Some uniform stability and convergence results for integral equations on the real line and projection methods for their solution

The paper considers second kind equations of the form (abbreviated x=y + K2x) in which and the factor z is bounded but otherwise arbitrary so that equations of Wiener-Hopf type are included as a special case. Conditions on a set are obtained such that a generalized Fredholm alternative is valid: if W satisfies these conditions and I − Kz, is injective for each z ε W then I − Kz is invertible for each z ε W and the operators (I − Kz)−1 are uniformly bounded. As a special case some classical results relating to Wiener-Hopf operators are reproduced. A finite section version of the above equation (with the range of integration reduced to [−a, a]) is considered, as are projection and iterated projection methods for its solution. The operators (where denotes the finite section version of Kz) are shown uniformly bounded (in z and a) for all a sufficiently large. Uniform stability and convergence results, for the projection and iterated projection methods, are obtained. The argument generalizes an idea in collectively compact operator theory. Some new results in this theory are obtained and applied to the analysis of projection methods for the above equation when z is compactly supported and k(s − t) replaced by the general kernel k(s,t). A boundary integral equation of the above type, which models outdoor sound propagation over inhomogeneous level terrain, illustrates the application of the theoretical results developed.

Gradient recovery in adaptive finite-element methods for parabolic problems

We derive energy-norm a posteriori error bounds, using gradient recovery (ZZ) estimators to control the spatial error, for fully discrete schemes for the linear heat equation. This appears to be the �rst completely rigorous derivation of ZZ estimators for fully discrete schemes for evolution problems, without any restrictive assumption on the timestep size. An essential tool for the analysis is the elliptic reconstruction technique.Our theoretical results are backed with extensive numerical experimentation aimed at (a) testing the practical sharpness and asymptotic behaviour of the error estimator against the error, and (b) deriving an adaptive method based on our estimators. An extra novelty provided is an implementation of a coarsening error "preindicator", with a complete implementation guide in ALBERTA in the appendix.

The vertical structure of oceanic Rossby waves: a comparison of high-resolution model data to theoretical vertical structures

Tests of the new Rossby wave theories that have been developed over the past decade to account for discrepancies between theoretical wave speeds and those observed by satellite altimeters have focused primarily on the surface signature of such waves. It appears, however, that the surface signature of the waves acts only as a rather weak constraint, and that information on the vertical structure of the waves is required to better discriminate between competing theories. Due to the lack of 3-D observations, this paper uses high-resolution model data to construct realistic vertical structures of Rossby waves and compares these to structures predicted by theory. The meridional velocity of a section at 24° S in the Atlantic Ocean is pre-processed using the Radon transform to select the dominant westward signal. Normalized profiles are then constructed using three complementary methods based respectively on: (1) averaging vertical profiles of velocity, (2) diagnosing the amplitude of the Radon transform of the westward propagating signal at different depths, and (3) EOF analysis. These profiles are compared to profiles calculated using four different Rossby wave theories: standard linear theory (SLT), SLT plus mean flow, SLT plus topographic effects, and theory including mean flow and topographic effects. Our results support the classical theoretical assumption that westward propagating signals have a well-defined vertical modal structure associated with a phase speed independent of depth, in contrast with the conclusions of a recent study using the same model but for different locations in the North Atlantic. The model structures are in general surface intensified, with a sign reversal at depth in some regions, notably occurring at shallower depths in the East Atlantic. SLT provides a good fit to the model structures in the top 300 m, but grossly overestimates the sign reversal at depth. The addition of mean flow slightly improves the latter issue, but is too surface intensified. SLT plus topography rectifies the overestimation of the sign reversal, but overestimates the amplitude of the structure for much of the layer above the sign reversal. Combining the effects of mean flow and topography provided the best fit for the mean model profiles, although small errors at the surface and mid-depths are carried over from the individual effects of mean flow and topography respectively. Across the section the best fitting theory varies between SLT plus topography and topography with mean flow, with, in general, SLT plus topography performing better in the east where the sign reversal is less pronounced. None of the theories could accurately reproduce the deeper sign reversals in the west. All theories performed badly at the boundaries. The generalization of this method to other latitudes, oceans, models and baroclinic modes would provide greater insight into the variability in the ocean, while better observational data would allow verification of the model findings.

