are a natural set of coordinate lines on them. In practice, it is a difficult problem to determine these lines [13]; the film does not address these mat- ters explicitly. ... We call these slices (1, k) bifurcation diagrams. Figure 5 is an example of
Equivariantsystems can be cast into a skew product form whereby the dynamics on the symme-try group is driven by the so called shape dynamics which is orthogonal to the groupdynamics. ... or in finite domainswhen the size of the computational domain is
Consider the natural action. of the Brauer algebra Bn(ω) (with an appropriate specialization of the parameter ω) onthe tensor product space. ... and 3.3 admit their natural quantum analogues. Namely, all primitive idempotents of.
A common very natural assumption, which is fulfilled in many situations (in particular,where Px, x E, are the laws of the solutions of a stochastic differential equation (SDE) withrespective initial ... Let us recall the necessary details from [49,
A by-product of the construction is a one-parameter family of fusion procedures for Heckealgebras. ... j = 1, 2,. ; the empty product is equal to 1, the symbol (respectively, ) over.
A.1. Reducible Coxeter Groups 102. A.2. Direct Products of Chamber Systems 102. ... To do so we need to. understand products Bw1Bw2 of the averaging operators.
Synchronization has been observedin a diverse range of natural and engineered systems1–3, in-cluding in pace-maker cells of circadian rhythms4, networksof neurons5, in chemical oscillators6,7 and in power
However, it is possible to define the unstable manifold (resp. subspace)of a backward orbit (xn)nN: this can be achieved using the machinery of natural extensions. ... 2. They have explicit expression. Tk(x) = cos(k cos1 x),. from which falls out a