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

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 a census-designated place ( CDP ), Laguna West-Lakeside was annexed by Elk Grove in 2003.

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, it was ceded to Russia in the Treaty of Nystad in 1721, together with Swedish Estonia and Swedish Ingria.

Formally declared on October 9, 1970, the Khmer Republic was a right-wing pro-United States military-led government headed by General Lon Nol and Prince Sisowath Sirik Matak that took power in the March 18, 1970 coup against Prince Norodom Sihanouk, then the country's head of state.

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, the Cisalpine Republic was an independent state allied with France, but the treaty of alliance established the effective subalternity of the new republic to France.

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 known as the Kelowna Grizzlies, the club was purchased in

Formally speaking, the opportunity was extended to all classes to join China's project on its Leninist terms.

Formally known as the Inverurie Parish Church, a split in Church of Scotland over the appointment of ministers in 1843 ( The Disruption ) led to the creation of the West Parish Church ( known locally as " The West Kirk ") which was founded as a Free Church ( a church free from Edinburgh control ) thus causing the Inverurie Parish Church to change its name.

Formally, the group was called Studiengesellschaft für Geistesurgeschichte ‚ Deutsches Ahnenerbe e. V.

Formally a member of the country's collective head of state and, as president of parliament, holder of the third-highest office, he was left with little political influence.

Formally known as the " Long Tinh ", the flag was the official flag of the Nguyễn Court.

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

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 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, these prepositions are actually prepositional phrases.

Formally termed cladodes, these branchlets somewhat resemble pine needles, although sheoaks are actually flowering plants.

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 West Lilydale, the surrounding region became known as Chirnside Park in the 1970s, the Post Office opening on 25 September 1979.

Formally known as the Constitution of the Republic of Poland (), it replaced the temporary amendments put into place in 1992 designed to reverse the effects of Communism, establishing the nation as " a democratic state ruled by law and implementing the principles of social justice ".

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

* Formally appoints the Prime Minister of Finland selected by the Parliament, and formally appoints the rest of the cabinet ( Council of State ) as proposed by the Prime Minister

* 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, 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, this is a solution of the matrix equation by Jacobi iteration.

Formally it is defined by the equation

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, 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

Limits and colimits in a category C are defined by means of diagrams in C. Formally, a diagram of type J in C is a functor from J to C:

Formally, most of these people were convicted by NKVD troikas (" triplets ")– special courts martial.

Formally, collective noun forms such as “ a group of people ” are represented by second-order variables, or by first-order variables standing for sets ( which are well-defined objects in mathematics and logic ).

Formally, a decision problem is P-complete ( complete for the complexity class P ) if it is in P and that every problem in P can be reduced to it by using an appropriate reduction.

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 transductive support vector machine is defined by the following primal optimization problem:

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.

Formally, powers with positive integer exponents may be defined by the initial condition

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.