The number of primitive ideas in systematically-simple theories is reduced to a minimum.

Law enforcement intelligence applies a number of theories in crime analysis.

A number of theories have been proposed to explain the two figures, and there are occasional references to them in popular culture.

The latter etymology has resulted in a number of theories.

His construction of new cohomology theories has left deep consequences for algebraic number theory, algebraic topology, and representation theory.

Perhaps Grothendieck's deepest single accomplishment is the invention of the étale and l-adic cohomology theories, which explain an observation of André Weil's that there is a deep connection between the topological characteristics of a variety and its diophantine ( number theoretic ) properties.

While many indigenous Amazonian people say they received the instructions directly from plants and plant spirits, researchers have devised a number of alternative theories to explain its discovery.

The Wright brothers ' flight confirmed or disproved a number of aerodynamics theories.

These two factors combined with others have obscured the history of the Baltic languages, leading to a number of theories regarding their position in the Indo-European family.

Some grand unified theories of particle physics also predict that a single proton can decay, changing the baryon number by one ; however, this has not yet been observed under experiment.

For a number of years the support for these theories was evenly divided.

Christopher Hitchens represents conspiracy theories as the " exhaust fumes of democracy ", the unavoidable result of a large amount of information circulating among a large number of people.

There are also, however, a large number of idiosyncratic theories that cannot cleanly be assigned to any of these camps.

Gauss also made important contributions to number theory with his 1801 book Disquisitiones Arithmeticae ( Latin, Arithmetical Investigations ), which, among things, introduced the symbol ≡ for congruence and used it in a clean presentation of modular arithmetic, contained the first two proofs of the law of quadratic reciprocity, developed the theories of binary and ternary quadratic forms, stated the class number problem for them, and showed that a regular heptadecagon ( 17-sided polygon ) can be constructed with straightedge and compass.

According to Mircea Eliade, the medieval " Gioacchinian myth [...] of universal renovation in a more or less imminent future " has influenced a number of modern theories of history, such as those of Lessing ( who explicitly compares his views to those of medieval " enthusiasts "), Fichte, Hegel, and Schelling, and has also influenced a number of Russian writers.

While it is clear that the Christmas tree originates in Renaissance and early modern Germany, there are a number of speculative theories as to its ultimate origin.

These theories are criticized by those who fear an evolution of liberal democracies to post-democracy, and others who point out the high number of illiberal democracies.

In many of Plato's dialogues, such as the Meno, and in particular the Theaetetus, Socrates considers a number of theories as to what knowledge is, the last being that knowledge is true belief that has been " given an account of " — meaning explained or defined in some way.

Detractors note that a significant number of environmental theories and predictions have been inaccurate and suggest that the regulations recommended by environmentalists will more likely harm society rather than help nature.

While extending the notion of number by means of his revolutionary concept of infinite cardinality, Cantor was paradoxically opposed to theories of infinitesimals of his contemporaries Otto Stolz and Paul du Bois-Reymond, describing them as both " an abomination " and " a cholera bacillus of mathematics ".

There are a number of theories of its origin, including as an Arab soup of bread, olive oil, water and garlic that arrived in Spain and Portugal with the Moors, or via the Romans with the addition of vinegar.

In bottom-up theories ( such as the Searle-Zinn model ), small structures such as globular clusters form first, and then a number of such bodies accrete to form a larger galaxy.

Although the United States and the U.S.S.R. have been arguing whether there shall be four, five or six top assistants, the most important element in the situation is not the number of deputies but the manner in which these deputies are to do their work.

Hence all teachers, good and bad, who have been teaching for a given number of years are paid the same salary.

To have any success in this effort, we must ourselves view it as an enterprise stretching over a considerable number of years, and we must encourage the recipients of our aid to view it in the same fashion.

For those communities which have financial difficulties in effecting adjustments, there are a number of alternatives any one of which alone, or in combination with others, would minimize if not even eliminate the problem.

There have been a number of sound plans proposed.

Thus, in the last few years, a number of programs which looked very promising at the time their development was commenced have since been completely eliminated.

To provide the continuous flow of information basic to administrative decisions, a number of institutions have established offices of institutional research.

A large number of these Juniors have 7 and 8 wins to their credit and are seasoned campaigners.

As America on wheels was responsible for an industry of motor courts, motels, and drive-in establishments where you can dine, see a movie, shop, or make a bank deposit, the ever-increasing number of boating enthusiasts have sparked industries designed especially to accommodate them.

Aside from the Ruger carbine, a number of hunting rifles have been introduced for the first time.

A number of them must have fallen into disfavor ; ;

Based on this phenomenon, a number of investigators have used this method to `` look through '' human organs.

In the GE plan, a number of individual contributors have positions and compensation higher than those of many managers.

`` These recent steps do not offer the possibility of extension to the great number of senior engineers who have displayed technical competence.

The railroads have responded by adding 20,000 more box cars with doors 12' or wider for forklift unloading ( a 21% increase while the total number of box cars was falling 6% ) and by cutting their freight rates twice on lumber shipped in heavily loaded cars.

However, whether you arrange to have a European or American model, if you rent a car with the proper seating capacity in relation to the number of people in your party, your transportation expense will average very close to $10.00 per day per passenger.

For the last two years, this frontier of the arts has produced a number of so-called `` non-dramas '' which have left indelible, bittersweet impressions on the psyche of this veteran theatregoer.

A number of semiempirical estimates by various workers lead to the conclusion that the Af bond becomes symmetric when the Af bond length is about 2.4 to 2.5 A, but aside from the possible example of nickel dimethylglyoxime there have been no convincing reports of symmetric Af bonds.

Since practical washing procedures are both lengthy and expensive, a number of laboratory tests have been developed for the numerical evaluation of detergents.

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.

The graph, as a set, may have a finite number of components.

Furthermore, one can find a neighborhood of Q in which the difference function is monotone, for since it is analytic it can have only a finite number of extrema in any interval.

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.

A number of strong independent agencies, established in some cases with governmental or royal support, have conducted large medical, social, educational and research operations in particular parts of the Congo and Ruanda-Urundi.