Physical Sciences and Mathematics Commons^™

Discrete Maximum Principle For Nonsmooth Optimal Control Problems With Delays, Boris S. Mordukhovich, Ilya Shvartsman

Mathematics Research Reports

We consider optimal control problems for discrete-time systems with delays. The main goal is to derive necessary optimality conditions of the discrete maximum principle type in the case of nonsmooth minimizing functions. We obtain two independent forms of the discrete maximum principle with transversality conditions described in terms of subdifferentials and superdifferentials, respectively. The superdifferential form is new even for non-delayed systems and may be essentially stronger than a more conventional subdifferential form in some situations.

The Fine Structure Of The Kasparov Groups I: Continuity Of The Kk-Pairing, Claude Schochet

Mathematics Faculty Research Publications

In this paper it is demonstrated that the Kasparov pairing is continuous with respect to the natural topology on the Kasparov groups, so that a KK-equivalence is an isomorphism of topological groups. In addition, we demonstrate that the groups have a natural pseudopolonais structure, and we prove that various KK-structural maps are continuous.

Ultraconvergence Of Zz Patch Recovery At Mesh Symmetry Points, Zhimin Zhang, Runchang Lin

Mathematics Research Reports

Ultraconvergence property of the Zienkiewicz-Zhu gradient patch recovery technique based on local discrete least squares fitting is established for a large class of even-order finite elements. The result is valid at all rectangular mesh symmetry points. Different smoothing strategies are discussed. Superconvergence recovery for the Q8 element is proved and ultraconvergence numerical examples are demonstrated.

Geometric Realization And K-Theoretic Decomposition Of C*-Algebras, Claude Schochet

Mathematics Faculty Research Publications

Suppose that A is a separable C*-algebra and that G∗ is a (graded) subgroup of the ℤ/2-graded group K∗(A). Then there is a natural short exact sequence

0 → G∗ → K∗(A) → K∗(A)/G∗ → 0.

In this note we demonstrate how to geometrically realize this sequence at the level of C*-algebras. As a result, we KK-theoretically decompose A as

0 → A ⊗ [cursive]K → A_ƒ → SA_t → 0

where K∗(A_t) is the torsion subgroup of …

Extended Powers Of Manifolds And The Adams Spectral Sequence, Robert R. Bruner

Mathematics Faculty Research Publications

The extended power construction can be used to create new framed manifolds out of old. We show here how to compute the effect of such operations in the Adams spectral sequence, extending partial results of Milgram and the author. This gives the simplest method of proving that Jones’ 30-manifold has Kervaire invariant one, and allows the construction of manifolds representing Mahowald’s classes η4 and η5, among others.