The prescribed mean curvature equation in weakly regular domains

We show that the characterization of existence and uniqueness up to vertical translations of solutions to the prescribed mean curvature equation, originally proved by Giusti in the smooth case, holds true for domains satisfying very mild regularity assumptions. Our results apply in particular to the non-parametric solutions of the capillary problem for perfectly wetting fluids in zero gravity. Among the essential tools used in the proofs, we mention a \textit{generalized Gauss-Green theorem} based on the construction of the weak normal trace of a vector field with bounded divergence, in the spirit of classical results due to Anzellotti, and a \textit{weak Young's law} for $(\Lambda,r_{0})$-minimizers of the perimeter.Comment: 23 pages, 1 figure --- The results on the weak normal trace of vector fields have been now extended and moved in a self-contained paper available at: arXiv:1708.0139

Two examples of minimal Cheeger sets in the plane

We construct two minimal Cheeger sets in the Euclidean plane, i.e., unique minimizers of the ratio \u201cperimeter over area\u201d among their own measurable subsets. The first one gives a counterexample to the so- called weak regularity property of Cheeger sets, as its perimeter does not coincide with the 1-dimensional Hausdorff measure of its topological boundary. The second one is a kind of porous set, whose boundary is not locally a graph at many of its points, yet it is a weakly regular open set admitting a unique (up to vertical translations) nonparametric solution to the prescribed mean curvature equation, in the extremal case corresponding to the capillarity for perfectly wetting fluids in zero gravity

Separated and overlapping neural coding of face and body identity

Recognising a person's identity often relies on face and body information, and is tolerant to changes in low-level visual input (e.g., viewpoint changes). Previous studies have suggested that face identity is disentangled from low-level visual input in the anterior face-responsive regions. It remains unclear which regions disentangle body identity from variations in viewpoint, and whether face and body identity are encoded separately or combined into a coherent person identity representation. We trained participants to recognise three identities, and then recorded their brain activity using fMRI while they viewed face and body images of these three identities from different viewpoints. Participants' task was to respond to either the stimulus identity or viewpoint. We found consistent decoding of body identity across viewpoint in the fusiform body area, right anterior temporal cortex, middle frontal gyrus and right insula. This finding demonstrates a similar function of fusiform and anterior temporal cortex for bodies as has previously been shown for faces, suggesting these regions may play a general role in extracting high-level identity information. Moreover, we could decode identity across fMRI activity evoked by faces and bodies in the early visual cortex, right inferior occipital cortex, right parahippocampal cortex and right superior parietal cortex, revealing a distributed network that encodes person identity abstractly. Lastly, identity decoding was consistently better when participants attended to identity, indicating that attention to identity enhances its neural representation. These results offer new insights into how the brain develops an abstract neural coding of person identity, shared by faces and bodies

Multidimensional Conservation Laws: Overview, Problems, and Perspective

Some of recent important developments are overviewed, several longstanding open problems are discussed, and a perspective is presented for the mathematical theory of multidimensional conservation laws. Some basic features and phenomena of multidimensional hyperbolic conservation laws are revealed, and some samples of multidimensional systems/models and related important problems are presented and analyzed with emphasis on the prototypes that have been solved or may be expected to be solved rigorously at least for some cases. In particular, multidimensional steady supersonic problems and transonic problems, shock reflection-diffraction problems, and related effective nonlinear approaches are analyzed. A theory of divergence-measure vector fields and related analytical frameworks for the analysis of entropy solutions are discussed.Comment: 43 pages, 3 figure

Long-term outcome of COVID-19 patients treated with helmet noninvasive ventilation vs. high-flow nasal oxygen: a randomized trial

Background: Long-term outcomes of patients treated with helmet noninvasive ventilation (NIV) are unknown: safety concerns regarding the risk of patient self-inflicted lung injury and delayed intubation exist when NIV is applied in hypoxemic patients. We assessed the 6-month outcome of patients who received helmet NIV or high-flow nasal oxygen for COVID-19 hypoxemic respiratory failure. Methods: In this prespecified analysis of a randomized trial of helmet NIV versus high-flow nasal oxygen (HENIVOT), clinical status, physical performance (6-min-walking-test and 30-s chair stand test), respiratory function and quality of life (EuroQoL five dimensions five levels questionnaire, EuroQoL VAS, SF36 and Post-Traumatic Stress Disorder Checklist for the DSM) were evaluated 6 months after the enrollment. Results: Among 80 patients who were alive, 71 (89%) completed the follow-up: 35 had received helmet NIV, 36 high-flow oxygen. There was no inter-group difference in any item concerning vital signs (N = 4), physical performance (N = 18), respiratory function (N = 27), quality of life (N = 21) and laboratory tests (N = 15). Arthralgia was significantly lower in the helmet group (16% vs. 55%, p = 0.002). Fifty-two percent of patients in helmet group vs. 63% of patients in high-flow group had diffusing capacity of the lungs for carbon monoxide < 80% of predicted (p = 0.44); 13% vs. 22% had forced vital capacity < 80% of predicted (p = 0.51). Both groups reported similar degree of pain (p = 0.81) and anxiety (p = 0.81) at the EQ-5D-5L test; the EQ-VAS score was similar in the two groups (p = 0.27). Compared to patients who successfully avoided invasive mechanical ventilation (54/71, 76%), intubated patients (17/71, 24%) had significantly worse pulmonary function (median diffusing capacity of the lungs for carbon monoxide 66% [Interquartile range: 47–77] of predicted vs. 80% [71–88], p = 0.005) and decreased quality of life (EQ-VAS: 70 [53–70] vs. 80 [70–83], p = 0.01). Conclusions: In patients with COVID-19 hypoxemic respiratory failure, treatment with helmet NIV or high-flow oxygen yielded similar quality of life and functional outcome at 6 months. The need for invasive mechanical ventilation was associated with worse outcomes. These data indicate that helmet NIV, as applied in the HENIVOT trial, can be safely used in hypoxemic patients. Trial registration Registered on clinicaltrials.gov NCT04502576 on August 6, 202