Thiocyanate complexes of uranium in multiple oxidation states: a combined structural, magnetic, spectroscopic, spectroelectrochemical, and theoretical study

A comprehensive study of the complexes A4[U(NCS)8] (A = Cs, Et4N, nBu4N) and A3[UO2(NCS)5] (A = Cs, Et4N) is described, with the crystal structures of [nBu4N]4[U(NCS)8]·2MeCN and Cs3[UO2(NCS)5]·O0.5 reported. The magnetic properties of square antiprismatic Cs4[U(NCS)8] and cubic [Et4N]4[U(NCS)8] have been probed by SQUID magnetometry. The geometry has an important impact on the low-temperature magnetic moments: at 2 K, μeff = 1.21 μB and 0.53 μB, respectively. Electronic absorption and photoluminescence spectra of the uranium(IV) compounds have been measured. The redox chemistry of [Et4N]4[U(NCS)8] has been explored using IR and UV–vis spectroelectrochemical methods. Reversible 1-electron oxidation of one of the coordinated thiocyanate ligands occurs at +0.22 V vs Fc/Fc+, followed by an irreversible oxidation to form dithiocyanogen (NCS)2 which upon back reduction regenerates thiocyanate anions coordinating to UO22+. NBO calculations agree with the experimental spectra, suggesting that the initial electron loss of [U(NCS)8]4– is delocalized over all NCS– ligands. Reduction of the uranyl(VI) complex [Et4N]3[UO2(NCS)5] to uranyl(V) is accompanied by immediate disproportionation and has only been studied by DFT methods. The bonding in [An(NCS)8]4– (An = Th, U) and [UO2(NCS)5]3– has been explored by a combination of DFT and QTAIM analysis, and the U–N bonds are predominantly ionic, with the uranyl(V) species more ionic that the uranyl(VI) ion. Additionally, the U(IV)–NCS ion is more ionic than what was found for U(IV)–Cl complexes.

An evaluation of the theoretical potential and practical opportunity for using greywater for domestic purposes in Ghana

Assessments concerning the effects of climate change, water resource availability and water deprivation in West Africa have not frequently considered the positive contribution to be derived from collecting and reusing water for domestic purposes. Where the originating water is taken from a clean water source and has been used the first time for washing or bathing, this water is commonly called “greywater”. Greywater is a prolific resource that is generated wherever people live. Treated greywater can be used for domestic cleaning, for flushing toilets where appropriate, for washing cars, sometimes for watering kitchen gardens, and for clothes washing prior to rinsing. Therefore, a large theoretical potential exists to increase total water resource availability if greywater were to be widely reused. Locally treated greywater reduces the distribution network requirement, lower construction effort and cost and, wherever possible, minimising the associated carbon footprint. Such locally treated greywater offers significant practical opportunities for increasing the total available water resources at a local level. The reuse of treated greywater is one important action that will help to mitigate the reducing availability of clean water supplies in some areas, and the expected mitigation required in future aligns well with WHO/UNICEF (2012) aspirations. The evaluation of potential opportunities for prioritising greywater systems to support water reuse takes into account the availability of water resources, water use indicators and published estimates in order to understand typical patterns of water demand. The approach supports knowledge acquisition regarding local conditions for enabling capacity building for greywater reuse, the understanding of systems that are most likely to encourage greywater reuse, and practices and future actions to stimulate greywater infrastructure planning, design and implementation. Although reuse might be considered to increase the uncertainty of achieving a specified quality of the water supply, robust methods and technologies are available for local treatment. Resource strategies for greywater reuse have the potential to consistently improve water efficiency and availability in water impoverished and water stressed regions of Ghana and West Africa. Untreated greywater is referred to as “greywater”; treated greywater is referred to as “treated greywater” in this paper.

