Inner tube formulas for polytopes
نویسندگان
چکیده
منابع مشابه
Inner diagonals of convex polytopes
An inner diagonal of a polytope P is a segment that joins two vertices of P and that lies, except for its ends, in P ’s relative interior. For 1 ≤ i ≤ d, an i-diagonal of a d-polytope P is a segment [x, y] whose ends are vertices of P and whose carrier in P (i.e., the smallest face of P that contains [x, y]) is of dimension i. The number of P ’s i-diagonals is denoted by δi(P ). Thus δ1(P ) is ...
متن کاملTube Formulas for Self-Similar Fractals
Tube formulas (by which we mean an explicit formula for the volume of an (inner) ε-neighbourhood of a subset of a suitable metric space) have been used in many situations to study properties of the subset. For smooth submanifolds of Euclidean space, this includes Weyl’s celebrated results on spectral asymptotics, and the subsequent relation between curvature and spectrum. Additionally, a tube f...
متن کاملExact Euler Maclaurin Formulas for Simple Lattice Polytopes
Euler Maclaurin formulas for a polytope express the sum of the values of a function over the lattice points in the polytope in terms of integrals of the function and its derivatives over faces of the polytope or its dilations. There are two kinds of Euler Maclaurin formulas: exact formulas, which apply to exponential or polynomial functions, and formulas with remainder, which apply to arbitrary...
متن کاملRecursive algorithms for inner ellipsoidal approximation of convex polytopes
In this paper, fast recursive algorithms for the approximation of an n-dimensional convex polytope by means of an inscribed ellipsoid are presented. These algorithms consider at each step a single inequality describing the polytope and, under mild assumptions, they are guaranteed to converge in a 5nite number of steps. For their recursive nature, the proposed algorithms are better suited to tre...
متن کاملSome Recurrence Formulas for Spherical Polynomials on Tube Domains
For a tube domain G/K we study the tensor products of two spherical representations of the maximal compact group K and the product of the corresponding spherical polynomials. When one of these is a fundamental representation, we prove that the spherical representations appear with multiplicity at most one and we then find all the coefficients in the recurrence formula for the product of the sph...
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: Proceedings of the American Mathematical Society
سال: 2012
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-2011-11307-8