A concise summary of the International System of Units, the SI

The Bureau International des Poids et Mesures, the BIPM, was established by Article 1 of the Convention du Mètre, on 20 May 1875, and is charged with providing the basis for a single, coherent system of measurements to be used throughout the world. The decimal metric system, dating from the time of the French Revolution, was based on the metre and the kilogram. Under the terms of the 1875 Convention, new international prototypes of the metre and kilogram were made and formally adopted by the first Conférence Générale des Poids et Mesures (CGPM) in 1889. Over time this system developed, so that it now includes seven base units. In 1960 it was decided at the 11th CGPM that it should be called the Système International d’Unités, the SI (in English: the International System of Units). The SI is not static but evolves to match the world’s increasingly demanding requirements for measurements at all levels of precision and in all areas of science, technology, and human endeavour. This document is a summary of the SI Brochure, a publication of the BIPM which is a statement of the current status of the SI. The seven base units of the SI, listed in Table 1, provide the reference used to define all the measurement units of the International System. As science advances, and methods of measurement are refined, their definitions have to be revised. The more accurate the measurements, the greater the care required in the realization of the units of measurement.

Redefinition of the kilogram, ampere, kelvin and mole: a proposed approach to implementing CIPM recommendation 1 (CI-2005)

The International System of Units (SI) is founded on seven base units, the metre, kilogram, second, ampere, kelvin, mole and candela corresponding to the seven base quantities of length, mass, time, electric current, thermodynamic temperature, amount of substance and luminous intensity. At its 94th meeting in October 2005, the International Committee for Weights and Measures (CIPM) adopted a recommendation on preparative steps towards redefining the kilogram, ampere, kelvin and mole so that these units are linked to exactly known values of fundamental constants. We propose here that these four base units should be given new definitions linking them to exactly defined values of the Planck constant h, elementary charge e, Boltzmann constant k and Avogadro constant NA, respectively. This would mean that six of the seven base units of the SI would be defined in terms of true invariants of nature. In addition, not only would these four fundamental constants have exactly defined values but also the uncertainties of many of the other fundamental constants of physics would be either eliminated or appreciably reduced. In this paper we present the background and discuss the merits of these proposed changes, and we also present possible wordings for the four new definitions. We also suggest a novel way to define the entire SI explicitly using such definitions without making any distinction between base units and derived units. We list a number of key points that should be addressed when the new definitions are adopted by the General Conference on Weights and Measures (CGPM), possibly by the 24th CGPM in 2011, and we discuss the implications of these changes for other aspects of metrology.

On logarithmic ratio quantities and their units

The use of special units for logarithmic ratio quantities is reviewed. The neper is used with a natural logarithm (logarithm to the base e) to express the logarithm of the amplitude ratio of two pure sinusoidal signals, particularly in the context of linear systems where it is desired to represent the gain or loss in amplitude of a single-frequency signal between the input and output. The bel, and its more commonly used submultiple, the decibel, are used with a decadic logarithm (logarithm to the base 10) to measure the ratio of two power-like quantities, such as a mean square signal or a mean square sound pressure in acoustics. Thus two distinctly different quantities are involved. In this review we define the quantities first, without reference to the units, as is standard practice in any system of quantities and units. We show that two different definitions of the quantity power level, or logarithmic power ratio, are possible. We show that this leads to two different interpretations for the meaning and numerical values of the units bel and decibel. We review the question of which of these alternative definitions is actually used, or is used by implication, by workers in the field. Finally, we discuss the relative advantages of the alternative definitions.

On defining base units in terms of fundamental constants

The definitions of the base units of the international system of units have been revised many times since the idea of such an international system was first conceived at the time of the French revolution. The objective today is to define all our units in terms of 'invariants of nature', i.e. by referencing our units to the fundamental constants of physics, or the properties of atoms, rather than the characteristics of our planet or of artefacts. This situation is reviewed, particularly in regard to finding a new definition of the kilogram to replace its present definition in terms of a prototype material artefact.

