Gaussian extended cubature formulae for polyharmonic functions

The purpose of this paper is to show certain links between univariate interpolation by algebraic polynomials and the representation of polyharmonic functions. This allows us to construct cubature formulae for multivariate functions having highest order of precision with respect to the class of polyharmonic functions. We obtain a Gauss type cubature formula that uses ℳ values of linear functional (integrals over hyperspheres) and is exact for all 2ℳ-harmonic functions, and consequently, for all algebraic polynomials of n variables of degree 4ℳ - 1.

Integration of polyharmonic functions

The results in this paper are motivated by two analogies. First, m-harmonic functions in R(n) are extensions of the univariate algebraic polynomials of odd degree 2m-1. Second, Gauss' and Pizzetti's mean value formulae are natural multivariate analogues of the rectangular and Taylor's quadrature formulae, respectively. This point of view suggests that some theorems concerning quadrature rules could be generalized to results about integration of polyharmonic functions. This is done for the Tchakaloff-Obrechkoff quadrature formula and for the Gaussian quadrature with two nodes.

Polinômios ortogonais em várias variáveis

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

The collapse of linear polyelectrolyte chains in a poor solvent: When does a collapsing polyelectrolyte collect its counter ions?

The collapse of linear polyelectrolyte chains in a poor solvent: When does a collapsing polyelectrolyte collect its counter ions? The collapse of polyions in a poor solvent is a complex system and is an active research subject in the theoretical polyelectrolyte community. The complexity is due to the subtle interplay between hydrophobic effects, electrostatic interactions, entropy elasticity, intrinsic excluded volume as well as specific counter-ion and co-ion properties. Long range Coulomb forces can obscure single molecule properties. The here presented approach is to use just a small amount of screening salt in combination with a very high sample dilution in order to screen intermolecular interaction whereas keeping intramolecular interaction as much as possible (polyelectrolyte concentration cp ≤ 12 mg/L, salt concentration; Cs = 10^-5 mol/L). This is so far not described in literature. During collapse, the polyion is subject to a drastic change in size along with strong reduction of free counterions in solution. Therefore light scattering was utilized to obtain the size of the polyion whereas a conductivity setup was developed to monitor the proceeding of counterion collection by the polyion. Partially quaternized PVP’s below and above the Manning limit were investigated and compared to the collapse of their uncharged precursor. The collapses were induced by an isorefractive solvent/non-solvent mixture consisting of 1-propanol and 2-pentanone, with nearly constant dielectric constant. The solvent quality for the uncharged polyion could be quantified which, for the first time, allowed the experimental investigation of the effect of electrostatic interaction prior and during polyion collapse. Given that the Manning parameter M for QPVP4.3 is as low as lB / c = 0.6 (lB the Bjerrum length and c the mean contour distance between two charges), no counterion binding should occur. However the Walden product reduces with first addition of non solvent and accelerates when the structural collapse sets in. Since the dielectric constant of the solvent remains virtually constant during the chain collapse, the counterion binding is entirely caused by the reduction in the polyion chain dimension. The collapse is shifted to lower wns with higher degrees of quaternization as the samples QPVP20 and QPVP35 show (M = 2.8 respectively 4.9). The combination of light scattering and conductivity measurement revealed for the first time that polyion chains already collect their counter ions well above the theta-dimension when the dimensions start to shrink. Due to only small amounts of screening salt, strong electrostatic interactions bias dynamic as well as static light scattering measurements. An extended Zimm formula was derived to account for this interaction and to obtain the real chain dimensions. The effective degree of dissociation g could be obtained semi quantitatively using this extrapolated static in combination with conductivity measurements. One can conclude the expansion factor a and the effective degree of ionization of the polyion to be mutually dependent. In the good solvent regime g of QPVP4.3, QPVP20 and QPVP35 exhibited a decreasing value in the order 1 > g4.3 > g20 > g35. The low values of g for QPVP20 and QPVP35 are assumed to be responsible for the prior collapse of the higher quaternized samples. Collapse theory predicts dipole-dipole attraction to increase accordingly and even predicts a collapse in the good solvent regime. This could be exactly observed for the QPVP35 sample. The experimental results were compared to a newly developed theory of uniform spherical collapse induced by concomitant counterion binding developed by M. Muthukumar and A. Kundagrami. The theory agrees qualitatively with the location of the phase boundary as well as the trend of an increasing expansion with an increase of the degree of quaternization. However experimental determined g for the samples QPVP4.3, QPVP20 and QPVP35 decreases linearly with the degree of quaternization whereas this theory predicts an almost constant value.

