منابع مشابه
Approximation by ruled surfaces
Given a surface or scattered data points from a surface in 3-space, we show how to approximate the given data by a ruled surface in tensor product B-spline representation. This leads us to a general framework for approximation in line space by local mappings from the Klein quadric to Euclidean 4-space. The presented algorithm for approximation by ruled surfaces possesses applications in archite...
متن کاملRuled Laguerre minimal surfaces
A Laguerre minimal surface is an immersed surface in R being an extremal of the functional ∫ (H/K− 1)dA. In the present paper, we prove that any ruled Laguerre minimal surface distinct from a plane is up to motion a convolution of the helicoid x = y tan z, the cycloid r(t) = (t− sin t, 1−cos t, 0) and the Plücker conoid (ax+ by) = z(x+y) for some a, b ∈ R. To achieve invariance under Laguerre t...
متن کاملNormal Presentation on Elliptic Ruled Surfaces
are surjective for all m ≥ 2. If L is normally generated, then we say that L satisfies property Np, if the matrices in the free resolution of R over S have linear entries until the pth stage. In particular, property N1 says that the homogeneous ideal I of X in P(H(L)) is generated by quadrics. A line bundle satisfying property N1 is also called normally presented. Let R = k⊕R1 ⊕R2 ⊕ . . . be a ...
متن کاملCovering Rational Ruled Surfaces
We present an algorithm that covers any given rational ruled surface with two rational parametrizations. In addition, we present an algorithm that transforms any rational surface parametrization into a new rational surface parametrization without affine base points and such that the degree of the corresponding maps is preserved.
متن کاملHardy Inequalities in Strips on Ruled Surfaces
Problems linking the geometry of two-dimensional manifolds and the spectrum of associated Laplacians have been considered for more than a century. While classical motivations come from theories of elasticity and electromagnetism, the same rather simple models can be also remarkably successful in describing even rather complicated phenomena in quantum heterostructures. Here, an enormous amount o...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1937
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1937-06572-4