Unique convex divisible domain found in Grassmannian.
problem Finding convex divisible domains in flag manifolds.
method Analyzing projective isomorphism and Lie groups.
result Only one convex divisible domain in Grassmannian.
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48 results for “convex divisible domain”
Uniform convexity in divisible domains leads to hyperbolic geometry.
problem Understanding the geometry of divisible convex sets in Finsler manifolds.
method Proving -uniform convexity of a specific Finsler metric.
result A strictly convex divisible domain induces a -uniformly convex Finsler metric.
Research shows how certain flat structures behave in specific convex domains.
problem Understanding the behavior of codimension-1 simplices in divisible convex domains.
method Analyzes the set of codimension-1 flats and their images in quotient manifolds.
result The set of codimension-1 flats forms a finite collection of disjoint virtual tori, leading to cusped convex projective manifolds.
New examples of hyperbolic manifolds with convex projective structures.
problem Finding new examples of hyperbolic manifolds with convex projective structures.
method Generalized Dehn filling and real projective structures.
result Infinitely many hyperbolic manifolds with cusps admit properly convex real projective structures.
New concept of coarse medians for higher rank symmetric spaces.
problem Understanding medians in higher rank symmetric spaces.
method Introducing coarse -median spaces and proving their existence.
result Existence of coarse higher medians on divisible and quasi-homogeneous convex domains.
Constructs examples of domains divided by groups in dimensions 3 and above.
problem Dividing convex sets with properly embedded cones.
method Uses Zariski dense relatively hyperbolic groups and properly embedded cones.
result Answers a question of Benoist and provides a topological criterion for convex projective structures.
An open convex set in real projective space is called divisible if there exists a discrete group of projective automorphisms which acts co-compactly. There are many examples of such sets and a theorem of Benoist implies that many of these examples are strictly convex, have boundary, and have word hyperbolic divid…
Study shows non-symmetric convex sets have full boundary limits.
problem Understanding boundaries of non-symmetric convex sets.
method Proved using proximal limit set analysis.
result Proximal limit set equals full projective boundary for non-symmetric irreducible divisible convex sets.
Affine deformations of convex cones on projective surfaces.
problem Understanding affine actions on convex cones.
method Geometric correspondence and convex tube domains.
result Quotients of convex domains are affine manifolds with convex surfaces.
Study of pseudometric properties on domains in Nagano spaces.
problem Characterize pseudometrics on domains in real-type Nagano spaces.
method Analyze Kobayashi-type pseudometrics on domains, proving properties and computing specific cases.
result The pseudometric is a genuine metric under certain conditions and has specific properties in higher rank.
Under certain integrability and geometric conditions, we prove division theorems for the exact sequences of holomorphic vector bundles and improve the results in the case of Koszul complex. By introducing a singular Hermitian structure on the trivial bundle, our results recover Skoda's division theorem for holomorphic …
Study of congestion in negative curvature manifolds using fair-division algorithms.
problem Estimating and predicting the size and location of congestion core in negative curvature manifolds.
method Introducing a novel fair-division algorithm to estimate congestion core.
result Demonstrated the effectiveness of fair-division algorithms in estimating congestion core.
New invariants from divisibility of Lee classes for slice-torus.
problem Determining slice-torus knots using Lee class divisibility.
method Defined new invariants from divisibility of reduced Lee class invariants.
result New invariants coincide with Rasmussen invariant for certain cases.
Affine deformations of convex cones yield special spacetime structures.
problem Deforming divisible convex cones in affine spaces.
method Analyzing the maximal convex domains and quotient structures.
result Quotients of affine actions are MGHCC affine spacetimes.
Let M be a compact manifold of dimension n with a strictly convex projective structure. We consider the geodesic flow of the Hilbert metric on it, which is known to be Anosov. We prove that its topological entropy is less than n-1, with equality if and only if the structure is Riemannian, that is hyperbolic. As a corol…
Completeness theorem for flat pseudo-Riemannian manifolds of signature (2,2).
problem Completeness of closed flat pseudo-Riemannian manifolds of signature (2,2).
method Geometric reduction and semidirect product constructions.
result Only the entire space is divisible by a discrete subgroup of isometries.
A new distributed algorithm for fitting sparse additive models with feature division and decorrelation.
problem Fitting high-dimensional sparse additive models efficiently and accurately.
method Divide, decorrelate, and conquer approach.
result Effective and efficient recovery of sparsity patterns and statistical inference for each component.
