Monotonically normal topological vector spaces are stratifiable

We prove that for any Hausdorff topological vector space E over the field R there exists A subset of E such that E is homeomorphic to a subset of A x R and A x R is homeomorphic to a subset of E. Using this fact we prove that E is monotonically normal if and only if E is stratifiable.

Decay measures on locally compact abelian topological groups

Source: PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS Volume: 131 Pages: 1257-1273 Part: Part 6 Published: 2001 Times Cited: 5 References: 23 Citation MapCitation Map beta Abstract: We show that the Banach space M of regular sigma-additive finite Borel complex-valued measures on a non-discrete locally compact Hausdorff topological Abelian group is the direct sum of two linear closed subspaces M-D and M-ND, where M-D is the set of measures mu is an element of M whose Fourier transform vanishes at infinity and M-ND is the set of measures mu is an element of M such that nu is not an element of MD for any nu is an element of M \ {0} absolutely continuous with respect to the variation \mu\. For any corresponding decomposition mu = mu(D) + mu(ND) (mu(D) is an element of M-D and mu(ND) is an element of M-ND) there exist a Borel set A = A(mu) such that mu(D) is the restriction of mu to A, therefore the measures mu(D) and mu(ND) are singular with respect to each other. The measures mu(D) and mu(ND) are real if mu is real and positive if mu is positive. In the case of singular continuous measures we have a refinement of Jordan's decomposition theorem. We provide series of examples of different behaviour of convolutions of measures from M-D and M-ND.

Universal Abelian topological groups

A topological group G is said to be universal in a class K of topological groups if G is an element of K and if for every group H is an element of K there is a subgroup K of G that is isomorphic to H as a topological group. A group is constructed that is universal in the class of separable metrizable topological Abelian groups.

Dietary glycaemic index, glycaemic load and breast cancer risk: a systematic review and meta-analysis

This systematic review aimed to examine if an association exists between dietary glycaemic index (GI) and glycaemic load (GL) intake and breast cancer risk. A systematic search was conducted in Medline and Embase and identified 14 relevant studies up to May 2008. Adjusted relative risk estimates comparing breast cancer risk for the highest versus the lowest category of GI/GL intake were extracted from relevant studies and combined in meta-analyses using a random-effects model. Combined estimates from six cohort studies show non-significant increased breast cancer risks for premenopausal women (relative risk (RR) 1.14, 95% CI 0.95-1.38) and postmenopausal women (RR 1.11, 95% CI 0.99-1.25) consuming the highest versus the lowest category of GI intake. Evidence of heterogeneity hindered analyses of GL and premenopausal risk, although most studies did not observe any significant association. Pooled cohort study results indicated no association between postmenopausal risk and GL intake (RR 1.03, 95% CI 0.94-1.12). Our findings do not provide strong support of an association between dietary GI and GL and breast cancer risk. © 2008 Cancer Research UK.


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Glycemic index, glycemic load, and risk of digestive tract neoplasms: a systematic review and meta-analysis

Background: Habitual consumption of diets with a high glycemic index (GI) and a high glycemic load (GL) may influence cancer risk via hyperinsulinemia and the insulin-like growth factor axis.
Objective: The objective was to conduct a systematic review to assess the association between GI, GL, and risk of digestive tract cancers.
Design: Medline and Embase were searched for relevant publications from inception to July 2008. When possible, adjusted results from a comparison of cancer risk of the highest compared with the lowest category of GI and GL intake were combined by using random-effects meta-analyses.
Results: Cohort and case-control studies that examined the risk between GI or GL intake and colorectal cancer (n = 12) and adenomas (n = 2), pancreatic cancer (n = 6), gastric cancer (n = 2), and squamous-cell esophageal carcinoma (n = 1) were retrieved. Most case-control studies observed positive associations between GI and GL intake and these cancers. However, pooled cohort study results showed no associations between colorectal cancer risk and GI intake [relative risk (RR): 1.04; 95% CI: 0.92, 1.12; n = 7 studies] or GL intake (RR: 1.06; 95% CI: 0.95, 1.17; n = 8 studies). Furthermore, no significant associations were observed in meta-analyses of cohort study results of colorectal cancer subsites and GI and GL intake. Similarly, no significant associations emerged between pancreatic cancer risk and GI intake (RR: 0.99; 95% CI: 0.83, 1.19; n = 5 studies) or GL intake (RR: 1.01; 95% CI: 0.86, 1.19; n = 6 studies) in combined cohort studies.
Conclusions: The findings from our meta-analyses indicate that GI and GL intakes are not associated with risk of colorectal or pancreatic cancers. There were insufficient data available regarding other digestive tract cancers to make any conclusions about GI or GL intake and risk.

Glycemic index, carbohydrate and fiber intakes and risk of reflux esophagitis, Barrett’s esophagus, and esophageal adenocarcinoma

Objective: To examine the association between dietary glycemic index (GI), glycemic load (GL), total carbohydrate, sugars, starch, and fiber intakes and the risk of reflux esophagitis, Barrett’s esophagus, and esophageal adenocarcinoma.

Methods: In an all-Ireland study, dietary information was collected from patients with esophageal adenocarcinoma (n = 224), long-segment Barrett’s esophagus (n = 220), reflux esophagitis (n = 219), and population-based controls (n = 256). Multiple logistic regression analysis examined the association between dietary variables and disease risk by tertiles of intake and as continuous variables, while adjusting for potential confounders.

Results: Reflux esophagitis risk was positively associated with starch intake and negatively associated with sugar intake. Barrett’s esophagus risk was significantly reduced in people in the highest versus the lowest tertile of fiber intake (OR 0.44 95%CI 0.25–0.80). Fiber intake was also associated with a reduced risk of esophageal adenocarcinoma, as was total carbohydrate intake (OR 0.45 95%CI 0.33–0.61 per 50 g/d increase). However, an increased esophageal adenocarcinoma risk was detected per 10 unit increase in GI intake (OR 1.42 95%CI 1.07–1.89).

Conclusions: Our findings suggest that fiber intake is inversely associated with Barrett’s esophagus and esophageal adenocarcinoma risk. Esophageal adenocarcinoma risk is inversely associated with total carbohydrate consumption but positively associated with high GI intakes.

Index of sources of stress in nursing students: a confirmatory factor analysis.

Aim. This paper is a report of a study to test the proposed factor structure of the Index of Sources of Stress in Nursing Students. Background. Research across many countries has identified a number of sources of distress in nursing students but little attempt has been made to understand and measure sources of eustress or those stressors likely to enhance performance and well-being. The Index of Sources of Stress in Nursing Students was developed to do this. Exploratory factor analysis suggested a three-factor structure, the factors being labelled: learning and teaching; placement-related and course organization. It is important, however, to subject the instrument to confirmatory factor analysis as a further test of construct validity. Method. A convenience sample of final year nursing students (n = 176) was surveyed in one university in Northern Ireland in 2007. The Index of Sources of Stress in Nursing Students, which measures sources of stress likely to contribute to distress and eustress, was completed electronically. The LISREL programme was used to carry out the confirmatory factor analysis and test the factor structure suggested in the exploratory analysis. Findings. The proposed factor structure for the items measuring ‘Uplifts’ proved to be a good fit to the data and the proposed factor structure for the items measuring ‘Hassles’ showed adequate fit. Conclusion. In nursing programmes adopting the academic model and combining university-based learning with placement experience, this instrument can be used to help identify the sources of stress or course demands that students rate as distressing and those that help them to achieve. The validity of the ISSN could be further evaluated in other education settings.