The continuity of the inversion and the structure of maximal subgroups in countably compact topological semigroups

In this paper we search for conditions on a countably compact (pseudo-compact) topological semigroup under which: (i) each maximal subgroup $H(e)$ in $S$ is a (closed) topological subgroup in $S$; (ii) the Clifford part $H(S)$(i.e. the union of all maximal subgroups) of the semigroup $S$ is a closed subset in $S$; (iii) the inversion $\operatorname{inv}\colon H(S)\to H(S)$ is continuous; and (iv) the projection $\pi\colon H(S)\to E(S)$, $\pi\colon x\longmapsto xx^{-1}$, onto the subset of idempotents $E(S)$ of $S$, is continuous

Drinking Water Salinity and Raised Blood Pressure: Evidence from a Cohort Study in Coastal Bangladesh.

BACKGROUND: Millions of coastal inhabitants in Southeast Asia have been experiencing increasing sodium concentrations in their drinking-water sources, likely partially due to climate change. High (dietary) sodium intake has convincingly been proven to increase risk of hypertension; it remains unknown, however, whether consumption of sodium in drinking water could have similar effects on health. OBJECTIVES: We present the results of a cohort study in which we assessed the effects of drinking-water sodium (DWS) on blood pressure (BP) in coastal populations in Bangladesh. METHODS: DWS, BP, and information on personal, lifestyle, and environmental factors were collected from 581 participants. We used generalized linear latent and mixed methods to model the effects of DWS on BP and assessed the associations between changes in DWS and BP when participants experienced changing sodium levels in water, switched from "conventional" ponds or tube wells to alternatives [managed aquifer recharge (MAR) and rainwater harvesting] that aimed to reduce sodium levels, or experienced a combination of these changes. RESULTS: DWS concentrations were highly associated with BP after adjustments for confounding factors. Furthermore, for each 100 mg/L reduction in sodium in drinking water, systolic/diastolic BP was lower on average by 0.95/0.57 mmHg, and odds of hypertension were lower by 14%. However, MAR did not consistently lower sodium levels. CONCLUSIONS: DWS is an important source of daily sodium intake in salinity-affected areas and is a risk factor for hypertension. Considering the likely increasing trend in coastal salinity, prompt action is required. Because MAR showed variable effects, alternative technologies for providing reliable, safe, low-sodium fresh water should be developed alongside improvements in MAR and evaluated in "real-life" salinity-affected settings. https://doi.org/10.1289/EHP659

BRCA2 polymorphic stop codon K3326X and the risk of breast, prostate, and ovarian cancers

Background: The K3326X variant in BRCA2 (BRCA2*c.9976A>T; p.Lys3326*; rs11571833) has been found to be associated with small increased risks of breast cancer. However, it is not clear to what extent linkage disequilibrium with fully pathogenic mutations might account for this association. There is scant information about the effect of K3326X in other hormone-related cancers. Methods: Using weighted logistic regression, we analyzed data from the large iCOGS study including 76 637 cancer case patients and 83 796 control patients to estimate odds ratios (ORw) and 95% confidence intervals (CIs) for K3326X variant carriers in relation to breast, ovarian, and prostate cancer risks, with weights defined as probability of not having a pathogenic BRCA2 variant. Using Cox proportional hazards modeling, we also examined the associations of K3326X with breast and ovarian cancer risks among 7183 BRCA1 variant carriers. All statistical tests were two-sided. Results: The K3326X variant was associated with breast (ORw = 1.28, 95% CI = 1.17 to 1.40, P = 5.9x10- 6) and invasive ovarian cancer (ORw = 1.26, 95% CI = 1.10 to 1.43, P = 3.8x10-3). These associations were stronger for serous ovarian cancer and for estrogen receptor–negative breast cancer (ORw = 1.46, 95% CI = 1.2 to 1.70, P = 3.4x10-5 and ORw = 1.50, 95% CI = 1.28 to 1.76, P = 4.1x10-5, respectively). For BRCA1 mutation carriers, there was a statistically significant inverse association of the K3326X variant with risk of ovarian cancer (HR = 0.43, 95% CI = 0.22 to 0.84, P = .013) but no association with breast cancer. No association with prostate cancer was observed. Conclusions: Our study provides evidence that the K3326X variant is associated with risk of developing breast and ovarian cancers independent of other pathogenic variants in BRCA2. Further studies are needed to determine the biological mechanism of action responsible for these associations

The translational hull of a topological semigroup

This paper is concerned with three aspects of the study of topological versions of the translational hull of a topological semigroup. These include topological properties, applications to the general theory of topological semigroups, and techniques for computing the translational hull. The central result of this paper is that if S is a compact reductive topological semigroup and its translational hull &(£) is given the topology of continuous convergence (which coincides with the topology of pointwise convergence and the compact- open topology in this case), then £l(S) is again a compact topological semigroup. Results pertaining to extensions of bitranslations are given, and applications of these together with the central result to semigroup compactifications and divisibility are presented. Techniques for determining the translational hull of certain types of topological semigroups, along with numerous examples, are set forth in the final section. © 1976 American Mathematical Society

On the multilinear Hausdorff problem of moments

Given a multi-index sequence necessary and sufficient conditions are given for the existence of a regular Borel polymeasure on the unit interval such that . This problem will be called the weak multilinear Hausdorff problemof moments for . Comparison with classical results will allow us to relate the weak multilinear Hausdorff problem with the multivariate Hausdorff problem. A solution to the strong multilinear Hausdorff problem of moments will be provided by exhibiting necessary and sufficient conditions for the existence of a Radon measure on such that where is the -linear moment functional on the space of continuous functions on the unit interval defined by the sequence . Finally the previous results will be used to provide a characterization of a class of weakly harmonizable stochastic processes with bimeasures supported on compact sets