Quantities, units and symbols in physical chemistry, 3rd edition

The first IUPAC Manual of Symbols and Terminology for Physicochemical Quantities and Units (the Green Book) of which this is the direct successor, was published in 1969, with the object of 'securing clarity and precision, and wider agreement in the use of symbols, by chemists in different countries, among physicists, chemists and engineers, and by editors of scientific journals'. Subsequent revisions have taken account of many developments in the field, culminating in the major extension and revision represented by the 1988 edition under the simplified title Quantities, Units and Symbols in Physical Chemistry. This 2007, third edition, is a further revision of the material which reflects the experience of the contributors with the previous editions. The book has been systematically brought up to date and new sections have been added. It strives to improve the exchange of scientific information among the readers in different disciplines and across different nations. In a rapidly expanding volume of scientific literature where each discipline has a tendency to retreat into its own jargon this book attempts to provide a readable compilation of widely used terms and symbols from many sources together with brief understandable definitions. This is the definitive guide for scientists and organizations working across a multitude of disciplines requiring internationally approved nomenclature.

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.

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.

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).

Benchmarking or business opportunity: Using milk recording data to expose your clients' weaknesses

Routine milk recording data, often covering many years, are available for approximately half the dairy herds of England and Wales. In addition to milk yield and quality, these data include production events that can be used to derive objective Key Performance Indicators (KPI) describing a herd's fertility and production. Recent developments in information systems give veterinarians and other technical advisers access to these KPIs on-line. In addition to reviewing individual herd performance, advisers can establish local benchmark groups to demonstrate the relative performance of similar herds in the vicinity. The use of existing milk recording data places no additional demands on farmer's time or resources. These developments could also readily be exploited by universities to introduce veterinary undergraduates to the realities of commercial dairy production.