Solving the brachistochrone and other variational problems with soap films

We show a method to solve the problem of the brachistochrone as well as other variational problems with the help of the soap films that are formed between two suitable surfaces. We also show the interesting connection between some variational problems of dynamics, statics, optics, and elasticity.Comment: 16 pages, 11 figures. This article, except for a small correction, has been submitted to the American Journal of Physic

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

Topological monoids of monotone injective partial selfmaps of N\mathbb{N} with cofinite domain and image

In this paper we study the semigroup $\mathscr{I}_{\infty}^{\nearrow}(\mathbb{N})$ of partial cofinal monotone bijective transformations of the set of positive integers $\mathbb{N}$. We show that the semigroup $\mathscr{I}_{\infty}^{\nearrow}(\mathbb{N})$ has algebraic properties similar to the bicyclic semigroup: it is bisimple and all of its non-trivial group homomorphisms are either isomorphisms or group homomorphisms. We also prove that every locally compact topology $\tau$ on $\mathscr{I}_{\infty}^{\nearrow}(\mathbb{N})$ such that $(\mathscr{I}_{\infty}^{\nearrow}(\mathbb{N}),\tau)$ is a topological inverse semigroup, is discrete. Finally, we describe the closure of $(\mathscr{I}_{\infty}^{\nearrow}(\mathbb{N}),\tau)$ in a topological semigroup

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

Diagnostic Value of Lumbar Facet Joint Injection: A Prospective Triple Cross-Over Study

The diagnosis “lumbar facet syndrome” is common and often indicates severe lumbar spine surgery procedures. It is doubtful whether a painful facet joint (FJ) can be identified by a single FJ block. The aim of this study was to clarify the validity of a single and placebo controlled bilateral FJ blocks using local anesthetics. A prospective single blinded triple cross-over study was performed. 60 patients (31 f, 29 m, mean age 53.2 yrs (22–73)) with chronic low back pain (mean pain persistance 31 months, 6 months of conservative treatment without success) admitted to a local orthopaedic department for surgical or conservative therapy of chronic LBP, were included in the study. Effect on pain reduction (10 point rating scale) was measured. The 60 subjects were divided into six groups with three defined sequences of fluoroscopically guided bilateral monosegmental lumbar FJ test injections in “oblique needle” technique: verum-(local anaesthetic-), placebo-(sodium chloride-) and sham-injection. Carry-over and periodic effects were evaluated and a descriptive and statistical analysis regarding the effectiveness, difference and equality of the FJ injections and the different responses was performed. The results show a high rate of non-response, which documents the lack of reliable and valid predictors for a positive response towards FJ blocks. There was a high rate of placebo reactions noted, including subjects who previously or later reacted positively to verum injections. Equivalence was shown among verum vs. placebo and partly vs. sham also. With regard to test validity criteria, a single intraarticular FJ block with local anesthetics is not useful to detect the pain-responsible FJ and therefore is no valid and reliable diagostic tool to specify indication of lumbar spine surgery. Comparative FJ blocks with local anesthetics and placebo-controls have to be interpretated carefully also, because they solely give no proper diagnosis on FJ being main pain generator

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 Distribution of Oceangoing Canoes on the North Coast of California

In 1968, Richard Gould presented ethnographic evidence that certain canoes were specifically made for ocean navigation among native groups along California's northern coast. In his paper, "Seagoing Canoes Among The Indians Of Northwestern California," he postulated that oceangoing canoes did in fact exist, contrary to doubt expressed by certain scholars (Gould 1968:11-13). He further provided detailed information regarding their manufacture and physical/functional characteristics. This paper is an attempt to clarify certain points not thoroughly addressed by Gould and, subsequently, broaden the scope of his study. Three lines of evidence will be examined concerning the distribution of oceangoing canoes in an effort to define their southern geographical and cultural boundaries. Using this evidence, a descriptive model will be developed to characterize the occurrence of canoes used on the ocean along the north coast