The completeness of the connections provide that, for N people, there are Af lines of communication between the pairs, which can become a large number ( 1,225 ) for a party of fifty guests.

In spite of the dreams of the host for oneness in the group, the Af incoming messages for each guest overload his receiving system beyond comprehension if N exceeds about six.

Such items recall the California journalist who reported an accident involving a movie star: `` The area in which Miss N -- was injured is spectacularly scenic ''.

For example, to move ( as the score requires ) from the lowest F-major register up to a barely audible N minor in four seconds, not skipping, at the same time, even one of the 407 fingerings, seems a feat too absurd to consider, and it is to the flautist's credit that he remained silent throughout the passage.

The approximate equation is Af, where N is the number of Af with electron line-density greater than or equal to Af, and Q is proportional to the mass of the meteorite.

Therefore, N is inversely proportional to the radius cubed and in fair agreement with the inverse 7/2 power derived from 1958 Alpha and 1959 Eta data.

Let N be a linear operator on the vector space V.

We say that N is nilpotent if there is some positive integer R such that Af.

Then there is a diagonalizable operator D on V and a nilpotent operator N in V such that ( A ) Af, ( b ) Af.

The diagonalizable operator D and the nilpotent operator N are uniquely determined by ( A ) and ( B ) and each of them is a polynomial in T.

We have just observed that we can write Af where D is diagonalizable and N is nilpotent, and where D and N not only commute but are polynomials in T.

hence they commute with D and with N.

for, using the fact that N and N' commute Af and so when R is sufficiently large every term in this expression for Af will be 0.

Then every linear operator T in V can be written as the sum of a diagonalizable operator D and a nilpotent operator N which commute.

These operators D and N are unique and each is a polynomial in T.

Let N be a positive integer and let V be the space of all N times continuously differentiable functions F on the real line which satisfy the differential equation Af where Af are some fixed constants.

If Af denotes the space of N times continuously differentiable functions, then the space V of solutions of this differential equation is a subspace of Af.

Each of the N trials is either a success or a failure.

Each performance of an n-trial binomial experiment results in some whole number from 0 through N as the value of the random variable X, where Af.

We shall find a formula for the probability of exactly X successes for given values of P and N.

Since a ruled surface of order N with N concurrent generators is necessarily a cone, it follows finally that every line through a point, P, of **zg meets its image at P, as asserted.

Some predictions had been made concerning factors R, N, I and Co on these inventories which appeared to be directly related to control and security aspects of personality functioning which were hypothesized as being of importance in differential Kohnstamm reactivity.

Prior to 1954 I imagine that a majority of Southerners would have voted against the Confederacy.

Prior to 1942, automobiles were the individual responsibility of the agency to which assigned.

Prior to 1960, in order to provide matching for the minimum ( base ) allotment, State funds had to equal 1954 State funds.

Prior to and since 1960 the rest of the support allotment is matched at rates related to the fiscal capacity of the State, with a pivot of 40% State ( or 60% Federal ) participation in total program costs.

Prior to World War 2, there was a higher percentage of endogamous marriages than after World War 2.

Prior to the featured race, the stewards announced that apprentice James P. Verrone is suspended ten days for crowding horses and crossing the field sharply in two races on Wednesday.

Prior to that he was associated with Long Island University in Brooklyn.

With the Prior Analytics, Aristotle is credited with the earliest study of formal logic, and his conception of it was the dominant form of Western logic until 19th century advances in mathematical logic.

Prior to Kennedy Center, it screened films in the auditorium of the National Gallery of Art.

Prior to meeting Mallowan, Christie had not had any extensive brushes with archaeology, but once the two married they made sure to only go to sites where they could work together.

Alastair Cook scored 189 and both Ian Bell and Matt Prior made centuries.

Prior to this, the monastery would be a mere priory, headed by a prior who acts as superior but without the same degree of legal authority that an abbot has.

Abbot Francis Michael and Prior Anthony Delisi ( on the left ) of Monastery of the Holy Spirit, a Trappist monastery in Conyers, Georgia, USA.

* Accreditation of Prior Learning ( UK ) refers to a reduction in the amount of study required to pass a degree, due to previous experience or study.

Prior to modern times, there was no distinction between architects, engineers and often artists, and the title used varied depending on geographical location.

# Prior to being drawn and enabled, one is unable to believe … able only to resist.

Prior to leaving Mahallat, Hasan Ali Shah equipped himself with letters appointing him to the governorship of Kerman.

Prior to the Akkadian period the progressive salinisation of the soils, produced by poorly drained irrigation, had been reducing yields of wheat in the southern part of the country, leading to the conversion to more salt-tolerant barley growing.

He wrote many commentaries on the works of Aristotle, extant are those on the Prior Analytics, Topics, Meteorology, Sense and Sensibilia, and Metaphysics.

* J. Barnes, S. Bobzien, K. Flannery, K. Ierodiakonou, 1991, Alexander of Aphrodisias: On Aristotle Prior Analytics 1. 1-7.