Positive factorization found for a specific map on surfaces.
problem Balanced superelliptic rotation on surfaces.
method Positive factorization approach.
result Positive factorization for balanced superelliptic rotation.
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48 results for “balanced superelliptic rotation”
Finite presentation for a specific group in 3D handlebody topology.
problem Finding a finite presentation for a specific group in 3D handlebody topology.
method Constructed a finite presentation for the liftable Hilden group to derive the presentation for the balanced superelliptic handlebody group.
result A finite presentation was given for the balanced superelliptic handlebody group.
Three elements generate balanced superelliptic mapping class groups.
problem Generating balanced superelliptic mapping class groups.
method Proving groups are generated by three elements through normalizers and liftable mapping class groups.
result Balanced superelliptic mapping class groups are generated by three elements.
Finite presentations for mapping class groups of surfaces and surfaces with points/boundaries.
problem Finding finite presentations for balanced superelliptic mapping class groups.
method Construct finite presentations for corresponding liftable mapping class groups in a different generating set.
result Finite presentations for balanced superelliptic mapping class groups of various surfaces.
Proves a minimal generating set for a specific group of mapping classes.
problem Finding a minimal generating set for a specific group of mapping classes.
method Proved the group is generated by four elements, with minimal exceptions.
result Minimal generating set for the balanced superelliptic mapping class group.
The hyperelliptic mapping class group has been studied in various contexts within topology and algebraic geometry. What makes this study tractable is that there is a surjective map from the hyperelliptic mapping class group to a mapping class group of a punctured sphere. The more general family of superelliptic mapping…
Study infinite superelliptic curves and their Veech groups, providing geometric and algebraic insights.
problem Characterize Veech groups of infinite superelliptic curves.
method Analyzing geometric properties, differential equations, and group theory.
result Veech groups of infinite superelliptic curves are all matrices permuting branched points.
The paper constructs braiding structures for a specific subfactor.
problem The challenge is to understand the braiding structures of a Jones-Wassermann subfactor.
method The approach involves constructing braiding structures on the multi-interval Jones-Wassermann subfactor planar algebra.
result The braiding structures induce a projective unitary representation of the balanced superelliptic mapping class group.
The reduced Burau representation of the braid group is obtained from the action of on the homology of an infinite cyclic cover of the disc with punctures. The group homology of braid groups with coefficients in the complexified reduced Burau representation is calculated. Our topolog…
DeepSphere improves spherical CNNs by balancing efficiency and rotation equivariance.
problem Designing efficient and rotation-equivariant convolutional layers for spherical data.
method Graph-based approach to represent spherical data, focusing on the number of vertices and neighbors.
result DeepSphere achieves state-of-the-art performance and demonstrates efficiency and flexibility.
We consider the universal family of superelliptic curves: each curve in the family is a -fold covering of the unit disk, totally ramified over a set of distinct points; is a fibre bundle, where is the configuration space of distinct points. We fin…
The paper studies liftable mapping class groups of cyclic covers of spheres.
problem Understanding liftable mapping class groups of cyclic covers of spheres.
method Derived finite generating sets, provided algorithms, determined isomorphism classes, derived presentations, and calculated normalizers and centralizers.
result Presentations and isomorphism classes of liftable mapping class groups for various covers.
Sparse principal component analysis (sparse PCA) aims at finding a sparse basis to improve the interpretability over the dense basis of PCA, meanwhile the sparse basis should cover the data subspace as much as possible. In contrast to most of existing work which deal with the problem by adding some sparsity penalties o…
Market maker handles negative prices with unique asset swapping.
problem Handling negative prices in financial markets.
method Unique market mechanism with numeraire currency, liquidity extensions.
result Liquidity fingerprint and payoff compared to established models.
We study the problem of approximating orthogonal matrices so that their application is numerically fast and yet accurate. We find an approximation by solving an optimization problem over a set of structured matrices, that we call extended orthogonal Givens transformations, including Givens rotations as a special case. …
The Loch Ness Monster admits many regular dessins d'enfants and different holomorphic structures.
problem Classical theory of dessins d'enfants on compact surfaces extended to non-compact surfaces.
method Study of infinite genus surfaces and their connections to Riemann surfaces.
result The Loch Ness monster admits infinitely many regular dessins d'enfants.
