Dr. David Yost
Adjunct Associate Professor
Minimum Number of Edges of Polytopes with 2d + 2 Vertices
THE LOWER BOUND THEOREM FOR d -POLYTOPES WITH 2d + 1 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...
More Indecomposable Polyhedra
We apply combinatorial methods to a geometric problem: the classification of polytopes, in terms...
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
A Different Johnson-Lindenstrauss Space
Decomposability of Polytopes
Integration: Reversing traditional pedagogy
Uniformly non-hexagonal Banach spaces
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
Extending operators into L-infinity spaces under a twisted light
Reducible convex sets
Twisted sums with C(K) spaces
Applications of inverse limits to extensions of operators and approximation of Lipschitz functions