Related papers: Isotropic constants and regular polytopes

Results are presented for finding the optimal orientation of an anisotropic elastic material. The problem is formulated as minimizing the strain energy subject to rotation of the material axes, under a state of uniform stress. It is shown…

The paper is devoted to a systematic study and characterizations of notions of local maximal monotonicity and their strong counterparts for set-valued operators that appear in variational analysis, optimization, and their applications. We…

We study upper bounds on the number of lattice points for convex bodies having their centroid at the origin. For the family of simplices as well as in the planar case we obtain best possible results. For arbitrary convex bodies we provide…

The purpose of this paper is to provide a detailed description of the spaces that can be specified as $L^2$ domains for the operators of a first order elliptic complex on a compact manifold with conical singularities. This entails an…

Let G be a group. Two elements x,y are said to be in the same z-class if their centralizers are conjugate in G. Let V be a vector space of dimension n over a field F of characteristic different from 2. Let B be a non-degenerate symmetric,…

We prove tight lower bounds for the coefficients of the generalized $h$-vector of a rational polytope with a symmetry of prime order that is fixed--point--free on the boundary. These bounds generalize results of R.~Stanley and R.~Adin for…

Generalizing Milnor's result that an FTC (finite total curvature) knot has an isotopic inscribed polygon, we show that any two nearby knotted FTC graphs are isotopic by a small isotopy. We also show how to obtain sharper constants when the…

The underlying motivation of the present work lies on a cornerstone question in spectral optimization that consists of determining sharp lower and upper uniform estimates for fundamental frequencies of a set of uniformly elliptic operators…

Given $n+1$ unit vectors in $\mathbf{R}^n$ or $\mathbf{C}^n,$ consider the absolute values of the determinants of the vectors taken $n$ at a time. By taking a geometric perspective, we show that the minimum of these determinants is…

We study the geometry of dynamically defined Cantor sets in arbitrary dimensions, introducing a criterion for $\mathcal{C}^{1+\alpha}$ stable intersections of such Cantor sets, under a mild bunching condition. This condition is naturally…

We consider a continuous-time positive bilinear control system (PBCS), i.e. a bilinear control system with Metzler matrices. The positive orthant is an invariant set of such a system, and the corresponding transition matrix C(t) is…

In this paper we study a class of anisotropic equations with a lower order term whose coefficients lay in Marcinkiewicz spaces. We prove some regularity results for local solutions requiring any control on the norm of the coefficients.

In this paper we look for minimizers of the energy functional for isotropic compressible elasticity taking into consideration the effect of a gravitational field induced by the body itself. We consider the displacement problem in which the…

A theorem of Scott gives an upper bound for the normalized volume of lattice polygons with exactly $i>0$ interior lattice points. We will show that the same bound is true for the normalized volume of lattice polytopes of degree 2 even in…

In this article we provide examples, methods and algorithms to determine conditions on the parameters of certain type of parametric optimization problems, such that among the resulting local minima and maxima there is at least one which…

When the standard representation of a crystallographic Coxeter group is reduced modulo an odd prime p, one obtains a finite group G^p acting on some orthogonal space over Z_p . If the Coxeter group has a string diagram, then G^p will often…

We define an abstract regular polytope to be internally self-dual if its self-duality can be realized as one of its symmetries. This property has many interesting implications on the structure of the polytope, which we present here. Then,…

In this paper, we will establish the best constants for certain classes of weighted Moser-Trudinger inequalities on the entire Euclidean spaces $\mathbb{R}^N$. We will also prove the existence of maximizers of these sharp weighted…

We investigate the iterative behaviour of continuous order preserving subhomogeneous maps that map a polyhedral cone into itself. For these maps we show that every bounded orbit converges to a periodic orbit and, moreover, that there exists…

For Gamma a finite, connected metric graph, we consider the space of configurations of n points in Gamma with a restraint parameter r dictating the minimum distance allowed between each pair of points. These restricted configuration spaces…