However, the state of matter and phase diagram usages are not commensurate with the formal definition given above and the intended meaning must be determined in part from the context in which the term is used.

A striking model of much interest in this context is the Azbel-Harper-Hofstadter model whose quantum phase diagram is the Hofstadter's butterfly shown in the figure.

Assuming that in the context cheese means some type of dairy product, the Euler diagram has the cheese zone entirely contained within the dairy-product zone — there is no zone for ( non-existent ) non-dairy cheese.

Interestingly, the above " Sharkovskii ordering " of the positive integers also occurs in a slightly different context in connection with the logistic map: the stable cycles appear in this order in the bifurcation diagram, starting with 1 and ending with 3, as the parameter is increased.

Example of a System context diagram.

The objective of a system context diagram is to focus attention on external factors and events that should be considered in developing a complete set of system requirements and constraints ".

The system context diagram is a necessary tool in developing a baseline interaction between systems and actors ; actors and system or systems and systems.

Alternatives of the system context diagram are:

* Problem Diagrams ( Problem Frames ): In addition to the kinds of things shown on a context diagram, a problem diagram shows requirements and requirements references.

A Conceptual schema | conceptual data model is developed based on the data requirement s for the application that is being developed, perhaps in the context of an activity diagram | activity model.

On the context diagram the system's interactions with the outside world are modelled purely in terms of data flows across the system boundary.

The context diagram shows the entire system as a single process, and gives no clues as to its internal organization.

* System context diagram

Depending on whether the diagram is intended for formal or informal use, certain details may be lacking and must be determined from context.

In the Steiners have busy lives without visiting relatives only context can indicate whether visiting relatives is equivalent in meaning to paying visits to relatives or to relatives who are visiting them, and in I looked up the number and I looked up the chimney only the meanings of number and chimney make it clear that up is syntactically a second complement in the first sentence and a preposition followed by its object in the second.

With a few important and a few more unimportant exceptions, no expression can be deemed le mot juste for its context, because each was very probably the only expression that long-established practice and ease of rapid recitation would allow.

In 2009, the American Anthropological Association's Commission on the Engagement of Anthropology with the US Security and Intelligence Communities released its final report concluding, in part, that, " When ethnographic investigation is determined by military missions, not subject to external review, where data collection occurs in the context of war, integrated into the goals of counterinsurgency, and in a potentially coercive environment – all characteristic factors of the HTS concept and its application – it can no longer be considered a legitimate professional exercise of anthropology.

Lexical ambiguity can be addressed by algorithmic methods that automatically associate the appropriate meaning with a word in context, a task referred to as word sense disambiguation.

Note that " completeness " has a different meaning here than it does in the context of Gödel's first incompleteness theorem, which states that no recursive, consistent set of non-logical axioms of the Theory of Arithmetic is complete, in the sense that there will always exist an arithmetic statement such that neither nor can be proved from the given set of axioms.

Abbreviations can also be used to give a different context to the word itself, such as " PIN Number " ( wherein if the abbreviation were removed the context would be invalid ).

As with many scientific fields, strict delineation can be highly contrived and atomic physics is often considered in the wider context of atomic, molecular, and optical physics.

From about 1955 he started to work on sheaf theory and homological algebra, producing the influential " Tôhoku paper " ( Sur quelques points d ' algèbre homologique, published in 1957 ) where he introduced Abelian categories and applied their theory to show that sheaf cohomology can be defined as certain derived functors in this context.

Several topics that might be covered here are instead covered there because much more can be said about them in a human context.

Because these two definitions can be transformed simply by into the other, some formulae have this alternatingly (- 1 )< sup > n </ sup >- term and others not depending on the context, but it is not possible to decide in favor of one of these definitions to be the correct or appropriate or natural one ( for the abstract Bernoulli numbers ).

Aspects of combinatorics include counting the structures of a given kind and size ( enumerative combinatorics ), deciding when certain criteria can be met, and constructing and analyzing objects meeting the criteria ( as in combinatorial designs and matroid theory ), finding " largest ", " smallest ", or " optimal " objects ( extremal combinatorics and combinatorial optimization ), and studying combinatorial structures arising in an algebraic context, or applying algebraic techniques to combinatorial problems ( algebraic combinatorics ).

