Showing papers by "University of Bath published in 2000"
TL;DR: In this article, the authors provide a comprehensive introduction to protection motivation theory and its application to health-related behavior, together with a quantitative review of the applications of PMT to healthrelated intentions and behavior.
Abstract: Protection motivation theory (PMT) was introduced by Rogers in 1975 and has since been widely adopted as a framework for the prediction of and intervention in health-related behavior. However. PMT remains the only major cognitive model of behavior not to have been the subject of a meta-analytic review. A quantitative review of PMT is important to assess its overall utility as a predictive model and to establish which of its variables would be most useful to address health-education interventions. The present paper provides a comprehensive introduction to PMT and its application to health-related behavior, together with a quantitative review of the applications of PMT to health-related intentions and behavior. The associations between threat- and coping-appraisal variables and intentions, and all components of the model and behavior were assessed both by meta-analysis and by vote-count procedures. Threat- and coping-appraisal components of PMT were found to be useful in the prediction of health-related intentions. The model was found to be useful in predicting concurrent behavior, but of less utility in predicting future behavior. The coping-appraisal component of the model was found to have greater predictive validity than was the threat-appraisal component. The main findings are discussed in relation to theory and research on social cognition models. The importance of the main findings to health education is also discussed, and future research directions are suggested.
1,205 citations
TL;DR: The frequency comb generated by a femtosecond mode-locked laser is used and broadened to more than an optical octave in a photonic crystal fiber to realize a frequency chain that links a 10 MHz radio frequency reference phase-coherently in one step to the optical region.
Abstract: We have used the frequency comb generated by a femtosecond mode-locked laser and broadened to more than an optical octave in a photonic crystal fiber to realize a frequency chain that links a 10 MHz radio frequency reference phase-coherently in one step to the optical region. By comparison with a similar frequency chain we set an upper limit for the uncertainty of this new approach to 5. 1x10(-16). This opens the door for measurement and synthesis of virtually any optical frequency and is ready to revolutionize frequency metrology.
1,136 citations
TL;DR: A simple classification system for lipid formulations, based on the polarity of the blend and reviewed here, will help comparison of data between laboratories and priorities for future work are discussed.
1,094 citations
TL;DR: Based on spectral measurements of the polarization mode beating, it is estimated that the strongly anisotropic photonic crystal fiber has a beat length of approximately 0.4 mm at a wavelength of 1540 nm, in good agreement with the results of modeling.
Abstract: We report a strongly anisotropic photonic crystal fiber. Twofold rotational symmetry was introduced into a single-mode fiber structure by creation of a regular array of airholes of two sizes disposed about a pure-silica core. Based on spectral measurements of the polarization mode beating, we estimate that the fiber has a beat length of approximately 0.4 mm at a wavelength of 1540 nm, in good agreement with the results of modeling.
860 citations
TL;DR: In this paper, the authors show that the activation of HO-1 is an ubiquitous cellular response to oxidative stress, and that the reaction products of HO activity, biliverdin, and its subsequent metabolite bilirubin, have antioxidant properties.
781 citations
TL;DR: In this paper, a supercontinuum light with a spectrum more than two octaves broad (370-1545 nm at the 20-dB level) was generated in a standard telecommunications fiber by femtosecond pulses from an unamplified Ti:sapphire laser.
Abstract: Supercontinuum light with a spectrum more than two octaves broad (370–1545 nm at the 20-dB level) was generated in a standard telecommunications fiber by femtosecond pulses from an unamplified Ti:sapphire laser. The fiber had been tapered to a diameter of ∼2 µm over a 90-mm length. The pulse energy was 3.9 nJ (average power, 300 mW). This source of high-intensity single-mode white light should find widespread applications in frequency metrology and spectroscopy, especially since no unconventional fibers are needed.
711 citations
Institute for Systems Biology1, University of Washington2, University of Massachusetts Amherst3, University of Bath4, Northern Illinois University5, University of Wisconsin-Madison6, University of Pennsylvania7, University of Texas Health Science Center at Houston8, Ohio State University9, University of British Columbia10, Stanford University11, Marine Biological Laboratory12
TL;DR: Analysis of the genome sequence shows the presence of pathways for uptake and utilization of amino acids, active sodium-proton antiporter and potassium uptake systems, sophisticated photosensory and signal transduction pathways, and DNA replication, transcription, and translation systems resembling more complex eukaryotic organisms.
