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# On metric heights

Periodica Mathematica Hungarica
Authors: A. Dubickas and C. Smyth

## Abstract

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
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\overline {\mathbb{Q}} ^*$$ \end{document}
. They have been defined with a view to eventually applying geometric methods to the study of
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\overline {\mathbb{Q}} ^*$$ \end{document}
. 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 na"ve 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.
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# Deflections of the vertical and geoid heights from gravity gradients

Acta Geodaetica et Geophysica Hungarica
Author: L. Völgyesi

In the 20th century more than 60000 torsion balance measurements were made in Hungary. At present efforts are made to rescue the historical torsion balance data; today 24544 torsion balance measurements are available for further processing in computer database. Previously only the horizontal gradients of gravity were used by geophysicists, but there is a good possibility in geodesy to interpolate deflections of the vertical, and to compute geoid heights from curvature gradients of gravity. First the theory of the interpolation method is discussed, than results of test computations are presented. We have selected a test area where all kinds of torsion balance measurements are available at 249 points. There were 3 astrogeodetic points providing initial data for the interpolation, and 10 checkpoints for controlling the results. The size of our test area is about 750 km2 and the average site distance of torsion balance data is 1.5-2 km. The standard deviations of geoid height and deflection of the vertical differences at checkpoints were about ±1-3 cm, and ± 0.6'' respectively; which confirm that torsion balance measurements give possibility to compute very precise deflections of the vertical and local geoid heights at least for flat areas.

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# Influence of the new Croatian height system on the benchmark heights in the national levelling control networks

Acta Geodaetica et Geophysica Hungarica
Author: N. Rožić

During the last ten years there were systematic works carried out in Croatia on the realisation and implementation of the new height system. The results of these works, based on the analysis and completely new processing of the existing archive data of geometric levelling measurements, are the basis for the introduction of the new Croatian height system into official usage. As the introduction of the new height system has direct impact on the changes of national control network benchmark heights, it is necessary to determine and investigate the changes and relations between the “old” and “new” heights of benchmarks. For this purpose, the benchmark heights in the national geometric levelling control networks have been compared and analysed at the north-western part of the territory of the Republic of Croatia chosen to be representative test area. Comparison results are achieved and presented in this paper.

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# Seismic retrofit of steel frame structures

Pollack Periodica
Author: Magdy Ismail

of beam-column connections [ 1 ]. In addition, excessive damage of non-structural elements should be avoided. The objective of this study is to investigate the seismic performance of three multi-story steel frame buildings with different heights that

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# Estimation of capillary rise in unsaturated gypseous sand soils

Pollack Periodica
Authors: Shaymaa Alsamia, Mohammed Sh. Mahmood, and Ali Akhtarpour

analysis. This paper has estimated all the heights using the proposed equations. The experiment consists of three pipes; each pipe has 1 m long and 4.5 cm diameter as well as a central slot of glass to track the rising water through the sandy soil. The real

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# Characterization of sugar palm (Arenga pinnata) fibres

## Tensile and thermal properties

Journal of Thermal Analysis and Calorimetry
Authors: M. R. Ishak, S. M. Sapuan, Z. Leman, M. Z. A. Rahman, and U. M. K. Anwar

thermal properties give significant contribution in understanding the behaviour of their fibres and composites [ 28 – 36 ]. This paper studies the tensile and thermal properties of sugar palm fibres obtained from different heights (1, 3, 5, 7, 9

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# Local geoid determination based on gravity gradients

Acta Geodaetica et Geophysica Hungarica
Author: L. Völgyesi

There is a good possibility tointerpolate a dense net of de ections of the vertical from Wgravity gradients measured by torsion balance and applying astronomical levelling to compute geoid heights. A new practical computation of astronomical levelling is suggested.

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# Development and validation of high-performance liquid chromatography method for determination of some pesticide residues in table grape

Acta Chromatographica
Authors: L. Velkoska-Markovska, B. Petanovska-Ilievska, M. S. Jankulovska, and U. Ilievski

was about 6 min. The results from the method validation revealed that the proposed method has a satisfactory linearity ( R 2 > 0.90) and excellent precision of retention times, peak areas, and heights (RSD ≤ 2.25%). The obtained values for recoveries

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# Effect of resin cross-linking and temperature on anion exchange separation of gallium and indium

Journal of Radioanalytical and Nuclear Chemistry
Author: R. Shabana

## Abstract

Anion exchange separation of Ga-In on Dowex 1 resins of 2, 4, 8, and 10 nominal cross-linkings, respectively, was investigated at tracer loadings. The influence of temperature on the exchange reaction was also studied on the different resins. Separation factors, plate heights, and resolutions for the two peaks were calculated from the elution curves. Best separations were achieved with Dowex 1X4 due to the most promising values for both plate height and resolution. It was also found that the separation factors as well as the plate heights decreased with growing temperature.

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# Determination of malathion and its residues by normal-phase high-performance liquid chromatography method

Acta Chromatographica
Authors: Lenche Velkoska-Markovska and Biljana Petanovska-Ilievska

from 30% less than MRL to 20% above ( Table 1 ), i.e. 0.014–0.024 mg/kg. For these concentration range and using the data for the peak areas and peak heights the curves were constructed and the multiple correlation coefficients ( R 2 ) were calculated

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