On metric heights
نویسندگان
چکیده
Metric heights are modified height functions on the non-zero algebraic numbers Q ∗ which can be used to define a metric on certain cosets of Q ∗ . They have been defined with a view to eventually applying geometric methods to the study of Q ∗ . In this paper we discuss the construction of metric heights in general. More specifically, we study in some detail the metric height obtained from the näıve height of an algebraic number (the maximum modulus of the coefficients of its minimal polynomial). In particular, we compute this metric height for some classes of surds.
منابع مشابه
Clustering mass spectrometry data using order statistics.
Mass spectrometry data is inherently uncertain. Rather than compare peak heights across samples, a comparison can be made of the relative ordering of the peak height across samples. Order statistics are used to provide a distance metric between each ordered list of peak heights from the samples. A principal component analysis is performed on the set of distance vectors to highlight to important...
متن کاملAllometric Scaling and Resource Limitations Model of Tree Heights: Part 2. Site Based Testing of the Model
The ultimate goal of this multi-article series is to develop a methodology to generate continuous fields of tree height and biomass. The first paper demonstrated the need for Allometric Scaling and Resource Limitation (ASRL) model optimization and its ability to generate spatially continuous fields of tree heights over the continental USA at coarse (1 km) spatial resolution. The objective of th...
متن کاملUse of a Non-metric Digital Camera for Tree Stem Evaluation
We are investigating the use of a commercially-available solid-state matrix camera as a dendrometer for tree stem measurements. Thirty-two images of four hardwood stems were used to measure 54 diameters at various heights on the stems ranging from 1.4 m to 21 m. These measurements were compared to caliper measurements taken at the same heights. The percent inaccuracy between diameters derived u...
متن کاملOn the topological equivalence of some generalized metric spaces
The aim of this paper is to establish the equivalence between the concepts of an $S$-metric space and a cone $S$-metric space using some topological approaches. We introduce a new notion of a $TVS$-cone $S$-metric space using some facts about topological vector spaces. We see that the known results on cone $S$-metric spaces (or $N$-cone metric spaces) can be directly obtained from...
متن کامل$C$-class and $F(psi,varphi)$-contractions on $M$-metric spaces
Partial metric spaces were introduced by Matthews in 1994 as a part of the study of denotational semantics of data flow networks. In 2014 Asadi and {it et al.} [New Extension of $p$-Metric Spaces with Some fixed point Results on $M$-metric paces, J. Ineq. Appl. 2014 (2014): 18] extend the Partial metric spaces to $M$-metric spaces. In this work, we introduce the class of $F(psi,varphi)$-contrac...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Periodica Mathematica Hungarica
دوره 46 شماره
صفحات -
تاریخ انتشار 2003