This, of course, results from the non-systematic, ' cellular ' character of Ptolemaic theory.

There results a study of literature freed from the tyranny of the contemporary.

There is now substantial evidence from several major studies of college students that the experience of the college years results in a certain, selective homogenization of attitudes and values.

Gen. Taylor will report to President Kennedy in a few days on the results of his visit to South Viet Nam and, judging from some of his remarks to reporters in the Far East, he is likely to urge a more efficient mobilization of Vietnamese military, economic, political and other resources.

Over a temperature range from 25 to 200 Af and at pressures up to 250 atm, an overload of 300 psi, applied for a period of one day, results in an uncertainty in the pressure of, at most, one millimeter of mercury.

The results of the study, based on collision integrals computed from the latest critically evaluated data on intermolecular forces in air, will be reported in the form of a table of viscosity, thermal conductivity, thermal diffusion, and diffusion coefficients at temperatures of 1,000 to 10,000 Af and of logarithm of pressure in atmospheres from Af to Af times normal density.

Exposure problems may occur in these forest areas where uneven lighting results from shafts of sunlight filtering through the overhead branches.

The results of present observations of the thermal radio emission of the moon are consistent with the very low thermal conductivity of the surface layer which was derived from the variation in the infrared emission during eclipses ( e.g., Garstung, 1958 ).

Radio observations of the moon have been made over the range of wave lengths from 4.3 mm to 75 cm, and the results are summarized in Table 1.

Since Af is ferromagnetic, we felt that any results obtained from the magnetically contaminated Af would be suspect.

We are reporting these investigations here briefly because of their relevancy to problems of the study of apparently simple exchange reactions of chlorine and because the results furnish some information on the activation energy for abstraction of chlorine atoms from carbon tetrachloride.

Many workers believe that the response is proportional to the incident momentum of the particles, a relation deduced from laboratory results linearly extrapolated to meteoritic velocities.

The best way to determine the correct figure ( in captives ) is by direct observation of pairs isolated from birth, a method that produced surprising results: maturing of a male Indian python in less than two years, his mate in less than three ; ;

Similar results might be expected from the influence of drugs or pathological conditions that limit iodide trapping, or organification, or accelerate thyroglobulin proteolysis.

The international unit ( u. ), adopted to make possible the comparison of results from different laboratories ( Mussett and Perry, 1955 ), has been defined as the amount of activity present in 13.5 mg of the International Standard Preparation.

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.

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.

The results of these inquiries were used to adjust compilations of data from the registers and to provide various ratios and rates by districts, including birth and death rates, general fertility rates, distributions by marital status, fertility of wives separately in polygynous and non-polygynous households, infant mortality, and migration.

He made it clear from the beginning that this was the students' opportunity, and that the future destiny of such groups depended on favorable results from this one.

This results in a separate record being made, distinguishing these trades from the overall volume of trading.

The research team was concerned that responses from firms in the state of Washington might not be typical of those throughout the country, or that the results might be different when no phone or personal follow-up was made.

Social theory has no more right to expect results from meaningless questions, than physics has the right to expect a theological solution to the wave-particle controversy.

The results of the election of 1859 found Republican candidates not only winning the offices of governor and lieutenant-governor but also obtaining the two Congressional offices from the eastern and western sections of the state.

Despite the fundamental importance and frequent necessity of statistical reasoning, there may nonetheless have been a tendency among biologists to distrust or deprecate results which are not qualitatively apparent.

The fundamental difference between a calculator and computer is that a computer can be programmed in a way that allows the program to take different branches according to intermediate results, while calculators are pre-designed with specific functions such as addition, multiplication, and logarithms built in.

Because it demonstrates the fundamental limitation of the observer to predict experimental results, Richard Feynman called it " a phenomenon which is impossible ... to explain in any classical way, and which has in it the heart of quantum mechanics.

Furthermore, Bob is only able to perform his measurement once: there is a fundamental property of quantum mechanics, known as the " no cloning theorem ", which makes it impossible for him to make a million copies of the electron he receives, perform a spin measurement on each, and look at the statistical distribution of the results.

Enumerative graph theory then rose from the results of Cayley and the fundamental results published by Pólya between 1935 and 1937 and the generalization of these by De Bruijn in 1959.

Since this also results in a prediction for the relative strengths of the fundamental interactions which we observe, in particular the weak mixing angle, Grand Unification ideally reduces the number of independent input parameters, but is also constrained by observations.

The most fundamental results of this theory are Shannon's source coding theorem, which establishes that, on average, the number of bits needed to represent the result of an uncertain event is given by its entropy ; and Shannon's noisy-channel coding theorem, which states that reliable communication is possible over noisy channels provided that the rate of communication is below a certain threshold, called the channel capacity.

The adoption of international standards results in the creation of equivalent, national standards that are substantially the same as international standards in technical content, but may have ( i ) editorial differences as to appearance, use of symbols and measurement units, substitution of a point for a comma as the decimal marker, and ( ii ) differences resulting from conflicts in governmental regulations or industry-specific requirements caused by fundamental climatic, geographical, technological, or infrastructural factors, or the stringency of safety requirements that a given standard authority considers appropriate.

The first half of the 20th century saw an explosion of fundamental results, accompanied by vigorous debate over the foundations of mathematics.

Classical measure theory makes deep usage of the axiom of choice, which is fundamental to, first, distinction between measurable and non-measurable sets, the existence of the latter being behind such famous results as the Banach – Tarski paradox, and secondly the hierarchies of notions of measure captured by notions such as Borel algebras, which are an important source of intuitions in set theory.

Pavel Samuilovich Urysohn, Pavel Uryson () ( February 3, 1898, Odessa – August 17, 1924, Batz-sur-Mer ) was a Jewish mathematician who is best known for his contributions in the theory of dimension, and for developing Urysohn's Metrization Theorem and Urysohn's Lemma, both of which are fundamental results in topology.

These forces, and also energy gained from the scattering particle by the lighter target, change the scattering results in fundamental ways which suggest structural information about the target.

However, results such as the fundamental theorem of algebra are simpler when expressed in terms of complex numbers.

Important results include the Bolzano – Weierstrass and Heine – Borel theorems, the intermediate value theorem and mean value theorem, the fundamental theorem of calculus, and the monotone convergence theorem.

Similar ideas are found in learning theories that developed from the same fundamental concepts, emphasizing how understanding results from knowing concepts both in part and as a whole.

Physics embodies the study of the fundamental constituents of the universe, the forces and interactions they exert on one another, and the results produced by these interactions.

The indistinguishability of all particles of each fundamental type ( say, electrons, or photons ) results in the Dirac and Bose quantum statistics which in turn result in the Pauli exclusion principle for fermions and in Bose-Einstein condensation for bosons.

Fermat's little theorem is the basis for the Fermat primality test and is one of the fundamental results of elementary number theory.

In cosmological models ( geometric 3-manifolds ), a compact space is either a spherical geometry, or has infinite fundamental group ( and thus is called " multiply connected ", or more strictly non-simply connected ), by general results on geometric 3-manifolds.

In computability theory, Kleene's recursion theorems are a pair of fundamental results about the application of computable functions to their own descriptions.

The fundamental results the researchers obtained established Turing computability as the correct formalization of the informal idea of effective calculation.

Inspired by the fundamental randomness in physics, Gregory Chaitin starts publishing results on Algorithmic Information theory ( measuring incompleteness and randomness in mathematics )

Intuition has no possible connection with an empirical calculation of results, and Hutcheson in adopting such a criterion practically denies his fundamental assumption.