We discuss different regularity notions for Lp-wellposed linear systems with 1 p < ∞: – compatibility in the sense of Helton (1976), – weak regularity in the sense of Weiss and Weiss (1997) or Staffans and Weiss (2000), – strong regularity in the sense of Weiss (1994a), – uniform regularity in the sense of Helton (1976) and Ober and Wu (1996). Compatibility is the minimal assumption if we want ...

In this paper we are concerned with a mathematical model which describes the electromagnetic interrogation of dielectric materials. We address the well-posedness of the system and regularity of solutions. Then we propose a semi-discrete nite element scheme for approximating the system and prove weak convergence under very mild regularity assumptions on the solutions of the original system. We a...

We show that the concept of strong Noether position for a polynomial ideal I CP is equivalent to δ-regularity and thus related to Pommaret bases. In particular, we provide explicit Pommaret bases for two of the ideal sequences used in Hashemi’s definition of strong Noether position and alternative proofs for a number of his statements. Finally, we show that one consequence of δ-regularity is th...

It is known that the Karush-Kuhn-Tucker (KKT) conditions of semidefinite programming can be reformulated as a nonsmooth system via the metric projector over the cone of symmetric and positive semidefinite matrices. We show in this paper that the primal and dual constraint nondegeneracies, the strong regularity, the nonsingularity of the B-subdifferential of this nonsmooth system, and the nonsin...

Introduction: The functionality and quality of any treatment planning system (TPS) strongly depends on the type of Algorithm which is used by it. Obviously, the role of dose distribution algorithms in calculation of prescribed dose inside the tumor in modern radiotherapy techniques has more important than past to achieve the best clinical outcomes, especially in tumors which ar...

Let I be a divisorial ideal of a strongly F-regular ring A. K.-i.Watanabe raised thequestionwhether the symbolicRees algebraRs(I) = ⊕n≥0I is Cohen-Macaulay whenever it is Noetherian. We develop the notion ofmulti-symbolic Rees algebras and use this to show thatRs(I) is indeedCohen-Macaulaywhenever a certain auxiliary ring is finitely generated over A.

The Abadie CQ (ACQ) for convex inequality systems is a fundamental notion in optimization and approximation theory. In terms of the contingent cone and tangent derivative, we extend the Abadie CQ to more general convex multifunction cases and introduce the strong ACQ for both multifunctions and inequality systems. Some seemly unrelated notions are unified by the new ACQ and strong ACQ. Relation...

As the main result of this paper it is proved that an interval matrix [Ac −∆, Ac +∆] is strongly regular if and only if the matrix inequality M(I − |I − RAc| − |R|∆) ≥ I has a solution, where M and R are real square matrices and M is nonnegative. Several consequences of this result are drawn.