The Representation of Polyhedra by Polynomial Inequalities
نویسندگان
چکیده
منابع مشابه
The Representation of Polyhedra by Polynomial Inequalities
A beautiful result of Bröcker and Scheiderer on the stability index of basic closed semi-algebraic sets implies, as a very special case, that every ^-dimensional polyhedron admits a representation as the set of solutions of at most d(d + l) /2 polynomial inequalities. Even in this polyhedral case, however, no constructive proof is known, even if the quadratic upper bound is replaced by any boun...
متن کاملextensions of some polynomial inequalities to the polar derivative
توسیع تعدادی از نامساوی های چند جمله ای در مشتق قطبی
15 صفحه اولPolynomial inequalities representing polyhedra
Our main result is that every ro-dimensional polytope can be described by at most (2n — 1) polynomial inequalities and, moreover, these polynomials can explicitly be constructed. For an n-dimensional pointed polyhedral cone we prove the bound 2n — 2 and for arbitrary polyhedra we get a constructible representation by 2n polynomial inequalities. 1. I N T R O D U C T I O N By a striking result of...
متن کاملThree-Dimensional Polyhedra Can Be Described by Three Polynomial Inequalities
Bosse et al. conjectured that for every natural number d ≥ 2 and every ddimensional polytope P in Rd there exist d polynomials p0(x), . . . , pd−1(x) satisfying P = { x ∈ Rd : p0(x) ≥ 0, . . . , pd−1(x) ≥ 0} . We show that for dimensions d ≤ 3 even every d-dimensional polyhedron can be described by d polynomial inequalities. The proof of our result is constructive. 2000 Mathematics Subject Clas...
متن کاملcontrol of the optical properties of nanoparticles by laser fields
در این پایان نامه، درهمتنیدگی بین یک سیستم نقطه کوانتومی دوگانه(مولکول نقطه کوانتومی) و میدان مورد مطالعه قرار گرفته است. از آنتروپی ون نیومن به عنوان ابزاری برای بررسی درهمتنیدگی بین اتم و میدان استفاده شده و تاثیر پارامترهای مختلف، نظیر تونل زنی(که توسط تغییر ولتاژ ایجاد می شود)، شدت میدان و نسبت دو گسیل خودبخودی بر رفتار درجه درهمتنیدگی سیستم بررسی شده اشت.با تغییر هر یک از این پارامترها، در...
15 صفحه اولذخیره 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: Discrete and Computational Geometry
سال: 2003
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-003-0782-y