A discrete approach to Wirtinger's inequality

Considering Wirtinger's inequality for piece-wise equipartite functions we find a discrete version of this classical inequality. The main tool we use is the theorem of classification of isometries. Our approach provides a new elementary proof of Wirtinger's inequality that also allows to study the case of equality. Moreover it leads in a natural way to the Fourier series development of $2\pi$-periodic functions.Comment: 9 page

A note on a result of Saks and Zygmund on additive functions of rectangles

We modify the proof of the basic lemma of a paper of Saks and Zygmund on additive functions of rectangles

On the angular limits of Bloch functions

This paper contains a method to associate to each function f in the little Bloch space another function f* in the Bloch space in such way that f has a finite angular limit where f* is radially bounded. The idea of the method comes from the theory of the lacunary series. An application to conformal mapping from the unit disc to asymptotically Jordan domains is given

Integration of optical and acoustic sensors for D underwater scene reconstruction.

Combination of optical and acoustic sensors to overcome the shortcomings presented by optical systems in underwater 3D acquisition is an emerging field of research. In this work, an opti-acoustic system composed by a single camera and a multibeam sonar is proposed, providing a simulation environment to validate its potential use in 3D reconstruction. Since extrinsic calibration is a prerequisite for this kind of feature-level sensor fusion, an effective approach to address the calibration problem between a multibeam and a camera system is presented.Peer Reviewe

Existence of principal values of some singular integrals on Cantor sets, and Hausdorff dimension

Consider a standard Cantor set in the plane of Hausdorff dimension 1. If the linear density of the associated measure $\mu$ vanishes, then the set of points where the principal value of the Cauchy singular integral of $\mu$ exists has Hausdorff dimension 1. The result is extended to Cantor sets in $\mathbb{R}^d$ of Hausdorff dimension $\alpha$ and Riesz singular integrals of homogeneity $-\alpha$, 0 < $\alpha$ < d : the set of points where the principal value of the Riesz singular integral of $\mu$ exists has Hausdorff dimension $\alpha$. A martingale associated with the singular integral is introduced to support the proof.Comment: 14 pages, minor revision after the referee's report, to appear in Pacific J. of Mat

Effectiveness of Statins as Primary Prevention in People With Different Cardiovascular Risk: A Population-Based Cohort Study

The purpose was to analyze statin effectiveness in a general population with differing levels of coronary heart disease (CHD) risk. Patients (35-74 years) without previous cardiovascular disease were included and stratified according to 10-year CHD risk ( < 5%, 5-7.4%, 7.5-9.9%, and 10-19.9%). New users were categorized according to their medical possession ratio (MPR). The main outcome was atherosclerotic cardiovascular disease (ASCVD) (myocardial infarction and ischemic stroke). In adherent patients (MPR 70%), statin treatment decreased ASCVD risk across the range of coronary risk (from 16-30%). The 5-year number needed to treat (NNT) was 470 and 204 in the risk categories < 5% and 5-7.4%, respectively, and 75 and 62 in the 7.5-9.9% category than in the 10-19.9% category, respectively. Statin therapy should remain a priority in patients at high 10-year CHD risk (10-19.9%). Most patients with intermediate risk could benefit from statin treatment, but the treatment decision should focus on the net benefit, safety, and patient preference, given the higher NNT

Different fatty acid metabolism effects of (−)-epigallocatechin-3-gallate and C75 in adenocarcinoma lung cancer

Background Fatty acid synthase (FASN) is overexpressed and hyperactivated in several human carcinomas, including lung cancer. We characterize and compare the anti-cancer effects of the FASN inhibitors C75 and (−)-epigallocatechin-3-gallate (EGCG) in a lung cancer model. Methods We evaluated in vitro the effects of C75 and EGCG on fatty acid metabolism (FASN and CPT enzymes), cellular proliferation, apoptosis and cell signaling (EGFR, ERK1/2, AKT and mTOR) in human A549 lung carcinoma cells. In vivo, we evaluated their anti-tumour activity and their effect on body weight in a mice model of human adenocarcinoma xenograft. Results C75 and EGCG had comparable effects in blocking FASN activity (96,9% and 89,3% of inhibition, respectively). In contrast, EGCG had either no significant effect in CPT activity, the rate-limiting enzyme of fatty acid β-oxidation, while C75 stimulated CPT up to 130%. Treating lung cancer cells with EGCG or C75 induced apoptosis and affected EGFR-signaling. While EGCG abolished p-EGFR, p-AKT, p-ERK1/2 and p-mTOR, C75 was less active in decreasing the levels of EGFR and p-AKT. In vivo, EGCG and C75 blocked the growth of lung cancer xenografts but C75 treatment, not EGCG, caused a marked animal weight loss. Conclusions In lung cancer, inhibition of FASN using EGCG can be achieved without parallel stimulation of fatty acid oxidation and this effect is related mainly to EGFR signaling pathway. EGCG reduce the growth of adenocarcinoma human lung cancer xenografts without inducing body weight loss. Taken together, EGCG may be a candidate for future pre-clinical development

Epithelial to Mesenchymal Transition by TGFβ-1 Induction Increases Stemness Characteristics in Primary Non Small Cell Lung Cancer Cell Line

Cancer Stem Cells (CSCs) hypothesis asserts that only a small subset of cells within a tumour is capable of both tumour initiation and sustainment. The Epithelial-Mesenchymal Transition (EMT) is an embryonic developmental program that is often activated during cancer invasion and metastasis. The aim of this study is to shed light on the relationship between EMT and CSCs by using LC31 lung cancer primary cell line.A549 and LC31 cell lines were treated with 2 ng/ml TGFβ-1 for 30 days, and 80 days, respectively. To evaluate EMT, morphological changes were assessed by light microscopy, immunofluorescence and cytometry for following markers: cytokeratins, e-cadherin, CD326 (epithelial markers) and CD90, and vimentin (mesenchymal markers). Moreover, RT-PCR for Slug, Twist and β-catenin genes were performed. On TGFβ-1 treated and untreated LC31 cell lines, we performed stemness tests such as pneumospheres growth and stem markers expression such as Oct4, Nanog, Sox2, c-kit and CD133. Western Blot for CD133 and tumorigenicity assays using NOD/SCID mice were performed.TGFβ-1 treated LC31 cell line lost its epithelial morphology assuming a fibroblast-like appearance. The same results were obtained for the A549 cell line (as control). Immunofluorescence and cytometry showed up-regulation of vimentin and CD90 and down-regulation of cytocheratin, e-cadherin and CD326 in TGFβ-1 treated LC31 and A549 cell lines. Slug, Twist and β-catenin m-RNA transcripts were up-regulated in TGFβ-1 treated LC31 cell line confirming EMT. This cell line showed also over-expression of Oct4, Nanog, Sox2 and CD133, all genes of stemness. In addition, in TGFβ-1 treated LC31 cell line, an increased pneumosphere-forming capacity and tumours-forming ability in NOD/SCID mice were detectable.The induction of EMT by TGFβ-1 exposure, in primary lung cancer cell line results in the acquisition of mesenchymal profile and in the expression of stem cell markers