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In this paper, we consider a model for the switching behaviour (determination) of a cell proposed by Meinhardt (1982) and observe that this two component system can create a pattern only in the presence of cross-diffusion. We also analyse the global behaviour of this model system by the...
This paper presents a solution to the problem to find isolated closed trajectories of two-dimensional dynamic systems. In contrast to the method of Bendixson’s ring regions, the new method is constructive. It allows the determination of the location of closed trajectories and therefore gives an...
The relation between matrix models and geometrical structures on moduli spaces of algebraic curves is reviewed. The description of discretized moduli spaces and the generating function for intersection indices (cohomological classes) on these spaces is presented by the matrix model with the...
The main notions and tools from white noise analysis are set up on the basis of the calculus of Gaussian random variables and the S -transform. A new proof of the formula for the S -transform of Itô integrals is given. Moreover, measurability and the martingale property with respect to the...
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