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

Formally trained specialists recognized by the American Dental Association undergo a minimum of 2 – 3 years full-time rigorous education program after dental school graduation.

Formally trained in music composition, Dargel studied with Oliveros, John Luther Adams, and Lewis Nielson, and received a B. A.

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 ).

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 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 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, 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 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, 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.

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

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, 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 ).

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.