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Page "Examples of differential equations" ¶ 19
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If and is
If the circumstances are faced frankly it is not reasonable to expect this to be true.
If his dancers are sometimes made to look as if they might be creatures from Mars, this is consistent with his intention of placing them in the orbit of another world, a world in which they are freed of their pedestrian identities.
If a work is divided into several large segments, a last-minute drawing of random numbers may determine the order of the segments for any particular performance.
If they avoid the use of the pungent, outlawed four-letter word it is because it is taboo ; ;
If Wilhelm Reich is the Moses who has led them out of the Egypt of sexual slavery, Dylan Thomas is the poet who offers them the Dionysian dialectic of justification for their indulgence in liquor, marijuana, sex, and jazz.
If he is the child of nothingness, if he is the predestined victim of an age of atomic wars, then he will consult only his own organic needs and go beyond good and evil.
If it is an honest feeling, then why should she not yield to it??
If he thus achieves a lyrical, dreamlike, drugged intensity, he pays the price for his indulgence by producing work -- Allen Ginsberg's `` Howl '' is a striking example of this tendency -- that is disoriented, Dionysian but without depth and without Apollonian control.
If love reflects the nature of man, as Ortega Y Gasset believes, if the person in love betrays decisively what he is by his behavior in love, then the writers of the beat generation are creating a new literary genre.
If he is good, he may not be legal ; ;
If the man on the sidewalk is surprised at this question, it has served as an exclamation.
If the existent form is to be retained new factors that reinforce it must be introduced into the situation.
If we remove ourselves for a moment from our time and our infatuation with mental disease, isn't there something absurd about a hero in a novel who is defeated by his infantile neurosis??
If many of the characters in contemporary novels appear to be the bloodless relations of characters in a case history it is because the novelist is often forgetful today that those things that we call character manifest themselves in surface behavior, that the ego is still the executive agency of personality, and that all we know of personality must be discerned through the ego.
If he is a traditionalist, he is an eclectic traditionalist.
If our sincerity is granted, and it is granted, the discrepancy can only be explained by the fact that we have come to believe hearsay and legend about ourselves in preference to an understanding gained by earnest self-examination.
If to be innocent is to be helpless, then I had been -- as are we all -- helpless at the start.

If and constant
If Af is the change per unit volume in Gibbs function caused by the shear field at constant P and T, and **yr is the density of the fluid, then the total potential energy of the system above the reference height is Af.
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 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 adiabats and isotherms are graphed severally at regular changes of entropy and temperature, respectively ( like altitude on a contour map ), then as the eye moves towards the axes ( towards the south-west ), it sees the density of isotherms stay constant, but it sees the density of adiabats grow.
Theorem: If K < sub > 1 </ sub > and K < sub > 2 </ sub > are the complexity functions relative to description languages L < sub > 1 </ sub > and L < sub > 2 </ sub >, then there is a constant c – which depends only on the languages L < sub > 1 </ sub > and L < sub > 2 </ sub > chosen – such that
If the valid element indices begin at 0, the constant B is simply the address of the first element of the array.
If the numbering does not start at 0, the constant B may not be the address of any element.
If the ratio a '/ a be sufficiently constant, as is often the case, the above relation reduces to the condition of Airy, i. e. tan w '/ tan w = a constant.
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 the domain of F is a disjoint union of two or more intervals, then a different constant of integration may be chosen for each of the intervals.
If the net force on some body is directed always toward some fixed point, the center, then there is no torque on the body with respect to the center, and so the angular momentum of the body about the center is constant.
If the pressure in a system remains constant ( isobaric ), a vapor at saturation temperature will begin to condense into its liquid phase as thermal energy ( heat ) is removed.
If these are linear with constant
If the resulting linear differential equations have constant coefficients one can take their Laplace transform to obtain a transfer function.
If we look for solutions that have the form, where C is a constant, we discover the relationship, and thus must be one of the complex numbers or.
If the subject could so judge his own superior, then all lawful superior authority could lawfully be overthrown by the arbitrary judgement of an inferior, and thus all law was under constant threat.
If the sources are constant ( DC ) sources, the result is a DC circuit.
If only the electric field () is non-zero, and is constant in time, the field is said to be an electrostatic field.
If the gain is not constant, e. g., by clipping the output signal at the limits of its capabilities, the output signal will be distorted.
If the firm is a perfect competitor in all input markets, and thus the per-unit prices of all its inputs are unaffected by how much of the inputs the firm purchases, then it can be shown that at a particular level of output, the firm has economies of scale if and only if it has increasing returns to scale, has diseconomies of scale if and only if it has decreasing returns to scale, and has neither economies nor diseconomies of scale if it has constant returns to scale.
If the frequency deviation is held constant and the modulation frequency increased, the spacing between spectra increases.
* If a pure function is called with parameters that cause no side-effects, the result is constant with respect to that parameter list ( sometimes called referential transparency ), i. e. if the pure function is again called with the same parameters, the same result will be returned ( this can enable caching optimizations such as memoization ).
If the diffusion coefficient is not a constant, but depends upon the coordinate and / or concentration, Fick's Second Law yields