Definitions of the units radian, neper, bel and decibel

The definition of coherent derived units in the International System of Units (SI) is reviewed, and the important role of the equations defining physical quantities is emphasized in obtaining coherent derived units. In the case of the dimensionless quantity plane angle, the choice between alternative definitions is considered, leading to a corresponding choice between alternative definitions of the coherent derived unit - the radian, degree or revolution. In this case the General Conference on Weights and Measures (CGPM) has chosen to adopt the definition that leads to the radian as the coherent derived unit in the SI. In the case of the quantity logarithmic decay (or gain), also sometimes called decrement, and sometimes called level, a similar choice of defining equation exists, leading to a corresponding choice for the coherent derived unit - the neper or the bel. In this case the CGPM has not yet made a choice. We argue that for the quantity logarithmic decay the most logical choice of defining equation is linked to that of the radian, and is that which leads to the neper as the corresponding coherent derived unit. This should not prevent us from using the bel and decibel as units of logarithmic decay. However, it is an important part of the SI to establish in a formal sense the equations defining physical quantities, and the corresponding coherent derived units.

An overview of Earth’s global electric circuit and atmospheric conductivity

The Earth’s global atmospheric electric circuit depends on the upper and lower atmospheric boundaries formed by the ionosphere and the planetary surface. Thunderstorms and electrified rain clouds drive a DC current (∼1 kA) around the circuit, with the current carried by molecular cluster ions; lightning phenomena drive the AC global circuit. The Earth’s near-surface conductivity ranges from 10−7 S m−1 (for poorly conducting rocks) to 10−2 S m−1 (for clay or wet limestone), with a mean value of 3.2 S m−1 for the ocean. Air conductivity inside a thundercloud, and in fair weather regions, depends on location (especially geomagnetic latitude), aerosol pollution and height, and varies from ∼10−14 S m−1 just above the surface to 10−7 S m−1 in the ionosphere at ∼80 km altitude. Ionospheric conductivity is a tensor quantity due to the geomagnetic field, and is determined by parameters such as electron density and electron–neutral particle collision frequency. In the current source regions, point discharge (coronal) currents play an important role below electrified clouds; the solar wind-magnetosphere dynamo and the unipolar dynamo due to the terrestrial rotating dipole moment also apply atmospheric potential differences. Detailed measurements made near the Earth’s surface show that Ohm’s law relates the vertical electric field and current density to air conductivity. Stratospheric balloon measurements launched from Antarctica confirm that the downward current density is ∼1 pA m−2 under fair weather conditions. Fortuitously, a Solar Energetic Particle (SEP) event arrived at Earth during one such balloon flight, changing the observed atmospheric conductivity and electric fields markedly. Recent modelling considers lightning discharge effects on the ionosphere’s electric potential (∼+250 kV with respect to the Earth’s surface) and hence on the fair weather potential gradient (typically ∼130 V m−1 close to the Earth’s surface. We conclude that cloud-to-ground (CG) lightning discharges make only a small contribution to the ionospheric potential, and that sprites (namely, upward lightning above energetic thunderstorms) only affect the global circuit in a miniscule way. We also investigate the effects of mesoscale convective systems on the global circuit.

Ranking efficiency units in DEA using bootstrapping an applied analysis for Slovenian farm data

This article explores how data envelopment analysis (DEA), along with a smoothed bootstrap method, can be used in applied analysis to obtain more reliable efficiency rankings for farms. The main focus is the smoothed homogeneous bootstrap procedure introduced by Simar and Wilson (1998) to implement statistical inference for the original efficiency point estimates. Two main model specifications, constant and variable returns to scale, are investigated along with various choices regarding data aggregation. The coefficient of separation (CoS), a statistic that indicates the degree of statistical differentiation within the sample, is used to demonstrate the findings. The CoS suggests a substantive dependency of the results on the methodology and assumptions employed. Accordingly, some observations are made on how to conduct DEA in order to get more reliable efficiency rankings, depending on the purpose for which they are to be used. In addition, attention is drawn to the ability of the SLICE MODEL, implemented in GAMS, to enable researchers to overcome the computational burdens of conducting DEA (with bootstrapping).