Abstract: We report the complete sequence of an extreme halophile, Halobacterium sp. NRC-1, harboring a dynamic 2,571,010-bp genome containing 91 insertion sequences representing 12 families and organized into a large chromosome and 2 related minichromosomes. The Halobacterium NRC-1 genome codes for 2,630 predicted proteins, 36% of which are unrelated to any previously reported. Analysis of the genome sequence shows the presence of pathways for uptake and utilization of amino acids, active sodium-proton antiporter and potassium uptake systems, sophisticated photosensory and signal transduction pathways, and DNA replication, transcription, and translation systems resembling more complex eukaryotic organisms. Whole proteome comparisons show the definite archaeal nature of this halophile with additional similarities to the Gram-positive Bacillus subtilis and other bacteria. The ease of culturing Halobacterium and the availability of methods for its genetic manipulation in the laboratory, including construction of gene knockouts and replacements, indicate this halophile can serve as an excellent model system among the archaea.
690 citations
TL;DR: In this paper, the authors describe the measured group-velocity dispersion characteristics of several air-silica photonic crystal fibers with anomalous group velocity dispersion at visible and near-infrared wavelengths.
Abstract: We describe the measured group-velocity dispersion characteristics of several air-silica photonic crystal fibers with anomalous group-velocity dispersion at visible and near-infrared wavelengths. The values measured over a broad spectral range are compared to those predicted for an isolated strand of silica surrounded by air. We demonstrate a strictly single-mode fiber which has zero dispersion at a wavelength of 700 mm. These fibers are significant for the generation of solitons and supercontinua using ultrashort pulse sources.
683 citations
TL;DR: This article proposes alternatives for Bayesian inference for permutation invariant posteriors, including a clustering device and alternative appropriate loss functions and shows that exploration of these modes can be imposed using tempered transitions.
Abstract: This article deals with both exploration and interpretation problems related to posterior distributions for mixture models. The specification of mixture posterior distributions means that the presence of k! modes is known immediately. Standard Markov chain Monte Carlo (MCMC) techniques usually have difficulties with well-separated modes such as occur here; the MCMC sampler stays within a neighborhood of a local mode and fails to visit other equally important modes. We show that exploration of these modes can be imposed using tempered transitions. However, if the prior distribution does not distinguish between the different components, then the posterior mixture distribution is symmetric and standard estimators such as posterior means cannot be used. We propose alternatives for Bayesian inference for permutation invariant posteriors, including a clustering device and alternative appropriate loss functions.
640 citations
TL;DR: It is proposed that inhibition of IRF-3 activation by a dsRNA binding protein significantly contributes to the virulence of influenza A viruses and possibly to that of other viruses.
Abstract: We present a novel mechanism by which viruses may inhibit the alpha/beta interferon (IFN-alpha/beta) cascade. The double-stranded RNA (dsRNA) binding protein NS1 of influenza virus is shown to prevent the potent antiviral interferon response by inhibiting the activation of interferon regulatory factor 3 (IRF-3), a key regulator of IFN-alpha/beta gene expression. IRF-3 activation and, as a consequence, IFN-beta mRNA induction are inhibited in wild-type (PR8) influenza virus-infected cells but not in cells infected with an isogenic virus lacking the NS1 gene (delNS1 virus). Furthermore, NS1 is shown to be a general inhibitor of the interferon signaling pathway. Inhibition of IRF-3 activation can be achieved by the expression of wild-type NS1 in trans, not only in delNS1 virus-infected cells but also in cells infected with a heterologous RNA virus (Newcastle disease virus). We propose that inhibition of IRF-3 activation by a dsRNA binding protein significantly contributes to the virulence of influenza A viruses and possibly to that of other viruses.
612 citations
TL;DR: This research identifies differing emphases that may be required for managing within supply networks, according to the nature of the products for which they are created, using the type of product as a differentiator.
Abstract: The articulation of supply networks, as an extension of supply chains, seeks to accommodate and explain the commercial complexity associated with the creation and delivery of goods and services from the source of raw materials to their destination in end‐customer markets. In place of the simplistic, linear and unidirectional model sometimes presented for supply chains, the supply network concept describes lateral links, reverse loops, two‐way exchanges and so on, encompassing the upstream and downstream activity, with a focal firm as the point of reference. A review of classifications of supply networks reveals that none of the existing approaches appears adequate for managers facing the practical problems of creating and operating them on a day‐to‐day basis. This research identifies differing emphases that may be required for managing within supply networks, according to the nature of the products for which they are created. Taking an established categorisation of supply chains as its starting point, the research first develops the conceptual basis, using strategy literature, and then tests the resultant initial model in 16 case studies. Finally, a new categorisation for supply networks is presented, using the type of product as a differentiator.
