Multiplying the result by the number of cylinders in the engine gives the engine's total displacement.

This number can be seen as equal to the one of the first definition, independently of any of the formulas below to compute it: if in each of the n factors of the power one temporarily labels the term X with an index i ( running from 1 to n ), then each subset of k indices gives after expansion a contribution X < sup > k </ sup >, and the coefficient of that monomial in the result will be the number of such subsets.

This result gives individual synagogues, rabbis, and rabbinical schools discretion to adopt either approach.

If the transaction was a " good bargain " contract generally gives a better result for the claimant.

If the transaction were a " bad bargain ", tort gives a better result for the claimant.

Thus, the conservation of electric charge, as expressed by the continuity equation, gives the result:

The result gives the impression of a dialogue led by an expert.

Applying the completeness theorem to this result, gives the existence of a model of T where the formula C < sub > T </ sub > is false.

* A unary operation ( or function ) is idempotent if, whenever it is applied twice to any value, it gives the same result as if it were applied once ; i. e.,.

* A binary operation is idempotent if, whenever it is applied to two equal values, it gives that value as the result.

* Given a binary operation, an idempotent element ( or simply an idempotent ) for the operation is a value for which the operation, when given that value for both of its operands, gives the value as the result.

Expressed in words, adding a to b first, and then adding the result to c gives the same final result as adding a to the sum of b and c, a property known as associativity.

A mondegreen is the mishearing or misinterpretation of a phrase as a result of near-homophony, in a way that gives it a new meaning.

In this text, probably as a result of confusion, he gives instead of Mieszko's name the name of his son Bolesław:

In general the result of multiplying two measurements gives a result of a new type depending on the measurements.

This climate is influenced by the monsoons originating from the South Atlantic ocean, which is brought into the country by the ( maritime tropical ) MT airmass, a warm moist sea to land seasonal wind. Its warmth and high humidity gives it a strong tendency to ascend and produce copious rainfall, which is a result of the condensation of water vapour in the rapidly rising air.

The Big Bang hypothesis, by contrast, predicts that the CBR should have the same energy density as the binding energy density of the primordial helium, which is much greater than the binding energy density of the non-primordial elements ; so it gives almost the same result.

The United States Supreme Court has stated that where a court gives multiple reasons for a given result, each alternative reason that is " explicitly " labeled by the court as an " independent " ground for the decision is not treated as " simply a dictum.

" The passage does not give enough information to determine which cubit Pliny meant ; however, any cubit gives the same general result.

( In fact, subtracting 1 and dividing the result by 9 always gives a triangular number, the sequence starting with 3, 55, 903, 3727815, ....) This can be reformulated as follows: adding the digits of any even perfect number ( except 6 ), then adding the digits of the resulting number, and repeating this process until a single digit ( called the digital root ) is obtained, always produces the number 1.

The court uses the Dunnigan based legal standard to determine if an accused person, " estifying under oath or affirmation violates this section if she gives false testimony concerning a material matter with the willful intent to provide false testimony, rather than as a result of confusion, mistake, or faulty memory.

Thus, measuring a quantum state described by complex coefficients ( a, b ,..., h ) gives the classical probability distribution and we say that the quantum state " collapses " to a classical state as a result of making the measurement.

Zero intensity for each component gives the darkest color ( no light, considered the black ), and full intensity of each gives a white ; the quality of this white depends on the nature of the primary light sources, but if they are properly balanced, the result is a neutral white matching the system's white point.

Surface forces or contact forces, expressed as force per unit area, can act either on the bounding surface of the body, as a result of mechanical contact with other bodies, or on imaginary internal surfaces that bound portions of the body, as a result of the mechanical interaction between the parts of the body to either side of the surface ( Euler-Cauchy's stress principle ).

Covalent bonds often result in the formation of small collections of better-connected atoms called molecules, which in solids and liquids are bound to other molecules by forces that are often much weaker than the covalent bonds that hold the molecules internally together.

Thus, one nucleus offers a more tightly bound position to an electron than does another nucleus, with the result that one atom may transfer an electron to the other.

In the Prose Edda, additional information is given about Fenrir, including that, due to the gods ' knowledge of prophecies foretelling great trouble from Fenrir and his rapid growth, the gods bound him, and as a result Fenrir bit off the right hand of the god Týr.

At this point, the formation of an open cluster will depend on whether the newly formed stars are gravitationally bound to each other ; otherwise an unbound stellar association will result.

Indeed, even if the photoelectric effect is the favoured reaction for a particular single-photon bound-electron interaction, the result is also subject to statistical processes and is not guaranteed, albeit the photon has certainly disappeared and a bound electron has been excited ( usually K or L shell electrons at nuclear ( gamma ray ) energies ).

The result is a polyubiquitin chain that is bound by the proteasome, allowing it to degrade the tagged protein.

This represented a departure from their earlier insistence that they would not be bound by any such result.

He is bound to take no decision or action, which is put into effect under the color of his sovereignty, without that action being as a result of the counsel and advisement of his responsible ministers.

Labour stated that it would not be bound by this result were it returned to power in the following general election that year.

Hitler overruled him, arguing that such harsh terms were bound to be rejected by the French and that the French fleet would sail over to Britain to continue the struggle if confronted by such a demand ; as a result of the armistice of 21 June 1940, the Kriegsmarine was only allowed to take over the French Navy's bases on the Atlantic coast.

::( a ) shall not be bound in law to infer that he intended or foresaw a result of his actions by reasons only of its being a natural and probable consequence of those actions ; but

By the result of the previous paragraph, the limit function is also Lipschitz, with the same bound for the Lipschitz constant.

--- are not brought about by androgens themselves, but rather are the result of androgens bound to androgen receptors ; the androgen receptor mediates the effects of androgens in the human body.

There he was interrogated with little result and sent bound to Caiaphas the high priest where the Sanhedrin had assembled ().

It has been mathematically proven that generalized chess ( chess played with an arbitrarily large number of pieces on an arbitrarily large chessboard ) is EXPTIME-complete, meaning that determining the winning side in an arbitrary position of generalized chess provably takes exponential time in the worst case ; however, this theoretical result gives no lower bound on the amount of work required to solve ordinary 8x8 chess.

This fact gave rise to the idea that spontaneous autoimmunity may result when the binding of antibody to certain antigens leads to aberrant signals being fed back to parent B cells through membrane bound ligands.

Thus, if energy is removed ( or emitted ) from the system at the time it is bound, the loss of energy from the system will also result in the loss of the mass of the energy, from the system.

One of the defendants, Bobby Seale, was disruptive in the court room and, as a result, was gagged and bound to his chair during the trial.

Marley ( who had died seven years earlier on Christmas Eve ) spent his life exploiting the poor and as a result is damned to walk the Earth for eternity bound in the chains of his own greed.

The lower peak temperatures result in more of the released energy remaining as sensible energy near TDC, rather than being bound up ( early in the expansion stroke ) in the dissociation of combustion products.

The first example below describes one such result from 1947 that gives a proof of a lower bound for the Ramsey number R ( r, r ).