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- Michael Frank, David R Larson
- 2008

We present a general approach to a module frame theory in C*-algebras and Hilbert C*-modules. The investigations rely on the idea of geometric dilation to standard Hilbert C*-modules over unital C*-algebras that possess orthonormal Hilbert bases, and of reconstruction of the frames by projections and other bounded module operators with suitable ranges. We… (More)

This paper describes a computer-assisted non-existence proof of 9-input sorting networks consisting of 24 comparators, hence showing that the 25-comparator sorting network found by Floyd in 1964 is optimal. As a corollary, we obtain that the 29-comparator network found by Waksman in 1969 is optimal when sorting 10 inputs. This closes the two smallest open… (More)

- Michael Frank, David R. Larson
- 1999

The goal of the present paper is a short introduction to a general module frame theory in C*-algebras and Hilbert C*-modules. The reported investigations rely on the idea of geometric dilation to standard Hilbert C*-modules over unital C*-algebras that possess orthonormal Hilbert bases, and of reconstruction of the frames by projections and other bounded… (More)

- Michael Frank, Vern I Paulsen, Terry R Tiballi
- 1998

We consider existence and uniqueness of symmetric approximation of frames by normalized tight frames and of symmetric orthogonalization of bases by orthonormal bases in Hilbert spaces. A crucial role is played by the Hilbert-Schmidt property of a certain operator related to the initial frame or basis.

Aversively motivated learning is more poorly understood than appetitively motivated learning in many aspects, including the role of dopamine receptors in different regions of the striatum. The present study investigated the roles of the D1-like DA receptors in the nucleus accumbens (NAc) and dorsolateral striatum (DLS) on learning and performance of… (More)

The objective of this study was to obtain estimates of the number of nerve fibers in the human crista ampullaris and utricular macula from normal individuals using unbiased stereology and immunohistochemistry. Vestibular endorgans with the attached vestibular nerve stump were microdissected from the temporal bones. Specimens were divided into two groups.… (More)

- M. Frank, P. Găvruţa, M. S. Moslehian
- 2008

Let X and Y be Hilbert C *-modules over a C *-algebra, and ϕ : X × Y → [0, ∞) be a function. A (not necessarily linear) mapping f : X → Y is called a ϕ-perturbation of an adjointable mapping if there exists a (not necessarily linear) corresponding mapping g : Y → X such that f (x), y − x, g(y) ≤ ϕ(x, y) x ∈ D(f) ⊆ X , y ∈ D(g) ⊆ Y. We prove that any… (More)

The number R(4, 3, 3) is often presented as the unknown Ramsey number with the best chances of being found “soon”. Yet, its precise value has remained unknown for almost 50 years. This paper presents a methodology based on abstraction and symmetry breaking that applies to solve hard graph edge-coloring problems. The utility of this methodology is… (More)

BACKGROUND
Optimal ECG triggering is of paramount importance for correct blood flow quantification during cardiovascular magnetic resonance (CMR). However, optimal ECG triggering and therefore blood flow quantification is impaired in many patients with congenital heart disease (CHD) due to complex QRS patterns. Therefore, a new ECG-trigger algorithm was… (More)

- MICHAEL FRANK
- 2006

B. Magajna and J. Schweizer showed in 1997 and 1999, respectively, that C*-algebras of compact operators can be characterized by the property that every norm-closed (and coinciding with its biorthogonal complement, resp.) submodule of every Hilbert C*-module over them is automatically an orthogonal sum-mand. We find out further generic properties of the… (More)