Cauchy integral and singular integral operator over closed Jordan curves

This paper is mostly a review paper. It contains a description of old and recent results concerning the regularity conditions on a Jordan curve in the plane that imply the boundedness of the singular integral operator as well as the boundary behavior of the Cauchy type integral. These results are of significance for boundary value problems in domains with non-smooth and non-rectifiable boundaries. © 2014 Springer-Verlag Wien

Cauchy integral and singular integral operator over closed Jordan curves

© Springer-Verlag Wien 2014. This paper is mostly a review paper. It contains a description of old and recent results concerning the regularity conditions on a Jordan curve in the plane that imply the boundedness of the singular integral operator as well as the boundary behavior of the Cauchy type integral. These results are of significance for boundary value problems in domains with non-smooth and non-rectifiable boundaries

Integration over non-rectifiable curves and Riemann boundary value problems

In this paper we introduce an alternative way of defining the curvilinear Cauchy integral over non-rectifiable curves in the case of complex functions of one complex variable. Especially the jump behavior on the boundary is considered. As an application, solvability conditions of the Riemann boundary value problem are derived on very weak conditions to the boundary. Besides the complex case the consideration can be extended to the theory of Douglis algebra valued functions. © 2011 Elsevier Inc

Evaluating eHealth: Undertaking Robust International Cross-Cultural eHealth Research

David Bates and Adam Wright discuss the opportunities and challenges of undertaking international collaborations in eHealth evaluation research, and make recommendations for moving forward

Deletion and Down-Regulation of HRH4 Gene in Gastric Carcinomas: A Potential Correlation with Tumor Progression

Background: Histamine is an established growth factor for gastrointestinal malignancies. The effect of histamine is largely determined locally by the histamine receptor expression pattern. Histamine receptor H4 (HRH4), the newest member of the histamine receptor family, is positively expressed on the epithelium of the gastrointestinal tract, and its function remains to be elucidated. Previously, we reported the decreased expression of HRH4 in colorectal cancers and revealed its correlation with tumor proliferation. In the current study, we aimed to investigate the abnormalities of HRH4 gene in gastric carcinomas (GCs). Methodology/Principal Findings: We analyzed H4R expression in collected GC samples by quantitative PCR, Western blot analysis, and immunostaining. Our results showed that the protein and mRNA levels of HRH4 were reduced in some GC samples, especially in advanced GC samples. Copy number decrease of HRH4 gene was observed (17.6%, 23 out of 131), which was closely correlated with the attenuated expression of H4R. In vitro studies, using gastric cancer cell lines, showed that the alteration of HRH4 expression on gastric cancer cells influences tumor growth upon exposure to histamine. Conclusions/Significance: We show for the first time that deletion of HRH4 gene is present in GC cases and is closely correlated with attenuated gene expression. Down-regulation of HRH4 in gastric carcinomas plays a role in histaminemediate

Benign follicular tumors

Benign follicular tumors comprise a large and heterogeneous group of neoplasms that share a common histogenesis and display morphological features resembling one or several portions of the normal hair follicle, or recapitulate part of its embryological development. Most cases present it as clinically nondescript single lesions and essentially of dermatological relevance. Occasionally, however, these lesions be multiple and represent a cutaneous marker of complex syndromes associated with an increased risk of visceral neoplasms. In this article, the authors present the microscopic structure of the normal hair follicle as a basis to understand the type and level of differentiation of the various follicular tumors. The main clinicopathological features and differential diagnosis of benign follicular tumors are then discussed, including dilated pore of Winer, pilar sheath acanthoma, trichoadenoma, trichilemmoma, infundibuloma, proliferating trichilemmal cyst/tumor, trichoblastoma and its variants, pilomatricoma, trichodiscoma/fibrofolliculoma, neurofollicular hamartoma and trichofolliculoma. In addition, the main syndromes presenting with multiple follicular tumors are also discussed, namely Cowden, Birt-Hogg-Dubé, Rombo and Bazex-Dupré-Christol syndromes, as well as multiple tumors of follicular infundibulum (infundibulomatosis) and multiple trichoepitheliomas. Although the diagnosis of follicular tumors relies on histological examination, we highlight the importance of their knowledge for the clinician, especially when in presence of patients with multiple lesions that may be the cutaneous marker of a cancer-prone syndrome. The dermatologist is therefore in a privileged position to recognize these lesions, which is extremely important to provide further propedeutic, appropriate referral and genetic counseling for these patients.info:eu-repo/semantics/publishedVersio

