In total, these increases in operating costs outweigh the savings that result from declining programs and from economy measures, such as reduced numbers of units and installations, smaller inventories of major equipment, and improvements in the supply and distribution systems of the Armed Forces.

While the particular limits of these groupings may seem artificially arbitrary, they do fairly express a corresponding grouping of more variable material, and they eventuate also in five classes, along a similar scale, containing approximately equal numbers of cases, namely 19, 14, 15, 11, 12 in Athabascan.

But, up to now, no one has attempted to analyze its inherent mathematical properties, or the numerical significance of its numbers -- singly or in combination -- and then tried to consider these in the light of Old Chinese cosmological concepts.

We have already seen that odd numbers were considered as being Yang, while the even numbers were Yin, so that the eight outer numbers of the Lo Shu represented these two principles in balanced equilibrium around the axial center.

`` I keep all these plays in this little black book, and I watch over a twelve-hour period to find out what numbers are repeating.

The expectation of obtaining these sinecures drew young men towards the church in considerable numbers, and the class of abbés so formed — abbés de cour they were sometimes called, and sometimes ( ironically ) abbés de sainte espérance, ( abbés of holy hope ; or the pun, of St. Hope )— came to hold a recognized position.

These include all quadratic surds, all rational numbers, and all numbers that can be formed from these using the basic arithmetic operations and the extraction of square roots.

This polynomial is irreducible over the rationals, and so these three cosines are conjugate algebraic numbers.

All of these numbers are solutions to polynomials of degree ≥ 5.

Most broadly, all numbers that can be defined explicitly or implicitly in terms of polynomials, exponentials, and logarithms are called " elementary numbers ", and these include the algebraic numbers, plus some transcendental numbers.

According to Lucas, Bayley, and Valli, each sign has a handshape ( see handshape section in American Sign Language grammar ) and these handshapes can resemble signs of numbers or letters.

All of these define the relative numbers of particles in a system as decreasing exponential functions of energy ( at the particle level ) over kT, with k representing the Boltzmann constant and T representing the temperature observed at the macroscopic level.

As the numbers of settlers from the mainland increased ( at first mostly prisoners and involuntary indentured labourers, later purposely recruited farmers ), these indigenous people lost territory and numbers in the face of punitive expeditions by British troops, land encroachment and the effects of various epidemic diseases.

No official lists of ANAC numbers are published as telephone companies believe overuse of these numbers could make them more likely to be busy when needed by installers.

As widespread inefficiencies in numbering ( such as the assignment of entire blocks of 10000 numbers to every competing carrier in every small village to support local number portability schemes ) have created shortages of available numbers, these prefixes are often " reclaimed " and issued as standard exchanges, moving the handful of numbers in them to one standard test exchange ( usually 958 ).

In 1 we investigate a new series of line involutions in a projective space of three dimensions over the field of complex numbers.

While women had always attended ball games in small numbers ( it was the part of a `` dead game sport '' in the early years of the twentieth century to be taken out to the ball park and to root, root, root for the home team ), they had often sat in patient martyrdom, unable even to read the scoreboard, which sometimes seemed to indicate that one team led another by a score of three hundred and eighty to one hundred and fifty-one.

I used the alias of Robert C. Richards, gave the first three letters and the first and last figure of the license number on the agency heap, but a couple of phony numbers in between.

A given ( hydrogen-like ) atomic orbital is identified by unique values of three quantum numbers: n, l, and m < sub > l </ sub >.

Ada Lovelace reported in her notes on the Analytical Engine: " Mr. Babbage believes he can, by his engine, form the product of two numbers, each containing twenty figures, in three minutes ".

Currently, Amaranthus includes three recognized subgenera and 70 species, although species numbers are questionable due to hybridization and species concepts.

Constitution of the Athenians, 4th century BCThere were three political bodies where citizens gathered in numbers running into the hundreds or thousands.

There are in round numbers three hundred and sixty uncompounded verbs in Beowulf, and forty of them are poetical words in the sense that they are unrecorded or rare in the existing prose writings.

