Sentence examples for a theorem on the characterization of from inspiring English sources

In this section, we will establish a theorem on the characterization of the folded Student's t distribution by upper record values.

As a corollary of the sum theorem, we state the characterization of the compact differences of two weighted composition operators on A. Theorem 2.5 Let u, v ∈ A and φ, ψ ∈ A*.

In the following theorem, we obtain the characterization of weighted almost regular matrices.

Using Theorem 5.1 we obtain the characterization of (1.2) and (1.3) for (0< p, r

Based on the characterizations of reproducing cones, some fixed point theorems for multi-valued increasing, decreasing, and mixed monotone operators are established.

) Based on these results, we now have the characterization of folded Student's t distribution by upper record values, as provided in Theorem 3.3.1 below.

So, the characterization of (lambda<0) follows from Theorem 2.12.

In the analytic setting, the structure theorem enables the explicit characterization of minimum-phase preserving operators on the half-line, a problem of importance in geophysical signal processing.

Special care must be taken with the characterization of the probability axioms when it comes to the Converse Dutch Book theorem.

The characterization of the characteristic values of these systems is also presented and a discussion on the stability theorems for ordinary differential equations is performed for the differential-algebraic case.

A theorem on independence.