For simplicity, we shall here use the shorthand notation for representing the over operator.

For simplicity, the following descriptions focus on continuous-time and discrete-time linear systems.

For the sake of simplicity, we might assume that the weights are normalized so that they sum up to 1 ( which can be easily done by dividing each weight by their sum ), thus allowing some terms in the above formulae to be omitted:

) For simplicity, consider a system composed of two identical particles.

For simplicity ’ s sake, the Germans designated any barge up to the size of a standard peniche as Type A1 and anything larger as Type A2.

For this reason, even the name The One isn't a positive name, but rather the most non-multiple name we can think of, a name derived from our own inadequate conception of the simplicity of the first principle.

For simplicity, we will first discuss second quantization for bosons, which form perfectly symmetric quantum states.

For Huxley ’ s biographer and friend, the author Sybille Bedford, the book combined sincerity with simplicity, passion with detachment.

Consider now the acceleration due to the sphere of mass M experienced by a particle in the vicinity of the body of mass m. With R as the distance from the center of M to the center of m, let ∆ r be the ( relatively small ) distance of the particle from the center of the body of mass m. For simplicity, distances are first considered only in the direction pointing towards or away from the sphere of mass M. If the body of mass m is itself a sphere of radius ∆ r, then the new particle considered may be located on its surface, at a distance ( R ± ∆ r ) from the centre of the sphere of mass M, and ∆ r may be taken as positive where the particle's distance from M is greater than R. Leaving aside whatever gravitational acceleration may be experienced by the particle towards m on account of ms own mass, we have the acceleration on the particle due to gravitational force towards M as:

For simplicity we neglect the neutrino ( neutrino accounting requires an exact calculation of all stages of the reaction, and the loss of neutrino energy make up only about one percent ), and annihilate the positrons with 2 electrons from hydrogen atoms remaining after the removal of these protons.

For the sake of simplicity, the frame is shown as a rectangular structure of 270 columns and nine rows but the protocol does not transmit the bytes in this order.

For the sake of simplicity, the frame is shown as a rectangular structure of 270 columns and nine rows.

For simplicity and durability, modern sousaphones almost definitively use three non-compensating piston valves in their construction, in direct contrast to their concert counterparts ' large variation in number, type, and orientation.

For simplicity, the example does not illustrate this.

For simplicity of description, most of this article assumes that the surface to be mapped is that of a sphere.

For many applications, FBA not only offered simplicity, but an increase in throughput.

For simplicity, we consider here only the spinless case.

For simplicity, assume that samples of the input and output are taken at evenly-spaced points in time separated by time.

For simplicity, assume that samples of the input and output are taken at evenly-spaced points in time separated by time.

For simplicity, adopt / adoption or adapt / adaption are used by many linguists, either in parallel to, or in preference to, these words.

For simplicity we consider only the case r = 1.

For some the simplicity of the mechanism, coupled with the large volume of ink it can encapsulate, compensates for the inconvenience of ink transfer.

For simplicity reasons, sometimes it is required that the hyperplane pass through the origin of the coordinate system.

For simplicity we assume unit price ( i. e. P = 1 ), and thus quantities also represent values in all equations.

For example, suppose a man wearing a $200 watch, driving a 1959 Rolls Royce, stops to ask a man on the sidewalk, `` What time is it ''??

For example, suppose another excess profits tax similar to prior laws is enacted, providing for carryover of excess profits credits.

For example, suppose at trial the judge found for the plaintiff and ordered the defendant to pay $ 50, 000.

For example, suppose that each member of the collection X is a nonempty subset of the natural numbers.

For example, suppose that X is the set of all non-empty subsets of the real numbers.

For example, suppose that we want to compute the rate of change in atmospheric pressure ten seconds after the skydiver jumps.

For example, suppose a mutation at a chromosome position is responsible for a recessive trait in a diploid organism ( where chromosomes come in pairs ).

For example, if we suppose at t = 0 the extension is a unit distance ( x = 1 ), and the particle is not moving ( dx / dt = 0 ).

For example, suppose that person S believes he saw Tom Grabit steal a book from the library and uses this to justify the claim that Tom Grabit stole a book from the library.

For example, suppose a and b are two sensible objects in a certain situation of affairs.

For instance, suppose one has a filter which, when presented with an impulse in a time series:

For example, suppose the word square is defined by " A figure is square if and only if it has four perpendicular sides of equal length.

For instance, suppose that each input is an integer z in the range 0 to N − 1, and the output must be an integer h in the range 0 to n − 1, where N is much larger than n. Then the hash function could be h

For example, suppose that the input data are file names such as < tt > FILE0000. CHK </ tt >, < tt > FILE0001. CHK </ tt >, < tt > FILE0002. CHK </ tt >, etc., with mostly sequential numbers.

For example, suppose we have a table like this, which gives some values of an unknown function f.

For example, suppose a free body ( one having no external forces on it ) is at rest at some instant.

For example, suppose the initial value of a variable is 3 and there is a sequence that reads the variable, then changes it to 5, and then reads it again.

For example, suppose that Sally is going to drink a glass of poison, because she wants to commit suicide and believes that she can do so by drinking the poison.

For example, suppose that Ike and Tina's mothers are identical twins and that Ike and Tina are raised in isolation from one another in indistinguishable environments.

' For ' Kubla Khan ' is as near enchantment, I suppose, as we are like to come in this dull world.

For example, suppose a country road in West Virginia is in disrepair.

For example, suppose a process commands that a computer card's voltage output be set high-low-high-low and so on at a rate of 1000 Hz.

For example, suppose we define another substitution action without the freshness condition.

For instance, suppose Portugal was a more efficient producer of wine than England, yet in England cloth could be produced more efficiently than it could in Portugal.

For example, suppose there are two bodies of equal mass, one stationary and one approaching the other at a speed ( as in the figure ).