Estimating numbers of infectious units from serial dilution assays

The paper concerns the design and analysis of serial dilution assays to estimate the infectivity of a sample of tissue when it is assumed that the sample contains a finite number of indivisible infectious units such that a subsample will be infectious if it contains one or more of these units. The aim of the study is to estimate the number of infectious units in the original sample. The standard approach to the analysis of data from such a study is based on the assumption of independence of aliquots both at the same dilution level and at different dilution levels, so that the numbers of infectious units in the aliquots follow independent Poisson distributions. An alternative approach is based on calculation of the expected value of the total number of samples tested that are not infectious. We derive the likelihood for the data on the basis of the discrete number of infectious units, enabling calculation of the maximum likelihood estimate and likelihood-based confidence intervals. We use the exact probabilities that are obtained to compare the maximum likelihood estimate with those given by the other methods in terms of bias and standard error and to compare the coverage of the confidence intervals. We show that the methods have very similar properties and conclude that for practical use the method that is based on the Poisson assumption is to be recommended, since it can be implemented by using standard statistical software. Finally we consider the design of serial dilution assays, concluding that it is important that neither the dilution factor nor the number of samples that remain untested should be too large.

Evaluation of the binding ability of a novel dioxatetraazamacrocyclic receptor that contains two phenanthroline units: selective uptake of carboxylate anions

The novel dioxatetraaza macrocycle [26]phen(2)N(4)O(2), which incorporates two phenanthroline units, has been synthesized, and its acid-base behavior has been evaluated by potentiometric and H-1 NMR methods. Six protonation constants were determined, and the protonation sequence was established by NMR. The location of the fifth proton on the phen nitrogen was confirmed by X-ray determinations of the crystal structures of the receptor as bromide and chloride salts. The two compounds have the general molecular formula {(H-5[26]phen(2)N(4)O(2))X-n(H2O)(5-n)}X(n-1)(.)mH(2)O, where X = Cl, n = 3, and m = 6 or X = Br, n = 4, and m = 5.5. In the solid state, the (H-5[26]phen(2)N(4)O(2))(5+) cation adopts a "horseshoe" topology with sufficient room to encapsulate three or four halogen anions through the several N-(HX)-X-... hydrogen-bonding interactions. Two supermolecules {(H-5[26]phen(2)N(4)O(2))X-n(H2O)(5-n)}((5-n)+) form an interpenetrating dimeric species, which was also found by ESI mass spectrum. Binding studies of the protonated macrocycle with aliphatic (ox(2-), mal(2-), suc(2-), cit(3-), cta(3-)) and aromatic (bzc(-), naphc(-), anthc(-), pyrc(-), ph(2-), iph(2-), tph(2-), btc(3-)) anions were determined in water by potentiometric methods. These studies were complemented by H-1 NMR titrations in D2O of the receptor with selected anions. The H-i[26]phen(2)N(4)O(2)(i+) receptor can selectively uptake highly charged or extended aromatic carboxylate anions, such as btc(3-) and pyrc(-), in the pH ranges of 4.0-8.5 and < 4.0, respectively, from aqueous solution that contain the remaining anions as pollutants or contaminants. To obtain further insight into these structural and experimental findings, molecular dynamics (MD) simulations were carried out in water solution.

New dioxadiaza-, trioxadiaza- and hexaaza-macrocycles containing dibenzofuran units

New dioxadiaza-, trioxadiaza-, and hexaaza-macrocycles containing rigid dibenzofuran groups (DBF) were prepared by a convenient synthetic route in high yields. The structures of the macrocycles were unequivocally established by electrospray mass spectrometry (ESIMS) studies together with NMR spectroscopy, with the exception of [14](DBF)N-3. The structures of the copper complex of [14](DBF)N-3 and of the diprotonated form of [22](DBF)N2O3 were determined by single crystal X-ray diffraction. Conformational analyses on the free macrocycles [14](DBF)N-3 and [22](DBF)N2O3 as well as on their larger counterparts containing two DBF units were undertaken in order to understand the synthetic findings. (c) 2006 Elsevier Ltd. All rights reserved.