μ is the Möbius function and the sums extend over all positive divisors d of n. In effect, the original f ( n ) can be determined given g ( n ) by using the inversion formula.
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where and μ
where μ < sub > i </ sub > is the chemical potential per particle for an i-type particle, and N < sub > i </ sub > is the number of such particles.
where the index i denotes the ith species, c is the concentration ( mol / m < sup > 3 </ sub >), R is the universal gas constant ( J /( K mol )), T is the absolute temperature ( K ), and μ is the chemical potential ( J / mol ).
where μ < sub > 4 </ sub > is the fourth moment about the mean and σ is the standard deviation.
where μ is the location parameter, θ represents additional parameters, and is a function of the additional parameters.
The theorem follows because * is ( commutative and ) associative, and 1 * μ = i, where i is the identity function for the Dirichlet convolution, taking values i ( 1 )= 1, i ( n )= 0 for all n > 1.
If μ is not a positive measure, then N is μ-null if N is | μ |- null, where | μ | is the total variation of μ ; equivalently, if every measurable subset A of N satisfies μ ( A )
where a sum over μ is performed according to the rules of Einstein notation.
where μ < sub > 3 </ sub > is the third moment about the mean μ, σ is the standard deviation, and E is the expectation operator.
The positive integer n is square-free if and only if μ ( n ) ≠ 0, where μ denotes the Möbius function.
The throughput can be analyzed mathematically by means of queueing theory, where the load in packets per time unit is denoted arrival rate λ, and the throughput in packets per time unit is denoted departure rate μ.
where μ < sub > α </ sub > and μ < sub > δ </ sub > are the components of proper motion in the R. A. and Declination, respectively, and δ is the Declination.
where the linear density μ is the mass per unit length of the string.
where μ < sub > i </ sub > is the chemical potential for the i-th component in the system.
where a is the semi-major axis, P is the orbital period, and μ is the geocentric gravitational constant, equal to approximately 398600. 4418 km < sup > 3 </ sup >/ s < sup > 2 </ sup >.
In this case the solutions are elliptically polarized electromagnetic waves with phase velocities ( where μ is the magnetic permeability ).
where μ = 255 ( 8 bits ) in the North American and Japanese standards.
where λ ' is the critical failure rate ( λ without the tick is the total failure rate ) and μ ' is the critical repair rate ( rate at which critical failures are repaired ).
where and is
But California is where we're goin ''.
He thought of the jungles below him, and of the wild, strange, untracked beauty there and he promised himself that someday he would return, on foot perhaps, to hunt in this last corner of the world where man is sometimes himself the hunted, and animals the lords.
Now I wish to enter the American market, where the competition is very strong.
from downstream, where the water level is much lower, it is a high, elaborately facaded pavilion.
The answers derived by these means may determine not only the temporal organization of the dance but also its spatial design, special slips designating the location on the stage where the movement is to be performed.
Even in domains where detailed and predictive understanding is still lacking, but where some explanations are possible, as with lightning and weather and earthquakes, the appropriate kind of human action has been more adequately indicated.
Robert Penn Warren puts it this way in `` Brother To Dragons '': `` The recognition of complicity is the beginning of innocence '', where innocence, I think, means about the same thing as redemption.
A dominant motive is the poet's longing for his homeland and its boyhood associations: `` Not men-folk, but the fields where I would stray, The stones where as a child I used to play ''.
In a society where everything is for sale, Marlowe is the only man who cannot be bought.
This is done for simplicity of commands and to bring the hidden redundancy up to where misunderstanding has almost zero possibility.
As to benefits to employees, it is notorious for its callous disregard except where it depends on them for services.
`` The Moral Creed '' and `` The Will To Risk '' live happily together, if we do not examine where the line is to be drawn.
Since the slogans have little application to reality and are sanctimonious to boot, the applause is faint even in areas of the world where we should expect to find the greatest affection for free government.
Ptolemy's problem is to forecast where, against the inverted bowl of night, some particular light will be found at future times.
She was exposing herself to temptation which it is best to avoid where it can consistently be done.
Such performance is a great tribute to American scientists and engineers, who in the past five years have had to telescope time and technology to develop these long-range ballistic missiles, where America had none before.
but it is perennially restructured in situations where anchors are dragged or lost.
`` History has this in common with every other science: that the historian is not allowed to claim any single piece of knowledge, except where he can justify his claim by exhibiting to himself in the first place, and secondly to any one else who is both able and willing to follow his demonstration, the grounds upon which it is based.
Finally we may note that the idea appears in educational theory where its influence is at present widespread.
where and Möbius
The diagonal of the square ( the points ( x, x ) where both coordinates agree ) becomes the boundary of the Möbius strip, and carries an orbifold structure, which geometrically corresponds to " reflection " – geodesics ( straight lines ) in the Möbius strip reflect off the edge back into the strip.
where μ is the Möbius function.
( where μ is the Möbius function and x is half the total of prime factors ), while for the former
This study became widely accessible through the Poincaré disc model where motions are given by Möbius transformations.
where μ ( k ) is the Möbius function, then the Mertens conjecture is that for all n > 1,
where μ ( n ) is the Möbius function.
where μ is the classic Möbius function.
where is the classic Möbius function.
where μ ( k ) is the Möbius function.
Because the Möbius function only takes the values − 1, 0, and + 1, the Mertens function moves slowly and there is no n such that | M ( n )| > n. The Mertens conjecture went further, stating that there would be no n where the absolute value of the Mertens function exceeds the square root of n. The Mertens conjecture was proven false in 1985 by Andrew Odlyzko and Herman te Riele.
where μ is the Möbius function.
* Futurama: on the episode Möbius Dick, where the aircraft tail, which couldn't be initially found in Lost, is shown to be placed in the fictional Bermuda Tetrahedron.
Shaped like a huge Möbius strip and patterned like pink-and-blue graph paper, this is where Bing and Bong solve problems involving arithmetic, logic and geometry.
Let g be a fuzzy measure, the Möbius representation of g is given by the set function M, where for every,
In 1888 Möbius became the director of the Zoological Collections of the Museum für Naturkunde in Berlin, and Professor of Systematic and Geographical Zoology at the Kaiser Wilhelm University, Berlin, where he taught until he retired in 1905, at the age of 80.
where A is a set of integers, P is a product of distinct primes, is the Möbius function, and is the set of integers in A divisible by d, and S ( A, P ) is defined to be:
0.187 seconds.