Guide for Continued Reading. You now have all the tools to go quickly through the classical material of Chapters IV and V of Hartshorne and related material. I suggest for a first read through: • IV §1, • IV §2 First three pages. Cor 2.4 is crucial. Try exercises 2.2, 2.3. Don’t be intimidated by differential forms–everything you need here we did in 631—now it should seem easy. Don’t use Hartsh...

A geometrically exact membrane formulation is presented that is based on curvilinear coordinates and isogeometric finite elements, and is suitable for both solid and liquid membranes. The curvilinear coordinate system is used to describe both the theory and the finite element equations of the membrane. In the latter case this avoids the use of local cartesian coordinates at the element level. C...

We introduce and begin the topological study of real rational plane curves, all of whose inflection points are real. The existence of such curves is a corollary of results in the real Schubert calculus, and their study has consequences for the important Shapiro and Shapiro conjecture in the real Schubert calculus. We establish restrictions on the number of real nodes of such curves and construc...

Let ⊂ R be a bounded, convex, and open set with real analytic boundary. Let T ⊂ C be the tube with base , and let B be the Bergman kernel of T . If is strongly convex, then B is analytic away from the boundary diagonal. In the weakly convex case this is no longer true. In this situation we relate the off-diagonal points where analyticity fails to the characteristic lines. These lines are contai...

Based on the hypothesis that reclaimed water for irrigating is the cardinal source of heavy metals pollution in soil, and the heavy metals leave from soil mainly by plant harvest, the article constructs a differential equation and simulates the cumulation of Cd in wheat soil of southeast suburb in Beijing based on simulink of matlab. With the data relative Cd mass proportion in soil as predicto...

We use a combination of both symbolic and numerical techniques to construct several degree bounded G 0 and G 1 continuous, piecewise approximations of real algebraic surfaces. These approximations are based upon an adaptive triangulation (a G 0 planar approximation) of the real components of the algebraic surface, and includes both singular points and singular curves on the surface. The approxi...

We present a novel framework for modeling hair using simplified representations. The set of representations, including individual strands, clusters and patches, are derived from Dynamic-NURBS and have the same underlying base skeleton. Our framework supports automatic simplification of dynamic simulation, collision detection and graphical rendering of hair, and offers flexibility to balance bet...

a r t i c l e i n f o a b s t r a c t Free boundary three-dimensional anisotropic pressure magnetohydrodynamic equilibria with nested magnetic flux surfaces are computed through the minimisation of the plasma energy functional W = V d 3 x [B 2 /(2μ 0) + p /(Γ − 1)]. The plasma–vacuum interface is varied to guarantee the continuity of the total pressure [p ⊥ + B 2 /(2μ 0)] across it and the vacu...

Our ongoing research in performance theory integrates methods for complex instrument parameter spaces and models for musical gestures. The latter are modelled as parametric curves residing in high-dimensional symbolic and physical gesture spaces. This article shortly exposes basic concepts of those spaces and the construction of symbolic gesture curves. It then discusses the problem of fitting ...

Garment virtual design has been evolved significantly with the rapid development of 3D CAD tools, especially with the convenient availability of NURBS surface modeling capability. Parametric development of clothes is demanded in line with the trend of mass customization according to the true measures of customers or regulated sizes of certain markets. Virtual design features with welldefined as...