On asymptotic behavior at infinity and the finite section method for integral equations on the half-line

e consider integral equations on the half-line of the form and the finite section approximation to x obtained by replacing the infinite limit of integration by the finite limit β. We establish conditions under which, if the finite section method is stable for the original integral equation (i.e. exists and is uniformly bounded in the space of bounded continuous functions for all sufficiently large β), then it is stable also for a perturbed equation in which the kernel k is replaced by k + h. The class of perturbations allowed includes all compact and some non-compact perturbations of the integral operator. Using this result we study the stability and convergence of the finite section method in the space of continuous functions x for which ()()()=−∫∞dttxt,sk)s(x0()syβxβx()sxsp+1 is bounded. With the additional assumption that ()(tskt,sk−≤ where ()()(),qsomefor,sassOskandRLkq11>+∞→=∈− we show that the finite-section method is stable in the weighted space for ,qp≤≤0 provided it is stable on the space of bounded continuous functions. With these results we establish error bounds in weighted spaces for x - xβ and precise information on the asymptotic behaviour at infinity of x. We consider in particular the case when the integral operator is a perturbation of a Wiener-Hopf operator and illustrate this case with a Wiener-Hopf integral equation arising in acoustics.

Late Barremian-Early Aptian palaeoenvironmental change: the Cassis-La Bedoule section (SE France)

The well-dated section of Cassis-La Bédoule in the South Provencal Basin (southern France) allows for a detailed reconstruction of palaeoenvironmental change during the latest Barremian and Early Aptian. For this study, phosphorus (P) and clay-mineral contents, stable-isotope ratios on carbonate (δ13Ccarb) and organic matter (δ13Corg), and redox-sensitive trace elements (RSTE: V, U, As, Co, and Mo) have been measured in this historical stratotype. The base of the section consists of rudist limestone, which is attributed to the Urgonian platform. The presence of low P and RSTE content, and content of up to 30% kaolinite indicate deposition under oligotrophic and oxic conditions, and the presence of warm, humid climatic conditions on the adjacent continent. The top of the Urgonian succession is marked by a hardground with encrusted brachiopods and bivalves, which is interpreted as a drowning surface. The section continues with a succession of limestone and marl containing the first occurrence of planktonic foraminifera. This interval includes several laminated, organic-rich layers recording RSTE enrichments and high Corg:Ptot ratios. The deposition of these organic-rich layers was associated with oxygen-depleted conditions and a large positive excursion in δ13Corg. During this interval, a negative peak in the δ13Ccarb record is observed, which dates as latest Barremian. This excursion is coeval with negative excursions elsewhere in Tethyan platform and basin settings and is explained by the increased input of light dissolved inorganic carbon by rivers and/or volcanic activity. In this interval, an increase in P content, owing to reworking of nearshore sediments during the transgression, is coupled with a decrease in kaolinite content, which tends to be deposited in more proximal areas. The overlying hemipelagic sediments of the Early Aptian Deshayesites oglanlensis and D. weissi zones indicate rather stable palaeoenvironmental conditions with low P content and stable δ13C records. A change towards marl-dominated beds occurs close to the end of the D. weissi zone. These beds display a long decrease in their δ13Ccarb and δ13Corg records, which lasted until the end of the Deshayesites deshayesi subzone (corresponding to C3 in Menegatti et al., 1998). This is followed by a positive shift during the Roloboceras hambrovi and Deshayesites grandis subzones, which corresponds in time to oceanic anoxic event (OAE) 1a interval. This positive shift is coeval with two increases in the P content. The marly interval equivalent to OAE 1a lacks organic-rich deposits and RSTE enrichments indicating that oxic conditions prevailed in this particular part of the Tethys ocean. The clay mineralogy is dominated by smectite, which is interpreted to reflect trapping of kaolinite on the surrounding platforms rather than indicating a drier climate.

