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 speaking, a collation method typically defines a total order on a set of possible identifiers, called sort keys, which consequently produces a total preorder on the set of items of information ( items with the same identifier are not placed in any defined order ).

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

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

Formally a random variable is considered to be a function on the possible outcomes.

Formally, in the finite-dimensional case, if the linear map is represented as a multiplication by a matrix A and the translation as the addition of a vector, an affine map acting on a vector can be represented as

Formally, a detailed balanced process is the one on which the probability to be in the state x and transit to x ' must be the same as to be in the state x ' and transit to x.

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

Formally, a function ƒ is real analytic on an open set D in the real line if for any x < sub > 0 </ sub > in D one can write

Formally, an elliptic function is a function meromorphic on for which there exist two non-zero complex numbers and with ( in other words, not parallel ), such that and for all.

Formally, if is an open subset of the complex plane, a point of, and is a holomorphic function, then is called a removable singularity for if there exists a holomorphic function which coincides with on.

Formally, the appointment remains a royal one made on the advice of the Lord Chancellor, but he / she no longer comments on individual applications, and merely supervises the process and reviews the panel's recommendations in general terms ( satisfying himself / herself that the process as operated is fair and efficient ).

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.

In late 1900s the day that of the City was founded is Jakin School is a Private School is Formally Part of Jakin School Board was Grades One through Twelve there is no Football field on this school. In 1966 When Jakin School was Closed were Sent to Blakely-Union Elementary, Junior High, and High School ( which later Became Early County High, Middle, and Elementary School ). while Carver school was built for African-American students grades One through Twelve. although late 1960s when Carver school was closed along with Kestler School was based in Damascus were sent to Washington High & Elementary at Blakely. In addition to small farm agriculture, Jakin's early economic growth resulted from turpentine.

Formally WPAZ, the station changed its call letters and name on October 28th, 2011.

Formally, the Sachs – Hornbostel is modeled on the Dewey Decimal classification.

Formally, a center of gravity is an application point of the resultant gravitational force on the body.

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, start with a set Ω and consider the sigma algebra Σ on Ω consisting of all subsets of Ω.

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.

Formally, the motion merely calls on parliament to thank the monarch or viceroy for the speech via an Address in Reply.

Formally, according to the Constitution, citizens of Turkmenistan have the right to set up political parties and other public associations, acting within the framework of the Constitution and laws, and public associations and groups of citizens have the right to nominate their candidates in accordance with the election law.

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, two variables are inversely proportional ( or varying inversely, or in inverse variation, or in inverse proportion or in reciprocal proportion ) if one of the variables is directly proportional with the multiplicative inverse ( reciprocal ) of the other, or equivalently if their product is a constant.

Formally, bending modulus is defined as the energy required to deform a membrane from its intrinsic curvature to some other curvature.

Formally known as Motion Picture Distribution LP, it was re branded and relaunched in 2007 due to the break-up of its preceding company, Alliance Atlantis, which was sold off piece by piece to Canwest Global, GS Capital Partners, along with several other smaller companies.

Formally, a mortgage lender ( mortgagee ), or other lien holder, obtains a termination of a mortgage borrower ( mortgagor )' s equitable right of redemption, either by court order or by operation of law ( after following a specific statutory procedure ).

The Force Act of 1870 ( Formally, " An Act to enforce the Right of Citizens of the United States to vote in the several States of this Union, and for other Purposes ," 41st Congress, Sess.

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

Formally, a byte stream is a certain abstraction, a communication channel down which one entity can send a sequence of bytes to the entity on the other end.

Formally, all members of the Ghelani family are Hindu Leuva Patel, although some have since chosen other religious beliefs.

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, if f is a harmonic function, then f cannot exhibit a true local maximum within the domain of definition of f. In other words, either f is a constant function, or, for any point inside the domain of f, there exist other points arbitrarily close to at which f takes larger values.

Formally, a redistribution of all agents ’ initial endowments of goods among all agents in the system is a core allocation if no group of agents can redistribute their own initial endowments among themselves so as to improve the satisfaction of someone in the group without impairing that of any other in the group.

Formally, he is also chief of staff of the air force and navy as well, but apparently the commanders of the other two services frequently report directly to the Minister of Defence / Commander-in-Chief.

Formally John William Friso of Nassau-Dietz, the other claimant of the principality, did not cede the territory in 1713.

Formally, the quick steps are full strides, with one foot passing the other on each step.

Formally, the outcomes Y < sub > i </ sub > are described as being Bernoulli-distributed data, where each outcome is determined by an unobserved probability p < sub > i </ sub > that is specific to the outcome at hand, but related to the explanatory variables.

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.