The definition of the Einstein 3-form Gα is motivated by means of the contracted 2nd Bianchi identity. This definition involves at first the complete curvature 2-form. The 1-form Lα is defined via Gα = L β ∧ (θβ ∧ θα) (here ⋆ is the Hodge-star, θα the coframe). It is equivalent to the Einstein 3-form and represents a certain contraction of the curvature 2-form. A variational formula of Salgado ...

The intersection body of a ball is again a ball. So, the unit ball Bd ⊂Rd is a fixed point of the intersection body operator acting on the space of all star-shaped origin symmetric bodies endowed with the Banach– Mazur distance. E. Lutwak asked if there is any other star-shaped body that satisfies this property. We show that this fixed point is a local attractor, i.e., that the iterations of th...

We report the discovery of a relatively faint (V = 15.5) early-type WN star in the SMC. The line strength and width of He II λ4686 emission is similar to that of the other SMC WNs, and the presense of N V λ4603, 19 emission (coupled with the lack of N III) suggests this star is of spectral type WN3-4.5, and thus is similar in type to the other SMC WRs. Also like the other SMC WN stars, an early...

A self-contained electromagnetic theory is developed on a simplicial lattice. Instead of dealing with vectorial field, discrete exterior calculus (DEC) studies the discrete differential forms of electric and magnetic fields, and circumcenter dual is adopted to achieve diagonal Hodge star operators. In this paper, Gauss’ theorem and Stokes’ theorem are shown to be satisfied inherently within DEC...

A new kind of spline geometric method approach is presented. Its main ingredient the use well established spaces forming a discrete de Rham complex to construct primal sequence $\{X^k_h\}^n_{k=0}$, starting from splines degree $p$, and dual $\{\tilde{X}^k_h\}_{k=0}^n$, $p-1$. By imposing homogeneous boundary conditions sequence, two sequences can be isomorphically mapped into one another. Withi...

We define cooperative games on general graphs and generalize Lloyd S. Shapley's celebrated allocation formula for those in terms of stochastic path integral driven by the associated Markov chain each graph. then show that value operator, one player defined integral, coincides with player's component game which is solution to least squares (or Poisson's) equation, light combinatorial Hodge decom...

We show that on the dual of a Lie algebra g of dimension d, the star-product recently introduced by M. Kontsevich is equivalent to the Gutt star-product on g *. We give an explicit expression for the operator realizing the equivalence between these star-products.

I show that Tremaine–Weinberg (TW) measurements of bar pattern speeds are sensitive to errors in the position angle of the disc, PAdisc. I use an N-body experiment to measure these errors; for typical random PAdisc errors, the resulting scatter in the measured values of the dimensionless bar speed parameter R (defined as the ratio of the corotation radius to the bar semi-major axis) is of the o...

This thesis explores new methods for geometric, structure-preserving Eulerian discretizations of dynamics, including Lie advection and incompressible fluids, and the manifolds in which these dynamics occur. The result is a novel method for discrete Lie advection of differential forms, a new family of structure-preserving fluid integrators, and a new set of energies for optimizing meshes appropr...

We present decision procedures for logical constraints involving collections such as sets, multisets, and fuzzy sets. Element membership in our collections is given by characteristic functions from a finite universe (of unknown size) to a user-defined subset of rational numbers. Our logic supports standard operators such as union, intersection, difference, or any operation defined pointwise usi...