If our freshness condition is not met, then we may simply alpha-rename with a suitably fresh variable.

If we wish to describe phenomena like chemical reactions, then the best we can do is to consider suitably chosen initial and final states in which the system is in ( metastable ) thermal equilibrium.

If we reverse the direction of the currents ( i. e. apply the current I < sub > 42 </ sub > and measure V < sub > 31, P </ sub >, and repeat for I < sub > 31 </ sub > and V < sub > 24, P </ sub >), then V < sub > 13, P </ sub > should be the same as V < sub > 31, P </ sub > to within a suitably small degree of error.

If necessary any suitably hard rock, such as quartzite, may be substituted for flint.

If the design parameters of a proposed new boat result in a formula output exceeding 5. 5 metres, then one or more of the parameters must be suitably adjusted.

If a crossing loop is several times the length of the trains using it, and is suitably signalled, then trains proceeding in opposite directions can pass ( cross ) each other without having to stop or even slow down.

If, for example a modeler would wish to achieve a troop from the same timeframe, but a different nation ( Most suitably from 1600 – 1800, particularly the 18th century ), they can simply paint it in the colours of the soldier, with very little accuracy flaws.

If the applicants were suitably impressive, they would earn an invitation to join the school at a cost of $ 3, 000 for six months training.

If the charts are suitably compatible ( namely, the transition from one chart to another is differentiable ), then computations done in one chart are valid in any other differentiable chart.

If the part is to be large and unable to have pressure transmit suitably for a uniform pressed density then isostatic pressing may be used.

If the system is suitably complex, like first-order arithmetic, then the set T of Gödel numbers of true sentences in the system will be a productive set, which means that whenever W is a recursively enumerable set of true sentences, there is at least one true sentence that is not in W. This can be used to give a rigorous proof of Gödel's first incompleteness theorem, because no recursively enumerable set is productive.

If the bead pattern is random, the only concern would generally be that one strand be sized shorter than the next, so they will all lay flat and not interfere with each other when worn or displayed.

If the resistance of the anode is too high, either a differently shaped or sized anode is chosen, or a greater quantity of anodes must be used.

If a buyer wanted a larger sleeper, Peterbilt worked with Mercury Sleepers for 40 " and 60 " and custom sized sleepers.

If the frame has a maximum sized address of 32 bits, a maximum sized control part of 16 bits and a maximum sized frame check sequence of 16 bits, the overhead per frame could be as high as 64 bits.

If you actually walked up to the houses it was easy to see they were normal sized.

If the groups of traders are differently sized, the outer limits of the contract curve will not shrink an equal amount.

If the functional allele originated from the mother, the offspring will exhibit dwarfism, whereas a paternal allele will generate a normal sized mouse.

If the accumulator, pump and plumbing are sized properly, the injection pressure and rate will be the same for each of the multiple injection events.

If it is possible to make at least a memory address sized variable thread local, it is in principle possible to make arbitrarily sized memory blocks thread local, by allocating such a memory block and storing the memory address of that block in a thread local variable.

If the turntable's surface is not completely flat, it is recommended that the flexi disc be placed on top of a full sized record.

If a particle and antiparticle are in the appropriate quantum states, then they can annihilate each other and produce other particles.

If denotes the quantum state of a particle ( n ) with momentum p, spin J whose component in the z-direction is σ, then one has

If the quantum state is initially symmetric ( antisymmetric ), it will remain symmetric ( antisymmetric ) as the system evolves.

If S contains two elements that are not pairwise orthogonal ( in particular, the set of all quantum states includes such pairs ) then an argument like that given above shows that the answer is no.

If the error rate is small enough, it is thought to be possible to use quantum error correction, which corrects errors due to decoherence, thereby allowing the total calculation time to be longer than the decoherence time.

If the theory of quantum gravity also achieves a grand unification of the other known interactions, it is referred to as a theory of everything ( TOE ).

If one used Planck's energy quanta, and demanded that electromagnetic radiation at a given frequency could only transfer energy to matter in integer multiples of an energy quantum hν, then the photoelectric effect could be explained very simply.

If certain quantum inequalities conjectured by Ford and Roman hold, then the energy requirements for some warp drives may be absurdly gigantic as well as negative, for example the energy equivalent of − 10 < sup > 64 </ sup > kg might be required to transport a small spaceship across the Milky Way galaxy.

If the universe is described by an effective local quantum field theory down to the Planck scale, then we would expect a cosmological constant of the order of.

:" If the essential frequency range is limited to B cycles per second, 2B was given by Nyquist as the maximum number of code elements per second that could be unambiguously resolved, assuming the peak interference is less half a quantum step.

If a quantum computer with a sufficient number of qubits were to be constructed, Shor's algorithm could be used to break public-key cryptography schemes such as the widely used RSA scheme.

If true, sonoluminescence may be the first observable example of quantum vacuum radiation.

If quantum electrodynamics were an exact theory, the fine-structure constant would actually diverge at an energy known as the Landau pole.

If more than one quantum mechanical state is at the same energy, the energy levels are " degenerate ".

If quantum mechanics were to be applicable to macroscopic objects, there must be some limit in which quantum mechanics reduces to classical mechanics.

If the effects of the quantum mechanical nuclear motion are to be studied, for instance because a vibrational spectrum is required, this electronic computation must be in nuclear coordinates.

If a more general measurement is made that detects the system in a state then the system makes a " jump " or quantum leap from the original state to the final state with probability of.

If the factor i were absent, the H matrix would be antihermitian and would have purely imaginary eigenvalues, which is not the traditional way quantum mechanics represents observable quantities like the energy.

If the middle layer is made thin enough, it acts as a quantum well.

If parity transforms a pair of quantum states into each other, then the sum and difference of these two basis states are states of good parity.

If we allow the elements of the system to use quantum computation, the system is called a quantum interactive proof system, and the corresponding complexity class is called QIP.

If we introduce a vector then each quantum state corresponds to a point in ' n-space ' with energy