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, 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 Want of a Genre ", article by Christopher M. Cevasco.

For more information, consult the Wikipedia article on affine transformations.

For a detailed discussion of the differences including a more comprehensive table ( several essential tables are given below ) of Biblical scripture for both Testaments and the intertestamental period with regard to canonical acceptance in Christendom's various major traditions, see Wikipedia's article on " Biblical canon ".

For example, in the U. S. state of Massachusetts an article of incorporation approved by the local state legislature distinguishes a city government from a town.

( For diagrams and full descriptions, see Contra Dance Form main article.

For more information on the efficiency of enzymatic catalysis, see the article on Enzymes.

For clarity, this article calls the two alternatives upper camel case and lower camel case.

For example, in the illustration shown in this article, the path < tt >/ Payroll / Salaries / Managers </ tt > uniquely identifies a file called < tt > Managers </ tt > in a folder called < tt > Salaries </ tt >, which in turn is contained in a folder called < tt > Payroll </ tt >.

For the purposes of this article, we call this constructed vector the transmitted vector.

For information on the specific challenges in the Amiga market of the time, see the Amiga Software article.

For the list of the members of the Holy Synod and their official titles see main article The Holy Synod of the Coptic Orthodox Patriarchate of Alexandria

For an overview of critical psychology in South Africa, see Desmond Painter and Martin Terre Blanche's article on Critical Psychology in South Africa: Looking back and looking forwards.

( For some more information about the early development, see the article " Gracht ", section " Delft as an example ").

For the purposes of this article, such reals will be called simply definable numbers.

For main article, see English and French Deism in the Eighteenth Century

For the sake of the example ( and this is a gross simplification ), let's assume that he values this particular risk at 5 % per annum ( we could perform a more precise probabilistic analysis of the risk, but that is beyond the scope of this article ).

For more information, see the main article on Bifurcation theory.

For these reasons, the Convention provides that neither marriage nor dissolution of marriage shall automatically affect the nationality of either spouse ( article 4d ).

For a thorough discussion of the valves and the compensation system, see the article on brass instruments.

For the purposes of this article then, a fugue state would occur while one is acting out a Dissociative Fugue.

For the names of the Uposatha days in Asian Buddhist countries see the article Uposatha.

For the culture and history of the island, see article Gotland.

: For an elementary introduction to how Lie algebras are related to particle physics, see the article Particle physics and representation theory.

For a more elementary discussion of Galois groups in terms of permutation groups, see the article on Galois theory.

For the purposes of this article, history is taken to mean written history recorded in a narrative format for the purpose of informing future generations about events.