Methods to assess the effectiveness of naturally ventilated classrooms in Gauteng, South Africa

There is a tendency to reduce ventilation rates and natural or hybrid ventilation systems to ensure the conservation of energy in school buildings. However, high indoor pollutant concentration, due to natural or hybrid ventilation systems may have a significant adverse impact on the health and academic performance of pupils and students. Reviewed evidence shows that this can be detrimental to health and wellbeing in schools because of the learner density within a small area, eventually indicating that CO2 concentrations can rise to very high levels (about 4000 ppm) in classrooms during occupancy periods. In South Africa’s naturally ventilated classrooms, it is not clear whether the environmental conditions are conducive for learning. In addition, natural ventilation will be minimized given the fact that in cold, wet or windy weather, doors and windows will commonly remain closed. Evidence from literature based studies indicates that the significance of ventilation techniques is not understood satisfactorily and additional information concerning naturally ventilated schools has to be provided for better design and policy formulation. To develop a thorough understanding of the environments in classrooms, many other parameters have to be considered as well, such as outdoor air quality, CO2 concentrations, temperature and relative humidity and safety issues that may be important drawbacks for naturally ventilated schools. The aim of this paper is to develop a conceptual understanding of methods that can be implemented to assess the effectiveness of naturally ventilated classrooms in Gauteng, South Africa. A theoretical concept with an embedded practical methodology have been proposed for the research programme to investigate the relationship between ventilation rates and learning in schools in Gauteng , a province in South Africa. It is important that existing and future school buildings must include adequate outdoor ventilation, control of moisture, and avoidance of indoor exposures to microbiologic and chemical substances considered likely to have adverse effects in South Africa. Adequate ventilation in classrooms is necessary to reduce and/or eradicate the transmission of indoor pollutants.

Theoretical insight into diagnosing observation error correlations using observation-minus-background and observation-minus-analysis statistics

To improve the quantity and impact of observations used in data assimilation it is necessary to take into account the full, potentially correlated, observation error statistics. A number of methods for estimating correlated observation errors exist, but a popular method is a diagnostic that makes use of statistical averages of observation-minus-background and observation-minus-analysis residuals. The accuracy of the results it yields is unknown as the diagnostic is sensitive to the difference between the exact background and exact observation error covariances and those that are chosen for use within the assimilation. It has often been stated in the literature that the results using this diagnostic are only valid when the background and observation error correlation length scales are well separated. Here we develop new theory relating to the diagnostic. For observations on a 1D periodic domain we are able to the show the effect of changes in the assumed error statistics used in the assimilation on the estimated observation error covariance matrix. We also provide bounds for the estimated observation error variance and eigenvalues of the estimated observation error correlation matrix. We demonstrate that it is still possible to obtain useful results from the diagnostic when the background and observation error length scales are similar. In general, our results suggest that when correlated observation errors are treated as uncorrelated in the assimilation, the diagnostic will underestimate the correlation length scale. We support our theoretical results with simple illustrative examples. These results have potential use for interpreting the derived covariances estimated using an operational system.

A priori error analysis of space–time Trefftz discontinuous Galerkin methods for wave problems

We present and analyse a space–time discontinuous Galerkin method for wave propagation problems. The special feature of the scheme is that it is a Trefftz method, namely that trial and test functions are solution of the partial differential equation to be discretised in each element of the (space–time) mesh. The method considered is a modification of the discontinuous Galerkin schemes of Kretzschmar et al. (2014) and of Monk & Richter (2005). For Maxwell’s equations in one space dimension, we prove stability of the method, quasi-optimality, best approximation estimates for polynomial Trefftz spaces and (fully explicit) error bounds with high order in the meshwidth and in the polynomial degree. The analysis framework also applies to scalar wave problems and Maxwell’s equations in higher space dimensions. Some numerical experiments demonstrate the theoretical results proved and the faster convergence compared to the non-Trefftz version of the scheme.

