Multiplicity of layered solutions for Allen-Cahn systems with symmetric double well potential

We study the existence of solutions $u:\R^{3}\to\R^{2}$ for the semilinear elliptic systems \begin{equation}\label{eq:abs} -\Delta u(x,y,z)+\nabla W(u(x,y,z))=0, \end{equation} where $W:\R^{2}\to\R$ is a double well symmetric potential. We use variational methods to show, under generic non degenerate properties of the set of one dimensional heteroclinic connections between the two minima \a_{\pm} of $W$, that (\ref{eq:abs}) has infinitely many geometrically distinct solutions $u\in C^{2}(\R^{3},\R^{2})$ which satisfy u(x,y,z)\to \a_{\pm} as ${x\to\pm\infty}$ uniformly with respect to $(y,z)\in\R^{2}$ and which exhibit dihedral symmetries with respect to the variables $y$ and $z$. We also characterize the asymptotic behaviour of these solutions as $|(y,z)|\to +\infty$

Credit Markets with Ethical Banks and Motivated Borrowers

This paper investigates banks’ corporate social responsibility. Two different competitive credit markets do exist: one for standard projects and one for ethical ones. Ethical projects have also a social profitability, but a lower (positive) expected revenue with respect to standard ones. Ethical projects are financed by ethical banks and undertaken by motivated borrowers. These borrowers obtain additional benefit (a social responsibility premium) from accomplishing ethical projects when trading with ethical banks. If the expected profitability of ethical project is sufficiently close to that of standard ones and/or the social responsibility premium of motivated borrowers is sufficiently high, the market for ethical projects is active and the credit market is fully segmented. This result holds true irrespective of the information structure: only moral hazard on the borrower side, moral hazard and screening on the borrower side, moral hazard on the borrower side and screening on the lender side. The optimal contract in our set-up is always a debt contract. However, its precise form and welfare properties depend on the information structure.corporate social responsibility; ethical banks; motivated borrowers; microfinance

Prescribed energy connecting orbits for gradient systems

We are concerned with conservative systems $\ddot{q}=\nabla V(q), \; q\in\mathbb{R}^N$ for a general class of potentials $V\in C^1(\mathbb{R}^N)$. Assuming that a given sublevel set $\{V\leq c\}$ splits in the disjoint union of two closed subsets $\mathcal{V}^c_-$ and $\mathcal{V}^c_+$, for some $c\in\mathbb{R}$, we establish the existence of bounded solutions $q_c$ to the above system with energy equal to $-c$ whose trajectories connect $\mathcal{V}^c_-$ and $\mathcal{V}^c_+$. The solutions are obtained through an energy constrained variational method, whenever mild coerciveness properties are present in the problem. The connecting orbits are classified into brake, heteroclinic or homoclinic type, depending on the behavior of $\nabla V$ on $\partial\mathcal{V}^c_{\pm}$. Next, we illustrate applications of the existence result to double-well potentials $V$, and for potentials associated to systems of Duffing type and of multiple-pendulum type. In each of the above cases we prove some convergence results of the family of solutions $(q_c)$.Comment: 34 pages, 2 figures, submitted to a journal for publication. KEYWORDS: conservative systems, energy constraints, variational methods, brake orbits, homoclinic orbits, heteroclinic orbits, convergence of solution

A randomized clinical trial about presence of pathogenic microflora and risk of peri-implantitis: comparison of two different types of implant-abutment connections

OBJECTIVE: The aim of this in vivo study was to evaluate two different types of implant-abutment connections: screwed connection and cemented connection, analyzing peri-implant bacteria microflora as well as other clinical parameters. PATIENTS AND METHODS: Twenty implants were selected, inserted in 20 patients, 10 with a screwed implant-abutment connection (Group 1) and 10 with a cemented implant-abutment connection (Group 2). The peri-implant microflora was collected, after at least 360 days from the prosthetic rehabilitation, using paper points inserted in peri-implant sulcus for 30 s. Polymerase chain reaction (PCR) Real-time analyzed the presence of 9 bacteria periodontal-pathogens and Candida albicans. RESULTS: Our findings showed that bacteria colonized all Groups analyzed, the average bacterial count was 3.7 E +08 (±1.19) in Group 1, compared to 2.1 E +08 (±0.16) in Group 2; no statistically significant differences were observed (p>0.0.5). In Group 1, however, bacterial colonization of peri-implant sulci was over the pathogenic threshold for 5 bacteria, indicating a high-risk of peri-implantitis. Also in Group 2, results showed a microflora composed by all bacteria analyzed but, in this case, bacterial colonization of peri-implant sulci was over the pathogenic threshold for only 1 bacterium, indicating a lower risk of peri-implantitis. Moreover, clinical parameters (PPD > 3 mm and m SBI > 0) confirmed a greater risk of peri-implantitis in Group 1 compared to Group 2 (p<0.05). CONCLUSIONS: We concluded that, also after only 360 days, implants with screwed connection showed a higher risk of peri-implantitis that implants with cemented connection