Study on rotating surfaces in 4D space with matrices.
problem Understanding rotational surfaces in pseudo-Euclidean 4-space.
method Defined hyperbolic and elliptic rotational surfaces using curves and matrices in 4D semi-Euclidean space.
result Generated rotated surfaces using specific rotation matrices.
A new transform links rotating calorons to solutions of a differential equation.
problem Existence and characterization of rotating calorons.
method Formulated a Nahm transform to relate rotating calorons to solutions of a delayed-differential equation.
result Existence of an eight-parameter family of rotating calorons with nontrivial holonomy.
We define general rotational surfaces of elliptic and hyperbolic type in the pseudo-Euclidean 4-space with neutral metric which are analogous to the general rotational surfaces of C. Moore in the Euclidean 4-space. We study Lorentz general rotational surfaces with plane meridian curves and give the complete classificat…
The paper defines and analyzes homotopic rotation sets for surfaces of higher genus.
problem Defining and analyzing homotopic rotation sets for surfaces of higher genus.
method Developed a definition and proved several results using the theory of Le Calvez and Tal.
result Found that the homotopic rotation set can imply the existence of infinitely many periodic orbits under certain conditions.
Basic Classes of Timelike General Rotational Surfaces in the Four-dimensional Minkowski Spacemath.DG
Study of timelike surfaces in Minkowski space with specific geometric properties.
problem Characterizing geometric properties of timelike surfaces in Minkowski space.
method Analytical study of two types of timelike general rotational surfaces.
result Explicit descriptions of minimal and surfaces with specific curvature properties.
The study characterizes loxodromes on specific rotational surfaces in 3D space.
problem Characterizing loxodromes on rotational surfaces with special geometric properties.
method Parametrizations and curvature/torsion calculations for loxodromes on various rotational surfaces.
result The loxodrome on a flat rotational surface is a general helix.
Overview of methods for rotating 2D and 3D data.
problem Processing data with equivariance/invariance under rotations.
method An overview of methods for 2D and 3D rotations.
result Identification of commonalities and links between methods.
Enhanced rotation prediction improves SSL models by capturing both shape and texture information.
problem Rotation prediction misses texture information, limiting model performance.
method Introduces image enhanced rotation prediction (IE-Rot) that combines rotation and image enhancement tasks.
result IE-Rot models outperform Rotation on various benchmarks.
General rotational surfaces as a source of examples of surfaces in the four-dimensional Euclidean space have been introduced by C. Moore. In this paper we consider the analogue of these surfaces in the Minkowski 4-space. On the base of our invariant theory of spacelike surfaces we study general rotational surfaces with…
The paper introduces REQNNs for robust 3D point cloud processing.
problem 3D point cloud processing robustness to rotations.
method Revised neural networks using quaternion features for rotation-equivariance.
result REQNNs exhibit higher rotation robustness compared to original networks.
Rotation systems can't always be drawn in surfaces.
problem Rotation systems and simple drawings in surfaces.
method Extended the plane result to all fixed surfaces.
result Existence of rotation systems not arising from simple drawings in any fixed surface.
RotEqNet preserves rotation symmetry in fluid systems using high-order tensors.
problem Lack of rotational symmetry in machine learning models for fluid systems.
method Introduces RotEqNet, a network that guarantees rotation-equivariance for high-order tensors.
result RotEqNet reduces errors and maintains rotation-equivariance in fluid systems.
The paper applies Clairaut's theorem to rotational surfaces in pseudo-Euclidean 4-space.
problem Exploring geodesic curves on rotational surfaces in pseudo-Euclidean 4-space.
method Expressing Clairaut's theorem and deriving equations for geodesic curves.
result Characterization of geodesic curves on hyperbolic and elliptic surfaces of rotation.
We consider -dimensional discrete motions such that any two neighbouring positions correspond in a pure rotation ("rotating motions"). In the Study quadric model of Euclidean displacements these motions correspond to quadrilateral nets with edges contained in the Study quadric ("rotation nets"). The main focus of ou…
Minimal sets of moves for rotational Reidemeister diagrams are identified.
problem Understanding the minimal sets of moves for rotational Reidemeister diagrams.
method Detailed description and proof of minimal generating sets for rotational Reidemeister moves.
result Minimal generating sets for oriented, framed links contain 5 moves.
