Characterizes toroidally alternating knots topologically.
problem Defining and characterizing toroidally alternating knots.
method Extending Howie's characterization to toroidally alternating knots and providing necessary and sufficient conditions.
result Necessary and sufficient conditions for a knot to be toroidally alternating.
Characterizes almost alternating knots from generalizations of alternating knots.
problem Characterizing almost alternating knots.
method Topological characterization based on generalizations of alternating knots.
result A topological characterization of almost alternating knots.
Paper characterizes generic transversality, improving on Mather's result.
problem Understanding and defining generic transversality.
method Characterization of transversality based on Mather's work.
result Improves on Mather's transversality result.
The simplest hyperbolic knot has no integral characterizing slopes.
problem Characterizing slopes for hyperbolic knots.
method Demonstrated the existence of infinitely many non-characterizing slopes for a specific hyperbolic knot.
result There are infinitely many non-characterizing slopes for the hyperbolic knot 8_6.
Study characterizes Einstein metrics in warped product spaces.
problem Characterizing Einstein metrics in warped product spaces.
method Local characterizations and global restatements of known results.
result Restated global characterizations of Einstein manifolds.
The study provides homological characterizations for Q-manifolds and l2-manifolds.
problem Density of maps in characterizing Q-manifolds and l2-manifolds. method Investigates weakening the density of Zn-maps and Z-maps to homological maps. result Obtains homological characterizations for Q-manifolds and l2-manifolds. The paper characterizes Alexander quandles of finite groups.
problem Characterizing Alexander quandles of finite groups.
method Using group theory and automorphism groups, the paper provides characterizations of Alexander quandles.
result Generalized Alexander quandles of finite groups are characterized in terms of automorphism groups and underlying groups.
No single parameter characterizes the learnability of probability distributions.
problem Finding a parameter to characterize the learnability of probability distributions.
method Analyzing various notions of learnability and showing impossibility results.
result No such parameter exists for characterizing learnability of probability distributions.
Characterizes the OU matrix for up to 5 strands in braids.
problem Understanding the structure of braid diagrams through their matrices.
method Characterization of the OU matrix for up to 5 strands in braids.
result Standard form of the OU matrix for general braids of up to 5 strands is given and characterized.
Study provides concrete examples of knot slopes.
problem Finding explicit characterizing slopes for knots.
method Concrete examples for the (-2,3,7)-pretzel knot.
result Explicit characterizing slopes for the knot 12n242. Jones slopes characterize adequate knots under the Strong Slope conjecture.
problem Characterizing adequate knots using colored Jones polynomials.
method Using the degree of colored Jones polynomials and essential surfaces.
result Jones slopes reformulate the characterization of adequate knots under the Strong Slope conjecture.
Characterizes the sample complexity of list regression tasks.
problem Understanding the sample complexity of list learning tasks in regression.
method Introducing two combinatorial dimensions: k-OIG dimension and k-fat-shattering dimension.
result These dimensions characterize realizable and agnostic k-list regression.
Characterizes geodesic laminations on surfaces.
problem Understanding geodesic laminations on surfaces.
method Topological characterization of geodesic laminations.
result Proved a topological characterization of geodesic laminations.
Study characterizes geodesic ray transform on surfaces, isolating and separating sub-ranges.
problem Characterizing the range of the attenuated geodesic ray transform on surfaces.
method Isolating and separating sub-ranges of sums of functions and one-forms, deriving new inversion formulas.
result Range characterizations and new inversion formulas for geodesic ray transform.
Establishes criterion for smooth and contact characterizing slopes of Legendrian knots.
problem Relating smooth and contact characterizing slopes for Legendrian knots.
method Criterion based on uniqueness of isotopy class and classical invariants.
result Criterion for smooth characterizing slopes to be contact characterizing slopes.
Study characterizes specific almost Kenmotsu metrics meeting Miao-Tam equation.
problem Characterizing almost Kenmotsu metrics.
method Characterization through Miao-Tam equation.
result Characterized specific almost Kenmotsu metrics.