Implant survival and success rates in patients with risk factors: results from a long-term retrospective study with a 10 to 18 years follow-up

OBJECTIVE: Risk factors for implant therapy are represented by all general and local conditions that through various mechanisms can increase either short-term and long-term failure risk. The aim of this study is to assess the implant survival and implant success rates with single and multiple risk factors. PATIENTS AND METHODS: To address the research purpose, a retrospective cohort study was designed and implemented, including a sample of 225 patients with a total of 871 implants placed. The following risk factors were considered: smoking, bruxism, bone augmentation procedures and the presence of load risk (implants with crown/implant relation > 0.8; angulation > 25°; presence of cantilever). Follow-up ranged from 10 years to 18 years (average follow-up 13.6 years). Failures were subdivided into short-term failures, before the prosthetic phase, and long-term failures, after definitive prosthesis. The success criteria published by Albrektsson and Zarb were adopted. A Cox proportional hazard regression model was used to calculate hazard ratio, with a statistically significant p-value <0.05. RESULTS: Out of the 871 implants placed, 138 did not meet the success criteria, (success rate 84.16%), sixty (43.47%) were classified as "early failure" and seventy-eight as "late failure" (56.53%). A total of 70 dental implants were removed, with a survival rate of 91.96%. CONCLUSIONS: The presence of a single risk factor does not imply a marked increase of failure risk. Among the analyzed factors, the one that proved to be the most dangerous was bruxism, even when presented as the only risk factor. Bruxism with load risk proved to be the most dangerous association (success rate 69.23%) and could be included among the absolute contraindications for implant treatment

Informed Principals in the Credit Market when Borrowers and Lenders Are Heterogeneous

Both borrowers and lenders can be socially responsible (SR). Ethical banks commit to financing only ethical projects, which have social profitability but lower expected revenues than standard projects. Instead, no credible commitment exists for SR borrowers. The matching between SR borrowers and ethical banks reduces the frictions caused by moral hazard. However, when the type of the borrowers is not observable, then standard borrowers have incentives to invest in ethical projects pretending to be SR. We show that the separation of borrowers entails costs that are paid by SR entrepreneurs but are relatively low because standard lenders offer an outside option that relaxes the self-selection constraint of the borrowers. Technically, we solve a Contract Proposal Game where informed principals (borrowers) offer different menus of contracts to heterogeneous agents (banks). We show that market segmentation improves efficiency and solves the problem of multiplicity of equilibria in Contract Proposal Games

A belief function theory based approach to combining different representation of uncertainty in prognostics

International audienceIn this work, we consider two prognostic approaches for the prediction of the remaining useful life (RUL) of degrading equipment. The first approach is based on Gaussian Process Regression (GPR) and provides the probability distribution of the equipment RUL; the second approach adopts a Similarity-Based Regression (SBR) method for the RUL prediction and belief function theory for modeling the uncertainty on the prediction. The performance of the two approaches is comparable and we propose a method for combining their outcomes in an ensemble. The least commitment principle is adopted to transform the RUL probability density function supplied by the GPR method into a belief density function. Then, the Dempster's rule is used to aggregate the belief assignments provided by the GPR and the SBR approaches. The ensemble method is applied to the problem of predicting the RUL of filters used to clean the sea water entering the condenser of the boiling water reactor (BWR) in a Swedish nuclear power plant. The results by the ensemble method are shown to be more satisfactory than that provided by the individual GPR and SBR approaches from the point of view of the representation of the uncertainty in the RUL prediction