In his scheme, three parallel stages were fired from lift-off, but all three engines were fueled from the outer two stages, until they are empty and could be ejected.

They were confident enough that this would be approved that they began repainting locomotives into a new unified paint scheme, including the letters SP or SF and an adjacent empty space for the other two ( as SPSF, the reverse order of the holding company ).

There were times when embalmers deviated from this scheme: during the 21st Dynasty they embalmed and wrapped the viscera and returned them to the body, while the Canopic jars remained empty symbols.

It remains a very difficult problem to describe these schemes explicitly, and there are few pairs of Chern numbers for which this has been done ( except when the scheme is empty ).

Even Julian's intellectual friends and fellow pagans were of a divided mind about this habit of talking to his subjects on an equal footing: Ammianus Marcellinus saw in that only the foolish vanity of someone " excessively anxious for empty distinction ", whose " desire for popularity often led him to converse with unworthy persons ".

The product of no factors at all is known as the empty product, and is equal to 1.

In particular, for a plane wave travelling through empty space, the wave impedance is equal to the impedance of free space.

In this case, the usual axiom of extensionality would then imply that every ur-element is equal to the empty set.

On occasions, an elder gives an empty soju shot glass ( usually his / hers ) to an equal or junior.

It is equal to the multiplicative identity 1, given that it exists for the multiplication operation in question, just as the empty sum — the result of adding no numbers — is zero, or the additive identity.

Using this property as definition, and extending this to the empty product, the right-hand side of this equation evaluates to b < sup > 0 </ sup > for the empty set, because the empty sum is defined to be zero, and therefore the empty product must equal one.

There are relations which are both symmetric and antisymmetric ( equality and its subrelations, including, vacuously, the empty relation ), there are relations which are neither symmetric nor antisymmetric ( the relation " divides " on the set ℤ ; the relation " preys on " in biological sciences ), there are relations which are symmetric and not antisymmetric ( congruence modulo n ), and there are relations which are not symmetric but are antisymmetric (" is less than or equal to ").

To reach from one square to another, only kings require the number of moves equal to the distance ; rooks, queens and bishops require one or two moves ( on an empty board, and assuming that the move is possible at all in the bishop's case ).

In particular, the rank of the empty set is zero, and every ordinal has a rank equal to itself.

Contemplate the five skandhas as originally empty and quiescent, non-arising, non-perishing, equal, without differentiation.

Only then does Death reveal that the Golden Globe is an empty instrument that needs to be powered by a life-force equal to that of the being who is to be restored.

The equal protection clause would indeed be a formula of empty words if such conspicuously artificial lines could be drawn.

If each Fourier mode of the equilibrium radiation in an otherwise empty cavity with perfectly reflective walls is considered as a degree of freedom capable of exchanging energy, then, according to the equipartition theorem of classical physics, there would be an equal amount of energy in each mode.

However, a string comparison function would indicate that all of these empty strings are equal to each other.

Some of his books of madrigals are in two versions: one for singing by equal voice parts, in the old Renaissance style, and another in what he calls the " empty " style, for single voice with instrumental accompaniment.

* At steady-state, the flow rate in must equal the mass flow rate out, otherwise the tank will overflow or go empty ( transient state ).

The difference between the full and empty weights is equal to the weight of the contents.

When scoring, it is important to note that although the number of moves remaining to a player is usually equal to the number of empty squares in the territories occupied by that player's amazons, it is nonetheless possible to have defective territories in which there are fewer moves left than there are empty squares.

When the ground assault began, the police academy was discovered to be empty of Jordanian troops, as they had taken shelter from the barrage in the bunker system of the hill, thereby enlarging the force defending the hill to one equal in size to the assault force rather than 1 / 3 of its size, as had been anticipated by Israeli Central Command.

If two numbers have no prime factors in common, their greatest common divisor is 1 ( obtained here as an instance of the empty product ), in other words they are coprime.

Following the normal convention for the empty product, The Legendre and Jacobi symbols are indistinguishable exactly when the lower argument is an odd prime, in which case they have the same value.

However, according to the book " France: 1815 – 2003 ", written by Martin Evans and Emmanuel Godwin, Raffarin was " a remarkably popular prime minister " despite his ability " to state the obvious and to make empty statements ".

More examples of the use of the empty product in mathematics may be found in the binomial theorem, factorial, fundamental theorem of arithmetic, birthday paradox, Stirling number, König's theorem, binomial type, difference operator, Pochhammer symbol, proof that e is irrational, prime factor, binomial series, and multiset.

The divisors of n are all products of some or all prime factors of n ( including the empty product 1 of no prime factors ).

This is much along the same lines of not considering 1 to be a prime number, an empty topological space to be connected, or the trivial group to be simple.

This is because it has no prime factors ; it is the empty product.

However, a number of prime ministers chose to live at Stormont House, the official residence of the Speaker of the House of Commons of Northern Ireland, which was empty as a number of speakers had chosen to live in their own homes.

The post was left empty until Abolhassan Banisadr became president in January 1980 and chose Mohammad Ali Rajai as his prime minister, mainly because of pressures imposed by Majlis representatives, specially those close to Islamic Republic Party.

For example, the spectrum of an element of a complex Banach algebra can never be empty, whereas in a real Banach algebra it could be empty for some elements.

a − λ1 is not invertible ( because the spectrum of a is not empty ) hence a = λ1: this algebra A is naturally isomorphic to C ( the complex case of the Gelfand-Mazur theorem ).

This insertion is possible because the spectrum of the monochrome TV signal is not continuous ( for most typical video content ), hence empty space exists which can be utilized.

Residual spectrum of a normal operator is empty.

If the spectrum were empty, then the resolvent function

The spectrum of an unbounded operator is in general a closed, possibly empty, subset of the complex plane.

The extra RDS subcarriers are placed in the upper empty part of the mpx spectrum and carry the extra data amount which can be used for arbitrary applications.

In the NMR spectrum of a dimethyl derivative, two nonequivalent signals are found for the two methyl groups indicating that the molecular conformation of this cation not perpendicular ( as in A ) but is bisected ( as in B ) with the empty p-orbital and the cyclopropyl ring system in the same plane:

The extra RDS subcarriers are placed in the upper empty part of the multiplex spectrum and carry the extra data payload.

* Spectrum sensing: Detecting unused spectrum and sharing it, without harmful interference to other users ; an important requirement of the cognitive-radio network to sense empty spectrum.

Detecting primary users is the most efficient way to detect empty spectrum.

The spectral theorem applies to self-adjoint operators and moreover, to normal operators, but not to densely defined, closed operators in general, since in this case the spectrum can be empty.