Formally, the theorem can be stated as follows:

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, 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, a Menger sponge can be defined as follows:

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, the Cantor function c: → is defined as follows:

Formally, the problem can be stated as follows: given a desired property, expressed as a temporal logic formula p, and a structure M with initial state s, decide if.

Formally, Turán's theorem may be stated as follows.

Formally, the sets of free and bound names of a process in π – calculus are defined inductively as follows.

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

a < sub > i </ sub >, a < sub > i + 1 </ sub >,..., which is a suffix of w. Formally, the satisfaction relation between a word and an LTL formula is defined as follows:

Formally, the construction is as follows.

Formally, the chain rule indeed follows from the above definition of conditional probability:

Formally, the expenditure function is defined as follows.

Formally, this can be expressed as follows.

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.

Formally, the extension of circumscription that incorporate varying and fixed variables is as follows, where is the set of variables to minimize, the fixed variables, and the varying variables are those not in:

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:

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

Formally, the word is applied to persons who are publicly accepted in a recognised capacity, such as professional employment, graduation from a course of study, etc., to give critical commentaries in one or any of a number of specific fields of public or private achievement or endeavour.

Formally, they are known as Ridunians, from the Latin Riduna.

Formally, it is a coalition of U. S. and European CEOs, largely from transnational corporations, launched at the urging of former United States Secretary of Commerce Ron Brown in Seville ( Spain ) in late 1995 at a conference attended by CEOs from more than 100 U. S. and EU companies and by top government representatives led by the Commissioners for Trade and Industry and by the U. S. Secretary of Commerce.

Formally reported from November 1944 onwards, witnesses often assumed that the foo fighters were secret weapons employed by the enemy, but they remained unidentified post-war and were reported by both Allied and Axis forces.

Formally, under Henry IV, Arundel served twice as Lord Chancellor, first in 1399 and again from 1407 to 1410.

Formally, a homotopy between two continuous functions f and g from a

It has been leased from the National Trust since 1974 by the Somerset Wildlife Trust ( Formally Somerset Trust for Nature Conservation ) and is run as a nature reserve and visitor centre.

Formally this approximation is founded on the variational principle, valid for Hamiltonians that are bounded from below.

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.

* Blades ( hip-hop group ) ( Formally Blades Of Hades ), Australian hip hop group from Newcastle, New South Wales

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

Formally, knowing the step response of a dynamical system gives information on the stability of such a system, and on its ability to reach one stationary state when starting from another.

Formally, it is the process of eliciting information from the government.

Formally known as Mickleham Grand it used to range from Mount Ridley Road to Crestmont Terrace, but now is connected to the urbanised areas of Craigieburn.

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, complexification is a functor Vect < sub > R </ sup > → Vect < sub > C </ sup >, from the category of real vector spaces to the category of complex vector spaces.

Formally, the Mahalanobis distance of a multivariate vector from a group of values with mean and covariance matrix is defined as:

Formally known as Thornhill, a gift from C. P.

Formally called " the Wigwam ", this immense edifice was located on Girard Avenue between 19th and 20th Streets, across from Philadelphia's Girard College.