The L p -Solvability of the Dirichlet Problem for Planar Elliptic Equations, Sharp Results

Assume that the elliptic operator L=div (A(x)∇) is L ^p -resolutive, p>1, on the unit disc \mathbbD ì \mathbb R²\mathbb{D}\subset \mathbb {R}^{2} . This means that the Dirichlet problem

Examples of Para-cocyclic Objects Induced by BD-Laws

In a recent paper (Böhm and Stefan, Commun Math Phys 282:239–286, 2008), we gave a general construction of a para-cocyclic structure on a cosimplex, associated to a so called admissible septuple—consisting of two categories, three functors and two natural transformations, subject to compatibility relations. The main examples of such admissible septuples were induced by algebra homomorphisms. In this note we provide more general examples coming from appropriate (‘locally braided’) morphisms of monads.     

Building addressable libraries: The use of a mass spectrometry cleavable linker for monitoring reactions on a microelectrode array

Time-of-flight secondary ion mass spectrometry (TOF SIMS) has been used in conjunction with a mass spectrometry cleavable linker to determine the percent conversion of reactions that were conducted site-selectively on an addressable microelectrode array. When combined with fluorescence techniques for analysis of the reactions, the TOF SIMS experiment provides a means for optimization of both reaction confinement and reaction efficiency on the microelectrode arrays.     

Gibbsian Stationary Non-equilibrium States

We study the structure of stationary non-equilibrium states for interacting particle systems from a microscopic viewpoint. In particular we discuss two different discrete geometric constructions. We apply both of them to determine non reversible transition rates corresponding to a fixed invariant measure. The first one uses the equivalence of this problem with the construction of divergence free flows on the transition graph. Since divergence free flows are characterized by cyclic decompositions we can generate families of models from elementary cycles on the configuration space. The second construction is a functional discrete Hodge decomposition for translational covariant discrete vector fields. According to this, for example, the instantaneous current of any interacting particle system on a finite torus can be canonically decomposed in a gradient part, a circulation term and an harmonic component. All the three components are associated with functions on the configuration space. This decomposition is unique and constructive. The stationary condition can be interpreted as an orthogonality condition with respect to an harmonic discrete vector field and we use this decomposition to construct models having a fixed invariant measure.     

Stiffness contribution of cellulose nanofibrils to composite materials

Nanocomposites, reinforced by different types of cellulose fibrils, have gained increased interest the last years due to the promising mechanical properties. There is a lack of knowledge about the mechanical properties of the cellulose fibrils, and their contribution to the often claimed potential of the impressive mechanical performance of the nanocomposites. This paper investigates the contribution from different types of cellulose nanofibril to the overall elastic properties of composites. A multiscale model is proposed, that allows back-calculation of the elastic properties of the fibril from the macroscopic elastic properties of the composites. The different types of fibrils used were nanofibrillated cellulose from wood, bacterial cellulose nano-whiskers and microcrystalline cellulose. Based on the overall properties of the composite with an unaged polylactide matrix, the effective longitudinal Young’s modulus of the fibrils was estimated to 65 GPa for the nanofibrillated cellulose, 61 GPa for the nano whiskers and only 38 GPa for the microcrystalline cellulose. The ranking and absolute values are in accordance with other studies on nanoscale morphology and stiffness estimates. Electron microscopy revealed that in the melt-processed cellulose nanofibril reinforced thermoplastics, the fibrils tended to agglomerate and form micrometer scale platelets, effectively forming a microcomposite and not a nanocomposite. This dispersion effect has to be addressed when developing models describing the structure–property relations for cellulose nanofibril composites.     

Has a fermiophobic Higgs boson been detected at the LHC?

We show that, in the present inclusive searches for the Higgs boson at the LHC, a fermiophobic Higgs mimics the standard-model-like Higgs if its mass is around 125 GeV. For that mass the order-of-magnitude reduction of fermiophobic Higgs production cross sections is compensated by a corresponding increase in the Higgs branching fraction into γγ  , while the WW^?$W{W}^{?}$, ZZ^?$Z{Z}^{?}$, Zγ signal yields are predicted to be somewhat smaller. The excess seen in the ATLAS and CMS fermiophobic Higgs boson searches in the γγ channel, including the exclusive vector-boson-fusion analysis, could point to a fermiophobic rather than a standard-model Higgs boson. If the Higgs boson will turn out to be fermiophobic, many of our present ideas of new physics should be revised.     

Competitors’ communities and taxonomy of products according to export fluxes

In this paper we use Complex Network Theory to quantitatively characterize and synthetically describe the complexity of trade between nations. In particular, we focus our attention on export fluxes. Starting from the bipartite countries-products network defined by export fluxes, we define two complementary graphs projecting the original network on countries and products respectively. We define, in both cases, a distance matrix amongst countries and products. Specifically, two countries are similar if they export similar products. This relationship can be quantified by building the Minimum Spanning Tree and the Minimum Spanning Forest from the distance matrices for products and countries. Through this simple and scalable method we are also able to carry out a community analysis. It is not gone unnoticed that in this way we can produce an effective categorization for products providing several advantages with respect to traditional classifications of COMTRADE [1]. Finally, the forests of countries allows for the detection of competitors’ community and for the analysis of the evolution of these communities.     

Configurational assignments of the diastereomers of 3,3′‐(1,2‐ethanediyl)bis[2‐(3‐fluorophenyl)‐5‐methyl‐4‐thiazolidinone] derivative with four stereogenic centers

Diastereomers of antiinflammatory/analgesic and antihistaminic 3,3′[(1,2‐ethanediyl)bis(2‐aryl‐4‐thiazo‐lidinone)] derivatives possessing two stereogenic centers (indicated as BIS 2*C) have been widely investigated in recent years. The 5,5′‐dimethyl analogues (BIS 4*C), now reported, have been synthesized by reaction of (±) α‐mercaptopropionic acid and N,N'‐di(3‐fluorobenzyliden)ethylenediamine. Because the 2 and 2′carbons bear the same groups and similarly the 5 and 5′ carbons, and the latter groups are different from the former, four enantiomeric pairs and two meso forms exist in this situation. These diastereomers were identified by the concerted use of nmr spectroscopy and hplc on chiral stationary phase.