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 this is part of the Army Militia, and is the ceremonial military band of San Marino.

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

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 named The King's College of Our Lady and Saint Nicholas in Cambridge, the college lies on the River Cam and faces out onto King's Parade in the centre of the city.

Formally, the city remained under Italian sovereignty until September 15, 1947 ( Paris Peace Treaties ).

Formally declared an enemy of the State, Caesar pursued the senatorial party, now led by Pompey, who abandoned the city to raise arms in Greece, with Cato among his companions.

Formally known as Bootle-cum-Linacre, the town is < span style =" white-space: nowrap "> 4 miles ( 6. 4 km )</ span > to the north of Liverpool city centre, and has a total resident population of 77, 640.

Formally, the city is composed of Eforie Sud, the administrative centre, and Eforie Nord, a dependent village.

Formally called the Mactaquac Generating Station, the dam and power house are located approximately upstream from the city of Fredericton.

Formally, the city has designations for each of the eight neighborhoods which are represented by neighborhood councils.

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

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 described as " Truck, Cargo: 10-Ton, 8x8 ", it has been nicknamed the " Dragon Wagon ".

Formally, we start with a category C with finite products ( i. e. C has a terminal object 1 and any two objects of C have a product ).

Formally, DFS is an uninformed search that progresses by expanding the first child node of the search tree that appears and thus going deeper and deeper until a goal node is found, or until it hits a node that has no children.

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.

It has been leased from the National Trust since 1974 by the Somerset Wildlife Trust ( Formally Somerset Trust for Nature Conservation ) and is run as a nature reserve and visitor centre.

Formally known as trilina, the armónico has seven strings, two of which form a doubled string.

Formally, this means that, for some function f, the image f ( D ) of a directed set D ( i. e. the set of the images of each element of D ) is again directed and has as a least upper bound the image of the least upper bound of D. One could also say that f preserves directed suprema.

Following a merger with the Furnishing Industry Trust ( Formally The Furnishing Trades Benevolent Association ) in 2011, the Company has become the most significant charity in the sector, supporting the needy and promoting welfare and education of those entering and working within the industry, as well as the wider support of the charitable work of the Mayoralty and the Corporation of the City of London.

Formally established in 1475, though in fact much older, it has 75, 000 codices from throughout history.

Formally, the situation has the characteristics of a prisoner's dilemma game that is played repeatedly between the same partners, and in this case " defection "-jumping the queue-would not be advantageous.

Formally, if R is a Noetherian ring and I is a principal, proper ideal of R, then I has height at most one.

* Formally real field, an algebraic field that has the so-called " real " property

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, an antihomomorphism between X and Y is a homomorphism, where equals Y as a set, but has multiplication reversed: denoting the multiplication on Y as and the multiplication on as, we have.

Formally, given two partially ordered sets ( S, ≤) and ( T, ≤), a function f: S → T is an order-embedding if f is both order-preserving and order-reflecting, i. e. for all x and y in S, one has

Formally described in Stephen Gilligan's article: The relational self: the expanding of love beyond desire ( 1996 ), and expanded on in his book: The Courage to Love ( 1997 ), it has become a major new approach in psychotherapy and healing.

Formally launched in 2004, the network currently has 16 members in nine states.

Enbridge currently has offices in Enbridge Place ( Formally ING Tower ), Manulife Place, and Royal Bank Building.

Formally, given a finite set X, a collection C of subsets of X, all of size n, has Property B if we can partition X into two disjoint subsets Y and Z such that every set in C meets both Y and Z.

Formally named " Olallie ", it has usually been marketed as olallieberry, just as " Marion " is sold as marionberry.