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If and number
If in any one calculation Ptolemy had had to invoke 83 epicycles all at once, while Copernicus never required more than one third this number, then ( in the sense obvious to Margenau ) Ptolemaic astronomy would be simpler than Copernican.
If your state has no provisions for the numbering of pleasure boats, you must apply for a number from the U.S. Coast Guard for any kind of boat with mechanical propulsion rated at more than 10 horsepower before it can be used on Federal waterways.
If a nation wished to get a head start in physical fitness over all other nations, it would start its kindergarten students on a program of gymnastics the day they entered and thus eliminate a large number of the problems that plague American schools.
If no specific organization plan exists limiting the number of scientists at each salary level, the result is a department top-heavy with high-level, high-salaried personnel ''.
If we thus spent our very first day in the midst of a large number of your people honoring a new hero and a great national achievement, our last day, to us at least, was equally impressive and very moving, even though the crowds were absent and there was almost complete silence.
If a wedge-shaped coating of increasing thickness is removed from a substrate by an instrument like the Hesiometer with a knife of constant rake angle, a number of removal mechanisms are often observed which depend upon the thickness of the coating.
If all the operating variables were varied simultaneously, Af operations would be required to do the same job, and as R increases this increases very much more rapidly than the number of operations required by the dynamic program.
If Rock shows up during the number -- or you hear anything -- give me the signal ''.
If one takes the middle number, 5, and multiplies it by 3 ( the base number of the magic square of three ), the result is 15, which is also the constant sum of all the rows, columns, and two main diagonals.
If so, it might be worth while to assign a future jazz show to a different department -- one with enough confidence in the musical material to cut down on the number of performers and give them a little room to display their talents.
* If it is required to use a single number X as an estimate for the value of numbers, then the arithmetic mean does this best, in the sense of minimizing the sum of squares ( x < sub > i </ sub > − X )< sup > 2 </ sup > of the residuals.
If its minimal polynomial has degree, then the algebraic number is said to be of degree.
If K is a number field, its ring of integers is the subring of algebraic integers in K, and is frequently denoted as O < sub > K </ sub >.
* Let Q be a set enclosed between two step regions S and T. A step region is formed from a finite union of adjacent rectangles resting on a common base, i. e. S ⊆ Q ⊆ T. If there is a unique number c such that a ( S ) ≤ c ≤ a ( T ) for all such step regions S and T, then a ( Q )
If a description of s, d ( s ), is of minimal length ( i. e. it uses the fewest number of characters ), it is called a minimal description of s. Thus, the length of d ( s ) ( i. e. the number of characters in the description ) is the Kolmogorov complexity of s, written K ( s ).
If a ) testimonies conflict one another, b ) there are a small number of witnesses, c ) the speaker has no integrity, d ) the speaker is overly hesitant or bold, or e ) the speaker is known to have motives for lying, then the epistemologist has reason to be skeptical of the speaker's claims.
If we take in our hand any volume ; of divinity or school metaphysics, for instance ; let us ask, Does it contain any abstract reasoning concerning quantity or number?
If a is algebraic over K, then K, the set of all polynomials in a with coefficients in K, is not only a ring but a field: an algebraic extension of K which has finite degree over K. In the special case where K = Q is the field of rational numbers, Q is an example of an algebraic number field.
If the two carbon atoms at the double bond are linked to a different number of hydrogen atoms, the halogen is found preferentially at the carbon with fewer hydrogen substituents ( Markovnikov's rule ).
If F is an antiderivative of f, and the function f is defined on some interval, then every other antiderivative G of f differs from F by a constant: there exists a number C such that G ( x ) = F ( x ) + C for all x.
If there is no number to its left, simply look at the column headed " 1 " in the previous row.
If the game has been scored correctly, the total number of plate appearances for a team should equal the total of that team's runs, men left on base, and men put out.
If the other player also knows to offer sacrifices, the expert also has to manipulate the number of available sacrifices through earlier play.

If and photons
If the photons reside mainly in the higher index material, the confinement is due to total internal reflection.
If light ( photons ) of frequency ν < sub > 12 </ sub > pass through the group of atoms, there is a possibility of the light being absorbed by atoms which are in the ground state, which will cause them to be excited to the higher energy state.
If the ground state has a higher population than the excited state ( N < sub > 1 </ sub > > N < sub > 2 </ sub >), the process of absorption dominates and there is a net attenuation of photons.
If we imagine the beam is made of photons, then every second numerous photons strike the surface and are absorbed.
If the light were totally reflected then the radiation pressure is doubled compared to total absorption, this is because the photons arrive with momentum E / c and depart with momentum-E / c ( the-ve sign indicates traveling in the opposite direction ), so the change of momentum is 2E / c.
If light falling on the device is of high enough frequency, photons absorbed by the semiconductor give bound electrons enough energy to jump into the conduction band.
If the bandgap is too high, most daylight photons cannot be absorbed ; if it is too low, then most photons have much more energy than necessary to excite electrons across the bandgap, and the rest is wasted.
Prior to any measurements being made, the polarizations of the photons are indeterminate ; If a measurement is made on one of the photons using a two-channel polarizer aligned with the axes of the coordinate system, the photon assumes either horizontal or vertical polarization, with 50 % probability for each orientation, and the other two photons immediately assume the identical polarization.
If photons of a particular wavelength are absorbed by matter, then when we observe light reflected from or transmitted through that matter, what we see is the complementary color, made up of the other visible wavelengths remaining.
If the photons are formed by the collision of a particle and an antiparticle, the invariant mass is the same as the total energy of the particle and antiparticle ( their rest energy plus the kinetic energy ), in the center of mass frame, where they will automatically be moving in equal and opposite directions ( since they have equal momentum in this frame ).
If the photons are formed by the disintegration of a single particle with a well-defined rest mass, like the neutral pion, the invariant mass of the photons is equal to rest mass of the pion.
If the Universe is dominated by radiation, or by dark energy, though, those potentials do evolve, subtly changing the energy of photons passing through them.
If their main purpose is radiation measurement, they are called radiation detectors, but as photons are also ( massless ) particles, the term particle detector is still correct.
If this is the case, some or all of the photons emitted by the fluorophore may be absorbed again.
If a Dp-brane is embedded in a spacetime of d spatial dimensions, the brane carries ( in addition to its Maxwell field ) a set of d-p massless scalars ( particles which do not have polarizations like the photons making up light ).
If the optical filter passed only that frequency band, then there would be a net transfer of photons, and their energy, from the second system to the first.
If this were true however, the radiometer would spin away from the non-black faces, since the photons bouncing off those faces impart even more momentum than the photons absorbed on the black faces.

