Singular behavior for a multi-parameter periodic Dirichlet problem

We consider a Dirichlet problem for the Poisson equation in a periodically perforated domain. The geometry of the domain is controlled by two parameters: a real number $\epsilon>0$ proportional to the radius of the holes and a map $\phi$, which models the shape of the holes. So, if $g$ denotes the Dirichlet boundary datum and $f$ the Poisson datum, we have a solution for each quadruple $(\epsilon,\phi,g,f)$. Our aim is to study how the solution depends on $(\epsilon,\phi,g,f)$, especially when $\epsilon$ is very small and the holes narrow to points. In contrast with previous works, we don't introduce the assumption that $f$ has zero integral on the fundamental periodicity cell. This brings in a certain singular behavior for $\epsilon$ close to $0$. We show that, when the dimension $n$ of the ambient space is greater than or equal to $3$, a suitable restriction of the solution can be represented with an analytic map of the quadruple $(\epsilon,\phi,g,f)$ multiplied by the factor $1/\epsilon^{n-2}$. In case of dimension $n=2$, we have to add $\log \epsilon$ times the integral of $f/2\pi$

The Dirichlet problem in a planar domain with two moderately close holes

We investigate a Dirichlet problem for the Laplace equation in a domain of $\mathbb{R}^2$ with two small close holes. The domain is obtained by making in a bounded open set two perforations at distance $|\epsilon_1|$ one from the other and each one of size $|\epsilon_1\epsilon_2|$. In such a domain, we introduce a Dirichlet problem and we denote by $u_{\epsilon_1,\epsilon_2}$ its solution. We show that the dependence of $u_{\epsilon_1,\epsilon_2}$ upon $(\epsilon_1,\epsilon_2)$ can be described in terms of real analytic maps of the pair $(\epsilon_1,\epsilon_2)$ defined in an open neighborhood of $(0,0)$ and of logarithmic functions of $\epsilon_1$ and $\epsilon_2$. Then we study the asymptotic behaviour of of $u_{\epsilon_1,\epsilon_2}$ as $\epsilon_1$ and $\epsilon_2$ tend to zero. We show that the first two terms of an asymptotic approximation can be computed only if we introduce a suitable relation between $\epsilon_1$ and $\epsilon_2$

Canaloplasty in the Treatment of Open-Angle Glaucoma: A Review of Patient Selection and Outcomes.

Canaloplasty is a relatively new non-penetrating surgery for the reduction of intraocular pressure in patients affected by glaucoma. The technique uses a microcatheter to perform a 360 º cannulation of Schlemm's canal and leaves in place a tension suture providing an inward distension. It aims to restore the physiological outflow pathways of the aqueous humour and is independent of external wound healing. Several studies have shown that canaloplasty is effective in reducing intraocular pressure and has a low rate of complications, especially compared with trabeculectomy, the gold standard for glaucoma surgery. Currently, canaloplasty is indicated in patients with open-angle glaucoma, having a mild to moderate disease, and the combination with cataract phacoemulsification may provide further intraocular pressure reduction. This article reviews canaloplasty indications, results and complications and analyses its outcomes compared with traditional penetrating and non-penetrating techniques

Multi-parameter perturbations for the space periodic heat equation

This paper is divided into three parts. The first part focuses on periodic layer heat potentials, demonstrating their smooth dependence on regular perturbations of the support of integration. In the second part, we present an application of the results from the first part. Specifically, we consider a transmission problem for the heat equation in a periodic two-phase composite material and we show that the solution depends smoothly on the shape of the transmission interface, boundary data, and conductivity parameters. Finally, in the last part of the paper, we fix all parameters except for the contrast parameter and outline a strategy to deduce an explicit expansion of the solution using a Neumann-type series