In this paper, we give some characterizations for spacelike helices in Minkowski space-time. We find the differential equations characterizing the spacelike helices and also give the integral characterizations for these curves in Minkowski space-time.
Research characterizes critical points of scalar curvature functionals.
problem Characterizing critical points of scalar curvature functionals.
method Translation and analysis of a previous Russian paper.
result Provides insights into critical points of scalar curvature functionals.
We review several results related to the characterization of polyhedra in hyperbolic 3-space. In particular we present Rivin's theorem that gives a characterization of compact convex hyperbolic polyhedra, and Hodgson's proof of the Adreev's theorem. We also review the analogous characterization of ideal polyhedra, and …
It is of interest to characterize algebraically the dynamical types of isometries of the complex and quaternionic hyperbolic planes. In the complex case, such a characterization is known from the work of Giraud-Goldman. In this paper, we offer an algebraic characterization of the isometries of the two-dimensional quate…
Characterizes learnability of multioutput functions in various settings.
problem Learning multioutput function classes in batch and online settings.
method Characterizes learnability based on single-output restrictions.
result Complete characterization of learnability in multioutput classification and regression.
New research shows that many slopes are characterizing for satellite knots.
problem Characterizing slopes for satellite knots.
method Detailed examination of the JSJ decomposition of a surgery along a knot, combined with other authors' constraints on surgery slopes.
result Many non-integral slopes are characterizing for composite knots.
Characterizes conditions for quotient spaces of decompositions to be manifolds.
problem Conditions for quotient spaces of decompositions to be manifolds.
method Generalized characterizations of upper semi-continuity for decomposition into one for a class decomposition.
result Characterizations of necessary and sufficient conditions for quotient spaces of decompositions to be k-manifolds (k=1,2). Characterizes alternating link exteriors using cubed complexes.
problem Understanding the structure of alternating link exteriors.
method Introducing signed BW cubed-complexes and characterizing their homeomorphism to link exteriors.
result Characterization of alternating link exteriors in terms of cubed complexes.
Characterizes paths minimizing anisotropic lengths in Euclidean space.
problem Finding paths of minimal anisotropic length between points.
method Characterization through geometric connection to anisotropic isoperimetric set.
result Established a connection between minimizing paths and anisotropic isoperimetric geometry.
Characterizes a specific type of spacetime using vector fields.
problem Classifying a specific type of spacetime.
method Using vector fields to characterize 1+n doubly twisted spacetimes.
result Simple classification of 1+n doubly-twisted spacetimes.
The paper characterizes Conway-Coxeter friezes using rational links.
problem Characterizing Conway-Coxeter friezes of zigzag type.
method Characterization via rational links and application to Jones polynomial.
result Jones polynomial can be defined for Conway-Coxeter friezes of zigzag type.
Characterizes Kerr spacetimes using conformal methods.
problem Understanding Kerr spacetimes through conformal transformations.
method Conformally covariant characterization approach.
result Ideal characterization of Kerr spacetimes.
Characterizes umbilic points in Riemannian and Lorentzian manifolds.
problem Understanding umbilic points in various geometric settings.
method New characterizations and proofs for Riemannian and Lorentzian manifolds.
result Obtained new characterizations of spheres and hyperbolic spaces.
The paper aims to develop new combinatorial dimensions for bounded memory learning.
problem Characterize bounded memory learning using combinatorial dimensions.
method Proposes a candidate solution based on the SQ dimension of neighboring distributions and proves upper and lower bounds.
result Characterizes bounded memory learning in a specific parameter regime, matching equivalence between bounded memory and SQ learning.
Characterizes the range of a tensor field transform in Schwartz space.
problem Range characterization of a tensor field transform in Schwartz space.
method Differential and integral equations for characterizing the range in different dimensions.
result Range characterization for the operator on Schwartz space of rank m tensor fields.
Characterizes projective submanifolds in high dimensions.
problem Characterizing projective submanifolds of specific codimensions.
method Uses Chern classes and ample line bundles.
result Generalizes earlier findings for hypersurfaces.
