We obtain this result as a consequence of certain weighted L2 Sobolev inequalities on the d-torus.
We obtain this as a consequence of a new property of almost transitive spaces with a Schauder basis, namely we prove that in such spaces the unit vector basis of ℓ22 belongs to the two-dimensional asymptotic structure and we obtain some information about the asymptotic structure in higher dimensions.
The interested reader can obtain this case as a consequence of the above corollary.
The main outcome measures sought were the identification of the information needs of women diagnosed with Polycystic Ovarian Syndrome (PCOS) during different periods of their lives; how and where they obtain this information, and the consequences of this information for future treatment and health outcomes.
This illustrates the advantages of using category theory and its tools for defining combination procedures as universal constructions: the same construction (in this case, algebraic fibring) can be performed in categories of logic systems with different features obtaining, as a consequence of this, stronger or weaker logic systems.
The main result obtained as consequence of this definition is some convergence results of multivariate Stieltjes series and a generalization of the Montessus De Ballore theorem for this class of multivariate functions.
This result is obtained as a consequence of a theorem stating that each orthogonal form on a C*-algebra is determined by two functionals on the algebra.
Proof-theoretic semantics has several roots, the most specific one being Gentzen's remarks that the introduction rules in his calculus of natural deduction define the meanings of logical constants, while the elimination rules can be obtained as a consequence of this definition (see section 2.2.1).
As a consequence of the previous result and their main theorems, the authors obtained the following consequence.
Again, when X n = X, for all n ∈ ℕ ̄, we obtain, as a consequence of Theorem 3.5, the following result.
AnL2inequality for the divergence is obtained as a consequence.
