Regular interval Cantor sets of <Emphasis Type="Italic">S</Emphasis><Superscript>1</Superscript> and minimality

It is known that not every Cantor set of S ¹ is C ¹-minimal. In this work we prove that every member of a subfamily of what we here call regular interval Cantor set is not C ¹-minimal. We also prove that no member of a class of Cantor sets that includes this subfamily is C ^1+∈-minimal, for any ∈ > 0. Partially supported by CNPq-Brasil and PEDECIBA-Uruguay.     

On the problem of the elastic plate on one-sided foundation

Summary Solution existence, uniqueness and regularity are analyzed for the elastic plate on unilateral elastic foundation problem. Some results are also given for the one-sided rigid foundation case.

---

Sommario Si studiano l'esistenza, l'unicità e la regolarità delle soluzioni del problema della piastra elastica su fondazione elastica unilaterale. Sono anche dati alcuni risultati per il caso di fondazione rigida unilaterale.

     

Interpreting technical evidence from spectral imaging of paintings by Édouard Manet in the Courtauld Gallery

The paintings by Édouard Manet in The Courtauld Gallery Déjeuner sur l'herbe (1863–68), Marguerite de Conflans en Toilette de Bal (1870–1880), Banks of the Seine at Argenteuil (1874), and A Bar at the Folies–Bergère (1882) were investigated for the first time using a range of non-invasive in situ analyses. The aims of the study were to investigate the painting techniques and materials used for this group of works and to critically evaluate the technical evidence derived from the integrated use of imaging techniques and portable spectroscopic methods in this context. The paintings were investigated by means of macro X-ray fluorescence (MA-XRF), reflection spectral imaging, portable UV–Vis–NIR spectroscopy, portable Raman spectroscopy, and reflection FTIR. MA-XRF and reflection spectral imaging allowed visualising elements in the compositions that were not visible using traditional methods of technical study. For example, MA-XRF analysis of Déjeuner sur l'herbe revealed elements of the development of the composition that provided new evidence to consider its relationship to other versions of the composition. The study also highlighted questions about the interpretation of elemental distribution maps and spectral images that did not correspond to the reworking visible in X-radiographs. For example, in A Bar at the Folies–Bergère Manet made numerous changes during painting, which were not clearly visualised with any of the techniques used. The research has wider implications for the study of Impressionist paintings, as the results will support technical studies of works by other artists of the period who used similar materials and painting methods.     

A random telegraph signal of Mittag-Leffler type

A general method is presented to explicitly compute autocovariance functions for non-Poisson dichotomous noise based on renewal theory. The method is specialized to a random telegraph signal of Mittag-Leffler type. Analytical predictions are compared to Monte Carlo simulations. Non-Poisson dichotomous noise is non-stationary and standard spectral methods fail to describe it properly as they assume stationarity.     

Computation of weak steady shock reflections by means of an unstructured shock-fitting solver

Weak steady Mach reflections are numerically simulated using unstructured grids by means of either “shock-fitting” or “shock-capturing” techniques. It is shown that shock-fitting allows using coarser meshes than those required by shock-capturing, since the latter needs mesh refinement in the direction normal to the discontinuities, which is not needed using the former approach. The shock-fitted solution is also free from the numerical disturbances that arise along the captured discontinuities and pollute the captured solution in the smooth flowfield region. Finally, the shock-fitting solutions show the presence of a small region next to the Mach stem and the reflected shock downstream of the triple point, characterized by very high gradients.     

Absence of Phase Transitions in a Class of Integer Spin Systems

We exhibit a class of integer spin systems whose free energy can be written in term of an absolutely convergent series at any temperature. This class includes spin systems on ℤ ^d interacting through infinite range pair potential polynomially decaying at large distances r at a rate 1/r ^d+ε with ε>0. It also contains the Blume-Emery-Griffiths model in the disordered phase at large values of the crystal field.     

The effect of process variables on the characteristics of carbon nanotubes obtained by spray pyrolysis

A simple spray pyrolysis setup is used to grow multi-walled carbon nanotubes (MWCNTs), from a ferrocene solution in benzene as precursor. The effects of process variables such as growth temperature, position of the aerosol generator and position in the reactor where the sample was formed were investigated. These variables have a strong influence on the graphitization degree, homogeneity, diameter and alignment of the nanotubes, as observed by TEM, SEM, XRD and Raman spectroscopy. Vertically aligned MWCNT arrays with high density were obtained in large areas (10 × 10 mm²), with high yield (2.1 mg cm⁻²) and at a growth rate at 1.43 μm min⁻¹, by a suitable choice of the experimental conditions.     

Substrates for flexible electronics: A practical investigation on the electrical,film flexibility,optical, temperature,and solvent resistance properties

Designing and developing flexible electronics requires a thorough investigation of the substrates available for the fabrication of devices. Here, we present a practical study on a variety of significant substrates: polyethylene terephthalate (PET), its heat‐stabilized (HS) derivative, HS‐PET, and polyethylene naphthalate (PEN) plastic insulating films; indium tin oxide (ITO)‐coated ITO/PEN and ITO/PET transparent conducting films; rigid ITO/glass and FTO/glass substrates; stainless steel and titanium foils. We put the substrates through a range of tests these actually undergo during device fabrication to determine their optical, mechanical flexibility (under different types of tensile and compressive stress bending with and without a PEDOT:PSS conducting polymer layer), solvent resistance, stability to temperature treatment (conductivity and deformation), and to UV irradiation. We highlight issues and propose solutions to improve substrate response. The results and thresholds extracted reveal limitations and windows of opportunity useful for the designer of flexible optoelectronics in determining manufacturing processes and the final applications under everyday operation. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

Intercalation of heterocyclic compounds in α-zirconium phosphate: Imidazole,benzimidazole, histamine and histidine

The intercalation of imidazole and some organic species containing the imidazole ring, between the layers of crystalline zirconium phosphate has been investigated. Fourteen new, well-ordered intercalation compounds are obtained with the batch procedure at r.t. and/or 60°C. A mechanism of formation of the various compounds is proposed on the basis of the interaction between the guest molecules (with their dimensions and geometries) and the free PO₃OH groups available between the layers of the host. The new phases have been characterized by TG and X-ray methods.