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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.

Zebrafish (Danio rerio) can serve as a model system to study heritable skin diseases. The skin is rapidly developed during the first 5-6 days of embryonic growth, accompanied by expression of skin-specific genes. Transmission electron microscopy (TEM) of wild-type zebrafish at day 5 reveals a two-cell-layer epidermis separated from the underlying… (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)

This study examines the use of high spatial resolution hyperspectral imagery in combination with light detection and ranging (LiDAR) data and digital aerial imagery for vegetation management of utility corridors. Two different classification methods, i.e. the support vector machines (SVM) and the spectral angle mapper (SAM) were applied on the datasets to… (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)