Colour is an important quality attribute in the food and bioprocess industries, and it influences consumer’s choice and preferences. Food colour is governed by the chemical, biochemical, microbial and physical changes which occur during growth, maturation, postharvest handling and processing. Colour measurement of food products has been used as an indirect measure of other quality attributes such as flavour and contents of pigments because it is simpler, faster and correlates well with other physicochemical properties. This review discusses the techniques and procedures for the measurement and analysis of colour in food and other biomaterial materials. It focuses on the instrumental (objective) and visual (subjective) measurements for quantifying colour attributes and highlights the range of primary and derived objective colour indices used to characterise the maturity and quality of a wide range of food products and beverages. Different approaches applied to model food colour are described, including reaction mechanisms, response surface methodology and others based on probabilistic and non-isothermal kinetics. Colour is one of the most widely measured product quality attributes in postharvest handling and in the food processing research and industry. Apart from differences in instrumentation, colour measurements are often reported based on different colour indices even for the same product, making it difficult to compare results in the literature. There is a need for standardisation to improve the traceability and transferability of measurements. The correlation between colour and other sensory quality attributes is well established, but future prospects exist in the application of objective non-destructive colour measurement in predictive modelling of the nutritional quality of fresh and processed food products.

Colour Measurement and Analysis in Fresh and Processed Foods: A Review

A Glimpse at Set Theory. The Real Numbers. The Topology of Cartesian Spaces. Convergence. Continuous Functions. Functions of One Variable. Infinite Series. Differentiation in RP Integration in RP.

The elements of real analysis (2nd edition), by Robert G. Bartle. Pp xv, 480. £10. 1976. SBM 0 471 05464 X (Wiley)

* Preliminaries* Numbers* Sequences and series* Limits and continuity* Differentiation* The elementary transcendental functions* Integration* Infinite series and infinite products* Trigonometric series* Bibliography* Other works by the author* Index

An introduction to classical real analysis, by Karl R. Stromberg. Pp 575. $29·95. 1981. ISBN 0-534-98012-0 (Wadsworth)

Introduction to real analysis

How Many People Can the Earth Support? By Joel E. Cohen. Norton: 1995. Pp. 532. $30, £22.50. UK publication date, 27 March.

Book of numbers

Lebesgue measure Measurable functions The Lebesgue integral Bounded variation and absolute continuity Darboux and Baire class one functions Functions of generalized bounded variation The Denjoy integral The Perron integral The Henstock integral The McShane integral Equivalence of integrals Integration by parts Convergence theorems Approximate derivatives The Khintchine integral The approximately continuous Henstock integral The approximately continuous Perron integral Solutions to exercises References Notation index Subject index

The Integrals of Lebesgue, Denjoy, Perron, and Henstock

It was noted in [1] that if a is any positive number other than 1, the tangent line to the curve y = ax at the point (/ In a, e) goes through the origin. The interesting feature here is that the y-coordinate is independent of a. We will show that this result is not as unique as it initially appears; there are many families of curves whose tangent lines at a fixed y-coordinate go through the origin. Shifting attention to the x-coordinate, it turns out that families of curves whose tangent lines at a fixed x-coordinate go through the origin have some interesting properties. In particular, these functions form the kernel of a linear transformation. The tangent line to a differentiable function f at the point (c, f(c)) with c :i 0 goes through the origin if and only if f'(c) = f(c)/c. By shifting, scaling, and tilting a given graph, it is possible to make the modified graph have a tangent line go through the origin at any given value of x or y. These geometric operations on a graph can be performed by modifying the original function by linear factors. This is the main idea used in the next paragraph. Let (a, b) be an open interval that contains the number 1. Suppose that f is differentiable and strictly increasing on (a, b) and that f'(1) < e. (There is nothing special about the choice of the numbers 1 and e; they could be replaced with any positive real numbers.) For each c :f 0, define a function gc on the open interval with endpoints ca and cb by

http://www.jstor.org/stable/pdfplus/3595849.pdf

Off on a Tangent

/pdf/the-mcshane-integral-of-banach-valued-functions-ebimzygbwe.pdf

The mcShane integral of Banach-valued functions

/pdf/the-denjoy-extension-of-the-bochner-pettis-and-dunford-21tj3g54e3.pdf

The Denjoy extension of the Bochner, Pettis, and Dunford integrals

(1998). The Use of Tagged Partitions in Elementary Real Analysis. The American Mathematical Monthly: Vol. 105, No. 2, pp. 107-117.

Russell A. Gordon

Papers

The Integrals of Lebesgue, Denjoy, Perron, and Henstock

Off on a Tangent

The mcShane integral of Banach-valued functions

The Denjoy extension of the Bochner, Pettis, and Dunford integrals

The Use of Tagged Partitions in Elementary Real Analysis