If man is actually the product of his environment and if science can discover the laws of human nature and the ways in which environment determines what people do, then someone -- a someone probably standing outside traditional systems of values -- can turn around and develop completely efficient means for controlling people.

If we try to study T using characteristic values, we are confronted with two problems.

If it is assumed that all color values are premultiplied by their alpha values (), we can rewrite the equation for output color as:

( If these values had been rounded they would have become 33K, 66K, and 131K, respectively.

If communities are developed based on something they share in common, whether that be location or values, then one challenge for developing communities is how to incorporate individuality and differences.

If F is clear from context then Ω < sub > F </ sub > may be denoted simply Ω, although different prefix-free universal computable functions lead to different values of Ω.

If are independent and identically distributed random variables, each with a standard Cauchy distribution, then the sample mean has the same standard Cauchy distribution ( the sample median, which is not affected by extreme values, can be used as a measure of central tendency ).

If the initial value of a polynomial ( and of its finite differences ) is calculated by some means for some value of X, the difference engine can calculate any number of nearby values, using the method generally known as the method of finite differences.

If people then experience other cultures that have different values and normal behaviors, they will find that the thought patterns appropriate to their birth culture and the meanings their birth culture attaches to behaviors are not appropriate for the new cultures.

If the values are, then the growth rate between measurement and is.

If attributes are not mentioned, default values are used in each case.

If the particles have the same physical properties, the n < sub > j </ sub >' s run over the same range of values.

If either the form or the parameters of F ( x ) are determined from the data X < sub > i </ sub > the critical values determined in this way are invalid.

If there is an additional magnitude of value or a loss of value after transformation compared with before then the relation between values ( proportional to labor ) and prices ( proportional to total capital advanced ) is incomplete.

If " this statement is false " is denoted by A and its truth value is being sought, it is necessary to find a condition that restricts the choice of possible truth values of A.

If there is an even number of observations, then there is no single middle value ; the median is then usually defined to be the mean of the two middle values.

If only the second and third conditions of the definition of measure above are met, and takes on at most one of the values, then is called a signed measure.

If the desired output values are often incorrect ( because of human error or sensor errors ), then the learning algorithm should not attempt to find a function that exactly matches the training examples.

If the feature vectors include features of many different kinds ( discrete, discrete ordered, counts, continuous values ), some algorithms are easier to apply than others.

If the feedback network is made of components with relatively constant, stable values, the variability of the op-amp's open loop response does not seriously affect the circuit's performance.

If c, h, and e were all changed so that the values they have in metric ( or any other ) units were different when we looked them up in our tables of physical constants, but the value of α remained the same, this new world would be observationally indistinguishable from our World.

If these quantities are signed, the length of the arc between any two points on the parabola is always shown by the difference between their values of

If the random variable is real-valued ( or more generally, if a total order is defined for its possible values ), the cumulative distribution function gives the probability that the random variable is no larger than a given value ; in the real-valued case it is the integral of the density.

* If asked to imagine the graph of the relationship y = ax < sup > 2 </ sup >, one typically visualizes a range of values of x, but only one value of a.

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 union cannot perform this function, then collective bargaining is being palmed off by organizers as a gigantic fraud.

If the Greek letter is used, it is assumed to be a Fourier transform of another function,

If the method is applied to an infinite sequence ( X < sub > i </ sub >: i ∈ ω ) of nonempty sets, a function is obtained at each finite stage, but there is no stage at which a choice function for the entire family is constructed, and no " limiting " choice function can be constructed, in general, in ZF without the axiom of choice.

If we try to choose an element from each set, then, because X is infinite, our choice procedure will never come to an end, and consequently, we will never be able to produce a choice function for all of X.

If the function R is well-defined, its value must lie in the range, with 1 indicating perfect correlation and − 1 indicating perfect anti-correlation.

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 we define the function f ( n ) = A ( n, n ), which increases both m and n at the same time, we have a function of one variable that dwarfs every primitive recursive function, including very fast-growing functions such as the exponential function, the factorial function, multi-and superfactorial functions, and even functions defined using Knuth's up-arrow notation ( except when the indexed up-arrow is used ).

