functions as real combinations of spherical harmonics Y < sub > lm </ sub >( θ, φ ) ( where l and m are quantum numbers ).

On the plane the most common alternative is polar coordinates, where every point is represented by its radius r from the origin and its angle θ.

where θ < sub > r, p </ sub > is the angle between r and p measured from r to p ; an important distinction because without it, the sign of the cross product would be meaningless.

where θ ∈ T < sub > f ( x )</ sub >< sup >*</ sup > N and X < sub > x </ sub > ∈ T < sub > x </ sub > M.

Consistent with the symmetry of the hyperbola, if the transverse axis is aligned with the x-axis of a Cartesian coordinate system, the slopes of the asymptotes are equal in magnitude but opposite in sign, ±, where b = a × tan ( θ ) and where θ is the angle between the transverse axis and either asymptote.

The contact angle, θ < sub > C </ sub >, is the angle formed by a liquid at the three-phase boundary where the liquid, gas, and solid intersect.

: where E is the energy, τ is magnitude of the torque, and θ is the angle moved ( in radians ).

where μ is the location parameter, θ represents additional parameters, and is a function of the additional parameters.

: where θ is the angle of inclination of the normal, and p is the length of the normal.

where A and θ < sub > 0 </ sub > are arbitrary constants.

where θ < sub > 1 </ sub > and θ < sub > 2 </ sub > are the angles of incidence of a ray crossing the interface between two media with refractive indices n < sub > 1 </ sub > and n < sub > 2 </ sub >.

where R is the distance to the particle, θ is the scattering angle, n is the refractive index of the particle, and d is the diameter of the particle.

The standard convention ( r, θ, φ ) conflicts with the usual notation for the two-dimensional polar coordinates, where θ is often used for the azimuth.

where r is the distance from the axis of rotation to the particle, F is the magnitude of the force applied, and θ is the angle between the position and force vectors.

where E is the energy, τ is magnitude of the torque, and θ is the angle moved ( in radians ).

where W is work, τ is torque, and θ < sub > 1 </ sub > and θ < sub > 2 </ sub > represent ( respectively ) the initial and final angular positions of the body.

where ( r, θ, φ ) correspond to a spherical coordinate system.

where the numerical aperture is defined as for θ being the half-angle of the cone of rays accepted by the microscope objective.

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.

The largest true alphabet where each letter is graphically independent is probably Georgian, with 41 letters.

The Catholic Encyclopedia ( 1909 ) called this confusion a " distortion of the true facts " and suggested that it arose because the " Liber Pontificalis ", which at this point may be registering a reliable tradition, says that this Felix built a church on the Via Aurelia, which is where the Roman martyr of an earlier date was buried.

gives the example of Groombridge 1830, where he estimates that the true position is displaced by approximately 3 arcminutes from the direction in which we observe it.

The book of Ruth portrays a perfect example of a true belief in the Creator God in that it propagates inclusion of all, even in the ancient world of the Israelites where separation is made obvious between Israelites and non-Israelites.

3-SAT can be further restricted to One-in-three 3SAT, where we ask if exactly one of the literals in each clause is true, rather than at least one.

The first true towns are sometimes considered to be large settlements where the inhabitants were no longer simply farmers of the surrounding area, but began to take on specialized occupations, and where trade, food storage and power was centralized.

For example, Australian left-wing " true believers " levelled it at supporters of the failed republic referendum of 1999 ( where the vote was split not along conventional party lines but very much along socio-economic divides, with the rich overwhelmingly supporting the change while the less well-off were opposed – a superficially bizarre pattern for a non-economic issue ).

Cultural imperialism is a term that is only used in discussions where cultural relativism and constructivism are generally taken as true.

Christian Science metaphysics teach that God is Spirit and cites the first chapter of Genesis as the true story of creation, where in the King James Bible, " man " is both " male and female ", created " in the image and likeness " of God.

In view of the success of her novels, particularly Jane Eyre, Charlotte was persuaded by her publisher to visit London occasionally, where she revealed her true identity and began to move in a more exalted social circle, becoming friends with Harriet Martineau and Elizabeth Gaskell, and acquainted with William Makepeace Thackeray and G. H. Lewes.

where he wrote that he had found " a true mathematical and mechanical form of all manner of Arches for Building.

The same is true of a simple suspension bridge or " catenary bridge ," where the roadway follows the cable.

This functional definition still holds true in North America, where two other sizeable groups, Unamended Christadelphians and the CGAF, are not received by most North American Amended ecclesias.

: Theorem ( A. Korselt 1899 ): A positive composite integer is a Carmichael number if and only if is square-free, and for all prime divisors of, it is true that ( where means that divides ).

A true duopoly ( from Greek duo δύο ( two ) + polein πωλεῖν ( to sell )) is a specific type of oligopoly where only two producers exist in one market.

Another significant development of EDuke32 in 2011 is true room over room ( TROR ), where sectors can be placed over other sectors, and can be seen at the same time.

If the panegyric detailing the ceremony implied that the true center of the Empire was not Rome, but where the Emperor sat ("... the capital of the Empire appeared to be there, where the two emperors met "), it simply echoed what had already been stated by the historian Herodian in the early third century: " Rome is where the emperor is ".

It cannot be said with certainty from where the megalithic culture of Korea originated, and therefore it is difficult to define its true cultural character.

These included criteria that the group maintains a myth or collective memory of their homeland ; they regard their ancestral homeland as their true home, to which they will eventually return ; being committed to the restoration or maintenance of that homeland ; and they relate " personally or vicariously " to the homeland to a point where it shapes their identity.

This caused many issues with incompatibility, where a true IBM-compatible third-party card ( designed for an 8 MHz or 4. 77 MHz bus ) might not work in a higher speed system ( or even worse, would work unreliably ).

The registered office of the SE designated in the statutes must be the place where it has its central administration, that is to say its true centre of operations.