Theoretical Analysis of Aggregation in Block-Copolymer Films: The Optical Signature

We focus this work on the theoretical investigation of the block-copolymer poly [oxyoctyleneoxy-(2,6-dimethoxy-1,4phenylene-1,2-ethinylene-phenanthrene-2,4diyl) named as LaPPS19, recently proposed for optoelectronic applications. We used for that a variety of methods, from molecular mechanics to quantum semiempirical techniques (AMI, ZINDO/S-CIS). Our results show that as expected isolated LaPPS19 chains present relevant electron localization over the phenanthrene group. We found, however, that LaPPS19 could assemble in a pi-stacked form, leading to impressive interchain interaction; the stacking induces electronic delocalization between neighbor chains and introduces new states below the phenanthrene-related absorption; these results allowed us to associate the red-shift of the absorption edge, seen in the experimental results, to spontaneous pi-stack aggregation of the chains. (C) 2009 Wiley Periodicals, Inc. Int J Quantum Chem 110: 885-892, 2010

Cyclocreatine, an anticancer and neuroprotective agent. Spectroscopic, structural and theoretical study

The structural, spectroscopic and theoretical study of cyclocreatine (1-carboxymethyl-2-iminoimidazolidine, CyCre) has been performed prompted by the biological relevance of the molecule and its potential role as a ligand in biometalic compounds. The crystal structure of CyCre has been determined by X-ray diffraction methods. The compound crystallizes as a zwitterion in the monoclinic system, space group P2(1)/c. The crystal is further stabilized by a network of N-H center dot center dot center dot O bonds. Infrared and Raman spectra of the solid, electronic spectra of aqueous solutions at different pH values and (1)H and (13)C NMR spectra have been recorded and analyzed. Band assignments were accomplished with the help of theoretical calculations. Optimized molecular geometries, harmonic vibrational frequencies and molecular electrostatic potentials were calculated using methods based on the density functional theory. (C) 2010 Elsevier B.V. All rights reserved.

Proximal methods for nonlinear programming: double regularization and inexact subproblems

This paper describes the first phase of a project attempting to construct an efficient general-purpose nonlinear optimizer using an augmented Lagrangian outer loop with a relative error criterion, and an inner loop employing a state-of-the art conjugate gradient solver. The outer loop can also employ double regularized proximal kernels, a fairly recent theoretical development that leads to fully smooth subproblems. We first enhance the existing theory to show that our approach is globally convergent in both the primal and dual spaces when applied to convex problems. We then present an extensive computational evaluation using the CUTE test set, showing that some aspects of our approach are promising, but some are not. These conclusions in turn lead to additional computational experiments suggesting where to next focus our theoretical and computational efforts.

Teaching grammar: A study of the common English grammar errors and grammar teaching methods that can be relevant for Swedish upper secondary schools

Grammar has always been an important part of language learning. Based on various theories, such as the universal grammar theory (Chomsky, 1959) and, the input theory (Krashen, 1970), the explicit and implicit teaching methods have been developed. Research shows that both methods may have some benefits and disadvantages. The attitude towards English grammar teaching methods in schools has also changed and nowadays grammar teaching methods and learning strategies, as a part of language mastery, are one of the discussion topics among linguists. This study focuses on teacher and learner experiences and beliefs about teaching English grammar and difficulties learners may face. The aim of the study is to conduct a literature review and to find out what scientific knowledge exists concerning the previously named topics. Along with this, the relevant steering documents are investigated focusing on grammar teaching at Swedish upper secondary schools. The universal grammar theory of Chomsky as well as Krashen’s input hypotheses provide the theoretical background for the current study. The study has been conducted applying qualitative and quantitative methods. The systematic search in four databases LIBRIS, ERIK, LLBA and Google Scholar were used for collecting relevant publications. The result shows that scientists’ publications name different grammar areas that are perceived as problematic for learners all over the world. The most common explanation of these difficulties is the influence of learner L1. Research presents teachers’ and learners’ beliefs to the benefits of grammar teaching methods. An effective combination of teaching methods needs to be done to fit learners’ expectations and individual needs. Together, they will contribute to the achieving of higher language proficiency levels and, therefore, they can be successfully applied at Swedish upper secondary schools.

