منابع مشابه
Class Groups, Totally Positive Units, and Squares
Given a totally real algebraic number field K, we investigate when totally positive units, U¿, are squares, u£. In particular, we prove that the rank of U¿ /Ují is bounded above by the minimum of (1) the 2-rank of the narrow class group of K and (2) the rank of Ul /U¿ as L ranges over all (finite) totally real extension fields of K. Several applications are also provided. 1. Notation and prelim...
متن کاملA Lattice-Ordered Skew Field Is Totally Ordered If Squares Are Positive
We show that a lattice-ordered field (not necessarily commutative) is totally ordered if and only if each square is positive, answering a generalized question of Conrad and Dauns [6] in the affirmative. As a consequence, any lattice-ordered skew-field in [5] is totally ordered. Furthermore , we note that each lattice order determined by a pre-positive cone P on a skew-filed F is linearly ordere...
متن کاملThe Tropical Totally Positive Grassmannian
Tropical algebraic geometry is the geometry of the tropical semiring (R,min,+). The theory of total positivity is a natural generalization of the study of matrices with all minors positive. In this paper we introduce the totally positive part of the tropicalization of an arbitrary affine variety, an object which has the structure of a polyhedral fan. We then investigate the case of the Grassman...
متن کاملGauss Interpolation Formulas and Totally Positive Kernels
This paper simplifies and generalizes an earlier result of the author's on Gauss interpolation formulas for the one-dimensional heat equation. Such formulas approximate a function at a point (x*, t*) in terms of a linear combination of its values on an initial-boundary curve in the (x, t) plane. The formulas are characterized by the requirement that they be exact for as many basis functions as ...
متن کاملTotally Positive Density Matrices and Linear Preservers
The intersection between the set of totally nonnegative matrices, which are of interest in many areas of matrix theory and its applications, and the set of density matrices, which provide the mathematical description of quantum states, are investigated. The single qubit case is characterized, and several equivalent conditions for a quantum channel to preserve the set in that case are given. Hig...
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: 1983
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1983-0687627-7