Related papers: Six topics on inscribable polytopes
There are many open problems and some mysteries connected to the realizations of the associahedra as convex polytopes. In this note, we describe three -- concerning special realizations with the vertices on a sphere, the space of all…
This note is an introduction to the properties of stable polynomials in several variables with real or complex coefficients. These polynomials are defined in terms of where the polynomial is non-vanishing. We do not cover well-known topics…
We collect here various conjectures on congruences made by the author in a series of papers, some of which involve binary quadratic forms and other advanced theories. Part A consists of 100 unsolved conjectures of the author while…
Sobolev orthogonal polynomials have been studied extensively in the past 20 years. The research in this field has sprawled into several directions and generates a plethora of publications. This paper contains a survey of the main…
Some Open Problems Concerning Orthogonal Polynomials.
The paper is devoted to perfect and almost perfect homogeneous polytopes in Euclidean spaces. We classified perfect and almost perfect polytopes among all regular polytopes and all semiregular polytopes excepting Archimedean solids and two…
We use a simple description of the outer automorphism of S_6 to cleanly describe the invariant theory of six points in P^1, P^2, and P^3.
Eberhard-type theorems are statements about the realizability of a polytope (or more general polyhedral maps) given the valency of its vertices and sizes of its polygonal faces up to a linear linear degree of freedom. We present new…
In which a review of the concept of countability is done in mathematics, subjecting review some of the theorems so far accepted, showing their inconsistency and also taking concrete elements on the countability of all the powers of the set…
Seventeen einsteinium isotopes have so far been observed; the discovery of these isotopes is discussed. For each isotope a brief summary of the first refereed publication, including the production and identification method, is presented.
I review progress that has been made in nuclear astrophysics over the past few years and summarize some of the questions that remain. Topics selected include solar neutrinos, supernovae (the explosion and associated nucleosynthesis),…
We propose a new contact relation between polytopes. Intuitively, we say that two polytopes are in strong contact if a small enough object can pass from one of them to the other while remaining in their union. In the first half of the paper…
This is an overview of various aspects of the 6-vertex model in statistical mechanics and related models.
We prove that seminormality of cut polytopes is equivalent to normality. This settles two conjectures regarding seminormality of cut polytopes.
Abstract polytopes are a combinatorial generalization of convex and skeletal polytopes. Counting how many flag orbits a polytope has under its automorphism group is a way of measuring how symmetric it is. Polytopes with one flag orbit are…
This work deals with the conformal transformations in six-dimensional spinorial formalism. Several conformally invariant equations are obtained and their geometrical interpretation are worked out. Finally, the integrability conditions for…
This work is devoted to the study of some important questions in general relativity. They include topics related to astrophysical shock waves, impulsive signals, gravitational memory effect, black hole geometries and integrable systems…
Our focus is upon {\it irreducible} nonnegative $n$-by-$n$ matrix realizations of nonnegatively realizable spectra or, equivalently, characteristic polynomials. After giving some general background, we make some useful new observations and…
Whether we live in a spatially finite universe, and what its shape and size may be, are among the fundamental long-standing questions in cosmology. These questions of topological nature have become particularly topical, given the wealth of…
Automated program verification often proceeds by exhibiting inductive invariants entailing the desired properties.For numerical properties, a classical class of invariants is convex polyhedra: solution sets of system of linear…