Purification, characterization, crystallization and theoretical molecular modeling of gyroxin fraction from Crotalus durissus terrificus venom (Laurenti, 1768)

The venom of Crotalus durissus terrificus snakes presents various substances, including a serine protease with thrombin-like activity, called gyroxin, that clots plasmatic fibrinogen and promote the fibrin formation. The aim of this study was to purify and structurally characterize the gyroxin enzyme from Crotalus durissus terrificus venom. For isolation and purification, the following methods were employed: gel filtration on Sephadex G75 column and affinity chromatography on benzamidine Sepharose 6B; 12% SDS-PAGE under reducing conditions; N-terminal sequence analysis; cDNA cloning and expression through RT-PCR and crystallization tests. Theoretical molecular modeling was performed using bioinformatics tools based on comparative analysis of other serine proteases deposited in the NCBI (National Center for Biotechnology Information) database. Protein N-terminal sequencing produced a single chain with a molecular mass of similar to 30 kDa while its full-length cDNA had 714 bp which encoded a mature protein containing 238 amino acids. Crystals were obtained from the solutions 2 and 5 of the Crystal Screen Kit (R), two and one respectively, that reveal the protein constitution of the sample. For multiple sequence alignments of gyroxin-like B2.1 with six other serine proteases obtained from snake venoms (SVSPs), the preservation of cysteine residues and their main structural elements (alpha-helices, beta-barrel and loops) was indicated. The localization of the catalytic triad in His57, Asp102 and Ser198 as well as S1 and S2 specific activity sites in Thr193 and Gli215 amino acids was pointed. The area of recognition and cleavage of fibrinogen in SVSPs for modeling gyroxin B2.1 sequence was located at Arg60, Arg72, Gln75, Arg81, Arg82, Lis85, Glu86 and Lis87 residues. Theoretical modeling of gyroxin fraction generated a classical structure consisting of two alpha-helices, two beta-barrel structures, five disulfide bridges and loops in positions 37, 60, 70, 99, 148, 174 and 218. These results provided information about the functional structure of gyroxin allowing its application in the design of new drugs.

A theoretical analysis on the intramolecular proton transfer of alpha-alanine in an aqueous medium

Intramolecular proton transfer from oxygen to nitrogen atoms in the alpha-alanine amino acid has been studied by ab initio methods at the HF/6-31G*, HF/6-31 ++ G** and MP2/6-31 ++ G** levels of calculation including the solvent effects by means of self-consistent reaction field theory. An analysis of the results based on the natural bond orbital charges shows that the transition structure presents an imbalance in the sense that the charge shift lags behind the proton transfer and that the bond formation is always in advance with respect to the bond cleavage. All calculation levels show that the barrier height associated with the conformational change on alpha-alanine is larger than the proton transfer process. (C) 1998 Elsevier B.V. B.V. All rights reserved.

A theoretical study on cytosine tautomers in aqueous media by using continuum models

B3LYP/6-31 + + G** and MP2/6-31 + + G** calculations have been carried out to study six tautomers of the nucleic acid base cytosine in aqueous media. Solvent effects have been analyzed using the self-consistent reaction field theory with two continuum methods. Relative stabilities and optimized geometries have been calculated for the tautomers and compared with experimental data. The present results show the importance of electrostatic solvent effects in determining observable properties of the cytosine tautomers. The amino-oxo form (C1) is the most abundant tautomer in aqueous media while the other amino-oxo form (C4) is the most energetically favored when solvent effects are included. These results can be justified by the larger values of the dipole moments for both C1 and C4 tautomers. Theoretical and experimental results of the harmonic vibrational frequencies and rotational constants show good agreement. (C) 2000 Elsevier B.V. B.V. All rights reserved.