If and solution
If we have five problems whose solution we seek in relatively united fashion, then there are twice as many issues which, I judge, sharply divide us, intergroup relations practitioners and lay people.
If one lives near a subway or an express parkway, the solution is to have one's wines stored with a dealer and brought home a few at a time.
If the differential equations are nonlinear and have a known solution, it may be possible to linearize the nonlinear differential equations at that solution.
If additional solute is added to a saturated solution, it will not dissolve, except in certain circumstances, when supersaturation may occur.
If the value of is not known a priori, it can be determined from two measurements of the solution.
If < math > c ^ 2 < 4km </ math > there are two complex conjugate roots a ± ib, and the solution ( with the above boundary conditions ) will look like this:
If very small amounts of solution are involved, most of the solution may be soaked up by the filter medium.
If the executor is merely following a solution ( e. g. sketch, script or instructions ) provided by another designer ( such as an art director ), then the executor is not usually considered the designer.
If a saline solution is used instead of water, a purer protein is obtained, with certain harmless impurities going into solution with the starch.
If un-aerated, the solution level is kept low enough that enough roots are above the solution so they get adequate oxygen.
If an equation can be put into the form f ( x ) = x, and a solution x is an attractive fixed point of the function f, then one may begin with a point x < sub > 1 </ sub > in the basin of attraction of x, and let x < sub > n + 1 </ sub > = f ( x < sub > n </ sub >) for n ≥ 1, and the sequence
If the example with the colored bricks above is viewed as an unbounded knapsack problem, then the solution is to take three yellow boxes and three grey boxes.
If the latter subgroup cools slowly from a melt, it forms exsolution lamellae because the two components — orthoclase and albite — are unstable in solid solution.
If that solution runs in polynomial time, then that problem is in BQP.
If, on the other hand, ranks of these two matrices are equal, the system must have at least one solution.
If an electron of energy E is incident upon an energy barrier of height U ( z ), the electron wave function is a traveling wave solution,
If both solute and solvent exist in equal quantities ( such as in a 50 % ethanol, 50 % water solution ), the concepts of " solute " and " solvent " become less relevant, but the substance that is more often used as a solvent is normally designated as the solvent ( in this example, water ).
# If alkaline transfer methods are used, the DNA gel is placed into an alkaline solution ( typically containing sodium hydroxide ) to denature the double-stranded DNA.
⟨ H ⟩, be the group generated by H. Then the word problem in H < sup >*</ sup > is solvable: given two words h, k in the generators H of H < sup >*</ sup >, write them as words in X and compare them using the solution to the word problem in G. It is easy to think that this demonstrates a uniform solution the word problem for the class K ( say ) of finitely generated groups that can be embedded in G. If this were the case the non-existence of a universal solvable word problem group would follow easily from Boone-Rogers.

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