Sentence examples for obtained algebra from inspiring English sources

The quasi-inequational characterization of the so obtained algebra provides the basis for an algebraic semantics for these logics.

Analogously, for the algebra, we obtain algebras and, a Hermitian -valued form on, a real Levi non-degenerate codimension 2 affine quadric in, the corresponding coordinates in, and a tube hypersurface in.

Potential distribution and electrical current lines of these configurations are obtained from algebra operations of complex variables owing to conformal mapping method.

The tensor algebra T V) is a formal way of adding products to any vector space V to obtain an algebra.

Therefore, when J ˆ + S ˆ + I ˆ > 0 and I ˆ > 0, namely R 0 ∗ > 1 and R 1 ∗ > 1, we can obtain that algebra equation (25) has a unique positive solution which are given in (26 - 29 26 - 29

We obtained the linearized algebra (mathcal{E}) from the two-dimensional nonlinear Heisenberg algebras by adding two generators.

According to the Galois Theory [18], p* cannot be obtained by elementary algebra.

On the second view of definition, we have expanded the language-as-algebra by adding a new fundamental operation → and can now consider the subalgebra generated by the propositional variables of the reduct of this algebra obtained by discarding the other fundamental operations.

The same description of the range is obtained for bounded algebra homomorphisms, this time when G and H are locally compact groups with G abelian.

The p.d.f.s of u i under hypotheses ℋ 0 and ℋ 1 can be obtained after some algebra as f u i | ℋ 0 ( x ) = L L exp - xL σ n 2 x L - 1 σ n 2 L Γ ( L ) (62). and f u i | ℋ 1 ( x ) = L L exp - xL σ hn 2 x L - 1 σ hn 2 L Γ ( L ), (63).

As shown in Figure 2B, our solution obtained using linear algebra is close to the actual solution (green and blue curves), even when the normal component was overwhelmingly abundant.