Since the mass numbers of these are 12, 13 and 14 respectively, the three isotopes of carbon are known as carbon-12, carbon-13, and carbon-14, often abbreviated to < sup > 12 </ sup > C, < sup > 13 </ sup > C, and < sup > 14 </ sup > C.

Gauss also discovered that every positive integer is representable as a sum of at most three triangular numbers on 10 July and then jotted down in his diary the famous note: " ΕΥΡΗΚΑ!

The legacy of Genghis Khan has been contested between China, Mongolia, and Russia, all three states having significant numbers of ethnic Mongols within their borders, and holding territory that was conquered by Khan.

The coordinates of a point p are obtained by drawing a line through p perpendicular to each coordinate axis, and reading the points where these lines meet the axes as three numbers of these number lines.

Carmichael numbers have at least three positive prime factors.

By 1943 however, large numbers of fleet and light carriers became available, which required larger formations of three or four carriers.

The reason why there were three cases to Diophantus, while today we have only one case, is that he did not have any notion for zero and he avoided negative coefficients by considering the given numbers to all be positive in each of the three cases above.

Because this geometrical interpretation of multiplication was limited to three dimensions, there was no direct way of interpreting the product of four or more numbers, and Euclid avoided such products, although they are implied, e. g., in the proof of book IX, proposition 20.

He proved equations for the volumes and areas of various figures in two and three dimensions, and enunciated the Archimedean property of finite numbers.

Training of Wh-sentences has lead improvements in three main areas of discourse for aphasics: increased average length of utterances, higher proportions of grammatical sentences, and larger ratios of numbers of verbs to nouns produced.

The GCD of three or more numbers equals the product of the prime factors common to all the numbers, but it can also be calculated by repeatedly taking the GCDs of pairs of numbers.

The modern definition has four points, which it numbers zero to three in compliance with zero-based numbering common to computer systems.

Plutarch isn't sure exactly how Fabius came up with this number, although he believes it was to honor of the perfection of the number three, as it is the first of the odd numbers, and one of the first of the prime numbers.

However, all of these legions were ' short ', and did not have the requisite numbers of troops.

Arminius, who had grown up in Rome as a citizen and become a Roman soldier, understood Roman tactics very well and could direct his troops to counter them effectively, using locally superior numbers against the dispersed Roman legions.

The three legion numbers were never used again by the Romans after this defeat, unlike other legions that were restructured – a case unique in Roman history except for the XXII Deiotariana legion, which may have been disbanded after heavy losses against the Jewish rebels in the Bar Kokba revolt ( 132 – 136 ) in Israel.

" He does not say that they were united, only that, if they were, these would be their numbers ; that is, 4 Roman legions and 4 allied alae.

The numbers stated to have fought the battle are problematic: a combined Roman army should have had 5 legions of 20, 000 men and all 30, 000 allies authorized by the Senate and yet if the armies were not combined Sempronius should have had only two legions of 8, 000 men.

This way, if the legions could not win a battle through military combat skill or superior numbers, they could simply outlast the invaders, who, as historian E. A.

Alongside the legions, Augustus established the auxilia, a regular corps of similar numbers to the legions, recruited from the peregrini ( non-citizen inhabitants of the empire – about 90 % of the empire's population in the 1st century ).

The numbers grew to a peak of about 450, 000 by 211 ( 33 legions and c. 400 auxiliary regiments ).

While still maintaining its own royal family, is far more democratic than the TOG, accepts women and aliens as equals, and even includes refugees from both the former Kess Rith empire, exiled or disgusted TOG military legions, and large numbers of TOG women who defect to the Commonwealth.

Each army corps of two legions was supported by greater numbers of Italian and other allied troops.

Possessed of no true intelligent thought and only very rarely transforming into robot mode, the Battle Ravage legions are sufficiently fragile, exploding under minimal artillery fire, but will swarm over their objective like insects, usually managing to tear down opposition through sheer numbers.

These Romans, largely out of need, have adopted a practice of Cultural Romanization more pronounced than the historical Romans did: large numbers of Germans have been adopted into the Roman society, forming a large proportion of both the legions and the Senate.