The numerical test bed example by considering the qualitative and quantitative criteria has been made to test the model.
For example, by considering the vortex effects, the amplitude of the system response at (alpha = 0.92) is demonstrated Fig. 9 in the case of using and not using the TMD.
We will illustrate the workings of this algorithm through a simple example, by considering the formula varphi equiv mathbf{G}, neg c vee mathbf{F},(a vee b)) evaluated on the trace a,c,a,d,c,d,b.
For example, by considering the second row in the RHS of (16), we add to the elements their corresponding powers which are,, and, respectively, and then we gather them to be.
For example: by considering the spherical designs which are orbits of a finite group in the real orthogonal group O(n), we get many connections with group theory; by considering those which are shells of Euclidean lattices, we get many unexpected connections with number theory, such as modular forms and Lehmer's conjecture about the zeros of the Ramanujan τ function.
If a more sensible prior is used, for example, by considering the empirical prior from the binding frequencies in the validation data, the proposed method can attain even higher accuracy than the regression method (results not shown).
The applicability and correctness of the proposed hybrid algorithm is demonstrated through different examples by considering the influence of the layers arrangement, the measurement errors and sensor numbers.
Example 1 By considering the matrix ℳ, one can give the following examples for Theorem 2: (i) For an odd prime p, if we take α 11 = 1, α 12 = t ( t ∈ Z + ), α 21 = 0 and α 22 = 1, then we get λ 1 λ 2 = 1 while M p + 1 ≡ M 1 mod p. Hence, we get an efficient presentation.
The good accuracy of the estimated internal pressure and heat flux is shown through different examples and by considering the influence of measurement errors, which validates the presented approach.
The fact that hybridizing ordinary modal logic actually does give more expressive power can for example be seen by considering the formula ↓c□¬c.
Application examples are shown by considering the construction of confidence regions and mixing models.
