An advanced geometric modeler GEMS4.0 has been developed, in whichfeature representation is used at the highest level abstraction of a productmodel. Boundary representation is used at the bottom level, while CSG model...An advanced geometric modeler GEMS4.0 has been developed, in whichfeature representation is used at the highest level abstraction of a productmodel. Boundary representation is used at the bottom level, while CSG modelis adopted at the median level. A BRep data structure capable of modelingnon-manifold is adopted. NURBS representation is used for all curved surfaces.Quadric surfaces have dual representations consisting of their geometric datasuch as radius, center point, and center tals. Boundary representation of freeform surfaces is easily built by sweeping and skinning method with NURBSgeometry Set operations on curved solids with boundary representation areperformed by an evaluation process consisting of four steps. A file exchangefacility is provided for the conversion between product data described by STEPand product information generated by GEMS4.0展开更多
We consider the tensor product π_α ? π_βof complementary series representations π_α and π_β of classical rank one groups SO_0(n, 1), SU(n, 1) and Sp(n, 1). We prove that there is a discrete component π_(α+β...We consider the tensor product π_α ? π_βof complementary series representations π_α and π_β of classical rank one groups SO_0(n, 1), SU(n, 1) and Sp(n, 1). We prove that there is a discrete component π_(α+β)for small parameters α and β(in our parametrization). We prove further that for SO_0(n, 1) there are finitely many complementary series of the form π_(α+β+2j,)j = 0, 1,..., k, appearing in the tensor product π_α ? π_βof two complementary series π_α and π_β, where k = k(α, β, n) depends on α, β and n.展开更多
文摘An advanced geometric modeler GEMS4.0 has been developed, in whichfeature representation is used at the highest level abstraction of a productmodel. Boundary representation is used at the bottom level, while CSG modelis adopted at the median level. A BRep data structure capable of modelingnon-manifold is adopted. NURBS representation is used for all curved surfaces.Quadric surfaces have dual representations consisting of their geometric datasuch as radius, center point, and center tals. Boundary representation of freeform surfaces is easily built by sweeping and skinning method with NURBSgeometry Set operations on curved solids with boundary representation areperformed by an evaluation process consisting of four steps. A file exchangefacility is provided for the conversion between product data described by STEPand product information generated by GEMS4.0
文摘We consider the tensor product π_α ? π_βof complementary series representations π_α and π_β of classical rank one groups SO_0(n, 1), SU(n, 1) and Sp(n, 1). We prove that there is a discrete component π_(α+β)for small parameters α and β(in our parametrization). We prove further that for SO_0(n, 1) there are finitely many complementary series of the form π_(α+β+2j,)j = 0, 1,..., k, appearing in the tensor product π_α ? π_βof two complementary series π_α and π_β, where k = k(α, β, n) depends on α, β and n.
