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 during the Han Dynasty, zhou continued to exist until the establishment of the Republic of China — a period of over 2000 years.

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 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 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 educated African Americans, on the other hand, either disregarded black minstrelsy or openly disdained it.

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

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 dedicated " as a memorial to the boys that were " on October 30, 1915, Alumni Field and its distinctive " maroon goal-posts on a field of green " were hailed in that evening's edition of the Boston Saturday Evening Transcript as " one of the sights in Boston.

Formally nicknamed the " Pacemaker " by a staffer at Peterbilt after an in-house name contest in 1969 ( the winner got a color TV ).

Formally, this definition includes as classical all objects with the current orbits that

Formally known as the ' Little Monsters Den of Mischief ', this area is mainly aimed at children, and includes the attractions Little Monster's Wacky Races and Mischief Mansion.

* South Korea Formally Declares End to Sunshine Policy, Voice of America, 18 November 2010

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

Formally, the 1772 Constitution was adopted by the Parliament ( Riksdag ) on 21 August 1772, but this took place as members of the Parliament and the Privy Council were under threat by the royal garrison on order by King Gustav III outside of Stockholm Palace, where the Parliament and Privy Council were assembled in different parts of the palace.

Formally, consider an economic model with different mathematical weightings placed on the utilities of each self.