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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 ...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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.
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...
Affine vector fields of Bianchi type IV space-times are investigated using holonomy and decomposability, the rank of the 6× 6 Riemann matrix and direct integration technique. From the above study it f...
The system of generators of the differential field of all G-invariant differential rational functions of a vector field in the n-dimensional Euclidean space Rn is described for groups G=M(n) and G=SM(...

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