TL;DR: Early events occurring during the hypersensitive resistance response (HR) were examined using the avrRpm1/RPM1 gene-for-gene interaction in Arabidopsis challenged by Pseudomonas syringae pv.
Abstract: Early events occurring during the hypersensitive resistance response (HR) were examined using the avrRpm1/RPM1 gene-for-gene interaction in Arabidopsis challenged by Pseudomonas syringae pv. tomato. Increases in cytosolic Ca2+ were measured in whole leaves using aequorin-mediated bioluminescence. During the HR a sustained increase in Ca2+ was observed which was dependent on the presence of both a functional RPM1 gene product and delivery of the cognate avirulence gene product AvrRpm1. The sequence-unrelated avirulence gene avrB, which also interacts with RPM1, generated a significantly later but similarly prolonged increase in cytosolic Ca2+. Accumulation of H2O2 at reaction sites, as revealed by electron microscopy, occurred within the same time frame as the changes in cytosolic Ca2+. The NADPH oxidase inhibitor diphenylene iodonium chloride did not affect the calcium signature, but did block H2O2 accumulation and the HR. By contrast, the calcium-channel blocker LaCl3 suppressed the increase in cytosolic Ca2+ as well as H2O2 accumulation and the HR, placing calcium elevation upstream of the oxidative burst.
TL;DR: In this paper, the authors argue that the HR strategies of firms are heavily shaped by contextual contingencies, including national, sectoral andorganizational factors, and conclude that the interconnection between HRM and organizational outcomes is achieved.
Abstract: Strategichumanresourcemanagement(SHRM)impliesaconcernwiththewaysinwhichHRM iscriticaltoorganizationaleffectiveness.Thisstraightforwardassertionisexaminedintheory andthroughresearchevidencetorevealhighlevelsofcomplexityinrelationtohow,whenand why the interconnection between HRM and organizational outcomes is achieved. The two dominant normative models of ‘best fit’ and ‘best practice’ are considered. The paper concludes that the HR strategies of firms are heavily shaped by contextual contingencies, includingnational,sectoralandorganizationalfactors.However,suchaconclusiondoesnot invalidate all ‘best-practice’ thinking. Although constrained in certain ways, underpinning principles of labour management still have relevance to practice as essential attributes of a firm’sabilityto competeinitschosenmarkets.Thepaper thenconsiderstheresource-based view (RBV) of the firm and asks whether this provides a better basis for the development of theory in SHRM and in understanding the contribution of HRM to the achievement of sustainedcompetitiveadvantage.WhilelimitstotheutilityofRBVinrespectofSHRMtheory are identified, important implications for research are signalled. Trends in the RBV literature are pushing all those interested in strategy towards studies of intellectual capital, learning processes and organizational adaptability. Researchers in HRM could, if they wished, play a centralroleinthesedevelopmentsbecausequestionsofhowtoattract,motivateanddevelop workerswithcriticalandscarceabilities,anddevelopeffectiveprocessesofworkorganization, mustbefundamentaltoanymodelofknowledge-basedcompetition.Greaterprogresswillbe madewhenorganizationsarestudiedinamuchmoreinterdisciplinaryorsystemicway.
TL;DR: It is shown that pancreatic cells can be converted into hepatocytes by treatment with a synthetic glucocorticoid, dexamethasone, and that a proportion of the hepatocytes arises directly from differentiated exocrine-like cells, with no intervening cell division.
Abstract: The appearance of hepatic foci in the pancreas has been described in animal experiments and in human pathology. Here we show that pancreatic cells can be converted into hepatocytes by treatment with a synthetic glucocorticoid, dexamethasone. This occurs both in a pancreatic cell line, AR42J-B13, and in organ cultures of pancreatic buds from mouse embryos. We have established several features of the mechanism behind this transdifferentiation. We show that a proportion of the hepatocytes arises directly from differentiated exocrine-like cells, with no intervening cell division. This conversion is associated with induction of the transcription factor C/EBPbeta and the activation of differentiated hepatic products. Transfection of C/EBPbeta into the cells can provoke transdifferentiation; conversely, a dominant-negative form of C/EBPbeta can inhibit the process. These results indicate that C/EBPbeta is a key component that distinguishes the liver and pancreatic programmes of differentiation.
