Related papers: The finite tiling problem is undecidable in the hy…
In this article, we consider mechanical billiard systems defined with Lagrange's integrable extension of Euler's two-center problems in the Euclidean space, on the sphere, and in the hyperbolic space of arbitrary dimension $n \ge 3$. In the…
A field $K$ in a ring language $\mathcal{L}$ is finitely undecidable if $\mbox{Cons}(\Sigma)$ is undecidable for every nonempty finite $\Sigma \subseteq \mbox{Th}(K; \mathcal{L})$. We extend a construction of Ziegler and (among other…
We consider the decidability of state-to-state reachability in linear time-invariant control systems over discrete time. We analyse this problem with respect to the allowable control sets, which in general are assumed to be defined by…
This is the third in a series of papers constructing hyperbolic structures on all Haken three-manifolds. This portion deals with the mixed case of the deformation space for manifolds with incompressible boundary that are not acylindrical,…
We show that the perimeter of the convex hull of finitely many disks lying in the hyperbolic or Euclidean plane, or in a hemisphere does not increase when the disks are rearranged so that the distances between their centers do not increase.…
We classify the solutions to an overdetermined elliptic problem in the plane in the finite connectivity case. This is achieved by establishing a one-to-one correspondence between the solutions to this problem and a certain type of minimal…
The Diophantine problem for a monoid $M$ is the decision problem to decide whether any given system of equations has a solution in $M$. In this note, we give a simple example of a context-free, word-hyperbolic, finitely presented, special…
The finite satisfiability problem of two-variable logic extended by a linear order successor and a preorder successor is shown to be undecidable.
V. Arnold's problem 1987-14 asks whether there exist smooth hypersurfaces in $R^N$ (other than the conics in odd-dimensional spaces) for which the volume of the segment cut by any hyperplane from the body bounded by such a hypersurface is…
We compare the flat geometry associated to a quadratic differential with the hyperbolic geometry associated to the underlying Riemann surface. We show that if a curve is contained in a thick subsurface, then its hyperbolic length is…
This paper shows the unique solvability of elliptic problems associated with two-phase incompressible flows, which are governed by the two-phase Navier-Stokes equations, in unbounded domains such as the whole space separated by a compact…
We show that the entailment problem, for a given entailment problem for DL-Lite$_{core}$ ontology, and given conjunctive query with inequalities, is undecidable. We also show that this problem remains undecidable if conjunctive queries with…
Several articles deal with tilings with squares and dominoes on 2-dimensional boards, but only a few on boards in 3-dimensional space. We examine a tiling problem with colored cubes and bricks of $(2\times2\times n)$-board in three…
We apply the topology of convergence on compact sets to define unpredictable functions [5, 6]. The topology is metrizable and easy for applications with integral operators. To demonstrate the effectiveness of the approach, the existence and…
We prove an existence result for the Backus interior problem in the Euclidean ball. The problem consists in determining a harmonic function in the ball from the knowledge of the modulus of its gradient on the boundary. The problem is…
In this thesis we will present and discuss various results pertaining to tiling problems and mathematical logic, specifically computability theory. We focus on Wang prototiles, as defined in [32]. We begin by studying Domino Problems, and…
We investigate the problem of finding complete strictly convex hypersurfaces of constant curvature in hyperbolic space with a prescribed asymptotic boundary at infinity for a general class of curvature functions.
The problem we are concerned with is whether singularities form in finite time in incompressible fluid flows. It is well known that the answer is ``no'' in the case of Euler and Navier-Stokes equations in dimension two. In dimension three…
We study the stability of capillary hypersurfaces in a unit Euclidean ball. It is proved that if the mass center of the generalized body enclosed by the immersed capillary hypersurface and the wetted part of the sphere is located at the…
The consistency problem for a class of algebraic structures asks for an algorithm to decide for any given conjunction of equations whether it admits a non-trivial satisfying assignment within some member of the class. By Adyan (1955) and…