Efficient incorporation of channel cross-section geometry uncertainty into regional and global scale flood inundation models

This paper investigates the challenge of representing structural differences in river channel cross-section geometry for regional to global scale river hydraulic models and the effect this can have on simulations of wave dynamics. Classically, channel geometry is defined using data, yet at larger scales the necessary information and model structures do not exist to take this approach. We therefore propose a fundamentally different approach where the structural uncertainty in channel geometry is represented using a simple parameterization, which could then be estimated through calibration or data assimilation. This paper first outlines the development of a computationally efficient numerical scheme to represent generalised channel shapes using a single parameter, which is then validated using a simple straight channel test case and shown to predict wetted perimeter to within 2% for the channels tested. An application to the River Severn, UK is also presented, along with an analysis of model sensitivity to channel shape, depth and friction. The channel shape parameter was shown to improve model simulations of river level, particularly for more physically plausible channel roughness and depth parameter ranges. Calibrating channel Manning’s coefficient in a rectangular channel provided similar water level simulation accuracy in terms of Nash-Sutcliffe efficiency to a model where friction and shape or depth were calibrated. However, the calibrated Manning coefficient in the rectangular channel model was ~2/3 greater than the likely physically realistic value for this reach and this erroneously slowed wave propagation times through the reach by several hours. Therefore, for large scale models applied in data sparse areas, calibrating channel depth and/or shape may be preferable to assuming a rectangular geometry and calibrating friction alone.

Equation for the microwave backscatter cross section of aggregate snowflakes using the self-similar Rayleigh–Gans approximation

In this paper an equation is derived for the mean backscatter cross section of an ensemble of snowflakes at centimeter and millimeter wavelengths. It uses the Rayleigh–Gans approximation, which has previously been found to be applicable at these wavelengths due to the low density of snow aggregates. Although the internal structure of an individual snowflake is random and unpredictable, the authors find from simulations of the aggregation process that their structure is “self-similar” and can be described by a power law. This enables an analytic expression to be derived for the backscatter cross section of an ensemble of particles as a function of their maximum dimension in the direction of propagation of the radiation, the volume of ice they contain, a variable describing their mean shape, and two variables describing the shape of the power spectrum. The exponent of the power law is found to be −. In the case of 1-cm snowflakes observed by a 3.2-mm-wavelength radar, the backscatter is 40–100 times larger than that of a homogeneous ice–air spheroid with the same mass, size, and aspect ratio.

Commodity risks and the cross-section of equity returns

The article examines whether commodity risk is priced in the cross-section of global equity returns. We employ a long-only equally-weighted portfolio of commodity futures and a term structure portfolio that captures phases of backwardation and contango as mimicking portfolios for commodity risk. We find that equity-sorted portfolios with greater sensitivities to the excess returns of the backwardation and contango portfolio command higher average excess returns, suggesting that when measured appropriately, commodity risk is pervasive in stocks. Our conclusions are robust to the addition to the pricing model of financial, macroeconomic and business cycle-based risk factors.

An Alternative Section Method for Casting and Posterior Laser Welding of Metallic Frameworks for an Implant-Supported Prosthesis

Purpose: The aim of this study was to compare the accuracy of fit of three types of implant-supported frameworks cast in Ni-Cr alloy: specifically, a framework cast as one piece compared to frameworks cast separately in sections to the transverse or the diagonal axis, and later laser welded. Materials and Methods: Three sets of similar implant-supported frameworks were constructed. The first group of six 3-unit implant-supported frameworks were cast as one piece, the second group of six were sectioned in the transverse axis of the pontic region prior to casting, and the last group of six were sectioned in the diagonal axis of the pontic region prior to casting. The sectioned frameworks were positioned in the matrix (10 N(.)cm torque) and laser welded. To evaluate passive fit, readings were made with an optical microscope with both screws tightened and with only one-screw tightened. Data were submitted to ANOVA and Tukey-Kramer`s test (p < 0.05). Results: When both screws were tightened, no differences were found between the three groups (p > 0.05). In the single-screw-tightened test, with readings made opposite to the tightened side, the group cast as one piece (57.02 +/- 33.48 mu m) was significantly different (p < 0.05) from the group sectioned diagonally (18.92 +/- 4.75 mu m) but no different (p > 0.05) from the group transversally sectioned (31.42 +/- 20.68 mu m). On the tightened side, no significant differences were found between the groups (p > 0.05). Conclusions: Results of this study showed that casting diagonally sectioned frameworks lowers misfit levels of prosthetic implant-supported frameworks and also improves the levels of passivity to the same frameworks when compared to structures cast as one piece.

