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Dr. David Yost

FedUni Associate

Academic, Technical Services and Program Support



Mt Helen Campus, Online

Minimum Number of Edges of Polytopes with 2d + 2 Vertices


Zero duality gap conditions via abstract convexity?

Using tools provided by the theory of abstract convexity, we extend conditions for zero duality...

Chebyshev Multivariate Polynomial Approximation and Point Reduction Procedure

We apply the methods of nonsmooth and convex analysis to extend the study of Chebyshev (uniform)...

Strictly convex banach algebras

We discuss two facets of the interaction between geometry and algebra in Banach algebras. In the...

Almost Simplicial Polytopes: The Lower and Upper Bound Theorems

We study -vertex -dimensional polytopes with at most one nonsimplex facet with, say, vertices,...

Observations on the separable quotient problem for banach spaces

The longstanding Banach-Mazur separable quotient problem asks whether every infinite-dimensional...

Polytopes Close to Being Simple

Schur Functions for Approximation Problems

In this paper we propose a new approach to least squares approximation problems. This approach is...

Lower bound theorems for general polytopes

For a d-dimensional polytope with v vertices, d+1≤v≤2d, we calculate precisely the minimum...

On the Reconstruction of Polytopes

Blind and Mani, and later Kalai, showed that the face lattice of a simple polytope is determined...

Thin sets of constant width

We prove that every Banach space which admits an unconditional basis can be renormed to contain a...

Chebyshev Multivariate Polynomial Approximation: Alternance Interpretation

In this paper, we derive optimality conditions for Chebyshev approximation of multivariate...

Compact Convex Sets with Prescribed Facial Dimensions

While faces of a polytope form a well structured lattice, in which faces of each possible...

The excess degree of a polytope

We define the excess degree \xi (P) of a d-polytope P as 2f1 - df0, where f0 and f1 denote the...

Almost simplicial polytopes: The lower and upper bound theorems

This is an extended abstract of the full version. We study n-vertex d-dimensional polytopes with...

  • Conference Proceedings

More Indecomposable Polyhedra

We apply combinatorial methods to a geometric problem: the classification of polytopes, in terms...

  • Journals

Quasilinear mappings, M-ideals and polyhedra

We survey the connection between two results from rather different areas: failure of the 3-space...

Lipschitz selections for multifunctions

  • Conference Proceedings

A Different Johnson-Lindenstrauss Space

  • Journals

Decomposability of Polytopes

Integration: Reversing traditional pedagogy

  • Journals

Uniformly non-hexagonal Banach spaces

  • Conference Proceedings

Some indecomposable polyhedra

Colocality and twisted sums of Banach spaces

Using the relation between subspaces of Banach spaces and quotients of their duals, we introduce...

Reducible polytopes

  • Conference Proceedings

Extending operators into L-infinity spaces under a twisted light

  • Conference Proceedings

Reducible convex sets

  • Conference Proceedings

Twisted sums with C(K) spaces

  • Journals

Applications of inverse limits to extensions of operators and approximation of Lipschitz functions

  • Journals