Sturm 3-ball global attractors 3: Examples of Thom-Smale complexes

Examples complete our trilogy on the geometric and combinatorial characterization of global Sturm attractors $\mathcal{A}$ which consist of a single closed 3-ball. The underlying scalar PDE is parabolic, $$u_t = u_{xx} + f(x,u,u_x)\,,$$ on the unit interval $0 < x<1$ with Neumann boundary conditions. Equilibria $v_t=0$ are assumed to be hyperbolic. Geometrically, we study the resulting Thom-Smale dynamic complex with cells defined by the fast unstable manifolds of the equilibria. The Thom-Smale complex turns out to be a regular cell complex. In the first two papers we characterized 3-ball Sturm attractors $\mathcal{A}$ as 3-cell templates $\mathcal{C}$. The characterization involves bipolar orientations and hemisphere decompositions which are closely related to the geometry of the fast unstable manifolds. An equivalent combinatorial description was given in terms of the Sturm permutation, alias the meander properties of the shooting curve for the equilibrium ODE boundary value problem. It involves the relative positioning of extreme 2-dimensionally unstable equilibria at the Neumann boundaries $x=0$ and $x=1$, respectively, and the overlapping reach of polar serpents in the shooting meander. In the present paper we apply these descriptions to explicitly enumerate all 3-ball Sturm attractors $\mathcal{A}$ with at most 13 equilibria. We also give complete lists of all possibilities to obtain solid tetrahedra, cubes, and octahedra as 3-ball Sturm attractors with 15 and 27 equilibria, respectively. For the remaining Platonic 3-balls, icosahedra and dodecahedra, we indicate a reduction to mere planar considerations as discussed in our previous trilogy on planar Sturm attractors.Comment: 73+(ii) pages, 40 figures, 14 table; see also parts 1 and 2 under arxiv:1611.02003 and arxiv:1704.0034

THE DYNAMIC HEDGING EFFECTIVENESS FOR SOYBEAN FARMERS OF MATO GROSSO WITH FUTURES CONTRACTS OF BM&F

Dynamic hedging effectiveness for soybean farmers in Rondonópolis (MT) with futures contracts of BM&F is calculated through optimal hedge determination, using the bivariate GARCH BEKK model, which considers the conditional correlations of the prices series, comparing the results with the minimum variance model effectiveness, calculated by OLS, the unhedged and the naïve hedge positions. The financial effectiveness of the dynamic hedge model is superior and can be used by farmers for several decision making purposes such as price discovery, hedging calibration, cash flow projections, market timing, among others.dynamic hedge, minimum variance, soybeans, Mato Grosso, Agribusiness, Agricultural Finance, Industrial Organization,

Lunar subsurface architecture enhanced by artificial biosphere concepts

The integration of artificial biosphere technology with subselene architecture can create a life-enhancing, productive habitat that is safe from solar radiation and extreme temperature fluctuations while maximizing resources brought from Earth and derived from lunar regolith. In the short term, the resulting biotectural (biosphere and architectural) designs will not only make the structures more habitable, productive, and manageable, but will ultimately provide the self-sufficiency factors necessary for the mature lunar settlement. From a long-term perspective, this biotecture approach to astronautics and extraterrestrial development (1) helps reduce mass lift requirements, (2) contributes to habitat self-sufficiency, and (3) actualizes at least one philosophy of solar system exploration, which is to exploit nonterrestrial resources in an effort to conserve our natural resources on this planet

Liberdade e totalitarismo : os movimentos totalitários modernos e o estado de exceção como seu instrumento

Trata do princípio da liberdade e dos movimentos totalitários modernos sob o ponto de vista de Hannah Arendt