At first glance, this might suggest that for full pure-state controllability the system algebra has to be isomorphic to so ( 2 d ).
Even so, by drawing the plane, we have shown it to be isomorphic to parts of the Euclidean plane.
It is well known that any model of these sentences must be isomorphic to the ordered field of real numbers.
In current treatments it is sometimes added that any other set-theoretically constructed system that is isomorphic to the system of Dedekind cuts or to the system of finite von Neumann ordinals, respectively, would do as well, i.e., be usable, for all mathematical purposes, as "the real numbers" or "the natural numbers".
Not because the model trajectories are isomorphic to the system trajectories; rather, because there is a topological or geometric similarity or correspondence between the models and the systems being modeled.
forms a basis in L p t ≡ L p t , then this system is isomorphic to the classical system of exponents { e i n t } n ∈ Z, where the isomorphism is given by S f = e − i α t ∑ 0 ∞ ( f, e i n x ) e i n t + e i α t ∑ 1 ∞ ( f, e − i n x ) e − i n t, (4).
3.14) showed that any closure algebra is isomorphic to an algebraic system formed by a set equipped with a reflexive and transitive relation.[67] As a matter of fact, the relevant algebraic structure is precisely that of the propositional modal logic S4.
By Theorem 1, it is isomorphic to the classical system of exponents { e i n t } n ∈ Z in L p t. Therefore the spaces of coefficients of the bases { e i μ n t } n ∈ Z and { e i n t } n ∈ Z coincide.
Then the following properties of the system (1) are equivalent in L p t : (1.1) the system (1) is complete; (1.2) the system (1) is minimal; (1.3) the system (1) is ω-linear independent; (1.4) the system (1) is isomorphic to { e i n t } n ∈ N basis; (1.5) λ i ≠ λ j for i ≠ j. (II) Let β > 1 and α = − 1 2 p.
The system algebra is isomorphic to so ( 2 n + 1 ) and irreducibly embedded in su ( 2 n ).