Regardless of the context, doing computing well can be complicated and difficult.

Such ethnographers and their students promoted the idea of " cultural relativism ", the view that one can only understand another person's beliefs and behaviors in the context of the culture in which he or she lived or lives.

Conspiratorial accounts can be emotionally satisfying when they place events in a readily understandable, moral context.

Yì can be translated as righteousness, though it may simply mean what is ethically best to do in a certain context.

Many important constructions in mathematics can be studied in this context.

Many of the above concepts, especially equivalence of categories, adjoint functor pairs, and functor categories, can be situated into the context of higher-dimensional categories.

* Cell ( music ), a small rhythmic and melodic design that can be isolated, or can make up one part of a thematic context

In this fashion, one can prove many important theorems in the class of compact spaces, that do not hold in the context of non-compact ones.

The name context-sensitive is explained by the α and β that form the context of A and determine whether A can be replaced with γ or not.

( Indeed, every production of a context free grammar is of the form V → w where V is a single nonterminal symbol, and w is a string of terminals and / or nonterminals ( w can be empty )).

Players can gain a large advantage if their civilization is the first to learn a particular technology ( the secrets of flight, for example ) and put it to use in a military or other context.

Others such as Michael Johnston and Noam Chomsky assert that classical liberalism as such can no longer exist in a modern day context as its principles were only relevant at the time its founding thinkers conceptualised them ; and that classical liberalism has grown into two divergent philosophies since the beginning of the twentieth century: social liberalism and market liberalism.

This condition affects not only the conception but also the legislative and financial support of foreign policy, especially in the context of economic aid.

But when what is new in a particular context is also fairly obvious, there is normally only light stress or no stress at all.

Depending on the context, a Lewis acid may also be described as an oxidizer or an electrophile.

The axiom of choice has also been thoroughly studied in the context of constructive mathematics, where non-classical logic is employed.

Violence in this context means any unlawful touching, though there is some debate over whether the touching must also be hostile.

His first ( pre-IHÉS ) breakthrough in algebraic geometry was the Grothendieck – Hirzebruch – Riemann – Roch theorem, a far-reaching generalisation of the Hirzebruch – Riemann – Roch theorem proved algebraically ; in this context he also introduced K-theory.

* The being which manifests in Christianity also manifests in all faiths and religions, and each religion is valid and true for the time and cultural context in which it was born ;

The Dispensational viewpoint interprets biblical prophecy literally and expects that the fulfillment of prophecy will also be literal, depending upon the context of scripture.

Depending on the context, jumping may also involve capturing or conquering an opponent's game piece.

Being is also understood as one's " state of being ," and hence its common meaning is in the context of human ( personal ) experience, with aspects that involve expressions and manifestations coming from an innate " being ", or personal character.

Connolly also suggests that in context the marriage metaphor was necessary in that it truly exemplified the unequal interaction between Yahweh and the people Israel.

Computing Curricula 2005 also recognizes that the meaning of " computing " depends on the context:

Computing also has other meanings that are more specific, based on the context in which the term is used.

In this article, he also defended a comment made by Professor Griff in the past that he says was taken out of context by the media.

In this context, it is more readily construed as meaning " school of thought ", since it is also used to construct the names of philosophical schools contemporary with Confucianism: for example, the Chinese names for Legalism and Mohism end in jiā.

In On War, Clausewitz sees all wars as the sum of decisions, actions, and reactions in an uncertain and dangerous context, and also as a socio-political phenomenon.

The addition of the empty string allows the statement that the context sensitive languages are a proper superset of the context free languages, rather than having to make the weaker statement that all context free grammars with no → λ productions are also context sensitive grammars.

However, depending on the operating system, a context switch may also take place at this time.

Mather also viewed Hayy as a noble savage and applied this in the context of attempting to understand the Native American Indians in order to convert them to Puritan Christianity.

The ISO 8601 standard also has the advantage of being language independent and is therefore useful when there may be no language context and a universal application is desired ( expiration dating on export products, for example ).