Sentence examples for main theorem shows from inspiring English sources

The main theorem shows, under a regularity hypothesis, that Cϑ∗ is subnormal if and only if ϑ is in a restricted class of linear fractional transformations.

Our main theorem shows that the functional F is in general a non-local one; this unexpected feature occurs even in very simple examples, when μ is the one-dimensional Hausdorff measure over a closed Lipschitz curve in the plane.

In this section we present our main theorem, showing that the Pareto product always preserves Bellman's principle.

Combining Propositions 1 and 2, we can get the first main theorem which shows us the equivalence relationship between (l_{2,0} -minimization and (l_{2,0} -minimization. Figure 1 M-NSC in Exandl_{2,p} -minimization

Step 4. In this step, we give the numerical results that support our main theorem as shown by plotting graphs using Matlab 7.11.0.

The main theorem given below shows that the stability criteria can be expressed in terms of the feasibility of two LMIs.

As a non-trivial application of the main theorem it is shown that many sequences of number theoretic importance, such as the sequence of primes, have infinitely many positive and infinitely many negative squares.

The main theorem of this paper shows that foldover designs are the only (regular or nonregular) two-level factorial designs of resolution IV (strength 3) or more for n runs and n/3⩽m⩽n/2 factors.

Such curves do not lie in the sphere ∂ B 3. So we introduce a new surface M ˜ k, τ T : = M k, τ T ∩ B 3. To prove the main theorem we need to show that there exists Φ such that also the second equation of (3) is satisfied.

Now, we show the main theorem.

Now, we show our main theorem dealing with (3.1).