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 a continuation card follows a statement that does not permit continuation cards, the compiler will generate a NOP and issue an error message.

If, at any time during the assignment pass, the compiler finds that there are no more index words available for assignment, the warning message `` No More Index Words Available '' will be placed in the object program listing, the table will be altered to show that index words 1 through 96 are available, and the assignment will continue as before.

If the compiler finds that there are no more electronic switches available for assignment, the warning message `` No More Electronic Switches Available '' will be placed in the object program listing, the table will be altered to show that electronic switches 1 through 30 are available, and assignment will continue as before.

If the compiler does encounter such statements, a warning message will be issued.

If somebody tries to associate a second engine with a given car, we want the DBMS to deny such a request and display an error message.

If the baseband data signal ( the message ) to be transmitted is and the sinusoidal carrier is, where f < sub > c </ sub > is the carrier's base frequency and A < sub > c </ sub > is the carrier's amplitude, the modulator combines the carrier with the baseband data signal to get the transmitted signal:

If the player uses the " god mode " cheat from Doom, the game will display a message saying " Trying to cheat, eh?

If the resulting TTL is 0, the packet is discarded and an ICMP Time To Live exceeded in transit message is sent to the datagram's source address.

If the message is an ISDN level message, then a decoding of the message is attempted showing the various Information Elements that make up the message.

If a compression scheme is lossless — that is, you can always recover the entire original message by uncompressing — then a compressed message has the same quantity of information as the original, but communicated in fewer bits.

If the originating mail program doesn't add a message ID, a server handling the message later on probably will, since a number of programs ( both clients and servers ) want every message to have one to keep track of them.

If none was available, then the computer would perform tasks from other memory stores or display an error message, depending on the model and design of the computer and version of the BIOS.

If, as in L4, part or all of the message is passed in registers, this transfers the in-register part of the message without any copying at all.

If the alphabet consists of alternative symbols, each symbol represents a message consisting of N bits.

* If the message indicates, Bob would send his qubit through the unitary gate given by the Pauli matrix

* If Alice's message corresponds to, Bob applies the gate

If a pushwall exits the boundaries of the level, the game quits with the error message " PushWall Attempting to escape off the edge of the map ".

An anecdote has it that when Philip II sent a message to Sparta saying " If I enter Laconia, I will raze Sparta ", the Spartans responded with the single, terse reply: " If.

If his circumspection in regard to Philip's sensibilities went so far that he even refused to grant a dispensation for the marriage of Amadee's daughter, Agnes, to the son of the dauphin of Vienne -- a truly peacemaking move according to thirteenth-century ideas, for Savoy and Dauphine were as usual fighting on opposite sides -- for fear that he might seem to be favoring the anti-French coalition, he would certainly never take the far more drastic step of ordering the return of Gascony to Edward, even though, as he admitted to the English ambassadors, he had been advised that the original cession was invalid.

If the moments of the aligned and anti-aligned ions balance completely so as to have zero net magnetization, despite the magnetic ordering, then it is an antiferromagnet.

If the entire volume of the observable universe ( taken to be 3 × 10 < sup > 80 </ sup > m < sup > 3 </ sup >) were packed solid with fine dust particles about 1. 5 micrometres in size, then the number of different ways of ordering these particles ( that is, assigning the number 1 to one particle, then the number 2 to another particle, and so on until all particles are numbered ) would be approximately one googolplex.

In computer science, a heap is a specialized tree-based data structure that satisfies the heap property: If A is a parent node of B then key ( A ) is ordered with respect to key ( B ) with the same ordering applying across the heap.

If the temperature rise is too high, thermal motion will destroy the delicate cooperative ordering of the LC phase, pushing the material into a conventional isotropic liquid phase.

If lexicographic ordering is used to sort variable-length integer representations, then the representations of the numbers from 1 to 10 would be output as 1, 10, 2, 3, 4, 5, 6, 7, 8, 9, as if the shorter keys were left-justified and padded on the right with blank characters to make the shorter keys as long as the longest key for the purpose of determining sorted order.

If a thing is to be well established or founded, its arche or static point must be secure, and the most secure foundations are those provided by the gods: the indestructible, immutable and eternal ordering of things.

That means, define E ≤ F if E is an initial segment of F and the ordering of the members in E is the same as their ordering in F. If E is a chain in A, then the union of the sets in E can be ordered in a way that makes it a continuation of any set in E ; this ordering is a well ordering, and therefore, an upper bound of E in A.

On his deathbed, he committed a manuscript to his chaplain, ordering him to consult with Libert Fromondus, a theology professor at Leuven, and Henri Calenus, a canon at the metropolitan church, and to publish the manuscript if they agreed it should be published, adding " If, however, the Holy See wishes any change, I am an obedient son, and I submit to that Church in which I have lived to my dying hour.

If the move ordering for the search is optimal ( meaning the best moves are always searched first ), the number of leaf node positions evaluated is about O ( b * 1 * b * 1 *...* b ) for odd depth and O ( b * 1 * b * 1 *...* 1 ) for even depth, or.

If the input values to the spreadsheet change, all of the remaining values of the spreadsheet may be recomputed with a single evaluation per cell, by topologically ordering the cells and re-evaluating each cell in this order.

If one is only interested in stochastic ordering of the two populations ( i. e., the concordance probability P ( Y > X )), the U test can be used even if the shapes of the distributions are different.

If n is the degree of P, then the splitting type is a partition Π of n. Considering also the Galois group G of K over Q, each g in G is a permutation of the roots of P in K ; in other words by choosing an ordering of α and its algebraic conjugates, G is faithfully represented as a subgroup of the symmetric group S < sub > n </ sub >.

* If the axiom of constructibility holds then there is a subset of the product of the Baire space with itself which is and is the graph of a well ordering of Baire space.

If the axiom holds then there is also a well ordering of Cantor space.

( If there should be infinitely many indeterminates, this convention is incompatible with the condition of being a well ordering, and one would be forced to use the opposite ordering ; however the case of polynomials in infinitely many variables is rarely considered.

If the a < sub > i </ sub > are rationally independent numbers ( so in particular none of them are zero and all fractions are irrational ) then a tie can never occur, and the weight vector itself specifies a monomial ordering.

At the outbreak of the Civil War, he sent a telegram to the Treasury agents in New Orleans ordering that: " If any one attempts to haul down the American flag, shoot him on the spot.

Deviously ordering someone to accuse Lao Ai of a crime punishable by castration, Lü also privately told the queen dowager, " If we can fake the castration, we can make him a servant in the harem.

If the result consists of nodes, then duplicates are eliminated and the nodes are returned in document order, an ordering defined in terms of the relative positions of the nodes in the original XML tree.

If F is an ordered field ( not just orderable, but a definite ordering is fixed as part of the structure ), the Artin – Schreier theorem states that F has an algebraic extension, called the real closure K of F, such that K is a real closed field whose ordering is an extension of the given ordering on F, and is unique up to a unique isomorphism of fields ( note that every ring homomorphism between real closed fields automatically is order preserving, because x ≤ y if and only if ∃ z y = x + z < sup > 2 </ sup >).