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

It was built on a raised plateau overlooking the east bank of the river Strymon where it emerged from Lake Cercinitis, about 3 m. from the Aegean Sea.

), where heights of 1800 m to 2400 m ( 6000 to 8000 ft ) are reached.

where m is the slope of the line.

In Analytical Geometry a section of a line can be given by the formula where ( c, d )&( e, f ) are the endpoints of the line & m: n is the ratio of division

where m and n are nonnegative integers with, is the azimuthal angle in radians, and is the normalized radial distance.

where R < sub > i </ sub > is the position vector of particle i from the reference point, m < sub > i </ sub > is its mass, and V < sub > i </ sub > is its velocity.

where n > m > 0 are integers and p, q, and r are prime numbers, then 2 < sup > n </ sup >× p × q and 2 < sup > n </ sup >× r are a pair of amicable numbers.

Let ( m, n ) be a pair of amicable numbers with m < n, and write m = gM and n = gN where g is the greatest common divisor of m and n. If M and N are both coprime to g and square free then the pair ( m, n ) is said to be regular, otherwise it is called irregular or exotic.

For the case of a non-commutative base ring R and a right module M < sub > R </ sub > and a left module < sub > R </ sub > N, we can define a bilinear map, where T is an abelian group, such that for any n in N, is a group homomorphism, and for any m in M, is a group homomorphism too, and which also satisfies

* Every quadratic Bézier curve is also a cubic Bézier curve, and more generally, every degree n Bézier curve is also a degree m curve for any m > n. In detail, a degree n curve with control points P < sub > 0 </ sub >, …, P < sub > n </ sub > is equivalent ( including the parametrization ) to the degree n + 1 curve with control points P '< sub > 0 </ sub >, …, P '< sub > n + 1 </ sub >, where.

where α > − 1, δ < sub > m, n </ sub > is the Kronecker delta, and u < sub > α, m </ sub > is the m-th zero of J < sub > α </ sub >( x ).

This orthogonality relation can then be used to extract the coefficients in the Fourier – Bessel series, where a function is expanded in the basis of the functions J < sub > α </ sub >( x u < sub > α, m </ sub >) for fixed α and varying m.

For example, the cofinality of ω² is ω, because the sequence ω · m ( where m ranges over the natural numbers ) tends to ω² ; but, more generally, any countable limit ordinal has cofinality ω.

There are two forces ; one is the force of gravity vertically downward through the center of mass of the ball mg where m is the mass of the ball and g is the gravitational acceleration ; the second is the upward normal force exerted by the road perpendicular to the road surface ma < sub > n </ sub >.

where m is the mass of the molecule and v is its velocity.

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.

Chairman C. Richard Mears pointed out that perhaps this was not strictly a school board problem, in case of atomic attack, but that the board would cooperate so far as possible to get the children to where the parents wanted them to go.

The trial will be held, probably the first week of March, in the famous Old Bailey central criminal court where Klaus Fuchs, the naturalized British German born scientist who succeeded in giving American and British atomic bomb secrets to Russia and thereby changed world history during the 1950s, was sentenced to 14 years in prison.

Thus, the planetary model of the atom was discarded in favor of one that described atomic orbital zones around the nucleus where a given electron is most likely to be observed.

Thus the discovery report by the Berkeley group reads: " It is suggested that element 97 be given the name berkelium ( symbol Bk ) after the city of Berkeley in a manner similar to that used in naming its chemical homologue terbium ( atomic number 65 ) whose name was derived from the town of Ytterby, Sweden, where the rare earth minerals were first found.

The concept of reversed chirality also figured prominently in the plot of James Blish's Star Trek novel Spock Must Die !, where a transporter experiment gone awry ends up creating a duplicate Spock who turns out to be a perfect mirror-image of the original all the way down to the atomic level.

Interstitials can form ' split interstitial ' or ' dumbbell ' structures where two atoms effectively share an atomic site, resulting in neither atom actually occupying the site.

The concept of a database transaction ( or atomic transaction ) has evolved in order to enable both a well understood database system behavior in a faulty environment where crashes can happen any time, and recovery from a crash to a well understood database state.

Dubnium ( ), is a chemical element with the symbol Db and atomic number 105, named after the town of Dubna in Russia, where it was first produced.

The concept of a database transaction ( or atomic transaction ) has evolved in order to enable both a well understood database system behavior in a faulty environment where crashes can happen any time, and recovery from a crash to a well understood database state.

Erbium can form propeller-shaped atomic clusters Er < sub > 3 </ sub > N, where the distance between the erbium atoms is 0. 35 nm.

* In physics, nuclear fission is a process where a large atomic nucleus ( such as uranium ) is split into two smaller particles.

Unlike conventional microscopes, where the spatial resolution is limited by the wavelength of the particles which are used for imaging, the FIM is a projection type microscope with atomic resolution and an approximate magnification of a few million times.

where ' is the rest mass of the electron, and M is the mass of the atomic nucleus.

Before Moseley's discovery, the atomic numbers ( or elemental number ) of an element had been thought of as a semi-arbitrary sequential number, based on the sequence of atomic masses, but modified somewhat where chemists found this to be desirable, such as by the great Russian chemist, Dimitri Ivanovich Mendeleev.

It also became clear that such clauses could be restricted to definite clauses or Horn clauses, where < tt > H </ tt >, < tt > B < sub > 1 </ sub ></ tt >, …, < tt > B < sub > n </ sub ></ tt > are all atomic predicate logic formulae, and that SL-resolution could be restricted ( and generalised ) to LUSH or SLD-resolution.

An MRI scanner is a device in which the patient lies within a large, powerful magnet where the magnetic field is used to align the magnetization of some atomic nuclei in the body, and radio frequency fields to systematically alter the alignment of this magnetization.

where and are the molecular wavefunctions for the bonding and antibonding molecular orbitals, respectively, and are the atomic wavefunctions from atoms a and b, respectively, and and are adjustable coefficients.

Because the muon is a lepton, the atomic energy levels of muonium can be calculated with great precision from quantum electrodynamics ( QED ), unlike the case of hydrogen, where the precision is limited by uncertainies related to the internal structure of the proton.

Perfectly elastic " collisions " can occur when the objects do not touch each other, as for example in atomic or nuclear scattering where electric repulsion keeps them apart.

The Lindemann criterion states that melting occurs because of vibrational instability, e. g. crystals melt when the average amplitude of thermal vibrations of atoms is relatively high compared with interatomic distances, e. g. < δu < sup > 2 </ sup >> 1 / 2 > δ < sub > L </ sub > R < sub > s </ sub >, where δu is the atomic displacement, the Lindemann parameter δ < sub > L </ sub > ≈ 0. 20 ... 0. 25 and R < sub > s </ sub > is a half of the inter-atomic distance.

He next dropped behind German lines in occupied Norway, where he met with Free Norwegian guerrillas and gathered information leading to the destruction of a German plant being used to develop atomic weapons.

For instance, in a hydrogen Maser, the well-known " 21cm wave " transition in atomic hydrogen, where the lone electron flips its spin state from parallel to the nuclear spin to antiparallel, can be used to create a population inversion because the parallel state has a magnetic moment and the antiparallel state does not.

He was one of the atomic scientists who attended the famous Multan meeting in 1972 where he has privileged to meet personally with Prime Minister Zulfikar Ali Bhutto.

In 1976, he joined hands with another nuclear scientist, Dr. Abdul Qadeer Khan on the atomic weapon project, where he tried working on the centrifuge programme.