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 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, Gaussian curvature only depends on the Riemannian metric of the surface.

Informally, G has the above presentation if it is the " freest group " generated by S subject only to the relations R. Formally, the group G is said to have the above presentation if it is isomorphic to the quotient of a free group on S by the normal subgroup generated by the relations R.

Formally, the case where only a subset of parameters is defined is still a composite hypothesis ; nonetheless, the term point hypothesis is often applied in such cases, particularly where the hypothesis test can be structured in such a way that the distribution of the test statistic ( the distribution under the null hypothesis ) does not depend on the parameters whose values have not been specified under the point null hypothesis.

Formally, wives only join their husband's household after the birth of their first child.

Formally, though, the name only survives in Finland and Sweden, where provinces bear the name.

Formally, Mbenga – Mbuti Pygmy music consists of at most only four parts, and can be described as an, " ostinato with variations ," or similar to a passacaglia, in that it is cyclical.

Formally, the complexity class MA is the set of decision problems that can be decided in polynomial time by an Arthur – Merlin protocol where Merlin's only move precedes any computation by Arthur.

Formally, a cardinal number κ is λ-unfoldable if and only if for every transitive model M of cardinality κ of ZFC-minus-power set such that κ is in M and M contains all its sequences of length less than κ, there is a non-trivial elementary embedding j of M into a transitive model with the critical point of j being κ and j ( κ ) ≥ λ.

Formally, a system is said to be observable if, for any possible sequence of state and control vectors, the current state can be determined in finite time using only the outputs ( this definition is slanted towards the state space representation ).

Formally, the definition only requires some invertibility, so we can substitute for Q any matrix M whose eigenvalues do not include − 1.

Formally, if is a limit ordinal, then a set is closed in if and only if for every < math >

Formally Roman Kalyn is now the only member of the group, but de-facto GreenJolly exists in name only.

Formally, if and only if, for any given, there exists an such that

Formally, a number n is colossally abundant if and only if there is an ε > 0 such that for all k > 1,

Formally, a natural number n is called highly abundant if and only if for all natural numbers m < n,

Formally this mission was declared to be only in pursuit of the Russian vessels and ammunition taken to Anzali by the White Russian counter-revolutionary General Denikin, who had been given asylum by British forces in Anzali.

Formally known as Crown Point Airport, the airport was renamed the Arthur Napoleon Raymond Robinson International Airport on May 19, 2011 in honour of the only Prime Minister and President from the island of Tobago.

Formally named " United Press Associations " for incorporation and legal purposes, but publicly known and identified as United Press or UP, it was created by the 1907 uniting of three smaller news syndicates by the Midwest newspaper publisher E. W. Scripps.

Formally recognizing this point, the French government argued that the delivery stemmed from an old contract and hence was technically legal.

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, we are given a set of hypotheses and a set of manifestations ; they are related by the domain knowledge, represented by a function that takes as an argument a set of hypotheses and gives as a result the corresponding set of manifestations.

Formally, a statistic s is a measurable function of X ; thus, a statistic s is evaluated on a random variable X, taking the value s ( X ), which is itself a random variable.

; Electronics: Formally a fixture in radio shacks, now used for assembly and repair of all sorts of electronic equipment including communication, computer, and home entertainment items.

; Formally real field

Formally, Aff ( V ) is naturally isomorphic to a subgroup of, with V embedded as the affine plane, namely the stabilizer of this affine plane ; the above matrix formulation is the ( transpose of ) the realization of this, with the ( n × n and 1 × 1 ) blocks corresponding to the direct sum decomposition.

Formally, HPGCC is a cross-compiler ; it compiles code for the ARM-based HP calculators, but runs on a PC rather than the target system.

Formally, Korea's governmental FTC ( Fair Trade Commission: 공정거래위원회 ; 公正去來委員會 ) announces a limited Chaebol list every year as size of industrial assets ( not including financial companies ).

Formally, the algorithm's performance will be a random variable determined by the random bits ; thus either the running time, or the output ( or both ) are random variables.

Formally, a deterministic algorithm computes a mathematical function ; a function has a unique value for any given input, and the algorithm is a process that produces this particular value as output.

Formally, Chrétien and Martin have remained publicly respectful of each other ; while much of the verbal sparring was between their supporters.

Formally, a squeeze preserves the hyperbolic metric expressed in the form ; in a different coordinate system.

Bābak Khorram-Din ( Formally known as " Pāpak " meaning " Young Father ") (, alternative spelling: Bābak Xorramdin ; 795, according to some other sources 798 — January 838 ) was one of the main PersianArmenian historian Vardan Areweltsʻi, ca.

Formally described, it alternates slow sections in a modal F with faster sections, " Neue Kraft fühlend " ( with renewed strength ), in D. The slow sections each have two elements, ( 1 ) a passage reminiscent of the opening of the first movement in which the instruments overlap each other with a brief motive ; ( 2 ) a chorale, the actual song.

Formally, a Markov partition is used to provide a finite cover for the smooth system ; each set of the cover is associated with a single symbol, and the sequences of symbols result as a trajectory of the system moves from one of the covering sets to another.

Formally, citizen science has been defined as " the systematic collection and analysis of data ; development of technology ; testing of natural phenomena ; and the dissemination of these activities by researchers on a primarily avocational basis ".

Formally, at least, the European Commission has primarily a monitoring role ; in practice, however, there is considerable scope for it to help set the policy agenda and persuade reluctant Member States to implement agreed policies.

Formally, let P be a poset ( partially ordered set ), and let F be a filter on P ; that is, F is a subset of P such that:

Formally ;

Formally, a biased graph Ω is a pair ( G, B ) where B is a linear class of circles ; this by definition is a class of circles that satisfies the theta-graph property mentioned above.