The cohomology of the diffeomorphism group of a manifold is a Gelfand-Fuks cohomology
The compactness operator in general topology
The convergence of explicit Runge-Kutta methods combined with Richardson extrapolation
Runge-Kutta methods are widely used in the solution of systems of ordinary differential equations. Richardson extrapolation is an efficient tool to enhance the accuracy of time integration schemes. In this paper we investigate the convergence of the combination of any explicit Runge-Kutta method with active Richardson extrapolation and show that the obtained numerical solution converges under rather natural conditions.
The decomposition of tensor spaces with almost complex structure
The dimension of a set of singularities of weak solutions to the Navier-Stokes equations
The Dirichlet problem
The Dirichlet problem for sublaplacians on nilpotent Lie groups - geometric criteria for regularity
The double covering of the quantum group
The dynamics of living and thinking systems, biological networks, and the laws of physics.
The Educational Use of Mathematical Software: Techniques and Examples
The enveloping group of a lie algebra
The Euler characteristic and signature for open manifolds
The Evolving Digital Mathematics Network
The grand vision of a Digital Mathematics Library (DML), coordinated by a group of institutions that establish polices and practices regarding digitization, management, access, and preservation, has not come to pass. The project encountered two related problems: it was overly ambitious, and the approach to realizing it confused local and community responsibilities. While the vision called for a network of distributed, interoperable repositories, we approached and planned the project as if we were...
The Finnish-Polish-Ukrainian Summer School in Complex Analysis. Opening address
The fixed point property of superextensions
The future or graphical communication education in the new South Africa.
The generalized -algebra structure on BGG sequences and generalized associative operad
The genesis of mathematical structures, as exemplified in the work of Charles Ehresmann
The Geometric and Dynamic Essence of Phyllotaxis
We present a dynamic geometric model of phyllotaxis based on two postulates, primordia formation and meristem expansion. We find that Fibonacci, Lucas, bijugate and multijugate are all variations of the same unifying phenomenon and that the difference lies in the changes in position of initial primordia. We explore the set of all initial positions and color-code its points depending on the phyllotactic pattern that arises.
The geometric theory of Volterra integral equations - a preliminary report