Formally organized vocational programs supported by federal funds allow high school students to gain experience in a field of work which is likely to lead to a full-time job on graduation.

Formally, a binary operation on a set S is called associative if it satisfies the associative law:

Formally, their designation is the letter Ž and the number.

Formally, a topological space X is called compact if each of its open covers has a finite subcover.

Formally, the set of all context-free languages is identical to the set of languages accepted by pushdown automata ( PDA ).

Formally, the derivative of the function f at a is the limit

More rigorously, the divergence of a vector field F at a point p is defined as the limit of the net flow of F across the smooth boundary of a three dimensional region V divided by the volume of V as V shrinks to p. Formally,

Formally, the base is known as Naval Support Facility Diego Garcia ( the US activity ) or Permanent Joint Operating Base ( PJOB ) Diego Garcia ( the UK's term ).

Formally, there is a clear distinction: " DFT " refers to a mathematical transformation or function, regardless of how it is computed, whereas " FFT " refers to a specific family of algorithms for computing DFTs.

Formally, oxidation state is the hypothetical charge that an atom would have if all bonds to atoms of different elements were 100 % ionic.

Formally, a bifunctor is a functor whose domain is a product category.

Formally, a set S is called finite if there exists a bijection

Formally, the system is said to have memory.

Formally, an inner product space is a vector space V over the field together with an inner product, i. e., with a map

Formally, if M is a set, the identity function f on M is defined to be that function with domain and codomain M which satisfies

* Formally, when working over the reals, as here, this is accomplished by considering the limit as ε → 0 ; but the " infinitesimal " language generalizes directly to Lie groups over general rings.

Formally, a profinite group is a Hausdorff, compact, and totally disconnected topological group: that is, a topological group that is also a Stone space.

Formally, this sharing of dynamics is referred to as universality, and systems with precisely the same critical exponents are said to belong to the same universality class.

Formally, a frame is defined to be a lattice L in which finite meets distribute over arbitrary joins, i. e. every ( even infinite ) subset

Formally, Φ = kx − ωt is the phase.

Formally, they were part of the non-resident sections, but in fact constituted a separate division, largely autonomous in their activities.

Formally it was part of Arles, but in reality it was under the influence of the French king.

Formally it is a part of Novosibirsk city, and has never been a closed city.

Formally it was part of Serbia, but it actually was a virtually separate autonomous region ruled by its German minority.

Formally known as Sportsdesk, it was re-vamped to closer resemble ESPN's own SportsCenter ( including the use of its theme music, logo, and opening ) in the Fall of 2001 as part of a corporate restructuring, closer aligning itself with new minority owner ESPN.

Formally since 19 June 1971 when Lövenich ( now part of Cologne ) was an independent town.

Formally, a cumulativity predicate CUM can be defined as follows, where capital X is a variable over sets, U is the universe of discourse, p is a mereological part structure on U, and is the mereological sum operation.

Formally, a quantization predicate QUA can be defined as follows, where is the universe of discourse, and is a variable over sets, and is a mereological part structure on with < math > < _p </ math > the mereological part-of relation.

Also in August 2010, HMV opened a new Fopp store on the ground floor of the Waterstone's store ( Formally part of the HMV Group ) in Gower Street, London.

Formally, they have always been considered Orthodox Christians, but most of them followed shamanism and animism as a part of their culture.

Formally, for any dimension, the orientation of the image of an object under a direct isometry with respect to that object is the linear part of that isometry.

Formally designated as the Manhattan Engineer District, it refers specifically to the period of the project from 1941 – 1946 under the control of the U. S. Army Corps of Engineers, under the administration of General Leslie R. Groves.

Formally independent, the division was one of the most successful units fighting in the ranks of the Polish Army during the Polish-Bolshevik War.

Formally, the minimum age for front line fighter is eighteen, but apparently rear line fighters below that age limit have been captured by the Colombian Army or occasionally have deserted.

Formally the " head of state " can also personally be the " head of government " ( ex officio or by ad hoc cumulation such as an absolute monarch nominating himself ) but otherwise has formal precedence over the Head of Government and other ministers, whether he is their actual political superior ( absolute monarch, executive president ) or rather theoretical or ceremonial in character.

Formally, however, the role also carries the title of " Klingon supreme commander " ( TNG's " Reunion "), which presumably means commander-in-chief of the military.

Formally, the Ministry of Aeronautics was founded on January 20, 1941 and so its military branch called " National Air Forces ", changed to " Brazilian Air Force " ( Força Aérea Brasileira-FAB ) on May, 22.

However, shortly after this positive result, Kurt Gödel published On Formally Undecidable Propositions of Principia Mathematica and Related Systems ( 1931 ), showing that in any sufficiently strong axiomatic system there are true statements which cannot be proved in the system.

Formally, arbitrage transactions have negative skew – prices can get a small amount closer ( but often no closer than 0 ), while they can get very far apart.

Formally, the Congress serves two functions: to approve changes to the Party constitution regarding policy and to elect a Central Committee, about 300 strong.

Formally, one has an implication, not an equivalence, so the solution set may get larger.

Formally inaugurated in March 2004, the Global Leadership Foundation works to " promote good governance – democratic institutions, open markets, human rights and the rule of law – and to contribute to the prevention and resolution of conflict through mediation.

Formally given to bishop Philip of Senj, the permission to use the Glagolitic liturgy ( the Roman Rite conducted in Slavic language instead of Latin, not the Byzantine rite ), actually extended to all Croatian lands, mostly along the Adriatic coast.

Formally the Prince-Electors elected a King of the Romans, who was elected in Germany but became Holy Roman Emperor only when crowned by the Pope.

Formally neutral and reluctant to become involved with the great powers except as a last resort, Kuwait turned to the United States, the Soviet Union and Britain for naval protection of its tanker fleet after twenty-one ships were attacked in the gulf since late 1986.

Massiah: Formally Charged + Deliberate Elicitation.

*, see On Formally Undecidable Propositions of Principia Mathematica and Related Systems for details on English translations.

Formally, these failed when they were rejected by the Church of England's General Synod in 1972 ; conversations and co-operation continued, however, leading in 2003 to the signing of a covenant between the two churches.

Formally introduced in September 1979, Initial samples were released in February 1980, with production chips available over the counter in November.

* Nuclear bunker buster: Formally known as the Robust Nuclear Earth Penetrator ( RNEP ), this program aimed to modify an existing gravity bomb to penetrate into soil and rock in order to destroy underground targets.