Evidence of a Critical Histidine Residue in Soluble Aspartic Aminotransferase

Photooxidation of extramitochondrial α-aspartate aminotransferase in the presence of methylene blue or Rose bengal leads to a loss of enzymatic activity which follows first order kinetics. Amino acid analysis shows that histidine is the only amino acid residue significantly affected by photooxidation. Of the 8 histidine residues present in the enzyme monomer, 2 are oxidized rapidly at a rate identical with that of the activity loss, while the other 6 are destroyed much more slowly. The pH dependence of the rate of the photo-induced inactivation of the enzyme corresponds to that expected for the photooxidation of imidazole groups. The behavior of the enzyme in Sephadex G-200 is identical before and after extensive photooxidation, while the starch gel electrophoretic pattern changes after photooxidation. It is concluded that the loss of enzyme activity caused by photooxidation is related to the destruction of 1 histidine residue

Iginio Tansini (1855-1943): An Italian surgeon and an innovator between the 19th and the 20th centuries

The aim of this paper is to describe the figure of the Italian surgeon Iginio Tansini (1855-1943), who was full professor of surgery and director of the Department of Surgery at the University of Pavia (1903-1931). In that period, he modernized the School of Surgery founded by Antonio Scarpa (1752-1832) in the previous century; he introduced the experimental method in the discipline. One of his major contributions was an innovative technique of mastectomy followed by plastic reconstruction with myocutaneous flap. Tansini was a pioneer in oncology, supporting the importance of an early diagnosis based on a biopsy; he was also the first in Italy to practice a gastrectomy for stomach cancer with success in 1887

Technology options for earthquake resistant, eco-efficient buildings in Europe: Research needs

The built environment corresponds to the largest industrial sector not only in economic terms, but also in terms of resource flow. Moreover, European citizens spend most of their lives inside buildings, therefore buildings turn out to be at the centre of social and economic activity. In that light, Europe is involved in several initiatives and strategies aimed to make this sector one of the most competitive and innovative, focusing on the achievement of the environmental and energy targets in line with 2020 Europe Strategy and EU 2050 Roadmap, but also ensuring safety both in ordinary conditions and in presence of exceptional events, such as earthquakes. While new buildings can be constructed with high performance levels, the older buildings which are predominantly characterized by low energy performance and seismic vulnerability, typically need renovation measures. This report has the aim to define the research needs for exploiting old buildings potential to deliver energy and CO2-emission savings, as well as societal and economic benefits, so that energy efficient and earthquake resistant buildings can have a pivotal role in a sustainable future. In the first part of the report, a detailed analysis of the main characteristics of European buildings in terms of age, size, ownership, location, structural typology is presented in order to define the predominant typology of the European existing building stock. Secondly, the seismic hazard in Europe and the earthquake vulnerability of European buildings are analysed. Finally, energy consumptions and environmental impacts in terms of use of resources, construction and demolition (C&D) wastes and CO2 emissions are described. The analysis of the present situation turns out to be essential in order to define the starting point to assess the current and new technology options, examined in the second part of the report and necessary to obtain eco-efficient and seismic resistant buildings. In addition, the benefits that a renovation project could bring against a demolition and reconstruction programme have been underlined. Once these inputs have been defined, the requalification needs and the importance to improve renovation strategies, considered as outputs of the analysis, are examined for each of the two above-mentioned parts of this study. Finally, a critical discussion on the importance of considering research needs for this topic, with a focus on barriers and challenges which a renovation programme has to face, has been carried out.JRC.G.5-European laboratory for structural assessmen

Design and Development of a Planetary Gearbox for Electromechanical Actuator Test Bench through Additive Manufacturing

The development and validation of prognostic algorithms and digital twins for Electromechanical Actuators (EMAs) requires datasets of operating parameters that are not commonly available. In this context, we are assembling a test bench able to simulate different operating scenarios and environmental conditions for an EMA in order to collect the operating parameters of the actuator both in nominal conditions and under the effect of incipient progressive faults. This paper presents the design and manufacturing of a planetary gearbox for the EMA test bench. Mechanical components were conceived making extensive use of Fused Deposition Modelling (FDM) additive manufacturing and off-the-shelf hardware in order to limit the costs and time involved in prototyping. Given the poor mechanical properties of the materials commonly employed for FDM, the gears were not sized for the maximum torque of the electric motor, and a secondary torque path was placed in parallel of the planetary gearbox to load the motor through a disc brake. The architecture of the gearbox allowed a high gear ratio within a small form factor, and a bearingless construction with a very low number of moving parts