New link invariants derived from Lee's classes show divisibility by certain elements.
problem Understanding divisibility of Lee's classes and their relation to Rasmussen's invariant.
method Combining combinatorial constructions with homology theory to define new link invariants.
result The new invariants are link concordance invariants and coincide with Rasmussen's s-invariant in some cases.
From division to extensionmath.CV
A new proof of an extension theorem with bounded generators.
problem Extension theorems in complex analysis.
method Skoda-type division theorem with bounded generators.
result The new division theorem allows to be 1 in the norm of the datum.
Solves division problem for L. Hörmander's systems.
problem Division problem for L. Hörmander's overdetermined systems.
method Formulates and proves divisibility criterion, coherence theorem.
result Establishes effective divisibility criterion and extends coherence theorem.
Proves divisibility relations for symplectic curve polynomials.
problem Divisibility relations for symplectic curve polynomials.
method New proofs of divisibility relations for Oka and Alexander polynomials of symplectic curves.
result Proves Libgober's divisibility relations for symplectic curves.
Study proves Maximum Principles for unbounded Riemannian domains.
problem Proving Maximum Principles for unbounded Riemannian domains.
method Examines both ambient manifold and differential operator assumptions.
result Valid Maximum Principles established for unbounded domains.
Study on surface group representations in PU(2,1) leading to convex-cocompact examples.
problem Nonmaximal representations of surface groups in PU(2,1).
method Analysis of convex-cocompact representations with unique equivariant minimal surfaces.
result Existence of convex-cocompact representations with specific properties.
Tropical division approximates polynomial division for neural networks.
problem Approximating polynomial division in max-plus semiring.
method Approximating Newton Polytope of dividend by divisor, then applying to neural networks.
result Minimizes a two-layer fully connected network for binary classification.
Paper tackles division difficulty, proposing new methods to improve accuracy.
problem Division is the most challenging arithmetic operation for both humans and computers.
method Proposes two novel approaches: Neural Reciprocal Unit (NRU) and Neural Multiplicative Reciprocal Unit (NMRU), and improves an existing division module.
result Improves division accuracy from 70.2% to 91.6%.
Adopting a zonal structure of electricity market requires specification of zones' borders. In this paper we use social welfare as the measure to assess quality of various zonal divisions. The social welfare is calculated by Market Coupling algorithm. The analyzed divisions are found by the usage of extended Locational …
Division algorithm for surface group rings yields standard complexes and cohomological dimensions.
problem Understanding cohomological dimensions of surface group actions.
method Division algorithm for group rings of surface groups.
result Some 2-complexes with surface fundamental groups are standard.
funLOCI identifies clusters in functional data.
problem Identifying similar behavior in functional data.
method Divisive hierarchical clustering with additive model.
result funLOCI reduces the number of local clusters.
Geometrically explains divisibility of Euler classes for spin modules.
problem Divisibility of -theoretical Euler classes for spin modules.
method Geometric interpretation of divisibility using spin structures and Seiberg-Witten theory.
result Clarifies the role of reducibles in monopole equations.
The paper sets lower bounds on envy-free divisions in cake-cutting problems.
problem Finding the minimum number of envy-free divisions in cake-cutting problems.
method Analyzes two scenarios: classical and hybrid, with different constraints and allocations.
result Sharp bounds and examples for envy-free divisions in both scenarios.
New proof of divisibility property for certain algebraic varieties.
problem Divisibility property for LQEL varieties.
method Construction of Clifford algebra representations to Severi varieties.
result New proof of Russo's Divisibility Property for LQEL varieties.
Classification of Convex Ancient Solutions to Free Boundary Curve Shortening Flow in Convex Domainsmath.DG
Classifies ancient convex curves in convex domains.
problem Ancient convex curve shortening flows on convex domains.
method Classification of convex ancient solutions.
result Ancient convex curves in convex domains classified.
The paper revisits Rokhlin's divisibility theorem and its significance.
problem Rokhlin's divisibility theorem on signatures of manifolds.
method Overview and retrace of Rokhlin's proof and further developments.
result Reaffirms the importance of Rokhlin's theorem in manifold theory.
