Invariants of pairs of compact convex sets.
Invertible Relations on Polytopes.
Ionpackings in the space
Irregular and semi-regular polyhedral models for Rous sarcoma virus cores.
Irregularities of Point Distributions Relative to Homothetic Convex Bodies I.
Isocanted alcoved polytopes
Through tropical normal idempotent matrices, we introduce isocanted alcoved polytopes, computing their -vectors and checking the validity of the following five conjectures: Bárány, unimodality, , flag and cubical lower bound (CLBC). Isocanted alcoved polytopes are centrally symmetric, almost simple cubical polytopes. They are zonotopes. We show that, for each dimension, there is a unique combinatorial type. In dimension , an isocanted alcoved polytope has vertices, its face lattice is the lattice...
Isohedrally compatible tilings
Isometric classification of Sobolev spaces on graphs
Isometric Sobolev spaces on finite graphs are characterized. The characterization implies that the following analogue of the Banach-Stone theorem is valid: if two Sobolev spaces on 3-connected graphs, with the exponent which is not an even integer, are isometric, then the corresponding graphs are isomorphic. As a corollary it is shown that for each finite group and each p which is not an even integer, there exists n ∈ ℕ and a subspace whose group of isometries is the direct product × ℤ₂.
Isometric Embeddings of Pro-Euclidean Spaces
In [12] Petrunin proves that a compact metric space X admits an intrinsic isometry into En if and only if X is a pro-Euclidean space of rank at most n, meaning that X can be written as a “nice” inverse limit of polyhedra. He also shows that either case implies that X has covering dimension at most n. The purpose of this paper is to extend these results to include both embeddings and spaces which are proper instead of compact. The main result of this paper is that any pro-Euclidean space of rank...
Isometrien des Konvexringes
Isometrien des Raumes der konvexen Körper
Isometries of Spaces of Compact Convex Subsets of Metric Manifolds.
Isomorphismes de lattis de fermés convexes
Isonemality and mononemality of woven fabrics
The paper studies the diagrams of woven fabrics consisting of white and black squares as geometrical objects and described their symmetries. The concepts of isonemality and mononemality due to B. Grünbaum and G. C. Shephard are used. A conjecture of these authors is proved in a particular case.
Isoperimetric inequalities and identifties for k-dimensional cross-sections of convex bodies.
Isoperimetric Inequalities for Infinite Hyperplane Systems.
Isoperimetric inequalities for quermassintegrals
Isoperimetric numbers and spectral radius of some infinite planar graphs
Isoperimetric problem for uniform enlargement
We consider an isoperimetric problem for product measures with respect to the uniform enlargement of sets. As an example, we find (asymptotically) extremal sets for the infinite product of the exponential measure.
Isoperimetric Problems for Convex Bodies and a Localization Lemma.