Polysomnographic record and successful management of augmentation in restless legs syndrome/Willis-Ekbom disease

BACKGROUND: Dopamine agonists (DAs) represent the first-line treatment in restless legs syndrome (RLS); however, in the long term, a substantial proportion of patients will develop augmentation, which is a severe drug-related exacerbation of symptoms and the main reason for late DA withdrawal. Polysomnographic features and mechanisms underlining augmentation are unknown. No practice guidelines for management of augmentation are available. METHODS: A clinical case series of 24 consecutive outpatients affected by RLS with clinically significant augmentation during treatment with immediate-release DA was performed. All patients underwent a full-night polysomnographic recording during augmentation. A switchover from immediate-release DAs (l-dopa, pramipexole, ropinirole, rotigotine) to the long-acting, extended-release formula of pramipexole was performed. RESULTS: Fifty percent of patients presented more than 15 periodic limb movements per hour of sleep during augmentation, showing longer sleep latency and shorter total sleep time than subjects without periodic limb movements. In all patients, resolution of augmentation was observed within two to four weeks during which immediate-release dopamine agonists could be completely withdrawn. Treatment efficacy of extended-release pramipexole has persisted, thus far, over a mean follow-up interval of 13 months. CONCLUSIONS: Pramipexole extended release could be an easy, safe, and fast pharmacological option to treat augmentation in patients with restless legs syndrome. As such it warrants further prospective and controlled investigations. This observation supports the hypothesis that the duration of action of the drug plays a key role in the mechanism of augmentation.

A generalization of Hull and White formula and applications to option pricing approximation

By means of Malliavin Calculus we see that the classical Hull and White formulafor option pricing can be extended to the case where the noise driving thevolatility process is correlated with the noise driving the stock prices. Thisextension will allow us to construct option pricing approximation formulas.Numerical examples are presented.

Batchelor's theory extended to elongated cylindrical or ellipsoidal particles

Extensions to Batchelor's theory have been derived to take into account different shaped particles while relating extensional viscosity enhancement to three parameters - shape, volume fraction and particle aspect ratio. The extended theory now allows calculation of the extensional viscosity enhancement, at a given volume fraction of particles, for either ellipsoidal or cylindrical particles. The formula improves the predictive capability of Batchelor's theory when compared with measurements found in the literature for different rod-like polymer solutions. (c) 2005 Elsevier B.V. All rights reserved.

Emergence of Klebsiella pneumoniae carrying the novel extended-spectrum 'beta'-lactamase gene variants 'bla IND. SHV-40', 'bla IND. TEM-116' and the class I integron-associated 'bla IND. GES-7' in Brazil

A clinical Klebsiella pneumoniae isolate carrying the extended-spectrum beta-lactamase gene variants bla(SHV-40), bla(TEM-116) and bla(GES-7) was recovered. Cefoxitin and ceftazidime activity was most affected by the presence of these genes and an additional resistance to trimethoprim-sulphamethoxazole was observed. The bla(GES-7) gene was found to be inserted into a class 1 integron. These results show the emergence of novel bla(TEM) and bla(SHV) genes in Brazil. Moreover, the presence of class 1 integrons suggests a great potential for dissemination of bla(GES) genes into diverse nosocomial pathogens. Indeed, the bla(GES-7) gene was originally discovered in Enterobacter cloacae in Greece and, to our knowledge, has not been reported elsewhere

Extended-spectrum beta-lactamases among Enterobacteriaceae isolated in a public hospital in Brazil

