A recently found local-global principle for quadratic forms over function fields of curves over a complete discretely valued field is applied to the study of quadratic forms, sums of squares, and related field invariants.

No abstract

Following the start of exploration of the problem of the effect of neon isotopes on the triple-point temperature in 2005, further progress was achieved in 2006-2008, and published in 2008. This paper summarizes the advances to date in our understanding as obtained from further work done in 2008-2009 on five basic aspects of the problem: new isotopic assays; new thermal measurements on neon of "natural" composition; the feasibility of obtaining a value of the slope dT tp /dx( 22 Ne) with an accuracy sufficient for the purpose; the possible occurrence of isotopic fractionation during the process of sealing the samples in the cells; and new thermal measurements

The neon triple point is one of the defining fixed points of the International Temperature Scale of 1990 (ITS-90). Although recognizing that natural neon is a mixture of isotopes, the ITS-90 definition only states that the neon should be of 'natural isotopic composition', without any further requirements. A preliminary study in 2005 indicated that most of the observed variability in the realized neon triple point temperatures within a range of about 0.5 mK can be attributed to the variability in isotopic composition among different samples of 'natural' neon. Based on the results of an International Project (EUROMET Project No. 770), the Consultative Committee for Thermometry decided to improve the realization of the neon fixed point by assigning the ITS-90 temperature value 24.5561 K to neon with the isotopic composition recommended by IUPAC, accompanied by a quadratic equation to take the deviations from the reference composition into account. In this paper, the uncertainties of the equation are discussed and an uncertainty budget is presented. The resulting standard uncertainty due to the isotopic effect (k = 1) after correction of the calibration data is reduced to (4 to 40) μK when using neon of 'natural' isotopic composition or to 30 μK when using 20 Ne. For comparison, an uncertainty component of 0.15 mK should be included in the uncertainty budget for the neon triple point if the isotopic composition is unknown, i.e. whenever the correction cannot be applied.

Slow dissolution of the borosilicate container of triple-point-of-water (TPW) cell is widely recognized as the main cause of long-term drift in observed triple point temperature. We add to the available experimental data a comparison of two large batches of TPW cells (67 cells in total) of various ages (from 1 year to 64 years), manufacturers (NRC, VSL, Fluke, Isotech, etc), and materials (borosilicate glass and fused-silica) which was undertaken in 2018. After measuring the TPW temperatures realized by all 67 cells, 12 borosilicate cells were opened and their water was analyzed by Inductively Coupled Plasma-Mass Spectrometry (ICP-MS) in order to correlate their impurity content with their respective age and their realized TPW temperature. No direct correlation was observed between the TPW cells age/impurity content and their measured triple-point temperature for neither borosilicate cells nor fused silica cells (Pearson’s correlation coefficient rxy is within the range −0.60  ≤  rxy≤ +0.40 for all the pairs considered). For fused-silica cells, the results indicate that after the isotopic variation in the water source is taken into account, the long-term drift due to the dissolution of glass envelope, if any, is negligibly small: (+0.4(±0.6) µK·yr−1 reported herein). Given that all the fused-silica cells realize the TPW temperature within 100 µK of NRC and VSL national reference cells and since the analyzed time period of 15 years is equal to the average lifespan of a TPW cell, we conclude that fused-silica TPW cells are superior to those made from borosilicate glass.