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Geometric differentiation: for the intelligence of curves and surfaces

https://doi.org/10.5860/choice.32-4553
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The Changeable Power Law Singularity and its Application to Prediction of Catastrophic Rupture in Uniaxial Compressive Tests of Geomedia
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Rainbows with Positrons and Carbon Nanotubes
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Shape Interrogation
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Plane curves
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Smooth surfaces
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Image Structure
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The Sub-Parabolic Lines in the Minkowski 3-Space
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Generalized Sabban Curves in the Euclidean $${{\varvec{n}}}$$ n -Sphere and Spherical Duality
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Towards a singularity-based shape language: ridges, ravines, and skeletons for polygonal surfaces
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Spherical Orthotomic and Spherical Antiothotomic
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Modeling bladder mechanics with 4D reconstruction of murine ex vivo bladder filling
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The focal geometry of circular and conical meshes
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Multidimensional Poincaré construction and singularities of lifted fields for implicit differential equations
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Lower bound on the spectrum of the two-dimensional Schrödinger operator with a δ-perturbation on a curve
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Local Image Features Resulting from 3-Dimensional Geometric Features, Illumination, and Movement: I
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Reworking Geometric Morphometrics into a Methodology of Transformation Grids
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Kinematic geometry of a line trajectory in spatial motion
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Conformal invariants and spherical contacts of surfaces in ℝ4
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Singularities of caustics of surfaces in non-flat Riemannian 4-space form$$^\dag $$
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Dual relations between line congruences in $$\mathbb {R}^3$$ and surfaces in $$\mathbb {R}^4$$
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Ridges and Ravines on a Surface and Related Geometry of Skeletons, Caustics, and Wavefronts
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Bibliography
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Image Hierarchy in Gaussian Scale Space
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Landmark-Based Registration Using Features Identified Through Differential Geometry
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A kinematic cue for active haptic shape perception
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Principal curvature ridges and geometrically salient regions of parametric B -spline surfaces
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A robust conforming NURBS tessellation for industrial applications based on a mesh generation approach
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2D skeleton extraction based on heat equation
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Fast, robust, and faithful methods for detecting crest lines on meshes
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Computing lines of curvature for implicit surfaces
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Ridge extraction of a smooth 2-manifold surface based on vector field
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Subdivision surface fitting to a dense mesh using ridges and umbilics
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Linear interpolation of shape operators for umbilical points through local parametrization
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Efficient numerical differentiation of implicitly-defined curves for sparse systems
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Bour's theorem for helicoidal surfaces with singularities
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Geometric investigation of the three-coefficient Redlich-Kister expansion global phase diagram for binary mixtures
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Algorithms for optimal partial matching of free-form objects with scaling effects
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Duality between wavefronts and caustics
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Singularities of homogeneous deformations of constrained hyper-elastic materials
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On the singularities of a constrained (incompressible-like) tensegrity-cytoskeleton model under equitriaxial loading
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The hinge lines of non-cylindrical folds
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Microstructural characteristics of bijel-templated porous materials
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Singularities in diffusion tensor fields and their relevance in white matter fiber tractography
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Singularities of homogeneous deformations in finite elasticity
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Chapter 5 Singular Optics: Optical Vortices and Polarization Singularities
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Differential geometry of G1 variable radius rolling ball blend surfaces
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Bibliography
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The Structure of Relief
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Creases as local features of deformation grids
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A procedure to average 3D anatomical structures
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Singularities, Bifurcations and Catastrophes
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Preface
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What’s it all about?
