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Our motivation for studying this problem is threefold:
(i) When one fixes r = m = 0, the resulting two parameter family is a normal
form for a codimension two bifurcation within the class of planar ...
Phase Portraits of Planar Vector Fields: Computer Proofs
Computer Proofs Planar Vector Fields
2015/8/25
This paper presents an algorithm for computer veri cation of the
global structure of structurally stable planar vector elds. Constructing
analytical proofs for the qualitative properties of phase p...
Periodic Orbits of Vector Fields: Computational Challenges
Computational Challenges Vector Fields
2015/8/25
Simulation of vector elds is ubiquitous: examples occur in every discipline of
science and engineering. Periodic orbits are frequently encountered as trajectories.
We use solutions of initial value...
Reconstruction of vector fields for semi-Lagrangian advection on unstructured, staggered grids
Interpolation Vector fields Unstructured Staggered grids Semi-Lagrangian advection
2015/6/30
Applying the semi-Lagrangian method to discretize the advection of momentum eliminates the Courant number constraint associated with explicit Eulerian momentum advection in coastal ocean models. Key s...
Singularities of the divergence of continuous vector fields and uniform Hausdorff estimates
Removable singularity divergence Hausdorff measure Hausdorff content Radon measure Frostman’s lemma charges strong charges
2012/6/19
We prove that every closed set which is not sigma-finite with respect to the Hausdorff measure H^{N-1} carries singularities of continuous vector fields in the Euclidean space R^N for the divergence o...
Solving the inverse problem of high numerical aperture focusing using Slepian-type vector fields
High numerical aperture focusing Vector diffraction theory Inverse problem Slepian’s concentration problem
2012/5/29
A technique using vector Slepian harmonics and multipole fields is presented for a general treatment of the inverse problem of high numerical aperture focusing. A prescribed intensity distribution or ...
This is an announcement of our work [5] on introducing and studying a geometric heat flow to find Killing vector fields on closed Riemannian manifolds with positive sectional curvature. We study its v...
Leibniz algebras on symplectic plane and cohomological vector fields
Leibniz algebras symplectic-Poisson geometry anti-cyclic operads Quantum Algebra
2011/9/16
Abstract: By using help of algebraic operad theory, Leibniz algebra theory and symplectic-Poisson geometry are connected. We introduce the notion of cohomological vector field defined on nongraded sym...
Transitive Lie algebras of vector fields---an overview
Transitive Lie algebras vector fields Differential Geometry
2011/9/6
Abstract: This overview paper is intended as a quick introduction to Lie algebras of vector fields. Originally introduced in the late 19th century by Sophus Lie to capture symmetries of ordinary diffe...
A geometric heat flow for vector fields
Geometric heat flow Killing vector fields Yano’s theorem Navier-Stokes equations
2011/9/6
Abstract: This is an announcement of our work [5] on introducing and studying a geometric heat flow to find Killing vector fields on closed Riemannian manifolds with positive sectional curvature. We s...
On vector fields having properties of Reeb fields
Reeb field presymplectic form contact form geodesible field
2011/9/5
Abstract: We study constructions of vector fields with properties which are characteristic to Reeb vector fields of contact forms. In particular, we prove that all closed oriented odd-dimensional mani...
Estimates on the modulus of expansion for vector fields solving nonlinear equations
Estimates vector fields nonlinear equations Differential Geometry
2011/9/5
Abstract: By adapting methods of \cite{AC} we prove a sharp estimate on the expansion modulus of the gradient of the log of the parabolic kernel to the Sch\"ordinger operator with convex potential, wh...
Spheres with more than 7 vector fields: all the fault of Spin(9)
Spin(9) octonions vector fields on spheres
2011/8/24
Abstract: We give an interpretation in terms of the Lie group Spin(9) of the maximal number of linearly independent vector fields on odd dimensional spheres.
Locally Homogeneous Spaces, Induced Killing Vector Fields and Applications to Bianchi Prototypes
locally homogeneous spaces Killing equations & vector fields isometric embedding moving frames
2011/7/28
Abstract: An answer to the question: Can, in general, the adoption of a given symmetry induce a further symmetry, which might be hidden at a first level? has been attempted in the context of different...
Conformal Killing vector fields and Rellich type identities on Riemannian Manifolds, II
Riemannian Manifolds Killing vector fields Rellich identities
2011/1/21
We propose a general Noetherian approach to Rellich integral identities. Using this method we obtain a higher order Rellich type identity involving the polyharmonic operator on Riemannian manifolds ad...