Homotopically homogeneous polyhedra.
نویسندگان
چکیده
منابع مشابه
Mutual Potential of Homogeneous Polyhedra
The mutual gravitational potential between a pair of homogeneous polyhedra is expressed using an infinite series. The nested volume integrals are evaluated analytically and result in simple tensor expressions containing no special functions. However, complexity increases as Oð6Þ, where n is the term degree. An alternate formulation due to Liebenthal is also presented.
متن کاملHomotopically Periodic Maps of Model Aspherical Manifolds
For a closed orientable surface S, any map f : S→S whose n-th power is homotopic to the identity, is homotopic to a homeomorphism g of S of order n. This famous theorem of Nielsen is known to fail in general for aspherical manifolds. In this paper, for model aspherical manifolds M associated to a finitely extendable set of data, we, however, present a weaker version of Nielsen’s result. We show...
متن کاملNumerical integration of homogeneous functions on convex and nonconvex polygons and polyhedra
We present a method for the numerical integration of homogeneous functions over convex and nonconvex polygons and polyhedra. On applying Stokes’s theorem and using the property of homogeneous functions, we show that it suffices to integrate these functions on the boundary facets of the polytope. For homogeneous polynomials, this approach is used to further reduce the integration to just functio...
متن کاملIntersection homology and Poincaré duality on homotopically stratified spaces
We show that intersection homology extends Poincaré duality to manifold homotopically stratified spaces (satisfying mild restrictions). These spaces were introduced by Quinn to provide “a setting for the study of purely topological stratified phenomena, particularly group actions on manifolds.” The main proof techniques involve blending the global algebraic machinery of sheaf theory with local ...
متن کاملHomotopically Non-trivial Maps with Small K-dilation
We construct homotopically non-trivial maps from Sm to Sn with arbitrarily small 3-dilation for certain pairs (m,n). The simplest example is the case m = 4, n = 3, and there are other pairs with arbitrarily large values of both m and n. We show that a homotopy class in π7(S) can be represented by maps with arbitrarily small 4-dilation if and only if the class is torsion. The k-dilation of a map...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Michigan Mathematical Journal
سال: 1961
ISSN: 0026-2285
DOI: 10.1307/mmj/1028998515