Modularity in Science and Art
Modules of splines on polyhedral complexes.
Moduli of rotundity and smoothness for convex bodies.
Moments of inertia associated with the lozenge tilings of a hexagon.
Monomer-dimer tatami tilings of rectangular regions.
Monotone Valuations on the Space of Convex Functions
We consider the space Cn of convex functions u defined in Rn with values in R ∪ {∞}, which are lower semi-continuous and such that lim|x| } ∞ u(x) = ∞. We study the valuations defined on Cn which are invariant under the composition with rigid motions, monotone and verify a certain type of continuity. We prove integral representations formulas for such valuations which are, in addition, simple or homogeneous.
Monotonic rearrangements of functions with small mean oscillation
We obtain sharp bounds for the monotonic rearrangement operator from "dyadic-type" classes to "continuous" ones; in particular, for the BMO space and Muckenhoupt classes. The idea is to connect the problem with a simple geometric construction named α-extension.
Monotonicity of the maximum of inner product norms
Let be the field of real or complex numbers. In this note we characterize all inner product norms on for which the norm on is monotonic.
More classes of stuck unknotted hexagons.
More on exposed points and extremal points of convex sets in and Hilbert space
Let be a separable real Hilbert space, with , and let be convex and closed in . Let be a collection of linear -subspaces of . A point is called exposed by if there is a so that . We show that, under some natural conditions, can be reconstituted as the convex hull of the closure of all its exposed by points whenever is dense and . In addition, we discuss the question when the set of exposed by some points forms a -set.
More on k-Sets of Finite Sets in the Plane.
More than first-order developments of convex functions: primal-dual relations.
Morse index of a cyclic polygon
It is known that cyclic configurations of a planar polygonal linkage are critical points of the signed area function. In the paper we give an explicit formula of the Morse index for the signed area of a cyclic configuration. We show that it depends not only on the combinatorics of a cyclic configuration, but also on its metric properties.
Motion of spirals by crystalline curvature
Modern physics theories claim that the dynamics of interfaces between the two-phase is described by the evolution equations involving the curvature and various kinematic energies. We consider the motion of spiral-shaped polygonal curves by its crystalline curvature, which deserves a mathematical model of real crystals. Exploiting the comparison principle, we show the local existence and uniqueness of the solution.
Movable configurations.
Multiapplications boréliennes à valeurs convexes de
Multigrid-convergence of digital curvature estimators
Many methods have been proposed to estimate differential geometric quantities like curvature(s) on discrete data. A common characteristics is that they require (at least) one user-given scale or window parameter, which smoothes data to take care of both the sampling rate and possible perturbations. Digital shapes are specific discrete approximation of Euclidean shapes, which come from their digitization at a given grid step. They are thus subsets of the digital plane . A digital geometric estimator...
Multiobjective problems of convex geometry.
Multiple Lattice Packings and Coverings of Spheres.
Multiple tilings by cubes with no shared faces.