The (classical, small quantum, equivariant) cohomology ring of the grassmannianG(k, n) is generated by certain derivations operating on an exterior algebra of a free module of rank n (Schubert Calculus on a Grassmann Algebra). Our main result gives, in a unified way, a presentation of all such cohomology rings in terms of generators and relations. It also provides, by results of Laksov and Thor...

Ford of Europe’s Product Sustainability Index (PSI) is a sustainability management tool directly used by engineering, i.e. not by sustainability or life cycle experts. PSI is looking at eight indicators reflecting environmental (Life Cycle Global Warming Potential, Life Cycle Air Quality Potential, Sustainable Materials, Restricted Substances, Drive-by-Exterior-Noise), social (Mobility Capabili...

The primary function of the outermost, lipophilic layer of plant aerial surfaces, called the cuticle, is preventing non-stomatal water loss. Its exterior surface is often decorated with wax crystals, imparting a blue-grey color. Identification of the barley Cer-c, -q and -u genes forming the 101 kb Cer-cqu gene cluster encoding a novel polyketide synthase-the β-diketone synthase (DKS), a lipase...

We show that the algebra of the bicovariant differential calculus on a quantum group can be understood as a projection of the cross product between a braided Hopf algebra and the quantum double of the quantum group. The resulting super-Hopf algebra can be reproduced by extending the exterior derivative to tensor products. ∗ This work was supported in part by the Director, Office of Energy Resea...

The Pick cubic form is a fundamental invariant in the (equi)affine differential geometry of hypersurfaces. We study its role in the affine isometric embedding problem, using exterior differential systems (EDS). We give pointwise conditions on the Pick form under which an isometric embedding of a Riemannian manifold M3 into R4 is rigid. The role of the Pick form in the characteristic variety of ...

Phenol formaldehyde (PF) resins are widely used as wood adhesives in the industrial production of exterior-grade plywood panels, oriented strand board panels and particleboards due to their superior performance including high bonding strength, heat resistance, excellent water resistance and chemical stability1. However, phenol, one raw material for the synthesis of PF resins, is a petroleum-bas...

We define epsilon factors for irreducible representations of finite general linear groups using Macdonald's correspondence. These satisfy multiplicativity, and are expressible as products Gauss sums. The tensor product related to the Rankin-Selberg gamma factors, by which we prove that can be written exterior square relate Jacquet-Shalika Langlands-Shahidi level zero supercuspidal representatio...

In this paper, we present a numerical technique for performing Lie advection of arbitrary differential forms. Leveraging advances in high-resolution finite volume methods for scalar hyperbolic conservation laws, we first discretize the interior product (also called contraction) through integrals over Eulerian approximations of extrusions. This, along with Cartan’s homotopy formula and a discret...

The n-instanton contribution to the Seiberg-Witten prepotential of N = 2 supersymmetric d = 4 Yang Mills theory is represented as the integral of the exponential of an equivariantly exact form. Integrating out an overall scale and a U(1) angle the integral is rewritten as (4n − 3) fold product of a closed two form. This two form is, formally, a representative of the Euler class of the Instanton...

The primary function of the outermost, lipophilic layer of plant aerial surfaces, called the cuticle, is preventing non-stomatal water loss. Its exterior surface is often decorated with wax crystals, imparting a blue–grey color. Identification of the barley Cer-c, -q and -u genes forming the 101 kb Cer-cqu gene cluster encoding a novel polyketide synthase—the β-diketone synthase (DKS), a lipase...