On Hopf's Lemma and the Strong Maximum Principle

In this paper we consider Hopf's Lemma and the Strong Maximum Principle for supersolutions to a class of non elliptic equations. In particular we prove a sufficient condition for the validity of Hopf's Lemma and of the Strong Maximum Principle and we give a condition which is at once necessary for the validity of Hopf's Lemma and sufficient for the validity of the Strong Maximum Principle.Comment: 27 pages,4 figure

Anatomical variants of sphenoid sinuses pneumatisation: a CT scan study on a Northern Italian population

Sphenoid bone may be affected by different variants of pneumatisation, which have a relevant importance from a clinical and surgical point of view. The description of such variants in different populations may give useful information. However, few articles describe the variability of sphenoid pneumatised structures and none of them focuses on Northern Italian population. Variants of pneumatisation of sphenoid bone were described in a sample of 300 Northern Italian patients who underwent a CT scan. More than fifty-seven percent of patients showed a form of anatomical variant: the most common form was the pneumatised pterygoid processes (39.6%), followed by dorsum sellae (32.9%) and clinoid processes (20.3%), without statistically significant differences between males and females (p\ua0>\ua00.01). In 26.3% of patients, a combined pneumatisation of these three structures was observed, being the combination pterygoid processes-dorsum sellae the most frequent (11.3%). In 9.3%, all the three sphenoid structures were affected. This article is the first description of the prevalence of different variants of pneumatisation in a Northern Italian population: the occurrence of such forms has to be acknowledged for their possible clinical and surgical consequences

Optimal control for satellite attitude maneuvers. Volume 1 - Mathematical analysis

Mathematical analyses of suboptimal attitude maneuvering control for synchronous earth pointing satellite

Anatomical Characteristics Of Intrapetrous Carotid Artery : A 3d Segmentation Study On Head Ct-Scan

The intrapetrous portion of internal carotid artery (IPCA) is one of the most unexplored anatomical regions, and its three-dimensional reconstruction in living subjects is still missing. The present study aims at describing IPCA on 3D models extracted from head CT-scans. The intrapetrous carotid artery was manually segmented on head CT-scans of 100 healthy patients free from vascular and neurological pathologies (50 males and 50 females aged between 18 and 91 years). Angles of the posterior and anterior genu, diameter and length of the horizontal portion, and volume of the entire canal were calculated through VAM\uae software. Statistically significant differences according to sex and side were assessed through two-way ANOVA test (p<0.05). Correlation of each measurement with age was calculated as well. On average the angles of the posterior and anterior genu were 120.1\ub110.4\ub0 and 118.0\ub110.0\ub0 in males, 119.5\ub19.2\ub0 and 117.6\ub110.3\ub0 in females, respectively, without statistically significant differences according to sex or side (p>0.05). Average length and diameter of the horizontal part were respectively 25.5\ub12.9 mm and 5.8\ub10.8 mm in males, 24.0\ub12.3 mm and 5.3\ub10.8 mm in females. The volume of IPCA was 0.941\ub10.215 cm3 in males, and 0.752\ub10.159 cm3 in females. Length and diameter of horizontal portion, and volume of IPCA showed statistically significant differences according to sex (p<0.05). No correlation with age was found. This study first provided data concerning not only linear and angular measurements, but also volumes of IPCA, useful in planning surgical interventions of the cranial base

Leveraging realities of saving energy at home : contributions of co-design to behavioural interventions

While reducing individual energy consumption contributes to climate change mitigation, many individuals who share this belief fail to act on it. While behavioural interventions try to address such intention-behaviour gaps, few approaches have worked with consumers to understand the realities of their opportunities and limitations to save energy at home. We argue that co-design is well-suited to address the unique challenges of climate-relevant behaviour change and propose an abductive co-design methodology to develop a behavioural intervention with household members based on the Model of Action Phases (MAP) framework. We implement the methodology to design an energy savings app and behaviour change intervention in Switzerland. The methodology shifts participants into an expert role and elucidates their motivations, real-life challenges, and knowledge gaps to save energy. Through group problem-solving and self-reflection, participants provided design inputs which address the socio-psychological gaps to progress behaviour through the preaction, action and postaction phases of the MAP. We assess the originality and feasibility of the co-design inputs, as well as reflect on the experience of the researchers and participants during the process. We conclude that co-design provided novel inputs relevant for progressing through the behaviour change stages identified by the MAP framework

Second-order L2L^2-regularity in nonlinear elliptic problems

A second-order regularity theory is developed for solutions to a class of quasilinear elliptic equations in divergence form, including the $p$-Laplace equation, with merely square-integrable right-hand side. Our results amount to the existence and square integrability of the weak derivatives of the nonlinear expression of the gradient under the divergence operator. This provides a nonlinear counterpart of the classical $L^2$-coercivity theory for linear problems, which is missing in the existing literature. Both local and global estimates are established. The latter apply to solutions to either Dirichlet or Neumann boundary value problems. Minimal regularity on the boundary of the domain is required. If the domain is convex, no regularity of its boundary is needed at all

Symmetry of zygomatic bone through 3D segmentation on CT-scan and "mirroring" procedure: a novel approach for reconstructive maxillofacial surgery

Zygomatic bones are among those most frequently fractured facial bones [1]: symmetry is the golden standard for a correct restoration of zygomatic shape, but literature is divided about the best method for its quantification. Also, no information about the actual 3D symmetry of this bone in healthy subjects is available. This study aims at exposing an innovative approach for the assessment of zygomatic symmetry through 3D surface analysis. One hundred patients (50 males and 50 females) were selected from the CT-scans database from a Northern Italy hospital. Zygomatic bones from each patient were segmented, the left bone was automatically mirrored according to the sagittal plane and registered on the right one according to the least point-to-point distance between the two surfaces. Mean and RMS (root mean square) distance between the two models was then calculated. Possible statistically significant differences according to sex and age groups were assessed respectively through two-way ANOVA test (p0.05). This study first provides an overall assessment of symmetry of zygomatic bone, based on surface analysis: results may provide a useful indication for the reconstruction of zygomatic bones in maxillofacial surgery

A version of Olech's lemma in a problem of the calculus of variations

This paper studies the solutions of the minimum problem for a functional of the gradient under linear boundary conditions. A necessary and sufficient condition, based on the facial structure of the epigraph of the integrand, is provided for the continuous dependence of the solutions on boundary data