arXiv research

Algorithm removes leaves to find root in uniform trees.

Study extends resolvent estimates for non-even metrics on hyperbolic spaces.

Motivated by the problem of finding an explicit description of a developable narrow Moebius strip of minimal bending energy, which was first formulated by M. Sadowsky in 1930, we will develop the theory of elastic strips. Recently E.L. Starostin and G.H.M. van der Heijden found a numerical description for an elastic Mo…

Proves an Euler-type formula for Möbius strip partitions.

Motivated by the theory of quantum waveguides, we investigate the spectrum of the Laplacian, subject to Dirichlet boundary conditions, in a curved strip of constant width that is defined as a tubular neighbourhood of an infinite curve in a two-dimensional Riemannian manifold. Under the assumption that the strip is asym…

We introduce the notion of strip complex. A strip complex is a special type of complex obtained by gluing "strips" along their natural boundaries according to a given graph structure. The most familiar example is the one dimensional complex classically associated with a graph, in which case the strips are simply copies…

Effective quantum dynamics on a thin Möbius strip approximated by a flat model.

Study on quantum strips in higher dimensions, focusing on essential and discrete spectra.

A simpler 3D Möbius strip design without twists.

Study strip deformations of hyperbolic polygons with decorated vertices.

Solves Dirichlet problem for translating solitons in a strip.

Ancient solutions on a strip are constant if polynomial, and have finite-dimensional space for slower growth.

We prove a flat strip theorem for 2-dimensional ptolemaic spaces.

New method weaves paper strips for designing curved surfaces with elasticity.

The strip map is a natural map from the arc complex of a bordered hyperbolic surface $S$ to the vector space of infinitesimal deformations of $S$. We prove that the image of the strip map is a convex hypersurface when $S$ is a surface of small complexity: the punctured torus or thrice punctured sphere.

We prove that the asymptotic completion of a developable Möbius strip in Euclidean three-space must have at least one singular point other than cuspidal edge singularities. Moreover, if the strip contains a closed geodesic, then the number of such singular points is at least three. These lower bounds are both sharp.

We consider the Dirichlet Laplacian in infinite two-dimensional strips defined as uniform tubular neighbourhoods of curves on ruled surfaces. We show that the negative Gauss curvature of the ambient surface gives rise to a Hardy inequality and use this to prove certain stability of spectrum in the case of asymptoticall…

Researchers found the first and second eigenvalues are Courant-sharp on a Möbius strip.

Study on disk configurations in strips shows stability patterns.

A criterion is given for cutting out disks with ribbons from a Möbius strip.

Study shows how a strip's twisting increases at infinity, affecting its spectrum.

All rational homology groups of unordered configuration spaces of the Moebius strip and the projective plane are calculated

Neural model predicts procedure names in stripped binaries.

The study solves conditions for minimal strips containing lightlike curves in 4D spacetime.

We construct real analytic flat Moebius strips of arbitrary isotopy types, whose centerlines are geodesics or lines of curvature.

Agents learning to act autonomously in real-world domains must acquire a model of the dynamics of the domain in which they operate. Learning domain dynamics can be challenging, especially where an agent only has partial access to the world state, and/or noisy external sensors. Even in standard STRIPS domains, existing …

New method eliminates domain size restrictions for X-ray transform inversion.

Let S be a C^2 H-minimal noncharacteristic hypersurface in the first Heisenberg group. We show that if S contains a graphical strip, then it is not a stable minimal surface. Moreover, we show that if S is a C^2 H-minimal noncharacteristic entire graph which is not itself a vertical plane, then S contains a graphical st…

New system studies trapped light paths in Euclidean space.

The paper proves optimal systolic inequalities for Möbius strip and Klein bottle.

New closed linkage mechanisms with Möbius strip properties.

Solves Björling problem for surfaces with given mean curvature.

Trojans can be inserted into deep neural networks without altering training data.

We study non-compact surfaces obtained by gluing strips $\mathbb{R}\times(-1,1)$ with at most countably many boundary intervals along some these intervals. Every such strip possesses a foliation by parallel lines, which gives a foliation on the resulting surface. It is proved that the identity path component of the gro…

New method constructs proper affine actions of groups in higher dimensions.

We address some global solvability issues for classes of smooth nonsingular vector fields $L$ in the plane related to cohomological equations $Lu=f$ in geometry and dynamical systems. The first main result is that $L$ is not surjective in $C^\infty(\R^2)$ iff the geometrical condition -- the existence of separatrix str…

New rings reveal surprising prime colorings.

We describe the family of minimal graphs on strips with boundary values $\pm\infty$ disposed alternately on edges of length one, and whose conjugate graphs are contained in horizontal slabs of width one in $\mathbb{R}^3$. We can obtain as limits of such graphs the helicoid, all the doubly periodic Scherk minimal surfac…

We study strip deformations of convex cocompact hyperbolic surfaces, defined by inserting hyperbolic strips along a collection of disjoint geodesic arcs properly embedded in the surface. We prove that any deformation of the surface that uniformly lengthens all closed geodesics can be realized as a strip deformation, in…

Let $X$ be a connected non-compact $2$-dimensional manifold possibly with boundary and $Δ$ be a foliation on $X$ such that each leaf $ω\inΔ$ is homeomorphic to $\mathbb{R}$ and has a trivially foliated neighborhood. Such foliations on the plane were studied by W. Kaplan who also gave their topological classification. H…

This paper provides a practical method to extract caplet volatilities from quoted data.

Researchers extend parametrization of Margulis spacetimes using strip deformations.

We consider the scattering and lens rigidity of compact surfaces with boundary that have a trapped geodesic. In particular we show that the flat cylinder and the flat Möbius strip are determined by their lens data. We also see by example that the flat Möbius strip is not determined by it's scattering data. We then cons…

We characterize subgroups of the mapping class group that stabilize a Teichmueller disk in terms of ellipses and strips that are immersed in the associated translation surface. In particular, we show that the space of immersed ellipses/strips that meet at least three cone points is naturally a (non-manifold) 2-dimensio…

In this paper we consider a free boundary problem in the 3-dimensional Lorentz-Minkowski space $ł^3$ which deals spacelike surfaces whose mean curvature is a linear function of the time coordinate and the boundary moves in a given support plane. We study spacelike surfaces that project one-to-one into a strip of the su…

Study flat flow solutions to Mullins-Sekerka and area-preserving curvature flows on planar flat torus.

The study constructs equivariant harmonic maps into symmetric spaces with applications to Willmore surfaces.

Proposes a method to improve skull stripping accuracy in MRI images.