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 ’ 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, suppose that the evidence used for the test has nothing to do with the collection of 100 objects dealt with here.

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, let's consider a standard 283 cubic inch Chevy Aj.

For example, to move ( as the score requires ) from the lowest F-major register up to a barely audible N minor in four seconds, not skipping, at the same time, even one of the 407 fingerings, seems a feat too absurd to consider, and it is to the flautist's credit that he remained silent throughout the passage.

For example, consider the sample space

For example, consider the following two strings of length 64, each containing only lowercase letters and digits:

For example, consider the matrix

For concreteness, consider the function

For example, consider the function.

For example, consider.

For example, consider English starve and Dutch sterven or German sterben (" to die "); these three words all derive from the same Proto-Germanic root, * sterƀ-(" die ").

For example, consider the following C ++ function:

For example, what Jews from Eastern Europe and from North Africa consider " Jewish food " has more in common with the cuisines of non-Jewish Eastern Europeans and North Africans than with each other, although for religious Jews all food-preparation must conform to the same laws of Kashrut.

For example, consider the problem of primality testing.

For example, consider the problem of finding an integer x such that

For example, consider these two definitions:

For example, consider the quadratic polynomial

For example, consider air as it is heated or cooled.

** For example, consider the map ( which is the " realification " of the complex square function ) where U

For example, consider an online bookseller whose customers maintain wishlists of books they'd like to have.

For example, consider the following sentence:

For example, consider an add-on library for regex support on String.

For example, consider, " My father's brother is my uncle.

For example, consider the following.

For instance, consider a damped harmonic oscillator such as a pendulum, or a resonant L-C tank circuit.

For example, he coined the programming phrase " two or more, use a for ," alluding to the rule of thumb that when you find yourself processing more than one instance of a data structure, it is time to consider encapsulating that logic inside a loop.

For example, consider Okun's law, which relates GDP growth to the unemployment rate.