Role of anatomical sites and correlated risk factors on the survival of orthodontic miniscrew implants:a systematic review and meta-analysis

Abstract Objectives The aim of this review was to systematically evaluate the failure rates of miniscrews related to their specific insertion site and explore the insertion site dependent risk factors contributing to their failure. Search methods An electronic search was conducted in the Cochrane Central Register of Controlled Trials (CENTRAL), Web of Knowledge, Scopus, MEDLINE and PubMed up to October 2017. A comprehensive manual search was also performed. Eligibility criteria Randomised clinical trials and prospective non-randomised studies, reporting a minimum of 20 inserted miniscrews in a specific insertion site and reporting the miniscrews’ failure rate in that insertion site, were included. Data collection and analysis Study selection, data extraction and quality assessment were performed independently by two reviewers. Studies were sub-grouped according to the insertion site, and the failure rates for every individual insertion site were analysed using a random-effects model with corresponding 95% confidence interval. Sensitivity analyses were performed in order to test the robustness of the reported results. Results Overall, 61 studies were included in the quantitative synthesis. Palatal sites had failure rates of 1.3% (95% CI 0.3–6), 4.8% (95% CI 1.6–13.4) and 5.5% (95% CI 2.8–10.7) for the midpalatal, paramedian and parapalatal insertion sites, respectively. The failure rates for the maxillary buccal sites were 9.2% (95% CI 7.4–11.4), 9.7% (95% CI 5.1–17.6) and 16.4% (95% CI 4.9–42.5) for the interradicular miniscrews inserted between maxillary first molars and second premolars and between maxillary canines and lateral incisors, and those inserted in the zygomatic buttress respectively. The failure rates for the mandibular buccal insertion sites were 13.5% (95% CI 7.3–23.6) and 9.9% (95% CI 4.9–19.1) for the interradicular miniscrews inserted between mandibular first molars and second premolars and between mandibular canines and first premolars, respectively. The risk of failure increased when the miniscrews contacted the roots, with a risk ratio of 8.7 (95% CI 5.1–14.7). Conclusions Orthodontic miniscrew implants provide acceptable success rates that vary among the explored insertion sites. Very low to low quality of evidence suggests that miniscrews inserted in midpalatal locations have a failure rate of 1.3% and those inserted in the zygomatic buttress have a failure rate of 16.4%. Moderate quality of evidence indicates that root contact significantly contributes to the failure of interradicular miniscrews placed between the first molars and second premolars. Results should be interpreted with caution due to methodological drawbacks in some of the included studies

Extremality and dynamically defined measures, part I: Diophantine properties of quasi-decaying measures

We present a new method of proving the Diophantine extremality of various dynamically defined measures, vastly expanding the class of measures known to be extremal. This generalizes and improves the celebrated theorem of Kleinbock and Margulis (’98) resolving Sprindžuk’s conjecture, as well as its extension by Kleinbock, Lindenstrauss, and Weiss (’04), hereafter abbreviated KLW. As applications we prove the extremality of all hyperbolic measures of smooth dynamical systems with sufficiently large Hausdorff dimension, of the Patterson–Sullivan measures of all nonplanar geometrically finite groups, and of the Gibbs measures (including conformal measures) of infinite iterated function systems. The key technical idea, which has led to a plethora of new applications, is a significant weakening of KLW’s sufficient conditions for extremality. In Part I, we introduce and develop a systematic account of two classes of measures, which we call quasi-decaying and weakly quasi-decaying. We prove that weak quasi-decay implies strong extremality in the matrix approximation framework, thus proving a conjecture of KLW. We also prove the “inherited exponent of irrationality” version of this theorem, describing the relationship between the Diophantine properties of certain subspaces of the space of matrices and measures supported on these subspaces. In subsequent papers, we exhibit numerous examples of quasi-decaying measures, in support of the thesis that “almost any measure from dynamics and/or fractal geometry is quasi-decaying”. We also discuss examples of non-extremal measures coming from dynamics, illustrating where the theory must halt