Strip maps are convex for small surfaces.
problem Understanding infinitesimal deformations of small surfaces.
method Analyzing the strip map from arc complexes to infinitesimal deformations.
result The strip map image is convex for small surfaces.
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48 results for “strip map”
Equivariant primitive harmonic maps into symmetric spaces, with applications to Willmore surfacesmath.DG
The study constructs equivariant harmonic maps into symmetric spaces with applications to Willmore surfaces.
problem Constructing harmonic maps into symmetric spaces.
method Equivariant primitive harmonic maps construction.
result Examples of -equivariant Willmore Moebius strips in .
Solves Björling problem for surfaces with given mean curvature.
problem Finding surfaces with prescribed mean curvature.
method Analytic function of Gauss map to construct surfaces.
result Existence of Möbius strip topological surfaces.
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…
Elastic stripsmath.DG
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.
problem No specific problem stated; focuses on a mathematical formula.
method Analyzes partitions of the Möbius strip.
result Proves an Euler-type formula for Möbius strip partitions.
Quantum strips on surfacesmath-ph
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…
Study calculates rational homology groups of configuration spaces for a Moebius strip and a projective plane.
problem Calculating rational homology groups of configuration spaces for specific topological spaces.
method Explicit calculation of all rational homology groups.
result All rational homology groups of configuration spaces for the Moebius strip and projective plane are determined.
Effective quantum dynamics on a thin Möbius strip approximated by a flat model.
problem Quantum dynamics on a Möbius strip with zero width.
method Norm-resolvent convergence to an unconventional flat model with explicit spectrum.
result Spectral properties of the curved Möbius strip are well approximated by a flat model.
Study on quantum strips in higher dimensions, focusing on essential and discrete spectra.
problem Location and existence of spectra in quantum strips of varying dimensions.
method Analysis of the Dirichlet Laplacian on ruled surfaces, considering conditions on Gauss curvature and curve type.
result Established existence of discrete spectrum under specific conditions and derived effective operators.
A simpler 3D Möbius strip design without twists.
problem Creating a Möbius strip without twists.
method A simple rational function on a polynomial subset of R^2.
result The new design is a union of a segment and a graph of a rational function.
Study strip deformations of hyperbolic polygons with decorated vertices.
problem Understanding deformations of hyperbolic polygons with decorated vertices.
method Analyzing strip deformations of ideal hyperbolic polygons with horoballs.
result Arc complexes parameterize uniformly lengthening deformations.
Solves Dirichlet problem for translating solitons in a strip.
problem Existence of classical solutions to the Dirichlet problem for -translating solitons.
method Perron method with grim reapers as barriers.
result Existence of classical solutions for the Dirichlet problem.
Ancient solutions on a strip are constant if polynomial, and have finite-dimensional space for slower growth.
problem Characterizing ancient solutions on an infinite strip with polynomial and exponential growth.
method Analyzing parabolic equations on an infinite strip, proving properties of ancient solutions.
result Ancient solutions on the strip are constant if they grow polynomially, and have a finite-dimensional space for slower exponential growth.
We prove a flat strip theorem for 2-dimensional ptolemaic spaces.
New method weaves paper strips for designing curved surfaces with elasticity.
problem Designing general curved surfaces with geometrical elasticity.
method Shape optimization of paper strips using nonlinear elasticity theory.
result Demonstrated creation of catenoid and helicoid surfaces with 54 paper strips.
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.
problem Determining Courant-sharp eigenvalues on a Möbius strip.
method Analyzing the eigenvalues and nodal patterns of the Möbius strip.
result Only the first and second eigenvalues are Courant-sharp on the Möbius strip.
Study on disk configurations in strips shows stability patterns.
problem Understanding stability patterns in disk configurations in strips.
method Finite presentation of rational homology groups, representation stability.
result Disk configuration space exhibits first-order representation stability.
A criterion is given for cutting out disks with ribbons from a Möbius strip.
problem Determining which hieroglyphs can be realized as disks with ribbons on a Möbius strip.
method Developed a criterion based on Mohar's realizability criterion, leading to a quadratic algorithm.
result A criterion for weak realizability of disks with ribbons on a Möbius strip.
Study shows how a strip's twisting increases at infinity, affecting its spectrum.
problem Understanding the spectrum of a strip with diverging twisting.
method Analyzing the Dirichlet Laplacian in a two-dimensional strip with segments rotating at increasing velocity.
result Essential spectrum forms a three-dimensional tube at infinity, with discrete eigenvalues possible if the tube's cross-section is a disk.
Neural model predicts procedure names in stripped binaries.
problem Reverse engineering stripped executables with limited debug information.
method Combines static analysis with neural models to predict procedure names.
result Improves prediction accuracy by 28% and 100% over state-of-the-art models.
The study solves conditions for minimal strips containing lightlike curves in 4D spacetime.
problem Existence and uniqueness of minimal timelike strips containing lightlike curves.
method Necessary and sufficient conditions derived for the existence of minimal strips.
result Conditions for the existence and uniqueness of minimal strips are provided.