Modified section method for laser-welding of ill-fitting cp Ti and Ni-Cr alloy one-piece cast implant-supported frameworks

P>This study aimed to verify the effect of modified section method and laser-welding on the accuracy of fit of ill-fitting commercially pure titanium (cp Ti) and Ni-Cr alloy one-piece cast frameworks. Two sets of similar implant-supported frameworks were constructed. Both groups of six 3-unit implant-supported fixed partial dentures were cast as one-piece [I: Ni-Cr (control) and II: cp Ti] and evaluated for passive fitting in an optical microscope with both screws tightened and with only one screw tightened. All frameworks were then sectioned in the diagonal axis at the pontic region (III: Ni-Cr and IV: cp Ti). Sectioned frameworks were positioned in the matrix (10-Ncm torque) and laser-welded. Passive fitting was evaluated for the second time. Data were submitted to anova and Tukey-Kramer honestly significant difference tests (P < 0 center dot 05). With both screws tightened, one-piece cp Ti group II showed significantly higher misfit values (27 center dot 57 +/- 5 center dot 06 mu m) than other groups (I: 11 center dot 19 +/- 2 center dot 54 mu m, III: 12 center dot 88 +/- 2 center dot 93 mu m, IV: 13 center dot 77 +/- 1 center dot 51 mu m) (P < 0 center dot 05). In the single-screw-tightened test, with readings on the opposite side to the tightened side, Ni-Cr cast as one-piece (I: 58 center dot 66 +/- 14 center dot 30 mu m) was significantly different from cp Ti group after diagonal section (IV: 27 center dot 51 +/- 8 center dot 28 mu m) (P < 0 center dot 05). On the tightened side, no significant differences were found between groups (P > 0 center dot 05). Results showed that diagonally sectioning ill-fitting cp Ti frameworks lowers misfit levels of prosthetic implant-supported frameworks and also improves passivity levels of the same frameworks when compared to one-piece cast structures.

Taxonomic survey of Paepalanthus section Diphyomene (Eriocaulaceae)

Paepalanthus is the largest genus in Eriocaulaceae, comprising about 400 species distributed mainly throughout the Neotropics. Through phylogenetic studies it has been demonstrated that the genus is polyphyletic, although many of its infrageneric categories are monophyletic. In an attempt to clarify the nomenclature and classification of Paepalanthus, we present a taxonomic survey of Paepalanthus section Diphyomene. This group consists of 10 species restricted to South America and is defined by inflorescences being arranged in the form of a tribotryum with terminal dibotryum, a terminal basic unit and pherophylls subtending the lateral dibotrya. Further important distinguishing characteristics are dimerous flowers, pistillate flowers with dolabriform sepals, bifid stigmatic branches and absent staminodes, and staminate flowers with an elongated anthophore. We hereby propose 19 new synonyms, six lectotypifications, one new status, one neotypification and one epitypification.

Five New and Narrowly Distributed Species of Paepalanthus Section Diphyomene (Eriocaulaceae) from Central Brazil

