Page "Modular representation theory" ¶ 75
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Formally and is
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, their designation is the letter Ž and the number.
Formally, a topological space X is called compact if each of its open covers has a finite subcover.
Formally, the set of all context-free languages is identical to the set of languages accepted by pushdown automata ( PDA ).
Formally, the derivative of the function f at a is the limit
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, the base is known as Naval Support Facility Diego Garcia ( the US activity ) or Permanent Joint Operating Base ( PJOB ) Diego Garcia ( the UK's term ).
Formally, there is a clear distinction: " DFT " refers to a mathematical transformation or function, regardless of how it is computed, whereas " FFT " refers to a specific family of algorithms for computing DFTs.
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 bifunctor is a functor whose domain is a product category.
Formally, a set S is called finite if there exists a bijection
Formally, the system is said to have memory.
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, 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, a profinite group is a Hausdorff, compact, and totally disconnected topological group: that is, a topological group that is also a Stone space.
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, a frame is defined to be a lattice L in which finite meets distribute over arbitrary joins, i. e. every ( even infinite ) subset
Formally, Φ = kx − ωt is the phase.

Formally and largest
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 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, the use of a reduction is the function that sends each natural number n to the largest natural number m whose membership in the set B was queried by the reduction while determining the membership of n in A.
Formally known as the Jodo-Shinshu Honganji-ha is the largest of all the Jodo Shinshu branches.

is and largest
The fact that sticks out in this voluminous record is that the bulk of Du Pont's production has always supplied the largest part of the requirements of the one customer in the automobile industry connected to Du Pont by a stock interest.
however, the anode is still the part receiving the largest heat flux.
It is often stated that the largest snakes require five years to attain maturity, but this apparently is an overestimation.
Bernard Heuvelmans also treats of the largest snakes, but on the third level, and is chiefly concerned with the anaconda.
In addition, the iodoamino acid formed in largest quantity in the intact thyroid is di-iodotyrosine.
This development is reflected in the action taken in February, 1961, by the general board of the National Council of Churches, the largest Protestant organization in the Aj.
The ultimate objective of American policy is to help establish a world in which there is the largest possible measure of freedom and justice and peace and material prosperity ; ;
I speak of `` the largest possible measure '' because any person who supposes that these conditions can be universally and perfectly achieved -- ever -- reckons without the inherent imperfectability of himself and his fellow human beings, and is therefore a dangerous man to have around.
The dome of the church is, outside of St. Peter's, one of the largest in Rome.
It is the second largest city in Japan, with about four million people.
The largest hurdle the Republicans would have to face is a state law which says that before making a first race, one of two alternative courses must be taken: 1
Behind this reply, and its many variations, is the ever-present budget problem all libraries must face, from the largest to the smallest.
Also, the state with the largest number of Negroes is New York -- not in the South at all.
The largest city by population is Birmingham.
The largest city by total land area is Huntsville.
The single largest organization of Anthropologists is the American Anthropological Association ( AAA ), which was founded in 1903.
The largest amphibian is the Chinese Giant Salamander, Andrias davidianus.
The suborder Neobatrachia is by far the largest group and includes the remaining families of modern frogs, including most common species.
The largest family in this group is Plethodontidae, the lungless salamanders, which includes sixty percent of all salamander species.
Alaska () is the largest state in the United States by area.
One of the largest problems that affect patients with disabilities is discomfort with prosthesis.
The largest segmental script is probably an abugida, Devanagari.
The largest known abjad is Sindhi, with 51 letters.

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