TL;DR: Xanthine oxidase was shown to catalyze the reduction of nitrite to nitric oxide (NO) in the presence of either NADH or xanthine as reducing substrate, and it is proposed that XO-derived NO fulfills a bactericidal role in the digestive tract.
TL;DR: Most, if not all, epithelial tissues contain stem cells, which are responsible for normal tissue renewal or for regeneration following damage.
Abstract: Most, if not all, epithelial tissues contain stem cells. They are responsible for normal tissue renewal or for regeneration following damage. Our present knowledge of their properties is limited and is mainly derived from studies of cell kinetics and from clonal analysis.
TL;DR: A review of the xenobiotic resistance literature shows that empirical evidence for this hypothesis is scarce, and it is postulate that such fitness costs can only be fully interpreted in the light of the molecular mutations that might underlie them.
Abstract: The nature and cost of single genes of major effect is one of the longest running controversies in biology. Resistance, whether to xenobiotics or to parasites, is often paraded as an obvious example of a single gene effect that must carry an associated fitness 'cost'. However, a review of the xenobiotic resistance literature shows that empirical evidence for this hypothesis is, in fact, scarce. We postulate that such fitness costs can only be fully interpreted in the light of the molecular mutations that might underlie them. We also derive a theoretical framework both to encompass our current understanding of xenobiotic resistance and to begin to dissect the probable cost of parasite resistance.
TL;DR: In this article, a novel charge extraction method was developed to study the transport, trapping and back reaction of photogenerated electrons in dye sensitised nanocrystalline cells (Gratzel cells).
TL;DR: It is argued that ISS recommendations in small firms need to take account of organisational change issues as much as information system implementation as well as the role of information as a strategic resource.
Abstract: Information systems strategy (ISS) use is under-developed for, and under-researched in, small and medium sized enterprises (SMEs). This paper reviews existing approaches to ISS for SMEs, finding them now out-dated and technology-focussed. The paper develops an approach that reflects on the role of information as a strategic resource. It argues that ISS recommendations in small firms need to take account of organisational change issues as much as information system implementation. The revised approach to ISS for SMEs is demonstrated through its application to over 40 cases in the UK West Midlands. The influences from the processes on outcomes are discussed and the effectiveness of tools and techniques recommended is assessed.
TL;DR: New deterministic methods that, given two eigenspace models-each representing a set of n-dimensional observations-will: merge the models to yield a representation of the union of the sets and split one model from another to represent the difference between the sets are presented.
Abstract: We present new deterministic methods that, given two eigenspace models-each representing a set of n-dimensional observations-will: 1) merge the models to yield a representation of the union of the sets and 2) split one model from another to represent the difference between the sets. As this is done, we accurately keep track of the mean. Here, we give a theoretical derivation of the methods, empirical results relating to the efficiency and accuracy of the techniques, and three general applications, including the construction of Gaussian mixture models that are dynamically updateable.
TL;DR: A long-standing discrepancy between experimental and theoretical values for the lifetimes of holes in the surface-state electron bands on noble metal surfaces is resolved; previous determinations of both are found to have been in error.
Abstract: A long-standing discrepancy between experimental and theoretical values for the lifetimes of holes in the surface-state electron bands on noble metal surfaces is resolved; previous determinations of both are found to have been in error. The ability of the scanning tunneling microscope to verify surface quality before taking spectroscopic measurements is used to remove the effects of defect scattering on experimental lifetimes, found to have been a significant contribution to prior determinations. A theoretical treatment of inelastic electron-electron scattering is developed that explicitly includes intraband transitions within the surface state band. In our model, two-dimensional decay channels dominate the electron-electron interactions that contribute to the hole decay and are screened by the electron states of the underlying three-dimensional electron system.
TL;DR: It is shown that if theoretically possible code structures are limited to reflect plausible biological constraints, and amino acid similarity is quantified using empirical data of substitution frequencies, the canonical code is at or very close to a global optimum for error minimization across plausible parameter space.
