Unified expressions of all integral variational principles

In terms of the quantitative causal principle, this paper obtains a general variational principle, gives unified expressions of the general, Hamilton, Voss, Holder, Maupertuis-Lagrange variational principles of integral style, the invariant quantities of the general, Voss, Holder, Maupertuis-Lagrange variational principles are given, finally the Noether conservation charges of the general, Voss, Holder, Maupertuis-Lagrange variational principles axe deduced, and the intrinsic relations among the invariant quantities and the Noether conservation charges of all the integral variational principles axe achieved.

We could make a meal out of nothing: contested explanations of inequalities in health

This paper reports on the qualitative findings from a comparative study of public health and lifestyles in South East England and Northern France, regions with similar geographic and economic characteristics. Data from health surveys showed that both countries had an increasing BMI with age, particularly in Northern France. This was despite the finding that the percentage eating fresh fruit and vegetable at least five days a week in Northern France increased with age (from well over 50% to over 90%) compared to around 50% to around 75% in South East England. Qualitative data on health inequalities and how they could be addressed were gathered by focus groups sampling from five tiers using the Townsend Index for comparability (14 in England with 106 participants overall; 13 in France with 143 participants). Both had about two thirds women participants, with a preponderance of middle aged and older people. There was a striking difference in the salience of diet between the two countries; in the French data it was raised only 14 times, whereas in England there were 165 occurrences, and these were often distinguished by their use of narrative. Older respondents contrasted the pressures on families today and the expense of fresh fruit and vegetables with their own childhood or childrearing, when cheap meals could be created using skills which have now been lost. These data therefore provide further evidence that providing food is a moral activity.

Selective migration from deprived areas in Northern Ireland and the spatial distribution of inequalities: implications for monitoring health and inequalities in health

Much of the evidence suggesting that inequalities in health have been increasing over the last two decades has come from studies that compared the changes in relative health status of areas over time. Such studies ignore the movement of people between areas. This paper examines the population movement between small areas in Northern Ireland in the year prior to the 1991 census as well as the geographical distribution of migrants to Northern Ireland over the same period. It shows that deprived areas tended to become depopulated and that those who left these areas were the more affluent residents. While immigrants differed a little from the indigenous population, the overall effect of their distribution would be to maintain the geographical socio-economic status quo. The selective movement of people between areas would result in the distribution of health and ill-health becoming more polarized, i.e. produce a picture of widening inequalities between areas even though the distribution between individuals is unchanged. These processes suggest potential significant problems with the area-based approaches to monitoring health and inequalities in health.

Joint measurements and Bell inequalities

Joint quantum measurements of noncommuting observables are possible, if one accepts an increase in the measured variances. A necessary condition for a joint measurement to be possible is that a joint probability distribution exists for the measurement. This fact suggests that there may be a link with Bell inequalities, as these will be satisfied if and only if a joint probability distribution for all involved observables exists. We investigate the connections between Bell inequalities and conditions for joint quantum measurements to be possible. Mermin's inequality for the three-particle Greenberger-Horne-Zeilinger state turns out to be equivalent to the condition for a joint measurement on two out of the three quantum systems to exist. Gisin's Bell inequality for three coplanar measurement directions, meanwhile, is shown to be less strict than the condition for the corresponding joint measurement.

A variational approach to the relaxation of single domain magnetic particles based on Brown's model

Brown's model for the relaxation of the magnetization of a single domain ferromagnetic particle is considered. This model results in the Fokker-Planck equation of the process. The solution of this equation in the cases of most interest is non- trivial. The probability density of orientations of the magnetization in the Fokker-Planck equation can be expanded in terms of an infinite set of eigenfunctions and their corresponding eigenvalues where these obey a Sturm-Liouville type equation. A variational principle is applied to the solution of this equation in the case of an axially symmetric potential. The first (non-zero) eigenvalue, corresponding to the largest time constant, is considered. From this we obtain two new results. Firstly, an approximate minimising trial function is obtained which allows calculation of a rigorous upper bound. Secondly, a new upper bound formula is derived based on the Euler-Lagrange condition. This leads to very accurate calculation of the eigenvalue but also, interestingly, from this, use of the simplest trial function yields an equivalent result to the correlation time of Coffey et at. and the integral relaxation time of Garanin. (C) 2004 Elsevier B.V. All rights reserved.