The Schr\"odinger operator on an infinite wedge with a tangent magnetic field

We study a model Schr\"odinger operator with constant magnetic field on an infinite wedge with Neumann boundary condition. The magnetic field is assumed to be tangent to a face. We compare the bottom of the spectrum to the model spectral quantities coming from the regular case. We are particularly motivated by the influence of the magnetic field and the opening angle of the wedge on the spectrum of the model operator and we exhibit cases where the bottom of the spectrum is smaller than in the regular case. Numerical computations enlighten the theoretical approach

Approximation of the critical buckling factor for composite panels

This article is concerned with the approximation of the critical buckling factor for thin composite plates. A new method to improve the approximation of this critical factor is applied based on its behavior with respect to lamination parameters and loading conditions. This method allows accurate approximation of the critical buckling factor for non-orthotropic laminates under complex combined loadings (including shear loading). The influence of the stacking sequence and loading conditions is extensively studied as well as properties of the critical buckling factor behavior (e.g concavity over tensor D or out-of-plane lamination parameters). Moreover, the critical buckling factor is numerically shown to be piecewise linear for orthotropic laminates under combined loading whenever shear remains low and it is also shown to be piecewise continuous in the general case. Based on the numerically observed behavior, a new scheme for the approximation is applied that separates each buckling mode and builds linear, polynomial or rational regressions for each mode. Results of this approach and applications to structural optimization are presented

A limit model for thermoelectric equations

We analyze the asymptotic behavior corresponding to the arbitrary high conductivity of the heat in the thermoelectric devices. This work deals with a steady-state multidimensional thermistor problem, considering the Joule effect and both spatial and temperature dependent transport coefficients under some real boundary conditions in accordance with the Seebeck-Peltier-Thomson cross-effects. Our first purpose is that the existence of a weak solution holds true under minimal assumptions on the data, as in particular nonsmooth domains. Two existence results are studied under different assumptions on the electrical conductivity. Their proofs are based on a fixed point argument, compactness methods, and existence and regularity theory for elliptic scalar equations. The second purpose is to show the existence of a limit model illustrating the asymptotic situation.Comment: 20 page

Piecewise Tensor Product Wavelet Bases by Extensions and Approximation Rates

Following [Studia Math., 76(2) (1983), pp. 1-58 and 95-136] by Z. Ciesielski and T. Figiel and [SIAM J. Math. Anal., 31 (1999), pp. 184-230] by W. Dahmen and R. Schneider, by the application of extension operators we construct a basis for a range of Sobolev spaces on a domain $\Omega$ from corresponding bases on subdomains that form a non-overlapping decomposition. As subdomains, we take hypercubes, or smooth parametric images of those, and equip them with tensor product wavelet bases. We prove approximation rates from the resulting piecewise tensor product basis that are independent of the spatial dimension of $\Omega$. For two- and three-dimensional polytopes we show that the solution of Poisson type problems satisfies the required regularity condition. The dimension independent rates will be realized numerically in linear complexity by the application of the adaptive wavelet-Galerkin scheme

“I’m only a dog!” : the Rwandan genocide, dehumanisation and the graphic novel

Graphic novels written in response to the 1994 Rwandan genocide do not confine their depictions of traumatic violence to humans, but extend their coverage to show how the genocide impacted on animals and the environment. Through analysis of the presentation of people and their relationships with other species across a range of graphic narratives, this article shows how animal imagery was used to justify inhumane actions during the genocide, and argues that representations of animals remain central to the recuperation processes in a post-genocide context too. Whilst novels and films that respond to the genocide have been the focus of scholarly work (Dauge-Roth, 2010), the graphic novel has yet to receive substantial critical attention. This article therefore unlocks the archive of French-, Dutch- and English-language graphic narratives written in response to the genocide by providing the first in-depth, comparative analysis of their animal representations. It draws on recent methodological approaches derived from philosophy (Derrida, [2008] trans. 2009), postcolonial ecocriticism (Huggan and Tiffin, 2010) and postcolonial trauma theory (Craps, 2012) in order show how human-centred strategies for recovery, and associated symbolic orders that forcefully position the animal outside of human law, continue to engender unequal and potentially violent relationships between humans, and humans and other species. In this way, graphic narratives that gesture towards more equitable relationships between humans, animals and the environment can be seen to support the processes of recovery and reconciliation in post-genocide Rwanda

