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 established in 1927, the Walker Art Center began as the first public art gallery in the Upper Midwest.

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

Formally established measures of centrality are degree centrality, closeness centrality, betweenness centrality, eigenvector centrality, and katz centrality.

Formally established in Los Angeles in 1922, the largest and most active Woodcraft organization is Los Angeles ' Woodcraft Rangers, which has a proud 87-year history of providing innovative and creative programs for children in the under-served areas of greater Los Angeles.

Formally established on October 21st, 1969, it includes 18 departments providing 31 different undergraduate courses, as well as a number of graduate programs.

Formally established in 1922, over the decades Woodcraft Rangers has modified Seton ’ s original emphasis on outdoor life to incorporate activities that meet the needs of an increasingly urban population, but the goal of changing behavior and encouraging positive outcomes through interaction and education remains central to its mission today.

Formally established in 1920 as the Aviation Ministry, the ROCAF was active during the tenure of the ROC on Mainland China.

Formally, the WOA was established during a meeting held in the Olympic Museum on 21 November 1995 by 25 founder members.

Formally, Training Group ceased to exist and No 22 Group was established.

Formally established in 1921, the Profintern was intended to act as a counterweight to the influence of the so-called " Amsterdam International ," the Social Democratic International Federation of Trade Unions, an organization branded as class collaborationist and an impediment to revolution by the Comintern.

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 Airframe Reconditioning Squadron RNZAF, the unit was commercialised in 1998 and is now managed by SAFE Air Ltd. No. 1 Repair Depot was also active at the base for a number of years, though during the war it appears to have been stationed at Hamilton.

Formally trained by Italian Futurist painter-sculptor Ambrogio Casati, Giorgini stayed on with his mentor as an apprentice, and assisted in the restoration of classic works by old masters damaged during the Second World War.

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 becoming a concert violinist following the completion of his musical education, Üngör continued to ascend the ranks of the Ottoman Imperial Orchestra, soon becoming first violinist, and ultimately, conductor in 1917.

Formally, Siddharta continued their work without a bass player.

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

Formally, the theorem is stated as follows: There exist unique integers q and r such that a = qd + r and 0 ≤ r < | d |, where | d | denotes the absolute value of d.

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 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, 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, her possessions and privileges ( including the government ) passed to her husband Robert Hathaway upon their marriage ( 1929 ) until his death ( 1954 ).

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

Formally based at the RHQ 95 Horseferry road until 2005 and now at the former RMP barracks on Rochester row.

Formally, it remained a state of the Holy Roman Empire until its dissolution in 1806.

By 1912, the Social Democrats, with an explicitly anti-antisemitic program, were the largest party in the German Reichstag, and the Progressives ran very strongly as well ... Formally, at least, the Jews had been fully emancipated with the establishment of the German Empire, although they were kept out of certain influential occupations, enjoyed extraordinary prosperity ... Germans intermarried with Jews: in the 1930s some 50, 000 Jews were living in mixed German-Jewish marriages, so at least 50, 000 Germans, and presumably parts of their families, had familial contact with the Jews.

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 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 ".

* A 06 Speech Sound Disorder — Formally Phonological Disorder

* General Headquarters United Nations Command ( Korea ) ( UNC ) — Formally activated 10 July 1950, before then Allied forces were formally under American operational control.

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.

Mid-West Arts Council — Formally known as the Royal Bank Building, the Heritage Arts Center was originally constructed as the Union Bank in 1905.

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 founded by the Virginia General Assembly in 1823, the Library of Virginia organizes, cares for, and manages the state's collection of books and official records, many of which date back to the early colonial period.

Formally, the Restoration period had a preferred rhyme scheme.

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

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

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 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 it is precisely in allowing quantification over class variables α, β, etc., that we assume a range of values for these variables to refer to.

If R is a ring, let R denote the ring of polynomials in the indeterminate X over R. Hilbert proved that if R is " not too large ", in the sense that if R is Noetherian, the same must be true for R. Formally,

Formally, the statement that " value decreases over time " is given by defining the linear differential operator as:

Formally, this effect is referred to as and is a process whereby the capture frame rate of the camera changes over time.

Formally, an analytic function ƒ ( z ) of the real or complex variables z < sub > 1 </ sub >,…, z < sub > n </ sub > is transcendental if z < sub > 1 </ sub >, …, z < sub > n </ sub >, ƒ ( z ) are algebraically independent, i. e., if ƒ is transcendental over the field C ( z < sub > 1 </ sub >, …, z < sub > n </ sub >).

Formally, a Lie superalgebra is a ( nonassociative ) Z < sub > 2 </ sub >- graded algebra, or superalgebra, over a commutative ring ( typically R or C ) whose product, called the Lie superbracket or supercommutator, satisfies the two conditions ( analogs of the usual Lie algebra axioms, with grading ):

Formally, a coalgebra over a field K is a vector space C over K together with K-linear maps Δ: C → C ⊗ C and ε: C → K such that

Formally, a Hopf algebra is a ( associative and coassociative ) bialgebra H over a field K together with a K-linear map S: H → H ( called the antipode ) such that the following diagram commutes:

Formally, an unlabelled state transition system is a tuple ( S, →) where S is a set ( of states ) and → ⊆ S × S is a binary relation over S ( of transitions ).

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 set of LTL formulas over AP is inductively defined as follows:

Formally, the theorem states that, for every Sperner family S over an n-set,

Formally trained in Rome and Paris, he exhibited in venues from Paris to New York to Beirut over his career.

Formally, an algebraic function in n variables over the field K is an element of the algebraic closure of the field of rational functions K ( x < sub > 1 </ sub >,..., x < sub > n </ sub >).

Formally, if there is a utility function that describes preferences over L commodities, the expenditure function

Formally, weakest-preconditions are defined recursively over the abstract syntax of statements.