Divide-and-conquer method speeds sparse factorization for large matrices.
problem Sparse factorization of large matrices for statistical learning.
method Statistical problem formulation, divide-and-conquer approach, stagewise learning.
result Efficient algorithm with lower complexity than existing methods.
Proves Skoda's Division Theorem using degeneration and positivity of direct image bundles.
problem Division Theorem in Skoda's context
method Degeneration approach inspired by B. Berndtsson and L. Lempert's extension theorem
result Simplified and extended proof of extension theorem
The paper divides minimal surfaces in a ball into two parts.
problem Characterizing minimal surfaces in a ball with free boundaries.
method Analyzing planes and mean convex regions to divide surfaces and proving their properties.
result Every plane through the origin divides a minimal surface into exactly two parts.
The paper explains the topological origin of the distinction between incidence theorems over division rings and fields.
problem Understanding the distinction between incidence theorems over division rings and fields.
method Extending the surface-graph approach to noncommutative settings, the paper analyzes the topological properties of graphs embedded on surfaces of different genera.
result Theorems associated with graphs on the sphere hold over any division ring, while those on surfaces of positive genus typically hold only if the ground ring is a field.
Constructs projective plane over octonions, proving no higher real division algebras.
problem Existence of higher-dimensional real division algebras.
method Using Adams' solution of the Hopf invariant 1 problem, constructs projective plane over octonions.
result No higher-dimensional real division algebras exist.
The study shows how strictly convex domains in Euclidean spaces are rigid.
problem Understanding the rigidity of strictly convex domains in Euclidean spaces.
method Proved a rigidity theorem for smooth strictly convex domains in Euclidean spaces.
result Smooth strictly convex domains in Euclidean spaces are rigid.
Researchers infer gene activity in dividing cells, accounting for protein inheritance and division history.
problem Inferring protein production kinetics in dividing cells due to protein inheritance and division history.
method Adapted conditional normalizing flows to approximate intractable likelihoods from simulated data.
result Glc3 gene is mostly inactive under stress, with brief and transient expression.
Symplectic homology matches dual capacities for convex domains.
problem Understanding symplectic capacities and Reeb flows on convex domains.
method Isomorphic filtered symplectic homology to dual singular homology.
result Gutt-Hutchings capacities match spectral invariants for convex domains.
Study on non-Gromov hyperbolic tube domains and their geometric properties.
problem Characterizing non-Gromov hyperbolic tube domains with convex bases.
method Provided a criterion for non-Gromov hyperbolicity, studied Hilbert metric, and continuity properties of complex geodesics.
result Similarity of geometry of tube domains and convex domains, connections between metrics.
This paper converts ADMM to proximal gradient for efficient sparse estimation.
problem Sparse estimation problems like fused lasso and convex clustering.
method General method converting ADMM to proximal gradient, assuming Lipschitz continuity of derivative.
result Significant improvement in efficiency for sparse estimation problems.
Some universal inequalities for Dirichlet eigenvalues of the Laplacian on a Euclidean convex domainmath.SP
Universal inequalities found for Laplacian eigenvalues on convex domains.
problem Finding bounds for Laplacian eigenvalues on convex domains.
method Established two universal inequalities.
result Found new bounds for Laplacian eigenvalues.
A note on the distribution of Neumann eigenvalues of the Laplacian on a Euclidean convex domainmath.SP
Universal inequalities for Laplacian eigenvalues on convex domains.
problem Eigenvalue distribution of the Laplacian on convex domains.
method Established two universal inequalities.
result Two new inequalities for Laplacian eigenvalues.
Two new universal inequalities for Neumann eigenvalues of the Laplacian on a planar convex domainmath.SP
New inequalities for planar convex domains' Laplacian eigenvalues.
problem Neumann eigenvalues of the Laplacian on planar convex domains.
method Established two new universal inequalities.
result New inequalities for Laplacian eigenvalues on convex domains.
Direct proof of Neumann isoperimetric inequality for convex domains.
problem Neumann isoperimetric inequality on convex domains.
method Direct proof using Riemannian manifold properties.
result New proof of Neumann isoperimetric inequality.
Geodesic connectedness proved for statistical manifolds with divisible cubic forms.
problem Geodesic connectedness of affine connections on statistical manifolds with divisible cubic forms.
method Analogy with Hopf-Rinow theorem in Riemannian geometry, establishing geodesic completeness.
result Geodesic connectedness established for statistical manifolds with divisible cubic forms.