Formally, the sequence of partial sums of some infinite summation converges if for every fixed power of X the coefficient stabilizes: there is a point beyond which all further partial sums have the same coefficient.

Formally, this follows from the convolution theorem in mathematics, which relates the Fourier transform of the power spectrum ( the intensity of each frequency ) to its autocorrelation.

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, a measurable cardinal is an uncountable cardinal number κ such that there exists a κ-additive, non-trivial, 0-1-valued measure on the power set of κ.

Formally titled ' An Act to protect all Persons in the United States in their Civil Rights, and furnish the Means of their vindication, the Act declared that people born in the United States and not subject to any foreign power are entitled to be citizens, without regard to race, color, or previous condition of slavery or involuntary servitude.

Formally, the game ( coalitional game ) consists of a finite set of players, called the grand coalition, and a characteristic function denotes the power set of .</ ref > from the set of all possible coalitions of players to a set of payments that satisfies.

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

Formally it can be seen just as an ordinary function from X to the power set of Y, written as φ: X → 2 < sup > Y </ sup >.

Formally the power resides with the Plenary Session ; in practice this approves the decisions of the Nomenclature Section.

Formally the Vice-President was appointed by the Governor-General on the " nomination " of the President of the Executive Council, but by convention the Governor-General could not refuse to appoint a Vice-President who the President had selected.

Formally known as the Organisation internationale de la Francophonie ( OIF ) or the International Organization of the Francophonie, the organization comprises 56 member states and governments, 3 associate members, and 19 observers.

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

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

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

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

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 neutral and reluctant to become involved with the great powers except as a last resort, Kuwait turned to the United States, the Soviet Union and Britain for naval protection of its tanker fleet after twenty-one ships were attacked in the gulf since late 1986.

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

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, 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 applying the Taylor series with respect to h, yields the formula

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, a Markov chain is a random process with the Markov property.

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, 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 it consists of a short lyric composed in a single metre with a single rhyme throughout.

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

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, they are partial derivatives of the option price with respect to the independent variables ( technically, one Greek, gamma, is a partial derivative of another Greek, called delta ).

Formally, the problem of supervised pattern recognition can be stated as follows: Given an unknown function ( the ground truth ) that maps input instances to output labels, along with training data assumed to represent accurate examples of the mapping, produce a function that approximates as closely as possible the correct mapping.

Formally the work is operatic, with the plot advanced entirely through dialogue sung with accompanying music.

Formally, the President is elected by the National People's Congress in accordance with Article 62 of the Constitution.

Formally the self-inductance of a wire loop would be given by the above equation with i

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.

However, shortly after this positive result, Kurt Gödel published On Formally Undecidable Propositions of Principia Mathematica and Related Systems ( 1931 ), showing that in any sufficiently strong axiomatic system there are true statements which cannot be proved in the system.

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, 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 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, a unique factorization domain is defined to be an integral domain R in which every non-zero and non-unit x of R can be written as a product ( including an empty product ) of irreducible elements p < sub > i </ sub > of R and a unit u:

Formally, dependence refers to any situation in which random variables do not satisfy a mathematical condition of probabilistic independence.

Formally, let P be an expression in which the variable x is free.

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 speaking, this then satisfies the premises of an axiom of well-founded induction, which asserts that these two conditions are sufficient for the proposition to hold for all x.

Formally, it is anything which when offered in payment extinguishes the debt.

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

Formally it consists of three groups of four measure phrases of three to four chords repeated four times each, ABC :|| ABC, which then merges with the next movement, " Floe " with the entrance of the horns.

Formally, let f: < sup > n </ sup > → be the cost function which must be minimized.

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 rigged Hilbert space consists of a Hilbert space H, together with a subspace Φ which carries a finer topology, that is one for which the natural inclusion

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.