Basic theories, such as arithmetic, real analysis and complex analysis are often introduced non-axiomatically, but implicitly or explicitly there is generally an assumption that the axioms being used are the axioms of Zermelo – Fraenkel set theory with choice, abbreviated ZFC, or some very similar system of axiomatic set theory like Von Neumann – Bernays – Gödel set theory, a conservative extension of ZFC.

He established the consistent use of the chemical balance, used oxygen to overthrow the phlogiston theory, and developed a new system of chemical nomenclature which held that oxygen was an essential constituent of all acids ( which later turned out to be erroneous ).

The system of Chinese astrology was elaborated during the Zhou dynasty ( 1046 – 256 BC ) and flourished during the Han Dynasty ( 2nd century BC to 2nd century AD ), during which all the familiar elements of traditional Chinese culture – the Yin-Yang philosophy, theory of the 5 elements, Heaven and Earth, Confucian morality – were brought together to formalise the philosophical principles of Chinese medicine and divination, astrology and alchemy.

The 9th-10th century master of the religious system known as " the nondual Shaivism of Kashmir " ( or " Kashmir Shaivism ") and aesthetician, Abhinavagupta brought rasa theory to its pinnacle in his separate commentaries on the Dhvanyāloka, the Dhvanyāloka-locana ( translated by Ingalls, Masson and Patwardhan, 1992 ) and the Abhinavabharati, his commentary on the Nātyashāstra, portions of which are translated by Gnoli and Masson and Patwardhan.

In theory the system could support the Z80 and the 8086 simultaneously.

The Copernican theory of the solar system – that the Earth revolved annually about the Sun – had received confirmation by the observations of Galileo and Tycho Brahe ( who, however, never accepted heliocentrism ), and the mathematical investigations of Kepler and Newton.

Aberrations occur because the simple paraxial theory is not a completely accurate model of the effect of an optical system on light, rather than due to flaws in the optical elements.

The Gaussian theory, however, is only true so long as the angles made by all rays with the optical axis ( the symmetrical axis of the system ) are infinitely small, i. e. with infinitesimal objects, images and lenses ; in practice these conditions are not realized, and the images projected by uncorrected systems are, in general, ill defined and often completely blurred, if the aperture or field of view exceeds certain limits.

Researchers at Bell developed radio astronomy, the transistor, the laser, information theory, the UNIX operating system, the C programming language and the C ++ programming language.

In signal processing and control theory the bandwidth is the frequency at which the closed-loop system gain drops 3 dB below peak.

In chaos theory, the butterfly effect is the sensitive dependence on initial conditions, where a small change at one place in a deterministic nonlinear system can result in large differences to a later state.

Bioinformatics also deals with algorithms, databases and information systems, web technologies, artificial intelligence and soft computing, information and computation theory, structural biology, software engineering, data mining, image processing, modeling and simulation, discrete mathematics, control and system theory, circuit theory, and statistics.

The bilinear transform ( also known as Tustin's method ) is used in digital signal processing and discrete-time control theory to transform continuous-time system representations to discrete-time and vice versa.

However, since piston-engined aircraft rely upon magnetos to provide spark to their cylinders rather than a battery powered ignition coil system, this theory is not strongly convincing.

Some believe that Georg Cantor's set theory was not actually implicated by these paradoxes ( see Frápolli 1991 ); one difficulty in determining this with certainty is that Cantor did not provide an axiomatization of his system.

Informal applications of set theory in other fields are sometimes referred to as applications of " naive set theory ", but usually are understood to be justifiable in terms of an axiomatic system ( normally the Zermelo – Fraenkel set theory ).

Lavoisier established the consistent use of the chemical balance, used oxygen to overthrow the phlogiston theory, and developed a new system of chemical nomenclature and made contribution to the modern metric system.

Once judges began to regard each other's decisions to be binding precedent, the pre-Norman system of local customs and law varying in each locality was replaced by a system that was ( at least in theory, though not always in practice ) common throughout the whole country, hence the name " common law.

Thus the cocktail party would appear to be the ideal system, but there is one weakness.

Bluntly, there never was a Ptolemaic system of astronomy.

Behind were privies, for there was no sewage system.

In the forest highway system, there are now 24,400 miles of public roads.

In the forest development road and trail system, there are now 162,400 miles of roads and 106,500 miles of supplemental foot and horse trails.

If you plan to add cooling later to your heating system, there are things to watch for.

Without a system of values there can be no society.

However, it cannot be presumed, informal though the structure of the population seems, that there are not well-defined roles within the system.

In the absence of a reservoir of political consensus each organized political group hopes that the elections will give them new prominence, but in a system where there is as yet no place for the less prominent.

It was there, in the course of trying to prepare new men for the `` culture shock '' they might encounter in remote overseas posts, that he first began to develop a system of charting the `` norms of human communication ''.

And there was the case of Tom Hepker, a machinist, who was referred by a friend to a health machine quack who treated him with a so-called diagnostic machine for what Doctor Fraud said was a system full of arsenic and strychnine.

-- Alfred Hayes, president of the Federal Reserve Bank of New York, said Tuesday `` there is no present need for far-reaching reforms '' which would basically alter the international financial system.

Hayes said that if a way can be found to deal effectively with short-term capital movements between nations, `` there is no reason, in my judgment why the international financial system cannot work satisfactorily for at least the foreseeable future ''.

Unlike bony fish, there is no direct control of the pigment cells by the nervous system, and this results in the colour change taking place more slowly than happens in fish.

Therefore no complete system, i. e. including the electromagnetic modes, can have negative temperatures, since there is no highest energy state, so that the sum of the probabilities of the states would diverge for negative temperatures.

Adiabatic processes can occur if the container of the system has thermally-insulated walls or the process happens in an extremely short time, so that there is no opportunity for significant heat exchange.

Because there is no external pressure for the gas to expand against, the work done by or on the system is zero.

ΑΒΡΑΣΑΞ, which is far more common in the sources than the variant form Abraxas, ΑΒΡΑΞΑΣ ) was a word of mystic meaning in the system of the Gnostic Basilides, being there applied to the “ Great Archon ” ( Gk., megas archōn ), the princeps of the 365 spheres ( Gk., ouranoi ).

Though there might be blocs of opinion, sometimes enduring, on important matters, there were no political parties and likewise no government or opposition ( as in the Westminster system ).

In 2005 there were 60, 275 students in the ACT school system.

Some ANACs are very regional or local in scope, while others are state -/ province-or area-code-wide: there appears to be no consistent national system for them.

After selling a few kits, MCP became convinced there was a much bigger market for an improved model sold as a completed working system.

Since algorithms are platform-independent ( i. e. a given algorithm can be implemented in an arbitrary programming language on an arbitrary computer running an arbitrary operating system ), there are significant drawbacks to using an empirical approach to gauge the comparative performance of a given set of algorithms.