Extended-spectrum beta-lactamases (ESBL) in enterobacteria are recognized worldwide as a great hospital problem. In this study, 127 ESBL-producing Enterobacteriaceae isolated in one year from inpatients and Outpatients at a public teaching hospital at Sao Paulo, Brazil, were Submitted to analysis by PCR with specific primers for bla(SHV), bla(TEM) and bla(CTX-M) genes. From the 127 isolates, 96 (75.6%) Klebsiella pneumoniae, 12 (9.3%) Escherichia coli, 8 (6.2%) Morganella morganii, 3 (2.3%) Proteus mirabilis, 2 (1.6%) Klebsiella oxytoca, 2 (1.6%) Providencia rettgeri, 2 (1.6%) Providencia stuartti, 1 (0.8%) Enterobacter aerogenes and 1 (0.8%) Enterobacter cloacae were identified as ESBL producers. Bla(SHV), bla(TEM), and bla(CTX-M) were detected in 63%, 17.3% and 33.9% strains, respectively. Pulsed field get eletrophoresis genotyping of K. pneumoniae revealed four main molecular patterns and 29 unrelated profiles. PCR results showed a high variety of ESBL groups among strains, in nine different species. The results Suggest the spread of resistance genes among genetically different strains of ESBL-producing K. pneumoniae in some hospital wards, and also that some strongly related strains were identified in different hospital wards, Suggesting clonal spread in the institutional environment

Crossover between the extended and localized regimes in stochastic partially self-avoiding walks in one-dimensional disordered systems

Consider N sites randomly and uniformly distributed in a d-dimensional hypercube. A walker explores this disordered medium going to the nearest site, which has not been visited in the last mu (memory) steps. The walker trajectory is composed of a transient part and a periodic part (cycle). For one-dimensional systems, travelers can or cannot explore all available space, giving rise to a crossover between localized and extended regimes at the critical memory mu(1) = log(2) N. The deterministic rule can be softened to consider more realistic situations with the inclusion of a stochastic parameter T (temperature). In this case, the walker movement is driven by a probability density function parameterized by T and a cost function. The cost function increases as the distance between two sites and favors hops to closer sites. As the temperature increases, the walker can escape from cycles that are reminiscent of the deterministic nature and extend the exploration. Here, we report an analytical model and numerical studies of the influence of the temperature and the critical memory in the exploration of one-dimensional disordered systems.

High Prevalence of bla(CTX-M) Extended Spectrum Beta-Lactamase Genes in Klebsiella pneumoniae Isolates from a Tertiary Care Hospital: First report of bla(SHV-12), bla(SHV-31), bla(SHV-38), and bla(CTX-M-15) in Brazil

The aim of this study was to investigate the presence and prevalence of bla(TEM), bla(SHV), and bla(CTX-M) and bla(GES)-like genes, responsible for extended spectrum beta-lactamases (ESBLs) production in clinical isolates of Klebsiella pneumoniae collected from a Brazilian tertiary care hospital. Sixty-five ESBL producing K. pneumoniae isolates, collected between 2005 and 2007, were screened by polymerase chain reaction (PCR). Identification of bla genes was achieved by sequencing. Genotyping of ESBL producing K. pneumoniae was performed by the enterobacterial repetitive intergenic consensus-PCR with cluster analysis by the Dice coefficient. The presence of genes encoding ESBLs was confirmed in 59/65 (90.8%) isolates, comprising 20 bla(CTX-M-2), 14 bla(CTX-M-59), 12 bla(CTX-M-15), 9 bla(SHV-12), 1 bla(SHV-2), 1 bla(SHV-2a), 1 bla(SHV-5), and 1 bla(SHV-31) genes. The ESBL genes bla(SHV-12), bla(SHV-31), and bla(CTX-M-15), and the chromosome-encoded SHV-type beta-lactamase capable of hydrolyzing imipenem were detected in Brazil for the first time. The analysis of the enterobacterial repetitive intergenic consensus-PCR band patterns revealed a high rate of multiclonal bla(CTX-M) carrying K. pneumoniae isolates (70.8%), suggesting that dissemination of encoding plasmids is likely to be the major cause of the high prevalence of these genes among the K. pneumoniae isolates considered in this study.

