منابع مشابه
The Surface Parametrizing Cuboids
We study the surface S̄ parametrizing cuboids: it is defined by the equations relating the sides, face diagonals and long diagonal of a rectangular box. It is an open problem whether a ‘rational box’ exists, i.e., a rectangular box all of whose sides, face diagonals and long diagonal have (positive) rational length. The question is equivalent to the existence of nontrivial rational points on S̄. ...
متن کاملTowards parametrizing word equations
Classically, in order to resolve an equation u ≈ v over a free monoid X∗, we reduce it by a suitable family F of substitutions to a family of equations uf ≈ vf , f ∈ F , each involving less variables than u ≈ v, and then combine solutions of uf ≈ vf into solutions of u ≈ v. The problem is to get F in a handy parametrized form. The method we propose consists in parametrizing the path traces in t...
متن کاملParametrizing Doubly Stochastic Measures
Doubly stochastic measures can be identi ed with the trace of a pair of (Lebesgue) measure preserving maps of the unit interval to itself. It has been of traditional interest in probability theory to produce a random vector (or metric space element), which has a given distribution and is de ned on a standard space, such as [0; 1] endowed with Lebesgue measure. In a classic work, L evy [4, secti...
متن کاملParametrizing complex Hadamard matrices
Abstract. The purpose of this paper is to introduce new parametric families of complex Hadamard matrices in two different ways. First, we prove that every real Hadamard matrix of order N ≥ 4 admits an affine orbit. This settles a recent open problem of Tadej and Życzkowski [11], who asked whether a real Hadamard matrix can be isolated among complex ones. In particular, we apply our construction...
متن کاملParametrizing Quantum States and Channels
This work describes one parametrization of quantum states and channels and several of its possible applications. This parametrization works in any dimension and there is an explicit algorithm which produces it. Included in the list of applications are a simple characterization of pure states, an explicit formula for one additive entropic quantity which does not require knowledge of eigenvalues,...
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: Topology and its Applications
سال: 2002
ISSN: 0166-8641
DOI: 10.1016/s0166-8641(01)00069-4