Cohen ( 1992 ) suggests effect sizes for various indexes, including ƒ ( where 0. 1 is a small effect, 0. 25 is a medium effect and 0. 4 is a large effect ).

where is ƒ < nowiki >'</ nowiki > s Laplace transform.

Condition numbers can be defined for any function ƒ mapping its data from some domain ( e. g. an m-tuple of real numbers x ) into some codomain an n-tuple of real numbers ƒ ( x ), where both the domain and codomain are Banach spaces.

The condition number of ƒ at a point x ( specifically, its relative condition number ) is then defined to be the maximum ratio of the fractional change in ƒ ( x ) to any fractional change in x, in the limit where the change δx in x becomes infinitesimally small:

where is a norm on the domain / codomain of ƒ ( x ).

where J denotes the Jacobian matrix of partial derivatives of ƒ and is the induced norm on the matrix.

0 is the polynomial equation corresponding to P. The solutions of this equation are called the roots of the polynomial ; they are the zeroes of the function ƒ ( corresponding to the points where the graph of ƒ meets the x-axis ).

More formally, # P is the class of function problems of the form " compute ƒ ( x )," where ƒ is the number of accepting paths of a nondeterministic Turing machine running in polynomial time.

The relation between the tangent vectors defined earlier and derivations is as follows: if γ is a curve with tangent vector γ '( 0 ), then the corresponding derivation is D ( ƒ ) = ( ƒ ∘ γ )'( 0 ) ( where the derivative is taken in the ordinary sense, since ƒ ∘ γ is a function from (- 1, 1 ) to R ).

where ƒ: M → R is an element of C < sup >∞</ sup >( M ).

Since < ƒ, ƒ > ≥ 0, φ ( f * f ) ≥ 0 for all ƒ in L < sup > 2 </ sup >( m ), where ƒ * is pointwise conjugate of ƒ.

where ƒ < sub > i </ sub > is the fugacity of the vapor of and indicates reference state.

where ƒ is frequency and 0 < α < 2, with α usually close to 1.

Let ( M, g ) be a Riemannian manifold and ƒ: M < sup > m </ sup > → R < sup > n </ sup > a short C < sup >∞</ sup >- embedding ( or immersion ) into Euclidean space R < sup > n </ sup >, where n ≥ m + 1.

** More generally, Rademacher's theorem extends the differentiability result to Lipschitz mappings between Euclidean spaces: a Lipschitz map ƒ: U → R < sup > m </ sup >, where U is an open set in R < sup > n </ sup >, is almost everywhere differentiable.

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.

Eventually, the whole surface consists of smooth, surface energy | stable faces, where new atoms cannot as easily attach themselves.

Let M be a smooth manifold and let x be a point in M. Let I < sub > x </ sub > be the ideal of all functions in C < sup >∞</ sup >( M ) vanishing at x, and let I < sub > x </ sub >< sup > 2 </ sup > be the set of functions of the form, where f < sub > i </ sub >, g < sub > i </ sub > ∈ I < sub > x </ sub >.

The pregroove is molded into the top side of the polycarbonate disc, where the pits and lands would be molded if it were a pressed ( nonrecordable ) Red Book CD ; the bottom side, which faces the laser beam in the player or drive, is flat and smooth.

The qualitative properties of dynamical systems do not change under a smooth change of coordinates ( this is sometimes taken as a definition of qualitative ): a singular point of the vector field ( a point where v ( x ) = 0 ) will remain a singular point under smooth transformations ; a periodic orbit is a loop in phase space and smooth deformations of the phase space cannot alter it being a loop.

: from where will a sun come into the smooth heaven

The farrier then uses a rasp ( large file ), to smooth the edge where it meets the shoe and eliminate any sharp edges left from cutting off the nails.

Jaggies are stairlike lines that appear where there should be smooth straight lines or curves.

The space of smooth vector fields on a differentiable manifold M forms a Lie algebra, where the Lie bracket is defined to be the commutator of vector fields.

where u and r are suitably smooth functions of t, and L is the operator defined on the relevant function space, that transforms u into r. That kind of equation can be used to constrain the output function u in terms of the forcing function r. The transfer function, written as an operator, is the right inverse of L, since.

At the high-end, where one is willing to trade-off higher rendering times for increased image quality and precision, smooth surface representations such as Bézier patches, NURBS or Subdivision surfaces are used.

It is created by specifying each edge of the physical object where two mathematically continuous smooth surfaces meet, or by connecting an object's constituent vertices using straight lines or curves.

These paintings — especially the Hell panel — are painted in a comparatively sketchy manner which contrasts with the traditional Flemish style of paintings, where the smooth surface — achieved by the application of multiple transparent glazes — conceals the brushwork.

In some species in this category, for example E. youngiana and E. viminalis, the rough basal bark is very ribbony at the top, where it gives way to the smooth upper stems.

The regularity becomes evident when changing to another coordinate system ( such as the Kruskal coordinates ), where the metric is perfectly smooth.

A conical singularity occurs when there is a point where the limit of every diffeomorphism invariant quantity is finite, in which case spacetime is not smooth at the point of the limit itself.

Now the sign has turned into a smooth symbolic sign where the signer makes two touches on the chest, one on each side, with a sweep of the wrist in between.

" A smooth low hand is one where the remaining cards after the highest card are themselves very low ; a rough low hand is one where the remaining cards are high.

Thinking of curvature as a measure, rather than as a function, Descartes ' theorem is Gauss – Bonnet where the curvature is a discrete measure, and Gauss – Bonnet for measures generalizes both Gauss – Bonnet for smooth manifolds and Descartes ' theorem.

For example, a smooth curve α ( t ): 1 → M has tangent vector α ′( t < sub > 0 </ sub >) in the tangent space TM ( α ( t < sub > 0 </ sub >)) at any point t < sub > 0 </ sub > ∈ ( 0, 1 ), and each such vector has length ‖ α ′( t < sub > 0 </ sub >)‖, where ‖·‖ denotes the norm induced by the inner product on TM ( α ( t < sub > 0 </ sub >)).

In particular one could define Riemannian manifold as a metric space which is isometric to a smooth submanifold of R < sup > n </ sup > with the induced intrinsic metric, where isometry here is meant in the sense of preserving the length of curves.

Also in German, where marmalade is much less popular than jam anyway, Marmelade is the traditional designation for any kind of jam and marmalade ( especially smooth jam without visible pieces of fruit ) regardless of fruit base, and remains so in everyday language, in spite of EU regulation which, in official commercial usage, limits the term Marmelade to citrus-based preserves to minimise international confusion.

Also abrasion commonly happens in areas where there are strong winds, loose sand, and soft rocks. The blowing of millions of sharp sand grains creates a sandblasting effects. This effect helps to erode, smooth and polish rocks. The definition of abrasion is grinding and wearing away of rock surfaces through the mechanical action of other rock or sand particles.