Abstract: The evolutionary forces that produced the canonical genetic code before the last universal ancestor remain obscure. One hypothesis is that the arrangement of amino acid/codon assignments results from selection to minimize the effects of errors (e.g., mistranslation and mutation) on resulting proteins. If amino acid similarity is measured as polarity, the canonical code does indeed outperform most theoretical alternatives. However, this finding does not hold for other amino acid properties, ignores plausible restrictions on possible code structure, and does not address the naturally occurring nonstandard genetic codes. Finally, other analyses have shown that significantly better code structures are possible. Here, we show that if theoretically possible code structures are limited to reflect plausible biological constraints, and amino acid similarity is quantified using empirical data of substitution frequencies, the canonical code is at or very close to a global optimum for error minimization across plausible parameter space. This result is robust to variation in the methods and assumptions of the analysis. Although significantly better codes do exist under some assumptions, they are extremely rare and thus consistent with reports of an adaptive code: previous analyses which suggest otherwise derive from a misleading metric. However, all extant, naturally occurring, secondarily derived, nonstandard genetic codes do appear less adaptive. The arrangement of amino acid assignments to the codons of the standard genetic code appears to be a direct product of natural selection for a system that minimizes the phenotypic impact of genetic error. Potential criticisms of previous analyses appear to be without substance. That known variants of the standard genetic code appear less adaptive suggests that different evolutionary factors predominated before and after fixation of the canonical code. While the evidence for an adaptive code is clear, the process by which the code achieved this optimization requires further attention.
TL;DR: The results from the comparison of apo and holo structures of LA provide high resolution structural evidence that the acceleration of folding by Ca2+ is mediated by an effect on interactions between the two subdomains.
Proceedings Article•
01 Jan 2000TL;DR: Work under way to extend and refine the WebQual instrument includes electronic commerce evaluation, where web-site service quality is proposed as a key issue.
Abstract: The issue of web-site quality is tackled from the perspective of the ‘voice of the customer’. Quality function deployment (QFD) is adopted as a framework for identifying web-site qualities demanded by users, which are gathered through a quality workshop. From the workshop an instrument for assessing web-site quality is developed (WebQual) and tested in the domain of UK business schools. The results of the WebQual survey are presented and analyzed, leading to the generation of a WebQual Index of web-site quality. Work under way to extend and refine the WebQual instrument includes electronic commerce evaluation, where web-site service quality is proposed as a key issue.
TL;DR: The observation that development is less severely affected if gametes of both sexes are 'neutralized' with respect to parent-of-origin effects supports the hypothesis that parental imprinting is not necessary to regulate development.
Abstract: Some genes in mammals and flowering plants are subject to parental imprinting, a process by which differential epigenetic marks are imposed on male and female gametes so that one set of alleles is silenced on chromosomes contributed by the mother while another is silenced on paternal chromosomes. Therefore, each genome contributes a different set of active alleles to the offspring, which develop abnormally if the parental genome balance is disturbed. In Arabidopsis, seeds inheriting extra maternal genomes show distinctive phenotypes such as low weight and inhibition of mitosis in the endosperm, while extra paternal genomes result in reciprocal phenotypes such as high weight and endosperm overproliferation. DNA methylation is known to be an essential component of the parental imprinting mechanism in mammals, but there is less evidence for this in plants. For the present study, seed development was examined in crosses using a transgenic Arabidopsis line with reduced DNA methylation. Crosses between hypomethylated and wild-type diploid plants produced similar seed phenotypes to crosses between plants with normal methylation but different ploidies. This is consistent with a model in which hypomethylation of one parental genome prevents silencing of alleles that would normally be active only when inherited from the other parent - thus phenocopying the effects of extra genomes. These results suggest an important role for methylation in parent-of-origin effects, and by inference parental imprinting, in plants. The phenotype of biparentally hypomethylated seeds is less extreme than the reciprocal phenotypes of uniparentally hypomethylated seeds. The observation that development is less severely affected if gametes of both sexes (rather than just one) are 'neutralized' with respect to parent-of-origin effects supports the hypothesis that parental imprinting is not necessary to regulate development.
TL;DR: Results are consistent with dopamine release mediated by beta2- containing nicotinic acetylcholine receptors on dopamine terminals, while non-beta2-containing nicotinIC acetyl choline receptors may enhance dopamine release indirectly by releasing glutamate from neighbouring terminals.
TL;DR: In this paper, a model of a strut-on-a-wool structural system with a subcritical post-buckling response is presented, with localized buckles first forming and then locking up in sequence.
