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.

In classical mathematics, analytic geometry, also known as coordinate geometry, or Cartesian geometry, is the study of geometry using a coordinate system and the principles of algebra and analysis.

Among active contemporary analytical chemistry research fields, micro total analysis system is considered as a great promise of revolutionary technology.

Other functions include, market supervision, oversight of the payment system and provision of settlement services, State treasury service, Central Credit Register, economic analysis and institutional consultancy.

2009, compared an analysis of blood and organ system data from trials with rats fed three main commercialized genetically modified types of maize which are present in food and feed in the world.

As a basic starting point it is normally assumed that, for the purposes of analysis, the general algorithm is known ; this is Shannon's Maxim " the enemy knows the system " -- in its turn, equivalent to Kerckhoffs ' principle.

Although the system established by the Sitges agreement was phased out by 1974, the 1886 Colombian constitution — in effect until 1991 — required that the losing political party be given adequate and equitable participation in the government which, according to many observers and later analysis, eventually resulted in some increase in corruption and legal relaxation.

A system can be mechanical, electrical, fluid, chemical, financial and even biological, and the mathematical modeling, analysis and controller design uses control theory in one or many of the time, frequency and complex-s domains, depending on the nature of the design problem.

The system analysis is carried out in time domain using differential equations, in complex-s domain with Laplace transform or in frequency domain by transforming from the complex-s domain.

In contrast to the frequency domain analysis of the classical control theory, modern control theory utilizes the time-domain state space representation, a mathematical model of a physical system as a set of input, output and state variables related by first-order differential equations.

Numerous tools exist for the analysis of the poles of a system.

Controllability and observability are main issues in the analysis of a system before deciding the best control strategy to be applied, or whether it is even possible to control or stabilize the system.

In 1936, Warner published his analysis of society in American deep south, and concluded it was a caste system.

In mathematics, the Cauchy – Riemann differential equations in complex analysis, named after Augustin Cauchy and Bernhard Riemann, consist of a system of two partial differential equations which must be satisfied if we know that a complex function is complex differentiable.

These methods are analogous to methods used in other areas of science, such as the field of system identification in systems analysis and control theory.

* James Martin's version of Information Engineering systems development methodology was automated to allow the input of the results of system analysis and design in the form of data flow diagrams, entity relationship diagrams, entity life history diagrams etc.

Through analysis of this and other of Hayek's works, Block purports, " in making the case against socialism, Hayek was led into making all sort of compromises with what otherwise appeared to be his own philosophical perspective – so much so, that if a system was erected on the basis of them, it would not differ too sharply from what this author explicitly opposed.

The despun section's instruments included the camera system ; the near infrared mapping spectrometer to make multi-spectral images for atmospheric and moon surface chemical analysis ; the ultraviolet spectrometer to study gases ; and the photo-polarimeter radiometer to measure radiant and reflected energy.

An ion implantation system at Laboratory for analysis and architecture of systems | LAAS technological facility in Toulouse, France.

Bloomfield used the materials collected in his descriptive work to undertake comparative studies leading to the reconstruction of Proto-Algonquian, with an early study reconstructing the sound system of Proto-Algonqian, and a subsequent more extensive paper refining his phonological analysis and adding extensive historical information on general features of Algonquian grammar.

The analysis of the contents of the digestive system of bog bodies had become one of the principal endeavours of investigating such remains.

In system analysis ( a subfield of mathematics ), linear prediction can be viewed as a part of mathematical modelling or optimization.

I knew that a conversation with the author would not settle such questions, because a man is not the same as his writing: in the last analysis, the questions had to be settled by the work itself.

Let me quote him even more fully, for his analysis is important to my theme.

It is a weakness of Gabriel's analysis that he never seems to realize that his so-called fundamental law had already been cut loose from its foundations when it was adapted to democracy.

Trevelyan accepts Italian nationalism with little analysis, he is unduly critical of papal and French policy, and he is more than generous in assessing British policy.

The research center of the University's School of Business and Public Administration is prepared to undertake the analysis Dr. Ellis has been talking about.

An analysis of the fiscal tax collection year calendars throughout the state indicates that transition may not be as painful as is commonly thought.

Another important source of evidence only recently receiving much attention is the analysis of atmospheric dust for a meteoritic component.

In the last analysis, religion is the means of inducing, formulating, expressing, enhancing, implementing, and perpetuating man's deepest experience -- the religious.

but the subsequent analysis of characteristics is reported only for the de jure population ( or, in some districts, only the de facto population ).

The criterion score used in the statistical analysis is an index of over- or under-achievement.

Tables 1 and 2 present the results of the statistical analysis of the data when compulsivity is used as the descriptive variable.

Finally, information is retrieved from the dictionary as required by stages of the translation process -- the grammatical description for sentence-structure determination, equivalent-choice information for semantic analysis, and target-language equivalents for output construction.

The first stage of translation after glossary lookup is structural analysis of the input text.

From the point of view of syntactic analysis the head word in the statement is the predicator has broken, and from the point of view of meaning it would seem that the trouble centers in the breaking ; ;

Tone analysis will continue to be difficult and unsatisfactory until a more representative selection of systems is familar to every practicing field linguist.

The great majority of present-day linguists fall into one or more of a number of overlapping types: those who are convinced that tone cannot be analysed, those who are personally scared of tone and tone languages generally, those who are convinced that tone is merely an unnecessary marginal feature in those languages where it occurs, those who have no idea how to proceed with tone analysis, those who take a simplistic view of the whole matter.

One issue that must be faced is the relative difficulty of analysis of different phonologic subsystems.

A third explanation is suggested by Richardson's analysis of Sukuma tone.

The difficulty of analysis of any subsystem in the phonology is an inverse function of the size -- smaller systems are more troublesome -- for any given degree of morphophonemic complexity.

The treatment seems unnecessarily loose-jointed and complex, largely because the method is lax and the analysis seems never to be pushed to a satisfactory or even a consistent stopping-point.

Mr. Alexander H. Wheelan's Study Helps In Point And Figure Technique tells the readers: `` We assure you that the total number of people using this method of market analysis is a very small portion of the sum total of those operating in the securities and commodities markets ''.

The threadbare notion that belief, unlike behaviour, is not subject to objective analysis, has placed intuitive metaphysics squarely against the sociology of knowledge, since it is precisely the job of the sociology of knowledge to treat beliefs as social facts no less viable than social behaviour.

It is rather that introducing them into social analysis reflects not so much a search for truth as for certainty.