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The results are analog to those obtained by Dette and Studden (2005) for moment matrices of matrix measures on a compact interval.
Consider the D-optimal designs for the dth-degree polynomial regression model with a continuous weight function on a compact interval.
Recently, Zayernouri and Karniadakis in (2013) [78] investigated two classes of fractional Sturm Liouville eigenvalue problems on compact interval [a,b] in more detail.
We develop mathematical framework and computational tools for calculating frequency responses of linear time-invariant PDEs in which an independent spatial variable belongs to a compact interval.
By utilizing the equivalence theorem and Descartes's rule of signs, we construct D-optimal designs for a weighted polynomial regression model of degree k, with specific weight function w(x)=1/(a2−x2)δ, on the compact interval [−1,1].
Until now, to the best of our knowledge, fractional Sturm Liouville eigenvalue problems on non-compact interval, such as [0,+∞) are not analyzed. So, our aim in this paper is to study these problems in detail.
Let be a compact interval.
Let Λ ⊂ R be a compact interval.
Let ([a,b]) be a compact interval.
Let J ⊂ R be a compact interval.
Let be any compact interval and as in Theorem 3.9.
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