Gromov hyperbolic cubic graphs

If X is a geodesic metric space and x ₁; x ₂; x ₃ ∈ X, a geodesic triangle T = {x ₁; x ₂; x ₃} is the union of the three geodesics [x ₁ x ₂], [x ₂ x ₃] and [x ₃ x ₁] in X. The space X is δ-hyperbolic (in the Gromov sense) if any side of T is contained in a δ-neighborhood of the union of the two other sides, for every geodesic triangle T in X. We denote by δ(X) the sharp hyperbolicity constant of X, i.e., δ(X) = inf {δ ≥ 0: X is δ-hyperbolic}. We obtain information about the hyperbolicity constant of cubic graphs (graphs with all of their vertices of degree 3), and prove that for any graph G with bounded degree there exists a cubic graph G* such that G is hyperbolic if and only if G* is hyperbolic. Moreover, we prove that for any cubic graph G with n vertices, we have δ(G) ≤ min {3n/16 + 1; n/4}. We characterize the cubic graphs G with δ(G) ≤ 1. Besides, we prove some inequalities involving the hyperbolicity constant and other parameters for cubic graphs.     

Generalized weighted Sobolev spaces and applications to Sobolev orthogonal polynomials II

We present a definition of general Sobolev spaces with respect to arbitrary measures, Wh,p (Ω,μ) for 1 ≤p≤∞. In [RARP] we proved that these spaces are complete under very light conditions. Now we prove that if we consider certain general types of measures, then Cc∞ (R) is dense in thee spaces. As an application to Sobolev orthogonal polynomials, we study the boundedness of the multiplication operator. This gives an estimation of the zeroes of Sobolev orthogonal polynomials.     

Fullerene derived molecularly imprinted polymer for chemosensing of adenosine-5′-triphosphate (ATP)

For molecular imprinting of oxidatively electroactive analytes by electropolymerization, we used herein reductively electroactive functional monomers. As a proof of concept, we applied C₆₀ fullerene adducts as such for the first time. For that, we derivatized C₆₀ to bear either an uracil or an amide, or a carboxy addend for recognition of the adenosine-5′-triphosphate (ATP) oxidizable analyte with the ATP-templated molecularly imprinted polymer (MIP-ATP). Accordingly, the ATP complex with all of the functional monomers formed in solution was potentiodynamically electropolymerized to deposit an MIP-ATP film either on an Au electrode of the quartz crystal resonator or on a Pt disk electrode for the piezoelectric microgravimetry (PM) or capacitive impedimetry (CI) determination of ATP, respectively, under the flow-injection analysis (FIA) conditions. The apparent imprinting factor for ATP was ∼4.0. After extraction of the ATP template, analytical performance of the resulting chemosensors, including detectability, sensitivity, and selectivity, was characterized. The limit of detection was 0.3 and 0.03 mM ATP for the PM and CI chemosensor, respectively. The MIP-ATP film discriminated structural analogues of ATP quite well. The Langmuir, Freundlich, and Langmuir–Freundlich isotherms were fitted to the experimental data of the ATP sorption and sorption stability constants appeared to be nearly independent of the adopted sorption model.     

Statistics of extremes for IID data and breakthroughs in the estimation of the extreme value index: Laurens de Haan leading contributions

In the last decades there has been a shift from the parametric statistics of extremes for IID random variables, based on the probabilistic asymptotic results in extreme value theory, towards a semi-parametric approach, where the estimation of the right tail-weight, under a quite general framework, is of major importance. After a brief presentation of classical Gumbel’s block methodology and of later improvements in the parametric framework (multivariate and multi-dimensional extreme value models for largest observations and peaks over threshold approaches), we present a coordinated overview, over the last three decades, of the developments on the estimation of the extreme value index under a semiparametric framework. Laurens de Haan has been one of the leading scientists in the field, (co-)author of many seminal ideas, that he generously shared with dozens (literally) of colleagues and students, thus achieving one of the main goals in a scientist’s life: he gathered around him a bunch of colleagues united in the endeavour of building knowledge. The last section is a personal tribute to Laurens, who fully lives his ideal that co-operation is the heart of Science. To Laurens de Haan, a token of friendship.     

A multi-analytical study of the fifteenth century mural paintings of the Batalha Monastery (Portugal) in view of their conservation

The systematic characterization of the painting’s palette and technique applied on the execution of the mural paintings of the Batalha Monastery (Batalha, Leiria, Portugal) is presented. These are the oldest mural paintings known in Portugal (apart from Roman frescoes) and represent the beginning of an artistic Portuguese tradition that continues until the nineteenth century. The aim of the study was to identify for the first time by adopting a multi-analytical physico-chemical approach of the pigments, binder, and alteration products (white veils, crusts, and pigment alteration) of these unique works of arts in order not only to better understand the painting technique, but also to support a conservation-restoration intervention that took place from April to August 2010. Micro-sampling of paint layers was performed on representative areas of the paintings. The characterization of the pigments and binders was carried out by microscopy and microanalysis of cross sections using optical microscopy, scanning electron microscopy coupled with energy dispersive X-ray spectrometry (SEM-EDS), micro-FTIR, and micro X-ray diffraction. The combined analysis of the paintings allowed the identification of the painting’s palette: Vermillion (HgS) and red ochre for the reds, yellow ochres for the yellows, green earths and malachite for the greens, azurite for the blues, and carbon for the blacks. The use of the pigment is dependent of the motive painted while the most expensive materials were used in the most important iconographic motives. Alteration of malachite was identified in darkened layers in green areas of the paintings. White veil areas on the surface of the paintings were identified as calcite from precipitation/dissolution processes due to water run-off on the sacristy dome ceiling and walls.     

