If Franklin was an authentic genius, then Alexander Hamilton, with his exceptional precocity, consuming energy, and high ambition, was a political prodigy.

If we grasp this opportunity to build an age of productive partnership between the less fortunate nations and those that have already achieved a high state of economic advancement, we will make brighter the outlook for a world order based upon security and freedom.

If the railroads, for example, regularly slaughtered 25,000 passengers each year, the high priests of the cult would have cause to tremble for their personal safety, for such a holocaust would excite demands for the hanging of every railroad president in the United States.

If we wait until children are in junior high or high school, we will never manage it.

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 high accuracy is required in preflight leveling, it is usually necessary to integrate or doubly integrate the accelerometer outputs ( this also minimizes the noise problem ).

If the platform is not too high off the ground, a transit can be mounted on a stand to raise it up to the platform.

If anyone thought of the John Harvey, it was to observe that she was straddled by a pair of ships heavily laden with high explosive and if they were hit the John Harvey would likely be blown up with her own ammo and whatever else it was that she carried.

If the farm is in an industrial area where wages are high, farm labor costs will also be high.

If William wished to continue operations for a year, why not simply leave the Negroes undisturbed and pay them `` as high wages to remain there as are ever paid the labor of persons of their sex & age.

If the student drops out of high school, the break with the school is even more complete.

If the concentration of element or compound in a sample is too high for the detection range of the technique, it can simply be diluted in a pure solvent.

If the brine regenerator uses high heat, they also partially sterilise the air.

" If the remainder of the Conservative Party could muster the electoral support necessary to form a government, then Disraeli was now guaranteed high office.

If the shuttlecock has dropped lower, then a smash is impossible and a full-length, high clear is difficult.

If the risk of asphyxiation is deemed to be high, doctors may use various devices ( such as an oropharyngeal airway, nasopharyngeal airway or endotracheal tube ) to safeguard the airway.

If the glass is damaged, atmospheric pressure can collapse the vacuum tube into dangerous fragments which accelerate inward and then spray at high speed in all directions.

If both high priority substituents are on the same side of the double bond, i. e. in the cis configuration, then the stereoisomer is assigned a Z or Zusammen configuration.

If a naive rendering algorithm is used without any filtering, high frequencies in the image function will cause ugly aliasing to be present in the final image.

If a team places high enough at selected USASF / IASF sanctioned national competitions, they could be included in the Cheerleading Worlds and compete against teams from all over the world, as well as receive money for placing.

If the signal matches the desired user's code then the correlation function will be high and the system can extract that signal.

If SR calcium stores become too high, some ions are released spontaneously through SR ryanodine receptors.

If the level of an attractant remains high, the level of phosphorylation of CheA ( and therefore CheY and CheB ) will remain low, the cell will swim smoothly, and the level of methylation of the MCPs will increase ( because CheB-P is not present to demethylate ).

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 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.