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, 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 several weeks we eyed one another almost like sparring partners, and then one day Uncle was slightly indisposed and stayed home ; ;

For better or for worse, we all now live in welfare states, the organizing principle of which is collective responsibility for individual well-being.

For better or worse we cannot regard `` imitation '' in the arts in the simple mode of classical rationalism or detached realism.

For answers to such questions we must turn to the anthropologists, the biologists, the historians, the psychologists, and the sociologists.

For what we propose, however, a psychoanalyst is not necessary, even though one aim is to enable the reader to get beneath his own defenses -- his defenses of himself to himself.

William Wimsatt and Cleanth Brooks, it seems to me, have a penetrating insight into the way in which this control is effected: `` For if we say poetry is to talk of beauty and love ( and yet not aim at exciting erotic emotion or even an emotion of Platonic esteem ) and if it is to talk of anger and murder ( and yet not aim at arousing anger and indignation ) -- then it may be that the poetic way of dealing with these emotions will not be any kind of intensification, compounding, or magnification, or any direct assault upon the affections at all.

For this purpose we now draw upon data from sociological and psychological studies of students in American colleges and universities, and particularly from the Cornell Values Studies.

For this concept of an Advisory Board, ancillary to the Board of Trustees, we are indebted to the late President of Harvard University, A. Lawrence Lowell, a master of the subject of the structure of cultural institutions and their administration.

For example, when the film is only four minutes old, Neitzbohr refers to a small, Victorian piano stool as `` Wilhelmina '', and we are thereupon subjected to a flashback that informs us that this very piano stool was once used by an epileptic governess whose name, of course, was Doris ( the English equivalent, when passed through middle-Gaelic derivations, of Wilhelmina ).

For vector spaces over non-algebraically closed fields, we still need to find some substitute for characteristic values and vectors.

For the marksman, we study sets of five shots ( Af ) ; ;

For example, we are interested in the number of bull's-eyes, not which shots were bull's-eyes.

For example, the marksman gets 5 shots, but we take his score to be the number of shots before his first bull's-eye, that is, 0, 1, 2, 3, 4 ( or 5, if he gets no bull's-eye ).

For purposes of sample selection only ( individual tests were given later ) we obtained group test scores of reading achievement and intelligence from school records of the entire third-grade population in each school system.

For our present purposes we assume that the sole subject of bargaining is the basic wage rate ( not including productivity improvement factors or cost-of-living adjustments ), and it is this basic wage rate which determines the level of costs.

For almost a hundred years we relied upon state courts ( subject to review by the Supreme Court ) for the protection of most rights arising under national law.

For the use of students and future restorers, a full, day-by-day record was kept of all three undertakings, complete technical reports on what we found and what we did.

For convenience we chose a stronger pigment, unknown to the early Italians or to Brumidi, titanium oxide, reserving the active lime white for highest lights, put on at the end of the day's stint.

For phosphor to fiber and fiber to air surfaces, and assuming Af, we obtain Af percent.

For the further discussion, we shall thus assume an electron optical resolution of 80 Af and phosphor screen resolution of 60 Af.

For the second we might have to choose the volume of reactor or amount of cooling to be supplied ; ;

For a single stage we may define Af where the maximization is by choice of Af.

For another moment we didn't talk, then she began to weep.

For it is primarily in community that we know and experience spirit.