On Harmonic Functions on Trees

We study the asymptotic behaviour of harmonic and p-harmonic functions (1<p<) on trees, obtaining estimates about the Hausdorff dimension of radial limits.     

GENERALIZED WEIGHTED SOBOLEV SPACES AND APPLICATIONS TO SOBOLEV ORTHOGONAL POLYNOMIALS Ⅱ

We present a definition of general Sobolev spaces with respect to arbitrary measures ,W^k,p(Ω,μ) for 1≤p≤∞,In[RARP] we proved that these spaces are complete under very light conditions.Now we prove that if we consider certain general types of measures,then Cc^∞(R) is dense in these spaces,As an application to Sobolev orthogonal polynomials,we study the boundedness of the multiplication poerator,THis gives an estimation of the zeroes of Sobolev orthogonal polynomials.     

Radial images by holomorphic mappings

Let be a nonexceptional Riemann surface, other than the punctured disk. We prove that if is a holomorphic mapping from the unit disk of the complex plane into , then the set of radial images that remain bounded in the Poincaré metric of has Hausdorff dimension at least , the exponent of convergence of . The result is best possible. This is a hyperbolic analog of the result of N. G. Makarov that Bloch functions are bounded on a set of radii of dimension one.

     

Assessment of Five SGS Models for Low-Rem MHD Turbulence

Assessment of three regularization-based and two eddy-viscosity-based subgrid-scale (SGS) turbulence models for large eddy simulations (LES) are carried out in the context of magnetohydrodynamic (MHD) decaying homogeneous turbulence (DHT) with a Taylor scale Reynolds number (Re_λ) of 120 and a MHD transition-to-turbulence Taylor-Green vortex (TGV) problems with a Reynolds number of 3000, through direct comparisons to direct numerical simulations (DNS). Simulations are conducted using the low-magnetic Reynolds number approximation (Re_m<<1). LES predictions using the regularization-based Leray- α,LANS- α, and Clark- α SGS models, along with the eddy viscosity-based non-dynamic Smagorinsky and the dynamic Smagorinsky models are compared to in-house DNS for DHT and previous results for TGV. With regard to the regularization models, this work represents their first application to MHD turbulence. Analyses of turbulent kinetic energy decay rates, energy spectra, and vorticity fields made between the varying magnetic field cases demonstrated that the regularization models performed poorly compared to the eddy-viscosity models for all MHD cases, but the comparisons improved with increase in magnitude of magnetic field, due to a decrease in the population of SGS eddies within the flow field.     

Supramolecular Tetrad Featuring Covalently Linked Bis(porphyrin)–Phthalocyanine Coordinated to Fullerene: Construction and Photochemical Studies

A multimodular donor–acceptor tetrad featuring a bis(zinc porphyrin)–(zinc phthalocyanine) ((ZnP–ZnP)–ZnPc) triad and bis‐pyridine‐functionalized fullerene was assembled by a “two‐point” binding strategy, and investigated as a charge‐separating photosynthetic antenna‐reaction center mimic. The spectral and computational studies suggested that the mode of binding of the bis‐pyridine‐functionalized fullerene involves either one of the zinc porphyrin and zinc phthalocyanine (Pc) entities of the triad or both zinc porphyrin entities leaving ZnPc unbound. The binding constant evaluated by constructing a Benesi–Hildebrand plot by using the optical data was found to be 1.17×10⁵ M ^?1, whereas a plot of “mole‐ratio” method revealed a 1:1 stoichiometry for the supramolecular tetrad. The mode of binding was further supported by differential pulse voltammetry studies, in which redox modulation of both zinc porphyrin and zinc phthalocyanine entities was observed. The geometry of the tetrad was deduced by B3LYP/6‐31G* optimization, whereas the energy levels for different photochemical events was established by using data from the optical absorption and emission, and electrochemical studies. Excitation of the zinc porphyrin entity of the triad and tetrad revealed ultrafast singlet–singlet energy transfer to the appended zinc phthalocyanine. The estimated rate of energy transfer (k_ENT) in the case of the triad was found to be 7.5×10¹¹ s^?1 in toluene and 6.3×10¹¹ s^?1 in o‐dichlorobenzene, respectively. As was predicted from the energy levels, photoinduced electron transfer from the energy‐transfer product, that is, singlet‐excited zinc phthalocyanine to fullerene was verified from the femtosecond‐transient spectral studies, both in o‐dichlorobenzene and toluene. Transient bands corresponding to ZnPc ^{? +} in the 850 nm range and C₆₀ ^{? ?} in the 1020 nm range were clearly observed. The rate of charge separation, k_CS, and rate of charge recombination, k_CR, for the (ZnP–ZnP)–ZnPc ^{? +}:Py₂C₆₀ ^{? ?} radical ion pair (from the time profile of 849 nm peak) were found to be 2.20×10¹¹ and 6.10×10⁸ s^?1 in toluene, and 6.82×10¹¹ and 1.20×10⁹ s^?1 in o‐dichlorobenzene, respectively. These results revealed efficient energy transfer followed by charge separation in the newly assembled supramolecular tetrad.