New method studies moving points on curves using rotating frames.
problem Understanding the motion of points on curves.
method Constructing rotating frames for curves and analyzing the motion of points within these frames.
result A new binary mathematical formation mechanism for curves based on linear and rotational motion.
Study on rotational hypersurfaces with constant Gauss-Kronecker curvature.
problem Exploring hypersurfaces with constant Gauss-Kronecker curvature.
method Solving ODE for generating curves and analyzing geometric properties.
result Discovery of non-compact rotational hypersurfaces with negative Gauss-Kronecker curvature and finite volume.
In-plane drill rotations are impossible for smooth shells.
problem In-plane drill rotations on smooth shells are impossible.
method Analyzing the differential geometry of surfaces and isometries.
result Any isometry that coincides with the given surface at a portion of the boundary is the identity.
Study of rotation angles in a rotating disc model.
problem Understanding geometric phase in rotating systems.
method Analyzes a simple kinematic model of rotating discs.
result Explicit form of geometric phase found using Baumkuchen lemma.
The study disproves rotating ancient flows in 4D space.
problem The existence of rotating ancient flows in .
method Analysis of ancient noncollapsed flows in .
result Nonexistence of rotating ancient flows among ancient noncollapsed flows in .
Study rotational surfaces with prescribed Gauss curvature in 3D space.
problem Classify and analyze rotational surfaces with prescribed Gauss curvature.
method Phase plane analysis and mild assumptions on the prescribed function.
result Existence of singular radial solutions intersecting orthogonally the axis of rotation.
In this work, we study a class of rotational surfaces in the pseudo-Euclidean space whose profile curves lie in two-dimensional planes. We solve the differential equation that characterizes the rotational surfaces with zero mean curvature to determine the profile curves of such rotational surfaces. The…
Rotational elasticitymath-ph
We consider an infinite 3-dimensional elastic continuum whose material points experience no displacements, only rotations. This framework is a special case of the Cosserat theory of elasticity. Rotations of material points are described mathematically by attaching to each geometric point an orthonormal basis which give…
The paper classifies CMC free boundary hypersurfaces in rotational domains.
problem Existence and uniqueness of free boundary constant mean curvature hypersurfaces in rotational domains.
method Classification and construction of CMC free boundary hypersurfaces under specific conditions.
result Classification of CMC free boundary hypersurfaces as topological disks or annuli.
Helicoidal surfaces rotate and translate under mean curvature flow.
problem Existence of helicoidal surfaces under mean curvature flow.
method One-parameter families of helicoidal surfaces rotating and translating.
result Existence of helicoidal surfaces under mean curvature flow.
We provide a new angle and obtain new results on a class of metrics on length-normalized curves in dimensions, represented by their unit tangents expressed as a function of arc-length, which are functions from the unit interval to the -dimensional unit sphere. These metrics are derived from the combined acti…
The study explores special surfaces in a normed space.
problem Constant Gaussian and mean curvature surfaces in normed spaces.
method Analyzes rotational surfaces with specific curvature properties.
result Generalizes catenoid, pseudo-sphere, and Delaunay surfaces.
Extends Euler class result to symplectic group.
problem Relationship between bounded Euler class and symplectic rotation number.
method Extends Ghys's result to symplectic group.
result Establishes relationship between bounded Euler class and symplectic rotation number.
The study characterizes helices in Euclidean and hyperbolic spaces.
problem Characterizing helices in Euclidean and hyperbolic spaces.
method Analyzing Killing vector fields associated with rotations in both spaces.
result Helices in hyperbolic space are geodesics on suitable surfaces.
We study the problem of learning representations of entities and relations in knowledge graphs for predicting missing links. The success of such a task heavily relies on the ability of modeling and inferring the patterns of (or between) the relations. In this paper, we present a new approach for knowledge graph embeddi…
In this paper we study general rotational surfaces in the 4- dimensional Euclidean space E4 and give a characterization of flat general rotation surface with pointwise 1-type Gauss map. Also, we show that a non-planar flat general rotation surface with pointwise 1-type Gauss map is a Lie group if and only if it is a Cl…
New quadratic forms expand and rotate linear endomorphisms in geometric theory.
problem Understanding the expansion and rotation properties of linear endomorphisms.
method Constructing new quadratic forms based on two-plane rotations.
result Established relations among eigenvalues, eigendirections, and matrix invariants.