If the polarities are correct, the platform rotates in such a direction as to reduce the accelerometer output to zero.

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

If, i. e., it has a large norm with each value of s, and if, then Y ( s ) is approximately equal to R ( s ) and the output closely tracks the reference input.

If u ( t ) is the control signal sent to the system, y ( t ) is the measured output and r ( t ) is the desired output, and tracking error, a PID controller has the general form

If a nation continues on this path without resistance, Gini claimed the nation would enter a final decadent stage where the nation would degenerate as noted by decreasing birth rate, decreasing cultural output, and the lack of imperial conquest.

If this output is then used as the clock signal for a similarly arranged D flip-flop ( remembering to invert the output to the input ), you will get another 1 bit counter that counts half as fast.

If the two input signals are both sinusoids of specified frequencies f < sub > 1 </ sub > and f < sub > 2 </ sub >, then the output of the mixer will contain two new sinsoids that have the sum f < sub > 1 </ sub > + f < sub > 2 </ sub > frequency and the difference frequency absolute value | f < sub > 1 </ sub >-f < sub > 2 </ sub >|.

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 high output powers are needed from a class-A circuit, the power waste ( and the accompanying heat ) will become significant.

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 magnetic field is applied by a solenoid, the sensor output is proportional to the product of the current through the solenoid and the sensor voltage.

In mathematics, an inverse function is a function that undoes another function: If an input x into the function ƒ produces an output y, then putting y into the inverse function g produces the output x, and vice versa.

* If the price is between average total cost and average variable cost at the profit-maximizing output, then the firm is said to be in a loss-minimizing condition.

* If the price is below average variable cost at the profit-maximizing output, the firm should go into shutdown.

If a and b are distances from the fulcrum to points A and B and if force F < sub > A </ sub > applied to A is the input force and F < sub > B </ sub > exerted at B is the output, the ratio of the velocities of points A and B is given by a / b, so the ratio of the output force to the input force, or mechanical advantage, is given by

If the distance from the fulcrum to the input force is less than from the fulcrum to the output force, then the lever reduces the input force.

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 each of the features makes an independent contribution to the output, then algorithms based on linear functions ( e. g., linear regression, logistic regression, Support Vector Machines, naive Bayes ) and distance functions ( e. g., nearest neighbor methods, support vector machines with Gaussian kernels ) generally perform well.

If the inverting input is held at ground ( 0 V ) directly or by a resistor, and the input voltage V < sub > in </ sub > applied to the non-inverting input is positive, the output will be maximum positive ; if V < sub > in </ sub > is negative, the output will be maximum negative.

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 a structuralist reading focuses on multiple texts, there must be some way in which those texts unify themselves into a coherent system.

If the only way to come by any approximately coherent conception of God is via a mystical experience, then it seems as though this formulation of God hasn't got enough objectivity to get it off the ground.

For Frye, this kind of coherent, critical integrity involves claiming a body of knowledge for criticism that, while independent of literature, is yet constrained by it: " If criticism exists ," he declares, " it must be an examination of literature in terms of a conceptual framework derivable from an inductive survey of the literary field " itself ( Anatomy 7 ).

" If you violate coherent rules of science you are in trouble.

If combined they can exhibit complete constructive interference / superposition at all times, then it follows that they are perfectly coherent.

If a wave has only 1 value of amplitude over an infinite length, it is perfectly spatially coherent.

" If the matter can be forced out of thermal equilibrium to a sufficient degree, so that the upper state has a higher population than the lower state ( population inversion ), then more stimulated emission than absorption occurs, leading to coherent growth ( amplification or gain ) of the electromagnetic wave at the transition frequency.

If this is not done, the pixels will gradually lose their coherent state, and the image will " fade " from the screen.

* If F is a coherent sheaf ( or G < sub > m </ sub >) then the étale cohomology of F is the same as Serre's coherent sheaf cohomology calculated with the Zariski topology ( and if X is a complex variety this is the same as the sheaf cohomology calculated with the usual complex topology ).

* If F is a quasi-coherent sheaf of finite presentation on Y ( in particular, if F is coherent ), and if J is the annihilator of F on Y, then, the pullback of the inclusion map, is an injection, and the image of f < sup >*</ sup > J in is the annihilator of f < sup >*</ sup > F </ sup > on X .< ref > EGA IV < sub > 2 </ sub >, Proposition 2. 1. 11 .</ ref >

If is coherent, then the converse is true and each sheaf of finite presentation over is coherent.

* Ideal sheaves: If Z is a closed complex subspace of a complex analytic space X, the sheaf I < SUB > Z </ SUB > of all holomorphic functions vanishing on Z is coherent.

If the support of F is proper over S, then for each the higher direct image is coherent.

If F is a coherent-module, then the higher direct images are coherent.

# If f: X → Y is an arbitrary morphism of schemes of finite type over C and is coherent then the natural map is injective.

If are two coherent algebraic sheaves on and if is a map of sheaves of modules then there exists a unique map of sheaves of modules with f =

If is a coherent analytic sheaf of modules over X < sup > an </ sup > then there exists a coherent algebraic sheaf of-modules and an isomorphism.

If no coherent excitation exists the state is called a squeezed vacuum.

If one is a voluntarist with respect to beliefs, it is coherent to simultaneously feel very certain about a particular proposition, P, and assign P a very low subjective probability.

If the wire is an infinite line, under conditions that the vacuum does not have winding number fluctuations which are coherent throughout the system, the conservation law is a superselection rule --- the probability that the winding will unwind is zero.

If X is coherent with any cover of compact subsets in the above sense then it is, in fact, coherent with all compact subsets.