In this paper, we mainly prove a theorem with a corollary establishing two characterizations of the Calabi composition of hyperbolic hyperspheres, where the second characterization (i.e., the corollary) has been given via a dual correspondence theorem earlier but now we would like to use a very direct method. Note that…
The paper characterizes geometric infiniteness for convergence group actions using orbit uniform metrics.
problem Characterizing geometric infiniteness for convergence group actions.
method Introducing orbit uniform metrics and proving properties of discrete orbits.
result Characterization of geometric infiniteness in terms of uncountability of non-conical limit points and existence of escaping sequences.
We characterize geometrically the Lyapunov exponents of a cocycle (of arbitrary rank) with respect to a harmonic current defined on a hyperbolic Riemann surface lamination. Our characterizations are formulated in terms of the expansion rates of the cocycle along geodesic rays.
The angle defect, which is the standard way to measure curvature at the vertices of polyhedral surfaces, goes back at least as far as Descartes. Although the angle defect has been widely studied, there does not appear to be in the literature an axiomatic characterization of the angle defect. We give a characterization …
Characterizes Lipschitz continuity using microlocal sheaf theory.
problem Understanding Lipschitz continuity on differential manifolds.
method Microlocal sheaf theory applied to the graph of continuous maps.
result Characterization of Lipschitz continuity in microlocal terms.
The study characterizes generalized Berwald surfaces with topological constraints.
problem Topological constraints on generalized Berwald surfaces.
method Intrinsic characterization and examples.
result Results on topological obstructions for the base manifold.
The paper characterizes upper bounds of Bakry-Emery curvature.
problem Characterizing upper bounds of Bakry-Emery curvature on Riemannian manifolds.
method Using functional inequalities on path space.
result Characterizations for upper bounds of Bakry-Emery curvature are provided.
New conditional risk measures called conditional generalized quantiles defined and characterized.
problem Developing new risk measures for dynamic risk assessment.
method Propose and characterize conditional generalized quantiles using expected utility model and equivalent conditions.
result Characterized conditional generalized quantiles as well-defined and equivalent to a conditional first order condition.
This note characterizes monohedral tilings of regular polygons with up to three tiles.
problem Characterizing monohedral tilings of regular polygons with up to three tiles.
method Connecting the results for squares and circles to generalize for any regular n-gon. result Characterization of monohedral tilings of any regular n-gon with up to three tiles. In this paper we characterize the degenerate elliptic equations F(D^2u)=0 whose viscosity subsolutions, (F(D^2u) \geq 0), satisfy the strong maximum principle. We introduce an easily computed function f(t) for t > 0, determined by F, and we show that the strong maximum principle holds depending on whether the integral …
Extended characterization of RAAGs with zero minimal volume entropy.
problem Characterizing RAAGs with vanishing minimal volume entropy.
method Extended characterization from geometric dimension 2 to higher dimensions.
result Extended characterization of RAAGs with zero minimal volume entropy.
Characterizes Milnor invariants with limited repetitions.
problem Understanding Milnor invariants with constraints on repetition.
method Algebraic and diagrammatic approaches using k-reduced free groups and welded knot theory. result Algebraic and diagrammatic characterizations of Milnor invariants.
Characterizes separable subgroups in 3-manifold groups.
problem Identifying which subgroups of 3-manifold groups are separable.
method Complete characterization using spirality and torus decomposition.
result Characterization generalizes previous work on surface subgroups.
Study characterizes kernel of mixed ray transform on simple surfaces.
problem Characterizing the kernel of mixed ray transform on simple surfaces.
method Characterization of the kernel through analysis of mixed ray transform on simple 2D Riemannian manifolds.
result Characterization of the kernel of the mixed ray transform on simple surfaces.
Characterizes specific harmonic manifolds using Laplacian eigenfunctions.
problem Characterizing harmonic manifolds.
method Using radial eigenfunctions of the Laplacian.
result Characterizes space forms, complex hyperbolic spaces, and quaternionic hyperbolic spaces as harmonic manifolds.
We formulate and prove an axiomatic characterization of conditional information geometry, for both the normalized and the nonnormalized cases. This characterization extends the axiomatic derivation of the Fisher geometry by Cencov and Campbell to the cone of positive conditional models, and as a special case to the man…