The paper proves shellability and sphericity of a complex related to the Möbius strip.
problem Shellability and sphericity of a specific complex related to the Möbius strip.
method Elementary proofs of shellability for related complexes, application of Danaraj and Klee's result.
result Shellability and sphericity of the quasi-arc complex of the Möbius strip.
Alexander polynomial derived from knot contact homology and Floer strips.
problem Calculating the Alexander polynomial of a knot.
method Contact homology and Floer theory applied to knot complements.
result Alexander polynomial expressed as an integral of partial derivatives.
We construct real analytic flat Moebius strips of arbitrary isotopy types, whose centerlines are geodesics or lines of curvature.
Study non-compact surfaces formed by gluing strips and their foliations.
problem Understanding foliations on non-compact surfaces formed by gluing strips.
method Examined surfaces formed by gluing strips and studied the resulting foliations.
result The identity path component of the group of homeomorphisms of the foliation is contractible.
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 …
Algorithm removes leaves to find root in uniform trees.
problem Finding the root in large uniform attachment trees.
method Leaf-stripping algorithm recursively removes leaves.
result Set of remaining vertices contains the root with high probability.
The central problem of strip theory is the calculation of potential flowaround 2D sections. One particular method of solutions to this problem is conformal mapping of the body section to the unit circle over which a solution of potential flow is available. Here, a new multiparameter conformal mapping method is presente…
The paper studies homeotopy groups of leaf spaces for specific foliations.
problem Identifying homeotopy groups of leaf spaces for non-compact surfaces with non-compact leaves.
method Identifying homeotopy groups with automorphisms of graphs and showing induced homomorphisms.
result The induced homomorphism between homeotopy groups is either injective or has a kernel of Z_2.
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…
Study on Rumin cohomology and Heisenberg orientability in Heisenberg group.
problem Analyzing Rumin cohomology and Heisenberg orientability in Heisenberg group.
method Careful description of Rumin cohomology, commutation of differential operators, pushforward and pullback definitions, and definition of Heisenberg orientability.
result Existence of Heisenberg regular non-Heisenberg orientable surfaces.
New system studies trapped light paths in Euclidean space.
problem Trapping of light paths in Euclidean space with negative refractive index.
method Introduces wind-tree tiling billiards system to study trajectories of rays in Euclidean space with rectangular obstacles.
result Almost every configuration of the system traps trajectories with initial vertical direction in an infinite strip.
Study extends resolvent estimates for non-even metrics on hyperbolic spaces.
problem Estimating resolvent for non-even metrics on asymptotically hyperbolic spaces.
method Extends Vasy's method for non-trapping geodesic flow, proving same strip size as Guillarmou.
result Same strip size for meromorphic continuation of resolvent as Guillarmou's result.
The paper proves optimal systolic inequalities for Möbius strip and Klein bottle.
problem Optimal systolic inequalities for Möbius strip and Klein bottle.
method Alternative proof using -distance of conformal factor.
result Estimates on systolic defect for Möbius strip and Klein bottle.
New closed linkage mechanisms with Möbius strip properties.
problem Designing closed linkage mechanisms with arbitrary number of hinges.
method Proposed a new family of closed linkage mechanisms with singular properties.
result These mechanisms can be considered as discrete Möbius strips.
New method constructs proper affine actions of groups in higher dimensions.
problem Finding proper affine actions of discrete groups in higher-dimensional spaces.
method Higher strip deformations and Margulis invariant for properness.
result Affine actions of convex cocompact groups and virtually free groups are constructed properly.
We address some global solvability issues for classes of smooth nonsingular vector fields in the plane related to cohomological equations in geometry and dynamical systems. The first main result is that is not surjective in iff the geometrical condition -- the existence of separatrix str…
New rings reveal surprising prime colorings.
problem Determining which primes can color rainbow rings.
method Linear algebra eigenvalues and knot theory colorability.
result Almost all primes admit 0, 1, or infinite colorings.
We describe the family of minimal graphs on strips with boundary values disposed alternately on edges of length one, and whose conjugate graphs are contained in horizontal slabs of width one in . 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…
Stability of non-abelian X-ray transform proven in higher dimensions.
problem Recovering matrix potentials from scattering data in higher dimensions.
method Injectivity proof using a novel method by Uhlmann-Vasy, with quantitative improvements.
result Hölder-type stability estimate established for non-abelian X-ray transform.
This paper provides a practical method to extract caplet volatilities from quoted data.
problem Extracting caplet volatilities from quoted data is complex and not straightforward.
method The paper presents a constructive algorithm based on criteria and robust outlier detection. It includes direct interpolation, bootstrap methods, and global search methods.
result The paper introduces methods to extract caplet volatilities that are arbitrage-free and consistent with quoted data.
Researchers extend parametrization of Margulis spacetimes using strip deformations.
problem Parametrize Margulis spacetimes with decorated horoballs.
method Use strip deformations to parametrize complete finite-area hyperbolic surfaces with spikes decorated with horoballs.
result Generalized parametrization of Margulis spacetimes with photons.
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…