If the expansion of the Universe continues to accelerate, there is a future horizon as well.

If the rational number's denominator has any prime factors other than 2 or 5, it cannot be expressed as a finite decimal fraction, and has a unique eventually repeating infinite decimal expansion.

If the source of Φ ( r ) is a dipole, as it is assumed here, this term is the only non-vanishing term in the multipole expansion of Φ ( r ).

If the energy density is positive, the associated negative pressure will drive an accelerated expansion of the universe, as observed.

If this type of energy were to exist, it would cause a big rip in the universe due to the growing energy density of dark energy which would cause the expansion of the universe to increase at a faster-than-exponential rate.

Based on Ginzburg – Landau theory, the free energy of a ferroelectric material, in the absence of an electric field and applied stress may be written as a Taylor expansion in terms of the order parameter, P. If a sixth order expansion is used ( i. e. 8th order and higher terms truncated ), the free energy is given by:

If this is so, the Sherden, pushed by Hittite expansionism of the Late Bronze Age and prompted by the famine that affected this region at the same time, may have been pushed to the Aegean islands, where shortage of space led them to seek adventure and expansion overseas.

* If the function pq u is expanded in terms of u at one of the corners, the leading term in the expansion has a coefficient of 1.

* If the expansion process is reversible, meaning that the gas is in thermodynamic equilibrium at all times, it is called an isentropic expansion.

If the growth continues, it is possible that Atoka could begin to see the type of expansion currently underway across the Red River to the south.

If, on top of that, the asker also doesn't know that they should search its expansion before asking someone, then once again, there may be legitimate resentment in his subordinates that they must " manage upward " to such a mollycoddling degree, because the very GIYF principle itself has been shifting into the area of " general knowledge that is lacked only by incompetents.

If one divides a change in proper distance by the interval of cosmological time where the change was measured ( or takes the derivative of proper distance with respect to cosmological time ) and calls this a " velocity ", then the resulting " velocities " of galaxies or quasars can be above the speed of light, c. This apparent superluminal expansion is not in conflict with special or general relativity, and is a consequence of the particular definitions used in cosmology.

:: Example: If the CSPRNG under consideration produces output by computing bits of π in sequence, starting from some unknown point in the binary expansion, it may well satisfy the next-bit test and thus be statistically random, as π appears to be a random sequence.

If the vortex's expansion is obstructed, and symmetry is broken, the vortex will break into cyclical form.

If one hopes to attain order in the state, he must first bring his own family and personal life into order through self-cultivation and the expansion of one's knowledge and the " investigation of things.

If the universe is finite in extent and the cosmological principle ( not to be confused with the cosmological constant ) does not apply, and the expansion speed does not exceed the escape velocity, then the mutual gravitational attraction of all its matter will eventually cause it to contract.

If entropy continues to increase in the contracting phase ( see Ergodic hypothesis ), the contraction would appear very different from the time reversal of the expansion.

If the kernels are over-dried, the expansion rate will suffer and the percentage of kernels that pop at all will decline.

If one were to step on an empty egg shell, its edges have to split in expansion before being flattened.

If true, this account would relate to the remains of the southern expansion of the Indo-Greeks into Gujarat:

* If is a matrix Lie group, then the exponential map coincides with the matrix exponential and is given by the ordinary series expansion:

If we define a decimal expansion such that some digit is dependent on some yet unsolved mathematical problem, we know beforehand that we cannot tell if this number is the same as some other decimal expansion which is independent of this problem.

If only this could be done more often -- with such heartening results -- many of the earth's `` big problems '' would shrink to the insignificances they really are.

If presented in this spirit, the response and the results will be immeasurably better.

If the carrier is only partially suppressed, a double-sideband reduced-carrier ( DSBRC ) signal results.

If a party has gained more direct mandates in a Land than it is entitled to according to the results of the second vote, it does not forfeit these mandates because all directly elected candidates are guaranteed a seat in the Bundestag.

If these preliminary results prove successful in larger trials, then At-DBF2 genes can help in engineering crops that can better withstand harsh environments.

In the words of Geoffrey Crowther, then editor of The Economist, " If the economic relationships between nations are not, by one means or another, brought fairly close to balance, then there is no set of financial arrangements that can rescue the world from the impoverishing results of chaos.

If the wave function is regarded as ontologically real, and collapse is entirely rejected, a many worlds theory results.

If untreated, it results in mild to severe impairment of both physical and mental growth and development.

If the cow does react, it would take at least four people to push it over, according to the results.

If the business ' debts exceed its assets, the bankruptcy restructuring results in the company's owners being left with nothing ; instead, the owners ' rights and interests are ended and the company's creditors are left with ownership of the newly reorganized company.

If objects are seen as moving within a rotating frame, this movement results in another fictitious force, the Coriolis force ; and if the rate of rotation of the frame is changing, a third fictitious force, the Euler force is experienced.

If people are immunized broadly, herd immunity results, with a decrease in the amount of contamination in the environment.

If a reaction results in a small energy release making way for more energy releases in an expanding chain, then the system will typically collapse explosively until much or all of the stored energy has been released.

If proteins in a living cell are denatured, this results in disruption of cell activity and possibly cell death.

Many results about plane figures are proved, e. g., If a triangle has two equal angles, then the sides subtended by the angles are equal.

If instrumentation is involved, the researcher is expected to calibrate his / her instrument by applying it to known standard objects and documenting the results before applying it to unknown objects.

If a project plan contains a significant portion of LOE, and the LOE is intermixed with discrete effort, EVM results will be contaminated.

If results were left unadjusted for factors such as race, gender, and free or reduced price lunch program eligibility, private schools performed significantly better than public schools.

If a better world results, we say it is " utopian ".

If this is prepared using only oil and vinegar ( i. e. without an emulsifier ), an unstable emulsion results

If the surgery is performed on very young patients ( 2 – 5 years old ), the remaining hemisphere may acquire some rudimentary motor control of the ipsilateral body ; in older patients, paralysis results on the side of the body opposite to the part of the brain that was removed.

If this is not accounted for, results can be erroneously attributed to the phenomenon under study rather than to the method of sampling.

If the beam of light is not orthogonal ( or rather normal ) to the boundary, the change in wavelength results in a change in the direction of the beam.

In his book, The God Particle: If the Universe Is the Answer, What Is the Question ?, Lederman writes that, although he was a chemistry major, he became fascinated with physics, because of the clarity of the logic and the unambiguous results from experimentation.

If matter and energy are seen as necessary to explain the physical world, but incapable of explaining mind, dualism results.