The evolution of the Greek sculpture can be observed in his depictions from the almost static formal Kouros type in early archaic period, to the representation of motion in a relative harmonious whole in late archaic period.

Computational models require a mathematically and logically formal representation of a problem.

Equivalent definitions can be given using μ-recursive functions, Turing machines or λ-calculus as the formal representation of algorithms.

** In some languages, the formal representation of aspect is optional, and can be omitted when the aspect is clear from context or does not need to be emphasized.

* How expressive is a representation scheme or formal language?

In the 1980s formal computer knowledge representation languages and systems arose.

One problem in knowledge representation is how to store and manipulate knowledge in an information system in a formal way so that it may be used by mechanisms to accomplish a given task.

An ontology is a formal representation of knowledge which includes the concepts ( such as objects, processes etc.

Like other theories, the theory of probability is a representation of probabilistic concepts in formal terms — that is, in terms that can be considered separately from their meaning.

However, the chart should not be regarded as an accurate representation of the relative prevalence of each mode in the present day, as it is not based on large-scale, formal surveys.

Ordinary character theory provides better arithmetic control, and uses simple CG modules to understand the structure of finite groups G. Modular representation theory uses Brauer characters to view modules as formal sums of simple modules, but is also interested in how those simple modules are joined together within composition series.

An automaton can be a finite representation of a formal language that may be an infinite set.

As stated in Brewer v. Williams,, the right to counsel “ at least that a person is entitled to the help of a lawyer at or after the time that judicial proceedings have been initiated against him, whether by formal charge, preliminary hearing, indictment, information, or arraignment .” Brewer goes on to conclude that once adversary proceeding have begun against a defendant, he has a right to legal representation when the government interrogates him and that when a defendant is arrested, “ arraigned on arrest warrant before a judge ,” and “ committed by the court to confinement ,” “ here can be no doubt that judicial proceedings ha been initiated .”

Another is that the formal representation of such points, the Kronecker delta function is unphysical, because it cannot be normalized.

In fact another theoretical representation of an amine oxide uses a dative covalent bond ≡ N → O with no formal charges.

In electronic design automation, until the 1980s schematics were virtually the only formal representation for circuits.

In formal terms, this representation is a wavelet series representation of a square-integrable function with respect to either a complete, orthonormal set of basis functions, or an overcomplete set or frame of a vector space, for the Hilbert space of square integrable functions.

As a theory of phonological representation, autosegmental phonology developed a formal account of ideas that had been sketched in earlier work by several linguists, notably Bernard Bloch ( 1948 ), Charles Hockett ( 1955 ) and J. R. Firth ( 1948 ).

The Carter Administration signed the Taiwan Relations Act to maintain commercial, cultural, and other relations through the unofficial relations in the form of American Institute in Taiwan without official Government representation and without formal diplomatic relations.

The formal rules enable representation of objects that are independent of machine-specific encoding techniques.

For general functions, the graphic representation cannot be applied and the formal definition of the graph of a function suits the need of mathematical statements, e. g., the closed graph theorem in functional analysis.

An automaton is a finite representation of a formal language that may be an infinite set.

Determining whether the principal is " disabled " enough to initiate this type of representation is a formal process.

By the 19th century, the settlement was officially uninhabited and yet still had formal parliamentary representation, making it the most notorious of the rotten boroughs that existed before the Reform Act 1832.

The formal ratification by all 13 states was completed in early 1781.

This force is used in the formal definition of the ampere, which states that it is " the constant current that will produce an attractive force of 2 × 10 < sup >– 7 </ sup > newton per metre of length between two straight, parallel conductors of infinite length and negligible circular cross section placed one metre apart in a vacuum ".

For many cytochromes, the metal ion present is that of iron, which interconverts between Fe < sup > 2 +</ sup > ( reduced ) and Fe < sup > 3 +</ sup > ( oxidised ) states ( electron-transfer processes ) or between Fe < sup > 2 +</ sup > ( reduced ) and Fe < sup > 3 +</ sup > ( formal, oxidised ) states ( oxidative processes ).

Adler states: " The three R's, which always signified the formal disciplines, are the essence of liberal or general education.

Since real political power belongs to the sole legal party, in certain states under Marxist constitutions of the constitutionally socialist state type inspired by the former Union of Soviet Socialist Republics ( USSR ) and its constitutive Soviet republics, there was no formal office of head of state, but rather the leader of the legislative branch was considered to be the closest common equivalent of a head of state as a natural person.

In some states the office of head of state is not expressed in a specific title reflecting that role, but constitutionally awarded to a post of another formal nature.

The Serbian crisis triggered a complex set of formal and secret military alliances between European states, causing most of the continent, including France, to be drawn into war within a few short weeks.

Malaysia participates in international politics and engages in formal relationships with international bodies as well as with foreign states adopting various policies.

Dual nationality is when a single person has a formal relationship with two separate, sovereign states.

* Protocol ( politics ), a formal agreement between nation states

In the theory of formal languages in computability theory, a pumping lemma or pumping argument states that, for a particular language to be a member of a language class, any sufficiently long string in the language contains a section, or sections, that can be removed, or repeated any number of times, with the resulting string remaining in that language.

Legal systems in all socialist states preserved formal criteria of the Romano-Germanic civil law ; for this reason, law theorists in post-socialist states usually consider the Socialist law as a particular case of the Romano-Germanic civil law.

The most common formal oxidation state of tungsten is + 6, but it exhibits all oxidation states from − 2 to + 6 .< ref > Tungsten typically combines with oxygen to form the yellow tungstic oxide, WO < sub > 3 </ sub >, which dissolves in aqueous alkaline solutions to form tungstate ions,.

A noteworthy difference between Thucydides ' method of writing history and that of modern historians is Thucydides ' inclusion of lengthy formal speeches that, as he himself states, were literary reconstructions rather than actual quotations of what was said — or, perhaps, what he believed ought to have been said.

A is a formal meeting of the representatives of different nations, constituent states, independent organizations ( such as trade unions ), or groups.

" This is used as a formal title in many states, but also informally a generic term to describe whichever office is formally the first amongst the executive " ministers " of an otherwise styled Head of State, as Minister — Latin for servants or subordinates — is a common title for members of a government ( but many other titles are in use, e. g. secretary ( of state )).

The doctrine was also invoked by U. S. Under-Secretary of State Sumner Welles in a declaration of July 23, 1940, that announced non-recognition of the Soviet annexation and incorporation of the three Baltic states — Estonia, Latvia, and Lithuania — and remained the official U. S. position until the Baltic states gained formal international recognition as independent states in 1991.

M. K. Lawson in his Dictionary of National Biography article on Harthacnut states that it is unclear whether Harthacnut was to have England as well as Denmark, but it was probably a reflection of a formal arrangement that mints south of the Thames produced silver pennies in his name, while those to the north were almost all Harold's.

Amy Devitt states this when she says, " A genre is named because of its formal markers " ( Devitt 10 ).

Interventionism found its formal articulation in the 1904 Roosevelt Corollary to the Monroe Doctrine, proclaiming the right of the United States to intervene in the affairs of weak states in the Americas in order to stabilize them, a moment that underlined the emergent U. S. regional hegemony.

The concept of fiscal federalism is not to be associated with fiscal decentralization in officially declared federations only ; it is applicable even to non-federal states ( having no formal federal constitutional arrangement ) in the sense that they encompass different levels of government which have defacto decision making authority ( Sharma, 2005a: 44 ).