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Families of functions
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The ring of germs of smooth functions
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Right equivalence
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Finite determinacy
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Classification of the elementary catastrophes
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Unfoldings and catastrophes
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Singularities of plane curves
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Even functions
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Families of maps and bifurcations
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Contact equivalence
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Tangent spaces
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Classification for contact equivalence
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Contact equivalence and unfoldings
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Geometric applications
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Preparation theorem
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Left–right equivalence
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Bifurcation problems and paths
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Vector fields tangent to a variety
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KV–equivalence
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Classification of paths
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Loose ends
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Constrained bifurcation problem
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Calculus of several variables
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Local geometry of regular maps
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Differential equations and flows
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Rings, ideals and modules
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Solutions to selected problem
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References
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Index
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Evolutes and focal surfaces of framed immersions in the Euclidean space
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Normal developable surfaces of surfaces along curves
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Constructing Invariant Fairness Measures for Surfaces
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Nose tip detection on three‐dimensional faces using pose‐invariant differential surface features
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Focal surfaces of hyperbolic cylinders
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Local Shape of Pictorial Relief
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Creating Noisy Stimuli
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Shortest Path Solution by Epitrochoid Machine
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Bifurcations of symmetrical caustics: the creation-annihilation of two symmetric butterflies
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Correlations and screening of topological charges in Gaussian random fields
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Vortex-free complex landscapes and umbilic-free real landscapes
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A general tool for the calculation of umbilical singularities using Thom’s singular set Σ2
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Legendre curves in the unit spherical bundle over the unit sphere and evolutes
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τ-curve: introduction of cusps to aesthetic curves☆
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An unbiased detector of curvilinear structures
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The support cone: a representational tool for the analysis of boundaries and their interactions
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Surface representation with deformable splines: using decoupled variables
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Ridges and ravines on implicit surfaces
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Hierarchic shape description via singularity and multiscaling
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Visualising Full Tensor Gradient Gravity Data Using Texture and Colour Cues
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Human eyeball model reconstruction and quantitative analysis
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Adaptive smoothing tangential direction fields on polygonal surfaces
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Fast and Faithful Geometric Algorithm for Detecting Crest Lines on Meshes
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Explicit Control of Vector Field Based Shape Deformations
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Image-Space Caustics and Curvatures
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On the representation of contact states between curved objects
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Fast algorithms for ridge detection
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On evolute cusps and skeleton bifurcations
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Degree Reduction for NURBS Symbolic Computation on Curves
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Ridge Extraction from Isosurfaces of Volumetric Data Using Implicit B-Splines
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Robust Feature Classification and Editing
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Visualization and Extraction of Carvings for Heritage Conservation
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Detection of Salient Curvature Features on Polygonal Surfaces
inferred← citeshttps://doi.org/10.1111/cgf.12172openalex-snapshot
Discrete Line Congruences for Shading and Lighting
inferred← citeshttps://doi.org/10.1111/opo.13008openalex-snapshot
Catastrophe optics theory unveils the localised wave aberration features that generate ghost images
inferred← citeshttps://doi.org/10.1117/12.428252openalex-snapshot
Geometry of phase and polarization singularities illustrated by edge diffraction and the tides
inferred← citeshttps://doi.org/10.1117/12.503952openalex-snapshot
Detection of salient curvature features on surfaces and their applications
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Combining heterogeneous features for colonic polyp detection in CTC based on semi-definite programming
inferred← citeshttps://doi.org/10.1134/s1995080225600232openalex-snapshot
Diagonalization of a Pair of Quadratic Differential Forms
inferred← citeshttps://doi.org/10.1137/090771053openalex-snapshot
Local Image Features Resulting from 3-Dimensional Geometric Features, Illumination, and Movement: II
inferred← citeshttps://doi.org/10.1142/9789812706812_0028openalex-snapshot
MAXWELL STRATA AND CAUSTICS
inferred← citeshttps://doi.org/10.1142/s0218127422500535openalex-snapshot
Kosambi–Cartan–Chern Analysis of the Nonequilibrium Singular Point in One-Dimensional Elementary Catastrophe
inferred← citeshttps://doi.org/10.1142/s0218654307000932openalex-snapshot
COMPLEXITY REDUCTION FOR SYMBOLIC COMPUTATION WITH RATIONAL B-SPLINES
inferred← citeshttps://doi.org/10.1142/s0219887819500762openalex-snapshot
Harmonic evolutes of B-scrolls with constant mean curvature in Lorentz–Minkowski space
inferred← citeshttps://doi.org/10.1142/s1469026810002744openalex-snapshot
COMBINING STATISTICAL AND GEOMETRIC FEATURES FOR COLONIC POLYP DETECTION IN CTC BASED ON MULTIPLE KERNEL LEARNING
inferred← citeshttps://doi.org/10.1145/1015706.1015768openalex-snapshot
Ridge-valley lines on meshes via implicit surface fitting
inferred← citeshttps://doi.org/10.1145/1060244.1060270openalex-snapshot
Fast and robust detection of crest lines on meshes
inferred← citeshttps://doi.org/10.1145/1141911.1141941openalex-snapshot
Geometric modeling with conical meshes and developable surfaces
inferred← citeshttps://doi.org/10.1145/1179352.1141941openalex-snapshot
Geometric modeling with conical meshes and developable surfaces
inferred← citeshttps://doi.org/10.1145/1186562.1015768openalex-snapshot
Ridge-valley lines on meshes via implicit surface fitting
inferred← citeshttps://doi.org/10.1145/1629255.1629263openalex-snapshot
Tracing ridges on B-Spline surfaces
inferred← citeshttps://doi.org/10.1145/2160749.2160762openalex-snapshot
Focal surfaces, skeletons, and ridges for shape analysis and processing
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A Qualitative Review on 3D Coarse Registration Methods
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Geometric Modeling with Conical Meshes and Developable Surfaces
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Phase Singularities to Polarization Singularities
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Grafos e aplicações de Gauss estáveis
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Extração de características robustas de superfícies NURBS
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Lines of axial curvature at critical points on surfaces mapped into R4
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Sobre a geometria diferencial do cross-cap no 3-espaço Euclidiano
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Between light and shadows—a brief history of caustics: retrospective
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Fold singularities on spacelike CMC surfaces in Lorentz-Minkowski space
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Characterizing singularities of a surface in Lie sphere geometry
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Global properties on spacelike submanifolds of codimension two in Minkowski space
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Tangent varieties and openings of map-germs
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Families of surfaces and conjugate curve congruences
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COMPORTAMENTO DAS LINHAS DE CURVATURA DE UMA SUPERFÍCIE NO 3-ESPAÇO EUCLIDIANO PRÓXIMO A UM PONTO UMBÍLICO
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Shape analysis of the human brain.