Five new species of Paepalanthus section Diphyomene are described and illustrated: P. brevis, P. flexuosus, P. longiciliatus, P. macer, and P. stellatus. Paepalanthus brevis, similar to P. decussus, is easily distinguished by its short reproductive axis, and pilose and mucronate leaves. Paepalanthus flexuosus, morphologically related to P. urbanianus, possesses a distinctive short and tortuous reproductive axis. Paepalanthus longiciliatus, morphologically similar to P. weddellianus, possesses long trichomes on the margins of the reproductive axis bracts, considered a diagnostic feature. Paepalanthus macer shares similarities with P. amoenus, differing by its sulfurous capitula and adpressed reproductive axis bracts. Paepalanthus stellatus also has affinity with P. decussus, but possesses unique, membranaceous, reproductive-axis bracts and a punctual inner-capitulum arrangement of pistillate flowers. Four of the described species are narrowly distributed in the state of Goias, whereas P. brevis is endemic to Distrito Federal. All are considered critically endangered. Detailed comparisons of these species are presented in tables. Comments on phenology, distribution, habitat and etymology, along with an identification key, are provided.

Baccharis scopulorum, a new species of section Caulopterae (Asteraceae: Astereae) from rocky cliffs of southern Brazil

A new species of Baccharis sect. Caulopterae endemic to rocky cliffs in southern Brazil, is here described as Baccharis scopulorum. This new species is characterized by the general presence of basal and persistent leaves, mostly solitary capitula born at the tips of the branches, and many flowered capitula, the pistillate capitula with an urceolate to campanulate involucres. The new species is morphologically most similar to B. altimontana and B. opuntioides, both inhabiting mountain summits in eastern Brazil. A description of B. scopulorum, together with illustrations, a distribution map, habitat description, conservation assessment and diagnostic comparison with B. altimontana and B. opuntioides is presented.

A new species of Croton section Cleodora (Euphorbiaceae s.s.) from Minas Gerais, Brazil

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Molecular phylogenetics and character evolution of the ""sacaca"" clade: Novel relationships of Croton section Cleodora (Euphorbiaceae)

Phylogenetic relationships of Croton section Cleodora (Klotzsch) Baill. were evaluated using the nuclear ribosomal ITS and the chloroplast trnl-F and trnH-psbA regions. Our results show a strongly supported clade containing most previously recognized section Cleodora species, plus some other species morphologically similar to them. Two morphological synapomorphies that support section Cleodora as a clade include pistillate flowers in which the sepals overlap to some degree, and styles that are connate at the base to varying degrees. The evolution of vegetative and floral characters that have previously been relied on for taxonomic decisions within this group are evaluated in light of the phylogenetic hypotheses. Within section Cleodora there are two well-supported clades, which are proposed here as subsections (subsection Sphaerogyni and subsection Spruceani). The resulting phylogenetic hypothesis identifies the closest relatives of the medicinally important and essential oil-rich Croton cajucara Benth. as candidates for future screening in phytochemical and pharmacological studies. (C) 2011 Elsevier Inc. All rights reserved.

Measurement of thermal neutron cross section and resonance integral for the (165)Ho(n, gamma)(166g)Ho reaction

The ground state thermal neutron cross section and the resonance integral for the (165)Ho(n, gamma)(166)Ho reaction in thermal and 1/E regions, respectively, of a thermal reactor neutron spectrum have been measured experimentally by activation technique. The reaction product, (166)Ho in the ground state, is gaining considerable importance as a therapeutic radionuclide and precisely measured data of the reaction are of significance from the fundamental point of view as well as for application. In this work, the spectrographically pure holmium oxide (Ho(2)O(3)) powder samples were irradiated with and without cadmium covers at the IEA-RI reactor (IPEN, Sao Paulo), Brazil. The deviation of the neutron spectrum shape from 1/E law was measured by co-irradiating Co, Zn, Zr and Au activation detectors with thermal and epithermal neutrons followed by regression and iterative procedures. The magnitudes of the discrepancies that can occur in measurements made with the ideal 1/E law considerations in the epithermal range were studied. The measured thermal neutron cross section at the Maxwellian averaged thermal energy of 0.0253 eV is 59.0 +/- 2.1 b and for the resonance integral 657 +/- 36b. The results are measured with good precision and indicated a consistency trend to resolve the discrepant status of the literature data. The results are compared with the values in main libraries such as ENDF/B-VII, JEF-2.2 and JENDL-3.2, and with other measurements in the literature.