Rotational Surfaces in L3\mathbb{L}^3 and Solutions in the Nonlinear Sigma Model

The Gauss map of non-degenerate surfaces in the three-dimensional Minkowski space are viewed as dynamical fields of the two-dimensional O(2,1) Nonlinear Sigma Model. In this setting, the moduli space of solutions with rotational symmetry is completely determined. Essentially, the solutions are warped products of orbits of the 1-dimensional groups of isometries and elastic curves in either a de Sitter plane, a hyperbolic plane or an anti de Sitter plane. The main tools are the equivalence of the two-dimensional O(2,1) Nonlinear Sigma Model and the Willmore problem, and the description of the surfaces with rotational symmetry. A complete classification of such surfaces is obtained in this paper. Indeed, a huge new family of Lorentzian rotational surfaces with a space-like axis is presented. The description of this new class of surfaces is based on a technique of surgery and a gluing process, which is illustrated by an algorithm.Comment: PACS: 11.10.Lm; 11.10.Ef; 11.15.-q; 11.30.-j; 02.30.-f; 02.40.-k. 45 pages, 11 figure

Quasistatic delamination of sandwich-like Kirchhoff-Love plates

A quasistatic rate-independent adhesive delamination problem of laminated plates with a finite thickness is considered. By letting the thickness of the plates go to zero, a rate-independent delamination model for a laminated Kirchhoff-Love plate is obtained as limit of these quasistatic processes. The same dimension reduction procedure is eventually applied to processes which are sensitive to delamination modes, namely opening vs. shearing is distinguishe

Existence theorems for multiple integrals of the calculus of variations for discontinuous solutions

The authors prove existence theorems for the minimum of multiple integrals of the calculus of variations with constraints on the derivatives in classes of BV possibly discontinuous solutions. To this effect the integrals are written in the form proposed by Serrin. Usual convexity conditions are requested, but no growth condition. Preliminary closure and semicontinuity theorems are proved which are analogous to those previously proved by Cesari in Sobolev classes. Compactness in L 1 of classes of BV functions with equibounded total variations is derived from Cafiero-Fleming theorems.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/47939/1/10231_2005_Article_BF01766143.pd

Quality of life and treatment satisfaction in adults with Type 1 diabetes: A comparison between continuous subcutaneous insulin infusion and multiple daily injections

Aims: The aim of this case-control study was to compare quality of life (QoL) and treatment satisfaction in adults with Type 1 diabetes (T1DM) treated with either continuous subcutaneous insulin infusion (CSII) or multiple daily injections (MDI). Methods: Consecutive patients aged between 18 and 55 years, and attending diabetes clinics for a routine visit, completed the Diabetes-Specific Quality-of-Life Scale (DSQOLS), the Diabetes Treatment Satisfaction Questionnaire (DTSQ) and the SF-36 Health Survey (SF-36). Case (CSII) and control subjects (MDI) were recruited in a 1 : 2 ratio. Results: Overall, 1341 individuals were enrolled by 62 diabetes clinics; 481 were cases and 860 control subjects. Cases had a longer diabetes duration and were more likely to have eye and renal complications. Age, school education, occupation and HbA1c were similar. Of control subjects, 90% followed glargine-based MDI regimens and 10% used NPH-based MDI regimens. On multivariate analysis, after adjusting for socioeconomic and clinical characteristics, scores in the following areas of the DSQOLS were higher in cases than control subjects: diet restrictions (β = 5.96; P < 0.0001), daily hassles (β = 3.57; P = 0.01) and fears about hypoglycaemia (β = 3.88; P = 0.006). Treatment with CSII was also associated with a markedly higher DTSQ score (β = 4.13; P < 0.0001) compared with MDI. Results were similar when CSII was compared separately with glargine- or NPH-based MDI regimens. Conclusions: This large, non-randomized, case-control study suggests quality of life gains deriving from greater lifestyle flexibility, less fear of hypoglycaemia, and higher treatment satisfaction, when CSII is compared with either glargine-based or NPH-based MDI regimens. © 2008 The Authors

Infrared imaging in liquid through an extrinsic optical microcavity

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