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Kinematische Schnittmaße bei gegebener Schnittsituation in der Integralgeometrie
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On the multiplicity of umbilic points
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Normal Developable Surfaces of A Surface Along A Direction Curve
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Caustics of translation surfaces in Euclidean 3-space
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Focal Surfaces of Discrete Geometry
inferred← citeshttps://doi.org/10.2748/tmj/1140727069openalex-snapshot
Isolated roundings and flattenings of submanifolds in Euclidean spaces
inferred← citeshttps://doi.org/10.2748/tmj/1347369369openalex-snapshot
Singularities of parallel surfaces
inferred← citeshttps://doi.org/10.28924/2291-8639-15-2017-114openalex-snapshot
Evolutes of Hyperbolic Dual Spherical Curve in Dual Lorentzian 3-Space
inferred← citeshttps://doi.org/10.2969/aspm/07810055openalex-snapshot
Singularities of frontals
inferred← citeshttps://doi.org/10.3934/mfc.2021038openalex-snapshot
Analysis of directional higher order jump discontinuities with trigonometric shearlets
inferred← citeshttps://doi.org/10.4064/-50-1-137-149openalex-snapshot
The rectifying developable and the spherical Darboux image of a space curve
inferred← citeshttps://doi.org/10.4064/-50-1-169-177openalex-snapshot
Topology and geometry of caustics in relation with experiments
inferred← citeshttps://doi.org/10.4064/-50-1-217-226openalex-snapshot
Some remarks on duality in $S^3$
inferred← citeshttps://doi.org/10.4064/-50-1-267-276openalex-snapshot
Properties of Conflict Sets in the Plane
inferred← citeshttps://doi.org/10.4064/-50-1-277-285openalex-snapshot
Curvatures of conflict surfaces in Euclidean 3-space
inferred← citeshttps://doi.org/10.4169/college.math.j.42.4.299openalex-snapshot
Do Dogs Know the Trammel of Archimedes?
inferred← citeshttps://doi.org/10.4213/tmf6477openalex-snapshot
Оценка снизу спектра двумерного оператора Шредингера с $\delta$-потенциалом на кривой
inferred← citeshttps://doi.org/10.48550/arxiv.0907.1543openalex-snapshot
Lower bound on the spectrum of the Schrödinger operator in the plane with delta-potential supported by a curve
inferred← citeshttps://doi.org/10.48550/arxiv.1501.07341openalex-snapshot
Affine connections and singularities of tangent surfaces to space curves
inferred← citeshttps://doi.org/10.48550/arxiv.2002.01084openalex-snapshot
On the analyticity of the value function in optimal investment and stochastically dominant markets
inferred← citeshttps://doi.org/10.48550/arxiv.math/0411303openalex-snapshot
New Coordinate Systems and Potentials on a Plane Providing Unusual Intergral of Motion
inferred← citeshttps://doi.org/10.53733/139openalex-snapshot
The conjugate locus in convex 3-manifolds
inferred← citeshttps://doi.org/10.5427/jsing.2012.6fopenalex-snapshot
Singularities of Tangent Varieties to Curves and Surfaces
inferred← citeshttps://doi.org/10.59490/abe.2022.03.6269openalex-snapshot
Design and Fabrication of Shell Structures
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