Maximum principles for vectorial approximate minimisers on non-convex functionals

We establish Maximum Principles which apply to vectorial approximate minimizers of the general integral functional of Calculus of Variations. Our main result is a version of the Convex Hull Property. The primary advance compared to results already existing in the literature is that we have dropped the quasiconvexity assumption of the integrand in the gradient term. The lack of weak Lower semicontinuity is compensated by introducing a nonlinear convergence technique, based on the approximation of the projection onto a convex set by reflections and on the invariance of the integrand in the gradient term under the Orthogonal Group. Maximum Principles are implied for the relaxed solution in the case of non-existence of minimizers and for minimizing solutions of the Euler–Lagrange system of PDE.

Differential effects of dietary fatty acids on genes associated with liver fat metabolism

Background – It has been recognized that specific fatty acids have the ability to directly influence the abundance of gene transcripts in organs such as the liver. However little comparison has been made between the effects of common dietary of fatty acids and there influence on gene expression.
Objectives – To determine the effect of diets rich saturated, monounsaturated and polyunsaturated on gene transcripts associated with liver fat metabolism. Specifically how these three classes of fatty acids influence mRNA levels of key transcriptional regulators (PGC1a, PPARa, PPARd, SREBP1C & ChREBP), fat oxidative (ACO, LCPT1, HMG-CoA lyase & UCP-2) and fat synthetic (ACC, MCD, GPAT & malic enzyme) genes were investigated.
Design - Rats (n=32) were evenly divided into four groups; a saturated fat diet, a monounsaturated fat diet, a polyunsaturated fat diet (each diet contained 23% fat) and standard rat chow (7% fat) diet and fed for 12 weeks. Real-time PCR analysis was performed on liver tissue.
Outcomes – PGC1a and SREBP1C increased 1.9 fold or greater in all groups. Conversely, PPARa, PPARd and ChREBP demonstrated variable changes with diet composition. Monounsaturated and polyunsaturated fat increased HMG-CoA lyase 2.8 fold, a response that was absent in the saturated fat fed animals. UCP-2 was decrease 3.0 fold by all dietary treatments. Malic enzyme was increased 2.8 and 2.4 fold with saturated and polyunsaturated diets respectively, yet was unaltered by the monounsaturated fat diet.
Conclusion – Modifications in common dietary fat composition initiated divergent gene responses in liver. These alterations were complex, with no uniform alteration in transcription factors with closely related functions (PPARfamily) and genes encoding proteins within the same metabolic pathway (fat oxidation or fat synthesis). Further studies are necessary to identify the predominant mechanisms regulating these differences in gene expression.

Rock slope risk analysis based on non-linear failure criterion

The probability of failure of a rock slope is generally estimated by using the Limit Equilibrium Method (LEM) in conjunction with a reliability analysis. Although the LEM is relatively simple and time efficient, recent studies have indicated that using the LEM may overestimate the factor of safety by 21%, when based on a non-linear failure criterion. Fortunately, the solutions presented by Li et al. (2008, 2009) can provide more accurate evaluations for rock slope stability as the numerical upper and lower bound limit analysis methods (2002a, 2002b, 2005) were employed. The advantages of these methods are used in this study to assess the rock slope probability of failure. The motivation is that with more accurate methods to evaluate the factor of safety, more economic designs can be performed.

A prospective study of the effect of education on non-compliant behaviour in contact lens wear

The contact lens practitioner and patient present a specific case for the study of non-compliance in areas such as hygiene, solution use, appointment attendance and wearing times. Education is one of the factors thought to influence compliance among patients in general health care situations and contact lens practitioners are encouraged to educate patients in the care and maintenance of contact lenses. A prospective, randomized, controlled and double masked study was performed to assess the effect of a‘compliance enhancement strategy’ on levels of compliance among contact lens wearers over twelve months. Eighty experienced contact lens patients were randomly allocated to two experimental groups. A standard level of contact lens instruction was applied to the first group and in addition the compliance enhancement strategy was applied to patients assigned to the second group. The strategy consisted of extra education for patients using a video, booklets, posters, a checklist and a health care contract. Patients were given free supplies of RelMu multipurpose solution and Medalist 38 soft contact lenses IBausch and Lomb, Rochester. New York). Compliance levels were assessed at a twelve month aftercare appointment by demonstration and questionnaire. The results indicate that the compliance enhancement strategy had little significant effect on the compliance levels of the patients to whom it was applied. The population of contact lens wearers were generally very compliant and the contact lenses and care regimen were clinically successful. The possibility that the assessment of non–compliance was not adequately sensitive to highlight small differences in non-compliant, behaviour is discussed. The standard level of eduction applied to this sample of contact lens patients was adequate to ensure generally high levels of compliance with the simple care and maintenance regimen recommended.