Asymptotic behaviour and numerical approximation of optimal eigenvalues of the Robin Laplacian

We consider the problem of minimising the $n^{th}-$eigenvalue of the Robin Laplacian in $\mathbb{R}^{N}$. Although for $n=1,2$ and a positive boundary parameter $\alpha$ it is known that the minimisers do not depend on $\alpha$, we demonstrate numerically that this will not always be the case and illustrate how the optimiser will depend on $\alpha$. We derive a Wolf-Keller type result for this problem and show that optimal eigenvalues grow at most with $n^{1/N}$, which is in sharp contrast with the Weyl asymptotics for a fixed domain. We further show that the gap between consecutive eigenvalues does go to zero as $n$ goes to infinity. Numerical results then support the conjecture that for each $n$ there exists a positive value of $\alpha_{n}$ such that the $n^{\rm th}$ eigenvalue is minimised by $n$ disks for all $0<\alpha<\alpha_{n}$ and, combined with analytic estimates, that this value is expected to grow with $n^{1/N}$

Absence of Gluonic Components in Axial and Tensor Mesons

A quarkonium-gluonium mixing scheme previously developed to describe the characteristic of the pseudoscalar mesons is applied to axial and tensor mesons. The parameters of the model are determined by fitting the eigenvalues of a mass matrix. The corresponding eigenvectors give the proportion of light quarks, strange quarks and glueball in each meson. However the predictions of the model for branching ratios and electromagnetic decays are incompatible with the experimental results. These results suggest the absence of gluonic components in the states of axial and tensor isosinglet mesons analyzed here.Comment: 12 page

Thermoelectric response of Fe1+y_{1+y}Te0.6_{0.6}Se0.4_{0.4}: evidence for strong correlation and low carrier density

We present a study of the Seebeck and Nernst coefficients of Fe$_{1+y}$Te$_{1-x}$Se$_{x}$ extended up to 28 T. The large magnitude of the Seebeck coefficient in the optimally doped sample tracks a remarkably low normalized Fermi temperature, which, like other correlated superconductors, is only one order of magnitude larger than T$_c$. We combine our data with other experimentally measured coefficients of the system to extract a set of self-consistent parameters, which identify Fe$_{1+y}$Te$_{0.6}$Se$_{0.4}$ as a low-density correlated superconductor barely in the clean limit. The system is subject to strong superconducting fluctuations with a sizeable vortex Nernst signal in a wide temperature window.Comment: 4 pages including 4 figure

On Logical Depth and the Running Time of Shortest Programs

The logical depth with significance $b$ of a finite binary string $x$ is the shortest running time of a binary program for $x$ that can be compressed by at most $b$ bits. There is another definition of logical depth. We give two theorems about the quantitative relation between these versions: the first theorem concerns a variation of a known fact with a new proof, the second theorem and its proof are new. We select the above version of logical depth and show the following. There is an infinite sequence of strings of increasing length such that for each $j$ there is a $b$ such that the logical depth of the $j$th string as a function of $j$ is incomputable (it rises faster than any computable function) but with $b$ replaced by $b+1$ the resuling function is computable. Hence the maximal gap between the logical depths resulting from incrementing appropriate $b$'s by 1 rises faster than any computable function. All functions mentioned are upper bounded by the Busy Beaver function. Since for every string its logical depth is nonincreasing in $b$, the minimal computation time of the shortest programs for the sequence of strings as a function of $j$ rises faster than any computable function but not so fast as the Busy Beaver function.Comment: 12 pages LaTex (this supercedes arXiv:1301.4451

Thoracic, abdominal and musculoskeletal involvement in Erdheim-Chester disease: CT, MR and PET imaging findings.