Synchrotron X-ray powder diffraction and extended X-ray absorption fine structure spectroscopy studies on nanocrystalline ZrO(2)-CaO solid solutions

The crystal structure and the local atomic order of a series of nanocrystalline ZrO(2)-CaO solid solutions with varying CaO content were studied by synchrotron radiation X-ray powder diffraction and extended X-ray absorption fine structure (EXAFS) spectroscopy. These samples were synthesized by a pH-controlled nitrate-glycine gel-combustion process. For CaO contents up to 8 mol%, the t' form of the tetragonal phase (c/a > 1) was identified, whereas for 10 and 12 mol% CaO, the t '' form (c/a=1; oxygen anions displaced from their ideal positions in the cubic phase) was detected. Finally, the cubic phase was observed for solid solutions with CaO content of 14 mol% CaO or higher. The t'/t '' and t ''/cubic compositional boundaries were determined to be at 9 (1) and 13 (1) mol% CaO, respectively. The EXAFS study demonstrated that this transition is related to a tetragonal-to-cubic symmetry change of the first oxygen coordination shell around the Zr atoms.

Two-dimensional supersonic nonlinear Schrodinger flow past an extended obstacle

Supersonic flow of a superfluid past a slender impenetrable macroscopic obstacle is studied in the framework of the two-dimensional (2D) defocusing nonlinear Schroumldinger (NLS) equation. This problem is of fundamental importance as a dispersive analog of the corresponding classical gas-dynamics problem. Assuming the oncoming flow speed is sufficiently high, we asymptotically reduce the original boundary-value problem for a steady flow past a slender body to the one-dimensional dispersive piston problem described by the nonstationary NLS equation, in which the role of time is played by the stretched x coordinate and the piston motion curve is defined by the spatial body profile. Two steady oblique spatial dispersive shock waves (DSWs) spreading from the pointed ends of the body are generated in both half planes. These are described analytically by constructing appropriate exact solutions of the Whitham modulation equations for the front DSW and by using a generalized Bohr-Sommerfeld quantization rule for the oblique dark soliton fan in the rear DSW. We propose an extension of the traditional modulation description of DSWs to include the linear ""ship-wave"" pattern forming outside the nonlinear modulation region of the front DSW. Our analytic results are supported by direct 2D unsteady numerical simulations and are relevant to recent experiments on Bose-Einstein condensates freely expanding past obstacles.

Spectroscopic evidence of extended states in the quantized Hall phase of weakly coupled GaAs/AlGaAs multilayers

The influence of interlayer coupling on the formation of the quantized Hall phase at the filling factor nu=2 was studied in multilayer GaAs/AlGaAs heterostructures. The disorder broadened Gaussian photoluminescence line due to localized electrons was found in the quantized Hall phase of the isolated multi-quanturn-well structure. On the other hand, the quantized Hall phase of weakly coupled multilayers emitted an unexpected asymmetrical line similar to that observed in metallic electron systems. We demonstrated that the observed asymmetry is caused by the partial population of extended electron states formed in the insulating quantized Hall phase due to spin-assisted interlayer percolation. A sharp decrease in the single-particle scattering time associated with these extended states was observed for the filling factor nu=2. (C) 2008 American Institute of Physics. [DOI: 10.1063/1.2978194]

An extended BEM formulation for plates reinforced by rectangular beams

This article presents a BEM formulation developed particularly for analysis of plates reinforced by rectangular beams. This is an extended version of a Previous paper that only took into account bending effects. The problem is now re-formulated to consider bending and membrane force effects. The effects of the reinforcements are taken into account by using a simplified scheme that requires application of ail initial stress field to locally correct the bending and stretching stiffness of the reinforcement regions. The domain integrals due to the presence of the reinforcements are then transformed to the reinforcement/plate interface. To reduce the number of degrees of freedom related to the presence of the reinforcement, the proposed model was simplified to consider only bending and stretching rigidities in the direction of the beams. The complete model can be recovered by applying all six internal force correctors, corresponding to six degrees of freedom per node. Examples are presented to confirm the accuracy of the formulation and to illustrate the level of simplification introduced by this strong reduction in the number of degrees of freedom. (C) 2008 Elsevier Ltd. All rights reserved.