Mass‐lumping or not mass‐lumping for eigenvalue problems

In this article we analyze the effect of mass‐lumping in the linear triangular finite element approximation of second‐order elliptic eigenvalue problems. We prove that the eigenvalue obtained by using mass‐lumping is always below the one obtained with exact integration. For singular eigenfunctions, as those arising in non convex polygons, we prove that the eigenvalue obtained with mass‐lumping is above the exact eigenvalue when the mesh size is small enough. So, we conclude that the use of mass‐lumping is convenient in the singular case. When the eigenfunction is smooth several numerical experiments suggest that the eigenvalue computed with mass‐lumping is below the exact one if the mesh is not too coarse. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 653–664, 2003     

The particle structure ofv-dimensional Ising models at low temperatures

In this work we study thev-dimensional Ising model at low temperatures and establish the existence of an upper gap in the energy-momentum spectrum of the two-point function forv3. Forv=2, it is known that this gap is absent.Supported in part by Conselho Nacional de Pesquisas (CNPq-Brazil), Universidade Federal de Minas Gerais (Brazil) and the National Science Foundation under Grant PHY76-17191     

Characterization of a β-glucanase produced by Rhizopus microsporus var. microsporus, and its potential for application in the brewing industry

Background  

In the barley malting process, partial hydrolysis of β-glucans begins with seed germination. However, the endogenous 1,3-1,4-β-glucanases are heat inactivated, and the remaining high molecular weight β-glucans may cause severe problems such as increased brewer mash viscosity and turbidity. Increased viscosity impairs pumping and filtration, resulting in lower efficiency, reduced yields of extracts, and lower filtration rates, as well as the appearance of gelatinous precipitates in the finished beer. Therefore, the use of exogenous β-glucanases to reduce the β-glucans already present in the malt barley is highly desirable.     

A unique tautomer of 1‐n‐hexyl‐3‐phenyl‐1H‐pyrazol‐5‐ol

In the title compound, C₁₅H₂₀N₂O, the bond distances and angles are consistent with the presence of the hydroxy tautomer. This tautomer was unambiguously determined by the clear presence of a H atom bonded to oxygen, as well as the total absence of any residual electron density around the N atom in the heterocycle, thus precluding any possibility of desmotropism.     

Cytotoxic and NF-κB inhibitory sesquiterpene lactones from Piptocoma rufescens

Six new (1-6) and eight known germacranolide-type sesquiterpene lactones, along with several known phenylpropanol coumarates and methylated flavonoids, were isolated from the leaves of Piptocoma rufescens, collected in the Dominican Republic. The new compounds were identified by analysis of their spectroscopic data, with the molecular structure of 3 being established by single-crystal X-ray diffraction. The absolute configurations of the sesquiterpene lactones isolated were determined from their CD and NOESY NMR spectra, together with the analysis of Mosher ester reactions. Bioassay screening results showed the majority of the sesquiterpene lactones isolated (1-13) to be highly cytotoxic toward the HT-29 human colon cancer cell line, with the most potent compound being 15-deoxygoyazensolide (10, IC(50), 0.26 μM). In addition, several of the sesquiterpene lactones exhibited NF-κB (p65) inhibitory activity.     

Synthesis of pentabromopseudilin and other arylpyrrole derivatives via Heck arylations

Pentrabromopseudilin and other 2 and 3-arylpyrrole derivatives were synthesized through the Heck–Matsuda reaction involving endocyclic enecarbamates and N-protected 3-pyrrolines, respectively. The overall processes permitted an easy and efficient access to these structural motifs present in several bioactive compounds. Attempts to synthesize the compound isopentabromopseudilin led to a tribromo aryl maleimide. We hypothesize that this latter compound is the putative product arising from the unusual thermal instability of isopentabromopseudilin.     

A branching process model for sand avalanches

An analytically solvable model for sand avalanches of noninteracting grains of sand, based on the Chapman-Kolmogorov equations, is presented. For a single avalanche, distributions of lifetimes, sizes of overflows and avalanches, and correlation functions are calculated. Some of these are exponentials, some are power laws. Spatially homogeneous distributions of avalanches are also studied. Computer simulations of avalanches of interacting grains of sand are compared to the solutions to the Chapman-Kolmogorov equations. We find that within the range of parameters explored in the simulation, the approximation of noninteracting grains of sand is a good one.     

Wavefront sensing with critical sampling

Different types of nonredundant sampling patterns are shown to guarantee completeness of the basis formed by the sampled partial derivatives of Zernike polynomials, commonly used to reconstruct the wavefront from its slopes (wavefront sensing). In the ideal noise-free case, this enables one to recover double the number of modes J than sampling points I (critical sampling J=2I). With real data, noise amplification makes the optimal number of modes lower I相似文献   

DFT study of NH3 dissociation on Si(1 1 1)-7 × 7. The role of intermolecular interactions

The adsorption of NH₃ molecule on the Si(1 1 1)-7 × 7 surface modelled with a cluster has been studied using density functional theory (DFT). The results indicate the existence of a precursor state for the non-dissociative chemisorption. The active site for the molecular chemisorption is the adatom; while the NH₃ molecule adsorbs on the Si restatom via this preadsorbed state, the adsorption on the Si adatom is produced practically without an energy barrier. The ammonia adsorption on the adatom induces an electron transfer from the dangling bond of this atom to the dangling bond of the adjacent Si restatom, hindering this site for the adsorption of a second NH₃ incoming molecule. However, this second molecule links strongly by means of two H-bonds. The dissociative chemisorption process was studied considering one and two ammonia molecules. For the dissociation of a lonely NH₃ molecule an energy barrier of ∼0.3 eV was calculated, yielding NH₂ on the adatom and H on the restatom. When two molecules are adsorbed, the NH₃-NH₃ interaction yields the weakening of a N-H bond of the ammonia molecule adsorbed closer the Si surface. As a consequence, the dissociation barrier practically disappears. Thus, the presence of a second NH₃ molecule at the adatom-restatom pair of the Si(1 1 1)-7 × 7 surface makes the dissociative reaction self-assisted, the total adsorption process elapsing with a negligible activation barrier (less than 0.01 eV).