Abstract: A long structural system with an unstable (subcritical)post-buckling response that subsequently restabilizes typically deformsin a cellular manner, with localized buckles first forming and thenlocking up in sequence. As buckling continues over a growing number ofcells, the response can be described by a set of lengthening homoclinicconnections from the fundamental equilibrium state to itself. In thelimit, this leads to a heteroclinic connection from the fundamentalunbuckled state to a post-buckled state that is periodic. Under suchprogressive displacement the load tends to oscillate between twodistinct values. The paper is both a review and a pointer tofuture research. The response is described via a typical system, asimple but ubiquitous model of a strut on a foundation which includesinitially-destabilizing and finally-restabilizing nonlinear terms. Anumber of different structural forms, including the axially-compressedcylindrical shell, a typical sandwich structure, a model of geologicalfolding and a simple link model are shown to display such behaviour. Amathematical variational argument is outlined for determining the globalminimum postbuckling state under controlled end displacement (rigidloading). Finally, the paper stresses the practical significance of aMaxwell-load instability criterion for such systems. This criterion,defined under dead loading to be where the pre-buckled and post-buckledstate have the same energy, is shown to have significance in the presentsetting under rigid loading also. Specifically, the Maxwell load isargued to be the limit of minimum energy localized solutions asend-shortening tends to infinity.
TL;DR: Data support a model in which alpha7* nAChRs on striatal glutamate terminals elicit glutamate release, which in turn acts at ionotropic glutamate receptors on dopamine terminals to stimulate dopamine release.
Abstract: Nicotinic agonists elicit the release of dopamine from striatal synaptosomes by acting on presynaptic nicotinic acetylcholine receptors (nAChRs) on dopamine nerve terminals. Both α3β2* and α4β2 nAChR subtypes (but not α7* nAChRs) have been implicated. Here, we compared nAChR-evoked [3H]dopamine release from rat striatal synaptosome and slice preparations by using the nicotinic agonist anatoxin-a. In the more integral slice preparation, the concentration-response curve for anatoxin-a-evoked [3H]dopamine release was best fitted to a two-site model, giving EC50 values of 241 nM and 5.1 μM, whereas only the higher-affinity component was observed in synaptosome preparations (EC50 = 134 nM). Responses to a high concentration of anatoxin-a (25 μM) in slices (but not in synaptosomes) were partially blocked by ionotropic glutamate receptor antagonists (kynurenic acid, 6,7-dinitroquinoxaline-2,3-dione) and by α7*-selective nAChR antagonists (α-bungarotoxin, α-conotoxin-ImI, methyllycaconitine) in a nonadditive manner. In contrast, the α3β2-selective nAChR antagonist α-conotoxin-MII partially inhibited [3H]dopamine release from both slice and synaptosome preparations, stimulated with both low (1 μM) and high (25 μM) concentrations of anatoxin-a. Antagonism by α-conotoxin-MII was additive with that of α7*-selective antagonists. These data support a model in which α7* nAChRs on striatal glutamate terminals elicit glutamate release, which in turn acts at ionotropic glutamate receptors on dopamine terminals to stimulate dopamine release. In addition, non-α7* nAChRs on dopamine terminals also stimulate dopamine release. These observations have implications for the complex cholinergic modulation of inputs onto the major efferent neurons of the striatum.
TL;DR: In this paper, a variational and asymptotic expansion for the energy of an infinitely extended periodic elastic medium with the periodicity cell of a small size e, in the presence of a fixed body force f, was derived via a combination of variational techniques.
Abstract: Higher order (so-called strain gradient) homogenised equations are rigorously derived for an infinitely extended periodic elastic medium with the periodicity cell of a small size e, in the presence of a fixed body force f, via a combination of variational and asymptotic techniques. The coefficients of these equations are explicitly related to solutions of higher order unit cell problems. The related higher order homogenised solutions are shown to be best possible in a certain variational sense, and it is shown that these solutions are close to the actual solutions up to higher orders in e. We derive a rigorous full asymptotic expansion for the energy I e, f and also show that its higher order terms are determined by the higher order homogenised solutions. The resulting variational construction generates higher order effective constitutive relations which are in agreement with those proposed by phenomenological strain gradient theories.
Book•
25 Feb 2000TL;DR: In this article, the authors consider a non-linear Poisson equation and show that positive solutions in a bounded set O are monotonically monotonous. But they do not consider the divergence theorem and the edge point lemma.
Abstract: Preface 0. Some notation, terminology and basic calculus 1. Introduction 2. Some maximum principles for elliptic equations 3. Symmetry for a non-linear Poisson equation 4. Symmetry for the non-linear Poisson equation in RN 5. Monotonicity of positive solutions in a bounded set O. Appendix A. On the Newtonian potential Appendix B. Rudimentary facts about harmonic functions and the Poisson equation Appendix C. Construction of the primary function of Siegel type Appendix D. On the divergence theorem and related matters Appendix E. The edge-point lemma Notes on sources References Index.