If f is not a function, but is instead a partial function, it is called a partial operation.

The tensor product X ⊗ Y from X and Y is a K-vector space Z with a bilinear function T: X × Y → Z which has the following universal property: If T ′: X × Y → Z ′ is any bilinear function into a K-vector space Z ′, then only one linear function f: Z → Z ′ with exists.

If your side has two aces and a void, then you are not at risk of losing the first two tricks, so long as ( a ) your void is useful ( i. e., does not duplicate the function of an ace that your side holds ) and ( b ) you are not vulnerable to the loss of the first two tricks in the fourth suit ( because, for instance, one of the partnership hands holds a singleton in that suit or the protected king, giving your side second round control ).

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

If wave function collapse is regarded as ontologically real as well, an objective collapse theory is obtained.

If we take the simple valence bond structure and mix in all possible covalent and ionic structures arising from a particular set of atomic orbitals, we reach what is called the full configuration interaction wave function.

If we take the simple molecular orbital description of the ground state and combine that function with the functions describing all possible excited states using unoccupied orbitals arising from the same set of atomic orbitals, we also reach the full configuration interaction wavefunction.

If the Af bond is linear then there are three reasonable positions for the hydrogen atoms: ( 1 ) The hydrogen atoms are centered and hence all lie on a sheet midway between the oxygen sheets ; ;

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 the rake angle **yc of the knife is high enough and the friction angle **yt between the front of the knife and the back of the chip is low enough to give a positive value for Af, the resultant vector R will lie above the plane of the substrate.

If so, Alcuin's origins may lie in the southern part of what was formerly known as Deira.

If there is refraction at a collective spherical surface, or through a thin positive lens, O ' 2 will lie in front of O ' 1 so long as the angle u2 is greater than u1 ( under correction ); and conversely with a dispersive surface or lenses ( over correction ).

If a throw lands out of bounds, unless defined by the hole, the thrower has the option of playing from the previous lie, or playing from the approximate spot where the disc crossed into the out-of-bound territory.

If the statement is a lie, then he is not actually lying, even though the statement is a lie.

If the radix point is omitted then it is implicitly assumed to lie at the right ( least significant ) end of the string ( that is, the number is an integer ).

In the Doctor Who serial The Green Death ( 1973 ), The Doctor temporarily stumps BOSS by asking it " If I were to tell you that the next thing I say would be true, but the last thing I said was a lie, would you believe me?

If the measured value does not lie in B, replace B by its complement for the above state.

If I hate a man because I am afraid of him, and if I am aware of my hate but not of my fear, we may say that my hate is conscious and that my fear is unconscious ; still my fear does not lie in that mysterious place: ' the ' unconscious.

If its density is similar to Amalthea's, Metis's orbit lies within the fluid Roche limit ; however, since it has not broken up, it must lie outside its rigid Roche limit.

If the ( light ) source, the massive lensing object, and the observer lie in a straight line, the original light source will appear as a ring around the massive lensing object.

If we use NC reductions, that is, reductions which can operate in polylogarithmic time on a parallel computer with a polynomial number of processors, then all P-complete problems lie outside NC and so cannot be effectively parallelized, under the unproven assumption that NC ≠ P. If we use the weaker log-space reduction, this remains true, but additionally we learn that all P-complete problems lie outside L under the weaker unproven assumption that L ≠ P. In this latter case the set P-complete may be smaller.

If the mancipium died a natural death while in the creditor's possession, no claim could lie against the latter ; but if he was the cause of death by cruelty, he had to give son for son, or pay for a slave.

If the width of the interval is doubled, then probably only 4. 6 % of the true values lie outside the doubled interval, and if the width is tripled, probably only 0. 3 % lie outside.

If the trajectory of the particle is constrained to lie on a cylinder, then the radius R is constant and the velocity and acceleration vectors simplify.

If a transverse wave is moving in the positive x-direction, its oscillations are in up and down directions that lie in the y – z plane.