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In this note we provide necessary small designs by using spherical geometries and a direct construction.
Furthermore, the approach, which provides a direct construction principle, grants the additional insight that the obtained solutions are Malliavin differentiable.
We also stress that our method does not involve a pathwise uniqueness argument but provides a direct construction of strong solutions.
Skolem's definable ultrapower construction from 1933 (see Skolem 1933) gives a direct construction of a non-standard model of True Arithmetic (which extends Peano arithmetic, being the set of arithmetic sentences true in the natural numbers).
The problem considered here, however, is simpler, and instead of analyzing those conditions, we shall define a synthesis of extremal controlled trajectories through a direct construction and then verify the optimality of the synthesis.
We illustrate the existence of spatio-temporally periodic solutions through a direct construction using ideas from coupled cell theory and the theory of weakly coupled oscillators, and show that these solutions can be stable in a very large region of parameter space.
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His temporary Tarantantara of 1999 (another jewel of Gateshead) was a wonderfully direct construction of two giant funnels that created striking optical effects.
Thus the system allows for direct construction of a Gateway Entry clone of a gDNA subclone from a BAC.
A suitable modification of the approach used for the recessive solution leads to the direct construction of a dominant solution.
As already mentioned, the first result is based on the direct construction of a winding trajectory.
Then a more efficient algorithm for direct construction of the explicit expression of response sensitivity is developed based on the physical meanings of the coefficient matrices in the formulation.
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