In Figure 2, the points in the network are designated by a letter accompanied by a number.

Each point on C, as a vertex, may possess a finite number of corresponding diagonal points by the above construction.

We note that two such curves C and Af, cannot coincide at more than a finite number of points ; ;

First, for any value of T for which all values of f{t} are ordinary points the number of values of f{t} must be odd.

Therefore, for any value of T the number of values of f{t} is equal to the ( finite ) number of tangent points corresponding to the argument T plus an odd number.

The remaining ( incomplete ) components all have an even number of ordinary points at any argument, and are defined only on a proper sub-interval of Aj.

The melting and boiling points of astatine are also expected to follow the trend seen in the halogen series, increasing with atomic number.

where is generally taken to be the duration of the time-history, or the number of points if is constant.

Anthemius assumes a property of an ellipse not found in Apollonius's work, that the equality of the angles subtended at a focus by two tangents drawn from a point, and having given the focus and a double ordinate he goes on to use the focus and directrix to obtain any number of points on a parabola — the first instance on record of the practical use of the directrix.

The coordinates of the points on the curve are of the form ( x, 1 / x ) where x is a number other than 0.

The celebration of deeds of ancient Danish and Swedish heroes, the poem beginning with a tribute to the royal line of Danish kings, but written in the dominant literary dialect of Anglo-Saxon England, for a number of scholars points to the 11th century reign of Canute, the Danish king whose empire included all of these areas, and whose primary place of residence was in England, as the most likely time of the poem's creation, the poem being written as a celebration of the king's heroic royal ancestors, perhaps intended as a form of artistic flattery by one of his English courtiers.

The award's only tie occurred in the National League in 1979, when Keith Hernandez and Willie Stargell received an equal number of points.

It can sometimes be advantageous to bid a contract that one does not expect to make and to be defeated, thus losing some points, rather than allow the opposing side to bid and make a contract which would score them an even greater number of points.

Bones can serve a number of uses such as projectile points or artistic pigments, and can be made from endoskeletal or external bones such as antler or tusk.

A technique called bootstrapping the simulation model is used, which bootstraps initial data points using a pseudorandom number generator to schedule an initial set of pending events, which schedule additional events, and with time, the distribution of event times approaches its steady state — the bootstrapping behavior is overwhelmed by steady-state behavior.

In their current form, Olympic and other amateur bouts are typically limited to three or four rounds, scoring is computed by points based on the number of clean blows landed, regardless of impact, and fighters wear protective headgear, reducing the number of injuries, knockdowns, and knockouts.

As the playing time for each individual game is short, it is often played in matches, where victory is awarded to the first player to reach a certain number of points.

Finite geometry is the study of geometric systems having only a finite number of points.

Thus if one chooses an infinite number of points in the closed unit interval, some of those points must get arbitrarily close to some real number in that space.

Though the number of people flowing in and out of our metropolitan areas each day has increased tremendously since World War 2,, total annual rail commutation dropped 124 million for 1947 to 1957.

Rather, such assignments are made, as they must be, on the basis of certain overall rules and standards, representing to some extent a statistical approach to the problem, taking into account for each situation some of the variables ( e.g., power and station separations ) and averaging out others in order to achieve the balance which must be struck between protection against destructive interference and the assignment of a number of stations large enough to afford optimum radio service to the Nation.

Since broadcast frequencies are very limited in number, these objectives are to some extent inconsistent in that not all of them can be fully realized, and to the extent that each is realized, there is a corresponding reduction of the possibilities for fullest achievement of the others.

Additional class 2, assignments for daytime operation can be made without causing destructive interference to the class 1, stations or to each other, and by their operation provide additional service on these channels and additional local outlets for a large number of communities.

If no specific organization plan exists limiting the number of scientists at each salary level, the result is a department top-heavy with high-level, high-salaried personnel ''.

One good way to cut your labor waste is to make sure you are using just the right number of men in each crew.

The bottom part of a burrow has a number of side tunnels or `` cells '', each of which is provided with an egg plus a store of beebread.

More generally, suppose that an experiment consists of a number of independent trials, that each trial results in either a `` success '' or a `` non-success '' ( `` failure '' ), and that the probability of success remains constant from trial to trial.

For an experiment to qualify as a binomial experiment, it must have four properties: ( 1 ) there must be a fixed number of trials, ( 2 ) each trial must result in a `` success '' or a `` failure '' ( a binomial trial ), ( 3 ) all trials must have identical probabilities of success, ( 4 ) the trials must be independent of each other.

When each number of successes X is paired with its probability of occurrence Af, the set of pairs Af, is a probability function called a binomial distribution.

The number of successes on each shot is a value of a random variable that has values 0 or 1, and there are 5 such random variables here.

In order to be able to properly relate the data for a single company each of the three cards comprising the set for each firm was identified with the appropriate serial number of the respondent.

We know that the number of radio and television impulses, sound waves, ultra-violet rays, etc., that may occupy the very same space, each solitary upon its own frequency, is infinite.

So we may conceive the coexistence of the infinite number of universal, apparently momentary states of matter, successive one after another in consciousness, but permanent each on its own basic phase of the progressive frequencies.

The body, senses and brain, in common with all matter, have their counterpart on each of a countless number of frequencies.

List the number of hours the family can be expected to work each month.

And while every writer must be dealt with as a special case, the interested student will want to ask himself a number of questions about each.

Having volunteered that he was a man of about sixty, he bounded up the stairs and with each leap rendered the number less credible.

The spokesman said the number to be furloughed cannot be estimated since the lay-offs must be carried out in each area depending on what men are most needed on the job.

The basic state grant is thirty cents for each person served, and there is a further book incentive grant that provides an extra twenty cents up to fifty cents per capita, if a library spends a certain number of dollars.

we cover each of these with our blanket of peas and then at last we have octillion peas corresponding in number to the atoms in the body.

The actual number of species in each group depends on the taxonomic classification followed.

The number of electrons in each element's electron shells, particularly the outermost valence shell, is the primary factor in determining its chemical bonding behavior.