BACKGROUND: Erdheim-Chester disease (ECD) is a rare, non-Langerhans cell histiocytosis with characteristic radiological and histological features. This entity is defined by a mononuclear infiltrate consisting of lipid-laden, foamy histiocytes that stain positively for CD68 and negatively for CD1a. Osseous involvement is constant and characteristic. Extra-osseous lesions may affect the retroperitoneum, lungs, skin, heart, brain and orbits. METHODS: Both radiography and technetium-99m bone scintigraphy may reveal osteosclerosis of the long bones, which is a typical finding in ECD. For visceral involvement, computed tomography (CT) is most useful, while magnetic resonance (MR) imaging is more sensitive for cardiovascular lesions; 2-[fluorine-18] fluoro-2-deoxy-d-glucose (FDG) positron emission tomography (PET)/CT scanning is useful in assessing the extension of ECD lesions. RESULTS: The prognosis is extremely variable and is often worse when there is cardiovascular system involvement. Diagnosis is based on the combination of radiographic, CT, MR imaging and nuclear medicine features and a nearly pathognomonic immunohistochemical profile. CONCLUSION: The aims of this work are to perform a systematic review of Erdheim-Chester disease as seen on imaging of the chest, abdomen and musculoskeletal system and to discuss the diagnostic workup and differential diagnoses according to the imaging presentation. Teaching points • Bone involvement is usually present in patients, and the imaging findings are pathognomonic of ECD. • The circumferential periaortic infiltration may extend to its branches, sometimes becoming symptomatic. • Cardiac involvement-the pericardium, right atrium and auriculoventricular sulcus-worsens its prognosis. • Perirenal infiltration extending to the proximal ureter is highly suggestive of this disease

Joints in pavements of industrial buildings

Os pavimentos de edifícios industriais são das obras de engenharia civil em que ocorrem maior número de patologias. Tal deve-se a deficiente empenho dos intervenientes na concepção, projecto e construção deste tipo de estruturas, muitas vezes associado ao sentimento de que a não verificação dos estados limites de utilização e últimos não está directamente ligado à ocorrência de acidentes trágicos. Porém, é reconhecido que, em muitos casos, o deficiente funcionamento deste tipo de estruturas conduz a prejuízos económicos significativos e, por vezes, a acidentes envolvendo seres humanos. De entre as patologias ocorridas em pavimentos industriais, as devidas directa ou indirectamente com juntas, são as mais correntes. Um deficiente traçado de juntas pode conduzir, em caso limite, à inutilização do pavimento, sendo a reabilitação deste bastante onerosa. Este trabalho é dedicado à temática das juntas em pavimentos de edifícios industriais, desde a sua concepção, traçado até ao dimensionamento de elementos de transferência de carga entre painéis adjacentes à junta.Pavements of industrial floors are one of the Civil Engineering realizations where higher number of pathologies occurred. This is caused by the deficient attitude of the intervenients in the conception, design, execution and quality control of this type of structural application. This behavior is related to the idea that a tragic accident will not occur even if the serviceability and ultimate limit analysis are not accomplished in the design practice. In several cases, however, a pavement with deficient operation leads to significant economical loses, and, sometimes to human injuries

Reforço de pavimentos de edifícios industriais com laminados de fibras de carbono

A eficácia da técnica de reforço constituída pela fixação de laminados de CFRP, com adesivo epoxy, no betão de recobrimento de elementos de betão armado tem sido comprovada nos últimos anos no reforço à flexão de vigas e pilares, e no reforço ao corte de vigas. No presente trabalho, esta técnica é aplicada no reforço à flexão de painéis de um pavimento de um edifício industrial. Os procedimentos e o cálculo do reforço são descritos no presente trabalho.Pisonort Lda (pavimentos industriais)

A new method based on noise counting to monitor the frontend electronics of the LHCb muon detector

A new method has been developed to check the correct behaviour of the frontend electronics of the LHCb muon detector. This method is based on the measurement of the electronic noise rate at different thresholds of the frontend discriminator. The method was used to choose the optimal discriminator thresholds. A procedure based on this method was implemented in the detector control system and allowed the detection of a small percentage of frontend channels which had deteriorated. A Monte Carlo simulation has been performed to check the validity of the method