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Page 1 of 3

Methods of Mathematical Physics
  • 3rd edition
  • Harold Jeffreys, Bertha Jeffreys
  • Published online:
    12 September 2018
    Print publication:
    18 November 1999
  • This well-known text and reference contains an account of those parts of mathematics that are most frequently needed in physics. As a working rule, it includes methods which have applications in at least two branches of physics. The authors have aimed at a high standard of rigour and have not accepted the often-quoted opinion that 'any argument is good enough if it is intended to be used by scientists'. At the same time, they have not attempted to achieve greater generality than is required for the physical applications: this often leads to considerable simplification of the mathematics. Particular attention is also paid to the conditions under which theorems hold. Examples of the practical use of the methods developed are given in the text: these are taken from a wide range of physics, including dynamics, hydrodynamics, elasticity, electromagnetism, heat conduction, wave motion and quantum theory. Exercises accompany each chapter.

  • Vitamin D status is associated with underweight and stunting in children aged 6–36 months residing in the Ecuadorian Andes

  • Rana R Mokhtar, Michael F Holick, Fernando Sempértegui, Jeffrey K Griffiths, Bertha Estrella, Lynn L Moore, Matthew P Fox, Davidson H Hamer
  • Journal:
    Public Health Nutrition / Volume 21 / Issue 11 / August 2018
    Published online by Cambridge University Press:
    22 November 2017, pp. 1974-1985
    • Article
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  • Objective

    There is limited knowledge on vitamin D status of children residing in the Andes and its association with undernutrition. We evaluated the vitamin D status of children residing in a low socio-economic status (SES) setting in the Ecuadorian Andes and assessed the association between vitamin D status, stunting and underweight. We hypothesized that children who were underweight would have lower serum 25-hydroxyvitamin D (25(OH)D) levels and lower 25(OH)D levels would be associated with a higher risk of stunting.

    Design

    We conducted a cross-sectional secondary analysis of a randomized controlled trial, the Vitamin A, Zinc and Pneumonia study. Children had serum 25(OH)D concentrations measured. A sensitivity analysis was undertaken to determine a vitamin D cut-off specific for our endpoints. Associations between serum 25(OH)D and underweight (defined as weight-for-age Z-score≤−1) and stunting (defined as height-for-age Z-score≤−2) were assessed using multivariate logistic regression.

    Setting

    Children residing in five low-SES peri-urban neighbourhoods near Quito, Ecuador.

    Subjects

    Children (n 516) aged 6–36 months.

    Results

    Mean serum 25(OH)D concentration was 58·0 (sd 17·7) nmol/l. Sensitivity analysis revealed an undernutrition-specific 25(OH)D cut-off of <42·5 nmol/l; 18·6 % of children had serum 25(OH)D<42·5 nmol/l. Children who were underweight were more likely to have serum 25(OH)D<42·5 nmol/l (adjusted OR (aOR)=2·0; 95 % CI 1·2, 3·3). Children with low serum 25(OH)D levels were more likely to be stunted (aOR=2·8; 95 % CI 1·6, 4·7).

    Conclusions

    Low serum 25(OH)D levels were more common in underweight and stunted Ecuadorian children.

  • Metabolic syndrome in the elderly living in marginal peri-urban communities in Quito, Ecuador

  • Fernando Sempértegui, Bertha Estrella, Katherine L Tucker, Davidson H Hamer, Ximena Narvaez, Mercy Sempértegui, Jeffrey K Griffiths, Sabrina E Noel, Gerard E Dallal, Jacob Selhub, Simin N Meydani
  • Journal:
    Public Health Nutrition / Volume 14 / Issue 5 / 15 April 2011
    Published online by Cambridge University Press:
    19 October 2010, pp. 758-767
    • Article
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  • Objective

    The proportion of the Latin American population aged >60 years is expected to double during the next few decades. Metabolic syndrome (MetS) is associated with high morbidity and mortality worldwide. However, little is known about MetS in Latin America in general, and in Ecuador in particular. The present study aimed to examine the prevalence of MetS and its association with blood micronutrient, homocysteine (Hcy) and C-reactive protein (CRP) concentrations in the elderly living in a low-income urban area.

    Design

    We performed a cross-sectional study. MetS, using the International Diabetes Federation definition, dietary intake and plasma micronutrient, CRP and Hcy concentrations were assessed.

    Subjects

    A total of 352 elderly (≥65 years) Ecuadorians.

    Setting

    Quito, Ecuador.

    Results

    MetS was prevalent (40 %) – considerably more so among women (81 %) than men (19 %; χ2 = 32·6, P < 0·0001). Further, 53 % of those without MetS exhibited two or more of its components. Micronutrient deficiencies were prevalent, including those of vitamin C, zinc, vitamin B12 and folate. Vitamin C and E concentrations were inversely (OR = 0·78, 95 % CI 0·71, 0·86; OR = 0·16, 95 % CI 0·03, 0·81, respectively) and CRP (OR = 1·79, 95 % CI 1·04, 3·06) was positively associated with MetS.

    Conclusions

    The coexistence of MetS with micronutrient deficiencies suggests that elderly Ecuadorians suffer from the double burden of diseases that are increasingly being observed in less developed countries. More research is needed to determine the causal factors, but results presented suggest that these older adults would benefit from interventions to reduce the risk factors for MetS, in particular higher consumption of micronutrient-rich foods.

  • Appendix on Notation

  • Harold Jeffreys, University of Cambridge and St John's College, Cambridge, Bertha Jeffreys, Girton College, Cambridge
  • Book:
    Methods of Mathematical Physics
    Published online:
    12 September 2018
    Print publication:
    18 November 1999, pp 706-710

  • Summary

    The difficulty of learning mathematical physics is much increased by confusion of notation, especially the overworking of certain letters and the introduction of awkward sign conventions. The only criterion usually recognized is conformity with ‘standard practice’. Unfortunately standard practice is not unique and students are put to much unnecessary trouble by having to accustom themselves to work with different conventions in rapid succession. Research workers in border-line subjects are also inconvenienced by finding the usual symbols in one subject pre-empted for different meanings in another.

    The following principles are important in choosing conventions:

  • (1) Complications should be reduced to a minimum. Negative signs should not be introduced without good reason.

  • (2) Genuine physical differences should be recognized as such and not disguised as conventions; attempts to disguise them always lead to later difficulties that should have been forestalled.

  • (3) Where a mathematical theory has applications in several subjects the notation should be such that it can be carried over into those subjects unchanged; so far as possible it should not use symbols already used with other meanings in those subjects.

    • The outstanding difficulty of notation at present is the ambiguous use of Y and φ. V is used for potential energy, which is a property of a complete system, but also for the various potential functions, which are functions of position within the system. It is also used for Hamilton's characteristic function, and, in hydrodynamics, for a component of the velocity at a great distance.

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