Correlation of three immunohistochemically detected markers of neuroendocrine differentiation with clinical predictors of disease progression in prostate cancer

<p>Abstract</p> <p>Background</p> <p>The importance of immuno-histological detection of neuroendocrine differentiation in prostatic adenocarcinoma with respect to disease at presentation and Gleason grade is gaining acceptance. There is limited literature on the relative significance of three commonly used markers of NE differentiation i.e. Chromogranin A (CgA), Neuron specific enolase (NSE) and Synaptophysin (Syn). In the current work we have assessed the correlation of immuno-histological detection of neuroendocrine differentiation in prostatic adenocarcinoma with respect to disease at presentation and Gleason grade and to determine the relative value of various markers.</p> <p>Materials and methods</p> <p>Consecutive samples of malignant prostatic specimens (Transurethral resection of prostate or radical retropubic prostatectomy) from 84 patients between January 1991 and December 1998 were evaluated by immunohistochemical staining (PAP technique) using selected neuroendocrine tumor markers i.e. Chromogranin A (CgA), Neuron specific enolase (NSE), and Synaptophysin (Syn). According to the stage at diagnosis, patients were divided into three groups. Group (i) included patients who had organ confined disease, group (ii) included patients with locally invasive disease, and group (iii) with distant metastasis. NE expression was correlated with Gleason sum and clinical stage at presentation and analyzed using Chi-Square test and one way ANNOVA.</p> <p>Results</p> <p>The mean age of the patients was 70 ± 9.2 years. Group I had 14 patients, group II had 31 patients and group III had 39 patients. CgA was detected in 33 cases, Syn in 8 cases, and NSE in 44 cases. Expression of CgA was seen in 7% of group I, 37% in group II and 35% of group III patients (p 0.059). CgA (p 0.024) and NSE (p 0.006) had a significantly higher expression with worsening Gleason grade.</p> <p>Conclusion</p> <p>CgA has a better correlation with disease at presentation than other markers used. Both NSE and CgA had increasing expression with worsening histological grade this correlation has a potential for use as a prognostic indicator. Limitations in the current work included small number and retrospective nature of work. The findings of this work needs validation in a larger cohort.</p

Bilevel Parameter Learning for Higher-Order Total Variation Regularisation Models.

We consider a bilevel optimisation approach for parameter learning in higher-order total variation image reconstruction models. Apart from the least squares cost functional, naturally used in bilevel learning, we propose and analyse an alternative cost based on a Huber-regularised TV seminorm. Differentiability properties of the solution operator are verified and a first-order optimality system is derived. Based on the adjoint information, a combined quasi-Newton/semismooth Newton algorithm is proposed for the numerical solution of the bilevel problems. Numerical experiments are carried out to show the suitability of our approach and the improved performance of the new cost functional. Thanks to the bilevel optimisation framework, also a detailed comparison between TGV 2 and ICTV is carried out, showing the advantages and shortcomings of both regularisers, depending on the structure of the processed images and their noise level.King Abdullah University of Science and Technology (KAUST) (Grant ID: KUKI1-007-43), Engineering and Physical Sciences Research Council (Grant IDs: Nr. EP/J009539/1 “Sparse & Higher-order Image Restoration” and Nr. EP/M00483X/1 “Efficient computational tools for inverse imaging problems”), Escuela Politécnica Nacional de Quito (Grant ID: PIS 12-14, MATHAmSud project SOCDE “Sparse Optimal Control of Differential Equations”), Leverhulme Trust (project on “Breaking the non-convexity barrier”), SENESCYT (Ecuadorian Ministry of Higher Education, Science, Technology and Innovation) (Prometeo Fellowship)This is the final version of the article. It first appeared from Springer via http://dx.doi.org/10.1007/s10851-016-0662-

Computational performance of Free Mesh Method applied to continuum mechanics problems

The free mesh method (FMM) is a kind of the meshless methods intended for particle-like finite element analysis of problems that are difficult to handle using global mesh generation, or a node-based finite element method that employs a local mesh generation technique and a node-by-node algorithm. The aim of the present paper is to review some unique numerical solutions of fluid and solid mechanics by employing FMM as well as the Enriched Free Mesh Method (EFMM), which is a new version of FMM, including compressible flow and sounding mechanism in air-reed instruments as applications to fluid mechanics, and automatic remeshing for slow crack growth, dynamic behavior of solid as well as large-scale Eigen-frequency of engine block as applications to solid mechanics