If you hold property for the production of rents or royalties you subtract, in computing Adjusted Gross Income, ordinary and necessary expenses and certain other deductions attributable to the property.

If the artist would study his work more thoroughly and move certain units in his design, often only slightly, finer pictures would result.

If you've travelled in Europe a time or two, it is quite certain that you've had that wanting-to-be-alone feeling or that you will get it on your next visit across the Atlantic.

If, in a certain part of the range, it starts life 1 foot longer than do any of the other ( relatively large ) giants, and reaches maturity at, let us guess, 18 inches longer than the others, a quadrupling of the maturity length would result in a maximum of ( nearly ) 40 feet.

If it were not for judicial development of certain exceptions, this section would prohibit a suit for refund by an acquiring corporation for taxes paid by a transferor corporation, even though the reorganization meets the requirements of section 381(a).

Chief Moore said, `` If I don't see you when I return, see you for certain at my road block, Inspector ''.

If it was, then it must have been God's intention to translate him at a certain point from time to eternity.

If an evil which is certain and extensive and immediate may rarely be compensated for by a problematic, speculative, future good, by the same token not every present, certain, and immediate good ( or lesser evil ) that may have to be done will be outweighed by a problematic, speculative, and future evil.

If the slowing down of certain seismic waves caused by the damp spot helped uncover the underground ocean, the unusual temperature variation with depth measured in 241 inactive oil wells helped locate the subterranean river.

* Continuity: If a certain mass of fluid enters a volume, it must either exit the volume or change the mass inside the volume.

If the heat of vaporization and the vapor pressure of a liquid at a certain temperature is known, the normal boiling point can be calculated by using the Clausius-Clapeyron equation thus:

* Indivisibility of certain goods: If a person wants to buy a certain amount of another's goods, but only has for payment one indivisible unit of another good which is worth more than what the person wants to obtain, a barter transaction cannot occur.

If the bankrupt fails to lodge the document within a certain period of time, he or she can be prosecuted and fined.

If a house or car is above a certain value, the bankrupt can buy the interest back from the estate in order to keep the asset.

If certain coordinate systems are used, for instance, polar-toroidal coordinates ( common in plasma physics ) using the notation ∇ × F will yield an incorrect result.

:: If patients fail to experience the healing power of Christian Science, and think they can be benefited by certain ordinary physical methods of medical treatment, then the Mind-physician should give up such cases, and leave invalids free to resort to whatever other systems they fancy will afford relief.

If additional solute is added to a saturated solution, it will not dissolve, except in certain circumstances, when supersaturation may occur.

If the computer controlling the display knows the exact position and color of all the subpixels on the screen, it can take advantage of this to improve the apparent resolution of the images on the screen in certain situations.

If it is assumed that social change is not only affected, but in some points of view, directed by the advancement of technology, is it ethical to hold these technologies from certain people?

If you find you have to sacrifice certain of those six things to make a cut, sacrifice your way up, item by item, from the bottom.

If the species concerned were short-lived ( in geological terms, lasting a few hundred thousand years ), then it is certain that the sediments in question were deposited within that narrow time period.

If a lock, let it have been made in whatever country, or by whatever maker, is not so inviolable as it has hitherto been deemed to be, surely it is to the interest of honest persons to know this fact, because the dishonest are tolerably certain to apply the knowledge practically ; and the spread of the knowledge is necessary to give fair play to those who might suffer by ignorance.

If the 3 generations are then put in a 3x3 hermitian matrix with certain additions for the diagonal elements then these matrices form an exceptional ( grassman -) Jordan algebra, which has the symmetry group of one of the exceptional Lie groups ( F < sub > 4 </ sub >, E < sub > 6 </ sub >, E < sub > 7 </ sub > or E < sub > 8 </ sub >) depending on the details.

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 a suitably sized quantum computer capable of running Grover's algorithm reliably becomes available, it would reduce a 128-bit key down to 64-bit security, roughly a DES equivalent.

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 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