In 3D for example y has length 4, I has size 3x3 and F has size 3x4, so the explicit forms are:
22.
There has been related recent work on the question of finding natural and explicit forms of Brauer's theorem, notably by Robert Boltje.
23.
In explicit form they are expressible in terms of Jacobian elliptic functions which are periodic functions ( effectively generalisations of trigonometrical functions ).
24.
This often yields a result giving a family of solutions implicitly, but in many examples does yield the general solution in explicit form.
25.
It is clear from the explicit form in terms of Euler angles that the map just described is a smooth, and onto group homomorphism.
26.
Then, using two proposed discretization operators for matrix functions results in an explicit form of solution for a system of linear FDEs with discrete delays.
27.
From a knowledge-based view, the design guideline represents an explicit form of knowledge, that contains information about " knowing-how-to " ( see Procedural knowledge ).
28.
Following work by Matorin and others, the extremising functions were found by Isaac Jacob Schoenberg, explicit forms for the sharp constants are however still unknown.
29.
During the last decade, studies have mainly focused on the minimal sector of the general theory, in which case the hamiltonian above takes the explicit form
30.
This explicit identification of the operators " e i " ( " T " ) in turn gives an explicit form of holomorphic functional calculus for matrices:
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