The turn of the century, or to be more precise, the two decades preceeding and following it, marks a great change in the history of early English scholarship.

Without a precise knowledge of Germanic philology, however, it is debatable whether their use was not more often a source of confusion and error than anything else.

The ledger was full of most precise information: date of laying, length of incubation period, number of chick reaching the first week, second week, fifth week, weight of hen, size of rooster's wattles and so on, all scrawled out in a hand that looked more Chinese than English, the most jagged and sprawling Alex had ever seen.

The Istiqlal found that the spontaneous solidarity of the independence struggle was not easily transposed to the more concrete, precise problems of internal politics.

When the power of the latter was made both limited and explicit -- when norms were clarified and made more precise and the creation of new norms was placed exclusively in parliamentary hands -- two purposes were served: Government was made subservient to an institutionalized popular will, and law became a rational system for implementing that will, for serving conscious goals, for embodying the `` public policy ''.

Uncertainty overcoming itself is the precondition of the quest for new and more precise information about the world.

In continuation of these theoretical studies, a more precise elucidation of the effects of imperfections in network structure is sought.

For more rigorous and precise analysis, the numerical approximations must be used.

A January 15, 1941 story in the Des Moines Register announced the ABC as " an electrical computing machine " with more than 300 vacuum tubes that would " compute complicated algebraic equations " ( but gave no precise technical description of the computer ).

A more precise way to measure resistance is to place an object within an artificial, uniform stream of air where the velocity is known.

The more precise meaning " three-masted ship " arose in the 17th century, and often takes the French spelling for disambiguation.

By World War II, the use of the smaller divisions, platoons and companies, became much more important as precise operations became vital.

Modifications to each aircraft include removal of the aircraft gun and replacement with the tank that contains smoke-oil used in demonstrations, and outfitting with the control stick spring system for more precise aircraft control input.

Other, more precise and robust methods have been developed For example, the truncated mean of the middle 24 % of the sample order statistics produces an estimate for x < sub > 0 </ sub > that is more efficient than using either the sample median or the full sample mean.

In June 2001, NASA launched a second CMB space mission, WMAP, to make much more precise measurements of the great scale anisotropies over the full sky.

The Jordan – Hölder theorem is a more precise way of stating this fact about finite groups.

The stories locate it somewhere in Britain and sometimes associate it with real cities, though more usually its precise location is not revealed.

In more precise language, the dependence of y upon x means that y is a function of x.

This more precise usage enables one to distinguish between varieties of a language, such as the French spoken in Nice, France, and local languages distinct from the superordinate language, e. g. Nissart, the traditional native Romance language of Nice, known in French as Niçard.

It provides a more precise guide for the actors, directors and technicians and can be used to complement the traditional ADR method.

Dziga Vertov believed his concept of Kino-Glaz, or " Cine Eye " in English, would help contemporary man evolve from a flawed creature into a higher, more precise form.

For the sake of the example ( and this is a gross simplification ), let's assume that he values this particular risk at 5 % per annum ( we could perform a more precise probabilistic analysis of the risk, but that is beyond the scope of this article ).

His theory of peripatric speciation ( a more precise form of allopatric speciation which he advanced ), based on his work on birds, is still considered a leading mode of speciation, and was the theoretical underpinning for the theory of punctuated equilibrium, proposed by Niles Eldredge and Stephen Jay Gould.

In order to distinguish esoteric currents based primarily on sources from late Antiquity and the European Middle Ages, from e. g. Islamic or Jewish currents with similar features, the more precise term " Western esotericism " is often employed.

A mathematical formula is nothing more than a pattern for solving a specific problem.

A more radical defense is to deny the separation of physical world and the platonic world, i. e. the mathematical universe hypothesis.

In computer science, an abstract data type ( ADT ) is a mathematical model for a certain class of data structures that have similar behavior ; or for certain data types of one or more programming languages that have similar semantics.

For those of the Cardinal, Melanchthon, and Dürer's final major work, a drawn portrait of the Nuremberg patrician Ulrich Starck, Dürer depicted the sitters in profile, perhaps reflecting a more mathematical approach.

The main disadvantage of abstraction is that highly abstract concepts are more difficult to learn, and require a degree of mathematical maturity and experience before they can be assimilated.

It was intended specifically for the new class of users that time-sharing systems allowed — that is, a less technical user who did not have the mathematical background of the more traditional users and was not interested in acquiring it.

In more general mathematical settings, the Boltzmann distribution is also known as the Gibbs measure.

A more general binomial theorem and the so-called " Pascal's triangle " were known in the 10th-century A. D. to Indian mathematician Halayudha and Persian mathematician Al-Karaji, in the 11th century to Persian poet and mathematician Omar Khayyam, and in the 13th century to Chinese mathematician Yang Hui, who all derived similar results .< ref > Al-Karaji also provided a mathematical proof of both the binomial theorem and Pascal's triangle, using mathematical induction.

A course in calculus is a gateway to other, more advanced courses in mathematics devoted to the study of functions and limits, broadly called mathematical analysis.

The actual degree of security achieved over time varies, as more computational power and more powerful mathematical analytic methods become available.

The term ' Copenhagen interpretation ' suggests something more than just a spirit, such as some definite set of rules for interpreting the mathematical formalism of quantum mechanics, presumably dating back to the 1920s.

Another application of category theory, more specifically: topos theory, has been made in mathematical music theory, see for example the book The Topos of Music, Geometric Logic of Concepts, Theory, and Performance by Guerino Mazzola.

This work showed that the quantum approach to chemical bonds could be fundamentally and quantitatively correct, but the mathematical methods used could not be extended to molecules containing more than one electron.

Compactness in this more general situation plays an extremely important role in mathematical analysis, because many classical and important theorems of 19th century analysis, such as the extreme value theorem, are easily generalized to this situation.

New mathematical techniques made it possible to control, more accurately, significantly more complex dynamical systems than the original flyball governor.

The " space " in cyberspace has more in common with the abstract, mathematical meanings of the term ( see space ) than physical space.

It is a constitutive equation which provides a mathematical relationship between two or more state functions associated with the matter, such as its temperature, pressure, volume, or internal energy.

It has often been categorized as science fiction although it could more precisely be called " mathematical fiction ".

He disliked complicated theories, and while he had great mathematical ability, he would never use it when the job could be done much more simply.

The greatest common divisor is often written as GCD ( a, b ) or, more simply, as ( a, b ), although the latter notation is also used for other mathematical concepts, such as two-dimensional vectors.

The word " fractal " often has different connotations for laypeople than mathematicians, where the layperson is more likely to be familiar with fractal art than a mathematical conception.

The term representation of a group is also used in a more general sense to mean any " description " of a group as a group of transformations of some mathematical object.