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

For both economic and political reasons all segments of the population must be able to share in the growth of a country.

For internal political reasons, the union asks for ( and accepts ) increases in the basic wage rate, and would vigorously oppose a reduction in this rate, but the adjustment of the basic wage rate upwards is essentially up to the discretion of the companies of the industry.

`` For these and other reasons '', says Dr. Brodie, `` orthodontics can prolong the life of teeth ''.

For many reasons, the demand to buy shares in the Dallas-headquartered company was tremendous.

This is one of the main reasons for National Library Week, April 16-22, and for its theme: `` For a richer, fuller life, read ''!!

For general morale reasons and to encourage the efforts of his supply officers, when food was short for combat troops he cut the rations of his headquarters staff accordingly.

For various reasons, however, poverty and personal inclination among others, he did not take a prominent part in the military operations of this period.

For these reasons, I appoint my grandson Karim, the son of my own son, Aly Salomone Khan to succeed to the title of Aga Khan and to the Imam and Pir of all Shia Ismailian followers.

For different reasons, various constitutionalists have praised the Act of Settlement: Henry Hallam called the act in the United Kingdom " the seal of our constitutional laws " and David Lindsay Keir placed its importance above the Bill of Rights 1689.

For unknown reasons, Plato never completed Critias.

For these reasons many CAD applications use the DWG format which can be licensed from AutoDesk or non-natively from the Open Design Alliance.

For these reasons and others the breeds overall production efficiency in an economic sense is still unclear.

For these reasons, a setup of bioleaching must be carefully planned, since the process can lead to a biosafety failure.

For these and other reasons, BCG was therefore given to time with the peak incidence of pulmonary disease.

For contingent reasons having to do with the Inquisition, Descartes spoke of motion as both absolute and relative.

For sparring, a bamboo shinai is typically used instead for obvious safety reasons.

For these reasons, legislative changes tend to be large, jarring and disruptive ( sometimes positively, sometimes negatively, and sometimes with unintended consequences ).

For these reasons, he was expected to seize opportunities during the 1990s to pursue closer ties with the Arab World.

For many reasons, including its age and its popularity among Western militaries, it is one of the most universally known card games in existence.

For all these reasons Costa Rica was by and large unappreciated and overlooked by the Spanish Crown and left to develop on its own.

For these reasons, paper currency was held in suspicion and hostility in Europe and America.

For these reasons, visiting caves inhabited by hibernating bats is discouraged during cold months ; and visiting caves inhabited by migratory bats is discouraged during the warmer months when they are most sensitive and vulnerable.

For these reasons, according to many commentators, Confucius's teachings may be considered a Chinese example of humanism.

For these reasons, rasterization is usually the approach of choice when interactive rendering is required ; however, the pixel-by-pixel approach can often produce higher-quality images and is more versatile because it does not depend on as many assumptions about the image as rasterization.

For these and other reasons, phylogenetic nomenclature has been developed ; it is still controversial.