If and being
If she, Pamela, were being held responsible for his crimes, then hers must be the final act of expiation.
If our national interest lies in being able to fight and win a war rather than committing national suicide, then we must take a much more penetrating look at ballistic missiles.
If, on the other hand, it is not settled, or while it is being debated and resolved, does the Federal government have a responsibility in situations like that in Prince Edward County??
If goodness and badness lie in attitudes only and hence are brought into being by them, those men who greeted death and misery with childishly merry laughter are taking the only sensible line.
If a union cannot perform this function, then collective bargaining is being palmed off by organizers as a gigantic fraud.
If we have not thought and made a decision entirely in these terms, then we need to submit ourselves to the following `` simple test '': `` Have we decided how we are to kill the other members of our household in the event of our being less injured than they are ''??
If two players tie for minority, they will share the minority shareholder bonus. Suppose Festival is the chain being acquired.
If anything, her poems suggest the opposite – they speak of quietly experienced but intensely felt emotions, hidden from others, without any indication of being requited.
" If the aircraft is not being hijacked, the pilot should not squawk 7500 and should inform the controller accordingly.
If Acorn had thought to include this small modification in the original Electron design it is likely the machine would have had a much greater impact as it would have nearly doubled the amount of motion possible in games and saved modes 0 – 3 ( including the only 16 colour mode ) from being nearly useless due to contended memory timings.
If, in an unsharp image, a patch of light corresponds to an object point, the center of gravity of the patch may be regarded as the image point, this being the point where the plane receiving the image, e. g., a focusing screen, intersects the ray passing through the middle of the stop.
If two equivalent amplifiers are being compared, the amplifier with higher gain settings would be more sensitive as it would take less input signal to produce a given amount of power.
If substance is the highest category and there is no substance, being, then the unity perceived in all beings by virtue of their existing must be viewed in another way.
If the first theory is correct ( see above ), then the absence of cavalry removed the main Athenian tactical disadvantage, and the threat of being outflanked made it imperative to attack.
If the slope / cliff being undercut is made of unconsolidated sediment it will erode at a much faster rate then a cliff made of bedrock.
If a cabal can be implicated in a sequence of events, there is always the hope, however tenuous, of being able to break the cabal's power – or joining it and exercising some of that power oneself.
If the experiment were done in English, since Searle knows English, he would be able to take questions and give answers without any algorithms for English questions, and he would be affectively aware of what was being said and the purposes it might serve: Searle passes the Turing test of answering the questions in both languages, but he's only conscious of what he's doing when he speaks English.
If evolutionary processes are blind to the difference between function F being performed by conscious organism O and non-conscious organism O *, it is unclear what adaptive advantage consciousness could provide.
If an atom A is double-bonded to an atom B, A is treated as being singly bonded to two atoms: B and a ghost atom that has the same atomic number as B but is not attached to anything except A.
If a 7 is rolled instead of the point being re-rolled, the don't pass bet wins and is paid even money.
If a demonstration of ability or knowledge is required by law before being allowed to perform a task or job, this is referred to as licensure.
If a compression test does give a low figure, and it has been determined it is not due to intake valve closure / camshaft characteristics, then one can differentiate between the cause being valve / seat seal issues and ring seal by squirting engine oil into the spark plug orifice, in a quantity sufficient to disperse across the piston crown and the circumference of the top ring land, and thereby effect the mentioned seal.
* If is the norm ( usually noted as ) defined in the sequence space ℓ < sup >∞</ sup > of all bounded sequences ( which also matches the non-linear distance measured as the maximum of distances measured on projections into the base subspaces, without requiring the space to be isotropic or even just linear, but only continuous, such norm being definable on all Banach spaces ), and is lower triangular non-singular ( i. e., ) then
Mather began to publicize and celebrate the trials well before they were put to an end: " If in the midst of the many Dissatisfaction among us, the publication of these Trials may promote such a pious Thankfulness unto God, for Justice being so far executed among us, I shall Re-joyce that God is Glorified ..." ( Wonders of the Invisible World ).
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.

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