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

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 the best results, feed this level to cattle 3 to 5 days preceding shipment and/or 3 to 5 days following their arrival in your feed lot.

For instance, the following statement was rated low in compulsivity, `` She's naturally quite neat about things, but it doesn't bother her at all if her room gets messy.

For example, one hebephrenic man used to annoy me, month after month, by saying, whenever I got up to leave and made my fairly steoreotyped comment that I would be seeing him on the following day, or whenever, `` You're welcome '', in a notably condescending fashion -- as though it were his due for me to thank him for the privilege of spending the hour with him, and he were thus pointing up my failure to utter a humbly grateful, `` thank you '' to him at the end of each session.

For example, property `` used in the trade or business '' of a transferor corporation, as defined in section 1231, presumably would not retain its special status following a non-taxable reorganization if it is not so used in the business of the acquiring corporation.

For the reason just suggested, I shall assume the use of the first subtype of fully distributed cost apportionment in the following simplified example.

For a time following the abandonment of the local plant, electric current for Manchester was brought in from the south with an emergency tie-in with the Vermont Marble Company system to the north.

For example, he cites the following data from two studies on job satisfaction: in the first study, 85 per cent of professionals and executives, 64 per cent of white collar people, and 41 per cent of factory workers expressed satisfaction with their jobs ; ;

7070/7074 Autocoder includes the following declarative statements: DA ( Define Area ), DC ( Define Constant ), DRDW ( Define Record Definition Word ), DSW ( Define Switch ), DLINE ( Define Line ), EQU ( Equate ), CODE,DTF ( Define Tape File ), DIOCS ( Define Input/Output Control System ), and DUF ( Descriptive Entry For Unit Records ).

Pope Pius the Sixth, at Rome, in April, 1778, wrote the following: `` The faithful should be excited to the reading of the Holy Scriptures: For these are the most abundant sources which ought to be left open to everyone, to draw from them purity of morals and of doctrine, to eradicate errors which are so widely disseminated in these corrupt times ''.

For example Connecticut applies the following standard to review unpreserved claims: 1. the record is adequate to review the alleged claim of error ; 2. the claim is of constitutional magnitude alleging the violation of a fundamental right ; 3. the alleged constitutional violation clearly exists and clearly deprived the defendant of a fair trial ; 4. if subject to harmless error analysis, the state has failed to demonstrate harmlessness of the alleged constitutional violation beyond a reasonable doubt.

For the algorithm above, one could use the following pseudocode:

For many centuries following his death Alboin's heroism and his success in battle were celebrated in Saxon and Bavarian epic poetry.

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

For any system, the following restrictions on measurement results apply, where is the reduced Planck constant and is any direction vector such as x, y, or z:

* James ` s Theorem For a Banach space the following two properties are equivalent:

For the following year the Duke proposed a campaign along the valley of the River Moselle to carry the war deep into France.

For a time, memory capacities were often expressed in K, even when M could have been used: The IBM System / 370 Model 158 brochure ( 1972 ) had the following: " Real storage capacity is available in 512K increments ranging from 512K to 2, 048K bytes.

Orpah reluctantly leaves ; however, Ruth says, " Entreat me not to leave you, or to turn back from following you ; For wherever you go, I will go ; And wherever you lodge, I will lodge ; Your people shall be my people, and your God, my God.

For instance, the momentum operator p has the following form:

For example, in the United Kingdom, the Companies Act 2006 requires directors of companies " to promote the success of the company for the benefit of its members as a whole " and sets out the following six factors regarding a director's duty to promote success:

For example, " UQJHSE " could be the code for " Proceed to the following coordinates ".

For example, following the American Revolution in 1776, one of the first legislative acts undertaken by each of the newly independent states was to adopt a " reception statute " that gave legal effect to the existing body of English common law to the extent that American legislation or the Constitution had not explicitly rejected English law.

For a quarter-century following independence, Cameroon was one of the most prosperous countries in Africa.

For example, the Pogo comic strip by Walt Kelly originally appeared only in the New York Star in 1948 and was not picked up for syndication until the following year.

For example, in one case, a prominent Chicana feminist writer and poet has indicated the following subjective meaning through her creative work.